transistors. The physical construction of ICs is the prime reason for this different approach. The most frequently used ICs are manufactured with either 14 or 16 pins, all of which may be soldered directly into the circuit. It can be quite a job for you to unsolder all of these pins, even with the special tools designed for this purpose. After unsoldering all of the pins, you then have the tedious job of cleaning and straightening all of them.
Although there are a few IC testers on the market, their applications are limited. Just as transistors must be removed from the circuit to be tested, some ICs must also be removed to permit testing. When ICs are used in conjunction with external components, the external components should first be checked for proper operation. This is particularly important in linear applications where a change in the feedback of a circuit can adversely affect operating characteristics of the component.
Any linear (analog) IC is sensitive to its supply voltage. This is especially the case among ICs that use bias and control voltages in addition to a supply voltage. If you suspect a linear IC of being defective, all voltages coming to the IC must be checked against the manufacturer’s circuit diagram of the equipment for any special notes on voltages. The manufacturer’s handbook will also give you recommended voltages for any particular IC.
When troubleshooting ICs (either digital or linear), you cannot be concerned with what is going on inside the IC. You cannot take measurements or conduct repairs inside the IC. You should, therefore, consider the IC as a black box that performs a certain function. You can check the IC, however, to see that it can perform its design functions. After you check static voltages and external components associated with the IC, you can check it for dynamic operation. If it is intended to function as an amplifier, then you can measure and evaluate its input and output. If it is to function as a logic gate or combination of gates, it is relatively easy for you to determine what inputs are required to achieve a desired high or low output. Examples of different types of ICs are provided in figure 2-23.
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Q-19. Why should you consider an IC as a black box? Digital ICs are relatively easy for you to troubleshoot and test because of the limited numbers of
input/output combinations involved. When using positive logic, the logic state of the inputs and outputs of a digital IC can only be represented as either a high (also referred to as a 1 state) or as a low (also referred to as a 0 state). In most digital circuitry, a high is a steady 5-vdc level, and a low is a 0-vdc level. You can readily determine the logic state of an IC by using high-input-impedence measuring devices, such as an oscilloscope. Because of the increased use of ICs in recent years, numerous pieces of test equipment have been designed specifically for testing ICs. They are described in the following paragraphs.
Q-20. What are the two logic states of an IC? LOGIC CLIPS
Logic clips, as shown in figure 2-24, are spring-loaded devices that are designed to clip onto a dual- in-line package IC while the IC is mounted in its circuit. It is a simple device that usually has 16 light emitting diodes (LEDs) mounted at the top of the clips. The LEDs correspond to the individual pins of the IC, and any lit LED represents a high logic state. An unlit LED represents a low logic state. Logic clips require no external power connections, and they are small and lightweight. Their ability to simultaneously monitor the input and output of an IC is very helpful when you are troubleshooting a logic circuit.
Q-21. A lighted LED on a logic clip represents what logic level? LOGIC COMPARATORS
The logic comparator, as shown in figure 2-25, is designed to detect faulty, in-circuit-DIP ICs by comparing them with ICs that are known to be good (reference ICs). The reference IC is mounted on a small printed-circuit board and inserted into the logic comparator. You then attach the logic comparator to the IC under test by a test lead, which is connected to a spring-loaded device similar in appearance to a logic clip. The logic comparator is designed to detect differences in logic states of the reference IC and the IC being tested. If any difference in logic states does exist on any pin, an LED corresponding to the pin in question will be lit on the logic comparator. The logic comparator is powered by the IC under test.
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Q-22. What does a lighted LED indicate on a logic comparator? LOGIC PROBES
Logic probes, as shown in figure 2-26, are extremely simple and useful devices that are designed to help you detect the logic state of an IC. Logic probes can show you immediately whether a specific point in the circuit is low, high, open, or pulsing. A high is indicated when the light at the end of the probe is lit and a low is indicated when the light is extinguished. Some probes have a feature that detects and displays high-speed transient pulses as small as 5 nanoseconds wide. These probes are usually connected directly to the power supply of the device being tested, although a few also have internal batteries. Since most IC failures show up as a point in the circuit stuck either at a high or low level, these probes provide a quick, inexpensive way for you to locate the fault. They can also display that single, short-duration pulse that is so hard to catch on an oscilloscope. The ideal logic probe will have the following characteristics:
1. Be able to detect a steady logic level
2. Be able to detect a train of logic levels
3. Be able to detect an open circuit
4. Be able to detect a high-speed transient pulse
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5. Have overvoltage protection
6. Be small, light, and easy to handle
7. Have a high input impedance to protect against circuit loading
Q-23. What is the purpose of a logic probe? LOGIC PULSERS
Another extremely useful device for troubleshooting logic circuits is the logic pulser. It is similar in shape to the logic probe and is designed to inject a logic pulse into the circuit under test. Logic pursers are generally used in conjunction with a logic clip or a logic probe to help you trace the pulse through the circuit under test or verify the proper operation of an IC. Some logic pursers have a feature that allows a single pulse injection or a train of pulses. Logic pursers are usually powered by an external dc power supply but may, in some cases, be connected directly to the power supply of the device under test. View A of figure 2-27 shows a typical logic pulser. View B shows a logic pulser (right) used with a logic probe (left).
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A relatively new device on the test equipment scene is the logic analyzer. A logic analyzer provides various functions that can assist you in maintenance, testing, and troubleshooting of equipment using digital circuitry. From your standpoint, they are extremely useful in performing timing analysis. Most logic analyzers have crt displays that can monitor up to 32 timing signals at the same time. A large percentage of today’s digital equipment is designed with the logic analyzer in mind and have built-in status or bus lines for your convenience in monitoring multiple signals at the same time. When monitoring a bus line, you can readily determine, through visual displays, such things as the presence of master clock signals or sequential timing events.
As a technician, you are primarily concerned with the uses of batteries; however, checking or testing of storage and dry cell batteries is an important part of your maintenance program. Proper preventive maintenance of batteries can significantly extend the useful life of a battery.
When you check a lead-acid type of storage battery for its condition of charge or discharge, you take a specific gravity reading of the electrolyte by using a hydrometer. A specific gravity reading between 1.275 and 1.300 indicates a full-charge condition and assures you that the battery is in good condition. A hydrometer reading of approximately 1.175 indicates a normal discharge condition, and a reading of approximately 1.250 indicates that the battery is half-discharged. Since the acids used in various batteries do not always have the same specific gravity and since electrode composition may differ, the hydrometer reading you obtain at the charged and discharged conditions will vary with the type of electrolyte and battery composition. A general rule for you to follow is not to discharge a battery more than 100 points (.100 specific gravity) before recharging.
Although readings of specific gravity are a reliable measure of the condition of a storage battery, cells that indicate normal may prove useless under load. This is usually caused by a high internal resistance. A load-voltage check of the cells with the use of a cell tester indicates the actual voltage
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charge held by each battery cell. Cell voltages should not differ by more than 0.15 volt for 6-volt or 12-volt batteries.
Use extreme caution whenever testing or working around lead-acid storage batteries. OPNAVINST 5100.23B emphatically states that you must wear eye protection devices at all times and that emergency eyewash facilities must be immediately adjacent to, or within 10 feet of, any eye-hazard area. Smoking and spark-producing tools or devices are also prohibited in enclosed spaces that contain lead-acid storage batteries. When charging, these batteries produce sufficient quantities of hydrogen to produce large explosions. Lead-acid storage batteries should only be charged in well-ventilated spaces.
Q-24. Emergency eyewash facilities must be located within what minimum number of feet of an eye- hazard area?
You must periodically check dry cell batteries that are used for test instruments and portable or field equipments for loss of power. For actual voltages of dry batteries, you should measure with a battery tester for a minimum acceptable voltage before installation. The TS-183/U series of battery testers incorporate a multiple-range voltmeter, battery-loading resistors, multiplier resistors, and a jack-switching arrangement that connects the load resistors across the voltmeter for a total of 32 different voltmeter-load resistor combinations. This type of tester permits you to complete a rapid and accurate measurement of battery potentials under load conditions, ranging in voltages from 1.5 to 180 volts. A data chart supplied with the battery tester provides information regarding the jack to be used and minimum acceptable voltages of various batteries used in Navy equipments.
Q-25. What is the advantage of using a battery test set versus a voltmeter to test batteries? Table 2-2 shows general standards of tolerance for dry batteries. Whenever practical, dry cell
batteries that are not in use should be stored in a refrigerated area to extend their shelf life.
Table 2-2.—Typical voltage Tolerances for Dry Cell Batteries
MAX. VOLTAGE TOLERANCE
1 to 2 0.1 3 to 10 0.3
11 to 15 0.5 16 to 25 1.0 26 to 50 2.0 50 to 70 3.0 70 to 99 5.0
Carbon-zinc and alkaline cells are used primarily in portable test equipment, vom’s, flashlights, some portable radios, and beacon equipment. The carbon-zinc cell provides 1.5 volts and holds its charge for approximately 1 year in normal service. The alkaline cell provides 1.2 volts and has about twice the stored energy of the carbon-zinc cell of the same size. It also has a longer life at a higher discharge rate than the carbon-zinc cell. You should discard both types of batteries at the first indication of weakness.
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The storage life of a mercury cell varies but is generally classified as long. The working life of the cell is extremely long relative to other types of batteries; and it maintains its full rated voltage (1.34 volts) until just before it is ready to expire, at which point its voltage will drop off sharply. Recharging of mercury cells is possible, but is not recommended because the recharging cycle can vary from one cell to another; and, after being recharged, their operating lifetime is uncertain.
NICKEL-CADMIUM BATTERIES (NICAD) Nickel-cadmium batteries have very high efficiency. They can be recharged hundreds of times; given
the proper conditions, they may even be recharged thousands of times. They can be stored for a number of years with no significant loss of performance. After just a few charge and discharge cycles, NICAD cells can be recharged to the point that they are just as good as new batteries. Since they are sealed, they are maintenance free and can be installed in any position. There are two types of nickel-cadmium batteries — vented and nonvented. This description deals with the nonvented exclusively because a vented NICAD would have extremely limited application in a shipboard environment.
The voltage at the terminals of a NICAD will normally be between 1.25 and 1.30 volts in an open- circuit condition. This value will vary, of course, depending on the state of charge. If the charge has dropped to a low of 1.1 volts, the NICAD should be regarded as being completely discharged and should not be permitted to be discharged further. The majority of small NICADs are rated in milliampere hours; the large ones are rated in ampere hours. The small NICAD is the one the technician will almost always be concerned with.
Q-26. At what voltage is a NICAD battery considered to be fully discharged? As a general rule, if the charging current is held to 10% of the milliampere-hour rating for the
NICAD and the time of charge is held at 150% of the time required to establish its full milliampere-hour rating, you will encounter no difficulty in maintaining NICADs at their maximum charge. For example, you should charge a battery rated at 300 milliampere hours for 15 hours at 30 milliamperes. You can leave the battery on extended charge for years, provided the charge rate is lowered to less than 10% of the NICAD's milliampere rating.
You should never place a NICAD in your pocket, because metal objects (such as keys) can short the cell and cause extreme heat. Never dispose of a NICAD by fire, because it can explode. Never solder a connection directly to the cell, because the heat of an iron can damage it. Never overcharge a NICAD cell, because an accumulation of gases within its case can destroy it.
NICADs are also subject to a phenomenon commonly referred to as cell memory. If a NICAD is consistently discharged to a minor extent (for example, 30 minutes per day) and then recharged after each use, the useful capacity of the cell will eventually be reduced to that level. To keep this from happening, you should fully discharge (1.1 volts) NICADs on a regular basis. In fact, some maintenance requirement cards and calibration laboratory procedures require this periodic full discharge of equipment containing NICADs.
All rf attenuators, decade or step attenuators, decade resistors, and 50/75-ohm loads are clearly marked to show their attenuation factor or resistance. In the case of precision rf attenuators, they are usually marked to show their useful frequency ranges. They are all basically resistive devices and are
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designed for a multitude of applications. None of these devices are user-repairable; however, you should be aware of the different methods of determining whether or not they are functioning properly.
Fixed rf attenuators (shown in fig. 2-28), such as the ones commonly found in power-measuring sets, are designed to provide a fixed-signal attenuation over a specific frequency range. Frequency ranges can be in excess of 30 gigahertz, and attenuation factors are typically in 1-, 3-, 6-, and 10-dB steps. Fixed attenuators can be connected in series to provide you with the desired attenuation. Most fixed rf attenuators are designed to handle only small amounts of rf power and are extremely susceptible to damage because of overloading. To test a fixed rf attenuator, you can either substitute it with a known good attenuator or perform basic measurements on the attenuator itself. With the rf substitution method, you connect an rf signal generator to a power meter and establish a suitable reference point on the meter by adjusting the power output of the signal generator. Once you establish the reference point, insert the rf attenuator between the signal generator and the power meter. You then determine the attenuation by noting the difference between the power meter reading and the initial reference point.
Q-27. What is the most common method of testing a fixed rf attenuator? DECADE RESISTORS
Decade resistors (also referred to as decade boxes) typically are precision devices. Depending on the make and model of the decade resistor, it may be capable of providing you with a selection of resistors ranging in value from a small fraction of an ohm to hundreds of megohms. Decade resistors are commonly used in calibration laboratories and in engineering design applications. Like the fixed rf attenuator, most decade resistors are capable of handling only small amounts of current. They are very limited in respect to frequency capabilities and are commonly used in dc-circuit applications. You may encounter specific equipment that requires the use of a decade resistor in performing your maintenance tests or alignments. To test a decade resistor, you can connect a standard multimeter or digital multimeter directly across its resistance terminals and read its resistance on the meter. This test will only indicate gross errors in the decade resistor such as an open or a badly damaged resistor. If you are performing a precision measurement or an alignment using a decade resistor and have any doubt as to its accuracy, you should submit it to your servicing calibration laboratory. Figure 2-29 shows a typical decade resistor.
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either a stand-alone piece of test equipment or as an integral part of an operational piece of electronic equipment. As the name implies, they are used to attenuate rf signals in incremental steps. Like the fixed rf attenuator, you can easily test them by using the rf substitution method, as previously described. Views A and B of figure 2-30 show two types of decade attenuators.
Terminations of 50 and 75 ohms are designed as either feedthrough, impedance-matching devices, or as rf loading devices. They are precision resistors sealed in small plastic or metal enclosures and are designed to be mounted on various rf connectors. In the case of feedthrough terminations, they are designed with rf connectors at both ends, which allows the rf signal to pass through them. They are impedance-matching devices designed primarily to reduce the voltage standing-wave ratio (vswr) that is produced when two pieces of equipment with dissimilar impedances are connected together.
You can test a feedthrough termination by measuring the resistance between the center conductor and the shield of either rf connector with an ohmmeter. As mentioned above, some terminations are manufactured as loading devices that are designed to shunt an rf signal to ground. A perfectly matched termination can be compared to a transmitting antenna in that it absorbs all of the rf signal with only a
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small amount of power being reflected back to the transmitting device. When using a termination as a load, you should ensure that its wattage rating exceeds the power output of the equipment to which it is connected. You can also measure this type of termination by using a standard ohmmeter to read the resistance between the center conductor and the shield of the rf connector.
Q-28. What is the most common method of testing resistive terminations?
Fiber optics are a relatively new type of transmission media. Figure 2-31 depicts a typical fiber-optic cable design. The core of the fiber-optic cable is the optical transmission path, which carries data from the optical transmitter to the optical receiver. The core is usually made of plastic, glass, or plastic-clad silica (PCS). Glass-core fibers are usually smaller in diameter than plastic or PCS cores. The major disadvantages of glass cores are that they have high attenuation (25 dB/km), require precision tools and connectors, and are extremely susceptible to mechanical damage. Plastic cores are typically more rugged than other types of cores, but their attenuation is high (35 dB/km). PCS cores are fairly rugged and have a relatively low attenuation (10 dB/km). A fiber-optic cable may consist of one fiber, multiples of single- optical fibers, or bundles of optical fibers. Fiber-optic cables are well suited for the transmission of high- speed data over relatively short distances. They are virtually immune to crosstalk or interference through inductance. (Interference is a characteristic of metallic cables.)
Testing techniques and the principles of measurement for fiber-optic and conventional cable are similar. For example, if both ends of the cable are exposed and can be used for testing, relatively unsophisticated equipment can be used to measure cable parameters, such as continuity and attenuation. This includes equipment such as optical multimeters and optical power meters (OPM). If only one cable end is available, then more sophisticated equipment such as an optical time-domain reflectometer (OTDR), is used. The following section lists and defines some common optical test equipment.
Q-29. What is the main disadvantage of using fiber-optic cables?
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connector, and of the entire system. Loss measurements are figured by using the same methods you would use for wire loss measurements. The OTDR injects a short, intense laser pulse into the fiber and monitors reflections caused by breaks, inclusions, microcracks, and discontinuities. Discontinuities appear as a spike on the OTDR display. The loss at the discontinuity point is directly related to the distance between the major pulse triggered by the laser and the spike. The manufacturer’s manual provides you with conversion factors to figure actual losses and locations of the discontinuities.
An oscilloscope is used with an OTDR to provide visual evidence of fiber faults, connector and splice locations, and attenuation locations.
The optical multimeter measures light sources and light in cable and at the detector, fiber cable transmission loss, and connector splice loss. For cable transmission measurements, transmission through a short length of cable is compared with transmission through a known longer length.
The optical ohmmeter measures the input versus the output of light in an optical fiber. It displays attenuation losses based on a comparison of known and unknown cable signals. It can be used in manufacturing, connecting, and installing cable. It is as simple to use as a digital voltmeter.
The optical power meter measures current by converting light power from plug-in units, such as light emitting diodes, into electrical current. In some models, the readout is in power units, watts. In other models, the readout is in absolute power levels and attenuation. Some units operate with a variety of power sensors for conventional coaxial and waveguide systems and fiber-optic systems.
The radiometer/photometer measures light power in watts from dc to unlimited ac response. It uses plug-in sensor heads and, for low-light displays, it uses spectrometers and fiber-optic measurements.
performance of a piece of equipment or printed circuit board (pcb). ATE assists you in troubleshooting a fault to the defective component. Basically, ATEs are state-of-the-art, computer devices in which software programs are specifically tailored to meet the requirements of the device being tested.
The AN/USM-465 Portable Service Processor (psp), shown in figure 2-32, is the Navy’s standard ATE for testing digital pcb’s.
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The AN/USM-465 is part of the Support and Test Equipment Engineering Program (STEEP). It provides on-site screen testing and fault isolation of digital pcb’s and modules. The psp is presently available on most ships and shore intermediate maintenance activities (SIMA) with Mini/Micro maintenance stations (2M). Psp’s come with maintenance-assist modules (spare parts kit) and diagnostic kits.
The psp is easy to use. You have a choice of three pcb connectors (located on the top panel of the test set) into which you insert the pcb being tested. The software program, which is provided on magnetic tape cartridges, is then loaded into the test set. The test set automatically tests the pcb by applying input signals to the appropriate pins while monitoring the output signal for a correct indication. An LED display will give you a pass or fail indication. If a pcb fails the operational test, the psp tells you (via LED display) what troubleshooting steps must be taken. The psp uses a guided probe fault isolation technique that tells you what test points to check on the faulty pcb. The software program guides you from the faulty output backwards toward the input until the fault is located. The probe is a standard 10 megohm, 10 to 1 oscilloscope probe. The guided probe circuitry and software is also unique because it is capable of locating faults within feedback loops and can sense when you have placed the probe at an incorrect test point.
An interesting advantage is that if the psp itself fails, the faulty board inside the psp can be identified by the test set’s own capability. After you replace the faulty pcb with a good one from the spare parts kit, you can use the psp to identify the faulty component on its own pcb.
The Huntron Tracker 2000, shown in figure 2-33, is a versatile troubleshooting tool used to statically test resistors, capacitors, inductors, diodes, transistors, multiple-component circuits, and integrated circuits. Its built-in features eliminate the use of multiple pieces of test equipment. These features and its lightweight portability make the 2000 a widely used tool for troubleshooting.
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We recommend you review setup and operating procedures discussed in NEETS Module 16, Introduction to Test Equipment, NAVEDTRA B72-16-00-95, before continuing with this chapter. Since the 2000 was covered in depth in module 16, we will cover only the most common troubleshooting procedures and provide a few troubleshooting tips.
Q-30. What two features make the Huntron Tracker 2000 a widely used troubleshooting tool? The Huntron Tracker 2000 has the following features:
• Multiple-test signal frequencies (2000 Hz, 400 Hz, and 50/60 Hz). • Four impedance ranges (low, medium 1, medium 2, high). • Automatic range scanning.
• Range control: High Lockout.
• Rate-of-channel alteration and/or range scanning is/are adjustable. • Dual-polarity pulse generator for dynamic testing of three terminal devices.
• LED indicators for all functions.
• Dual-channel capability for easy comparison.
• Large CRT display with easy-to-operate controls.
The device to be tested must have all power turned off, and have all high voltage capacitors discharged before connecting the Tracker 2000 to the device.
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Testing components by comparison is the most preferred method for troubleshooting. The ALT (alternate) mode setup is the most commonly used mode for this method. This mode allows the technician to compare a known good component to a suspect component. This is accomplished by connecting channel A to a known good device, channel B to the device under test, and a common test lead to COM as illustrated in figure 2-34. Select the ALT button, and the 2000 will alternately display the signature of the known good device and the device under test. By examining the signature differences, you can detect a defective component. Figure 2-35 is a typical example of the CRT display on the 2000 while testing the base to emitter on a good transistor. Figure 2-36 illustrates a defective transistor under the same test setup. Note that in the low range, the transistor appears to be good. Sometimes component defects are more obvious in one range than another, so is a suspect device appears normal for one range, try the other ranges.
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Q-31. What is the most preferred method of troubleshooting? Q-32. Why is it recommended to use more than one range while troubleshooting a device?
When you are testing individual components in a circuit, a parallel resistor or diode of similar value may cause a defective component to appear good. Therefore, you should, in most cases, electrically isolate the suspected component from the circuit while testing individual components. The best way to do this is to desolder all but one lead on the suspected component.
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Q-33. When you are testing individual components in a circuit, what may cause a defective component to appear good?
You should be aware that devices made by different manufacturers may appear to have slightly different signatures. This is normal, especially with digital integrated circuits, and does not necessarily indicate a failed device. When this occurs, the best way to verify this is to compare the outputs of the device under test with the equipment specifications to ensure the signals are adequate for proper equipment operation.
The information that follows summarizes the important points of this chapter.
ELECTRON TUBES are usually tested for SHORTS, TRANSCONDUCTANCE, and the presence of GAS. Several different types of tubes (i.e., twt’s, magnetrons, and klystrons) are normally tested in-circuit.
Most TRANSISTORS can be tested by measuring the forward-to-back resistance of their junctions using a standard ohmmeter. The resistance scale of the ohmmeter must be carefully selected to ensure that the current rating of the transistor is not exceeded.
ESD-SENSITIVE DEVICES are components that require special handling. Some of the more sensitive devices can be damaged by static charges as small as 35 volts.
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Most DIODES and MOSFETs can be tested by measuring the forward-to-back resistance of their junctions using a standard ohmmeter. MOSFETS, however, are classed as ESD-sensitive devices; and care should be exercised when handling or testing them.
INTEGRATED CIRCUITS (ICs) have revolutionized the electronics industry. They are rugged, compact, and inexpensive. There is a wide assortment of equipment on the market designed for testing ICs.
BATTERIES are common to a large number of both electronic test equipment and operational equipment. You should be familiar with the different types of batteries, their test requirements, and the safety precautions to be followed.
RF ATTENUATORS and RESISTIVE LOADS are common devices that are widely used for attenuating rf signals and impedance matching. Resistive loads can be tested with a standard ohmmeter, and rf attenuators are normally tested through the rf substitution method.
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FIBER-OPTIC CABLES are used primarily for the transmission of high-speed data over short distances. Their construction and theory of operation require that they be tested with a light source, usually a laser beam. There is a wide assortment of test equipment designed specifically for testing fiber- optic cables.
AUTOMATIC TEST EQUIPMENT (ATE) is test equipment designed to evaluate the operational performance of a piece of equipment or printed circuit board (pcb).
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The HUNTRON TRACKER 2000 is a versatile troubleshooting tool commonly used for statically testing resistors, capacitors, inductors, diodes, transistors, multiple-component circuits, and integrated circuits.
EIMB, Test Methods and Practices, NAVSEA 0967-LP-000-0130, Naval Sea Systems Command, Washington, D.C., 1980.
Fiber Optic Communication Cables and Connectors, (Navy) EE169-CA-GYD-010/E110 TSER E & I, (Published under the authority of the Secretaries of the Air Force, Army, and Navy), 1983.
Fire Control Technician G 3 & 2, NAVEDTRA 10207-B, Naval Education and Training Professional Development and Technology Center, Pensacola, Fla., 1981.
Huntron Tracker 2000 Operation and Maintenance Manual, P/N 21-1052, Huntron Instruments, Inc., 15720 Mill Creek Blvd., Mill Creek, WA 98012.
Introduction to Microelectronics, NAVEDTRA 172-14-00-84, Naval Education and Training Professional Development and Technology Center, Pensacola, Fla., 1984.
Logic Clip 548A, NAVAIR 16-45-3102, Naval Air Systems Command, Washington, D.C., 1979.
Logic Comparator 10529A, NAVAIR 16-45-3100, Naval Air Systems Command, Washington, D.C., 1979.
Logic Probe 545A, NAVAIR 16-45-3105, Naval Air Systems Command, Washington, D.C., 1979.
Logic Pulser 546A, NAVAIR 16-45-3104, Naval Air Systems Command, Washington, D.C., 1979.
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ANSWERS TO QUESTIONS Q1. THROUGH Q33. A-1. Lack of adequate storage space. A-2. Open filaments. A-3. Testing the tube in its circuit.
A-4. In their circuit.
A-5. Restore it to serviceable condition by operating it temporarily at reduced beam voltage.
A-6. Correct gain figure. A-7. Rugged design.
A-8. Sensitive to heat and minor overloads.
A-9. Any range setting that produces a current flow through the transistor that exceeds 1 milliamp (usually R x 1 range).
A-10. 3,500 to 4,000 volts.
A-11. 35 volts.
A-12. For your own safety. A-13. Voltages and resistances.
A-14. Greater than 10 to 1.
A-15. Gate and anode.
A-16. Current is allowed to flow in either direction. A-17. Solder suckers create an electrostatic charge capable of damaging a MOSFET. A-18. Low power consumption, compact size, and lower cost.
A-19. ICs cannot be repaired. All you need to test is output versus input.
A-20. A "1" or "0."
A-21. A "1" state.
A-22. A difference in logic states between the reference IC and the IC under test. A-23. They provide you with a visual indication of the logic state at any point you choose in the
circuit.
A-24. 10 feet. A-25. A battery test set will test batteries under load conditions.
A-26. At 1.1 volts.
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A-27. Rf substitution method. A-28. Reading their resistances with a standard ohmmeter.
A-29. High attenuation.
A-30. It eliminates the need for multiple pieces of test equipment and it is lightweight and portable. A-31. Testing components by comparison.
A-32. Some defective devices may appear to be good in certain ranges. A-33. A parallel resistor or diode of similar value.
3-1
Upon completion of this chapter, you will be able to do the following:
1. Explain the purposes and benefits of performing quantitative measurements.
2. Identify the various methods of performing impedance measurements.
3. Identify the various methods of performing power measurements.
4. Identify the various methods of performing frequency measurements.
You have already studied the basics of performing electronics measurements and how to determine if a component is or is not functioning properly. This chapter will cover techniques used in measurements of specific impedance, frequency, and power. These measurements are extremely important to you in evaluating the performance of a piece of electronic equipment.
Impedance measurements are often used during routine test procedures. Impedance-measuring equipment, such as impedance bridges, are mainly used in determining the capacitance and inductance of component parts. However, the values of combined circuit constants also may be obtained and used in direct calculations of impedance. An impedance measurement effectively totals the inductive and capacitive reactance together with the resistance in a circuit. In addition, impedance measurements are useful in testing and analyzing antenna and transmission line performance and for determining the figure of merit (Q) of electrical parts and resonant circuits.
Q meters are impedance-measuring instruments that determine the ratio of reactance to resistance of capacitors or inductors and resistors. Details of Q meters and impedance bridges as well as a number of other methods of measuring circuit impedance are described in the following paragraphs. Also discussed are methods of measuring the impedance of antennas and transmission lines.
Bridges are among the most accurate types of measuring devices used in the measurement of impedance. In addition, bridges are also used to measure dc resistance, capacitance, and inductance. Certain types of bridges are more suitable for measuring a specific characteristic, such as capacitance or inductance. Basic schematics for the various bridge circuits are shown in figure 3-1. The bridge circuits shown are similar in that they usually contain two branches in the measuring circuit, two branches in the comparing circuit, a detector circuit, and a power circuit, as shown in figure 3-2. The bridge shown in figure 3-2 is actually the dc Wheatstone bridge; however, the general principles of circuit operation for ac remain the same.
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The comparing circuit contains branches A and B and has provisions for changing the ratios of the branches with respect to each other, which enables various measuring ranges to be obtained. Comparison of figures 3-1 and 3-2 shows that either or both branches of the comparing circuit do not necessarily contain resistors alone. Branch B of the Hay bridge, containing CB and RB in series connection, provides a striking contrast with the parallel connection of CB and RB of the Maxwell bridge.
The measuring circuit in figure 3-2 also contains two branches. The resistance, capacitance, or inductance to be measured is connected to branch X of the bridge-measuring circuit. The subscript X is also used in figure 3-1 to designate the circuit parameters involved in computing the values of various electronic parts. Branch S contains the variable control used to bring the bridge into a balanced condition. A potentiometer is used for this purpose in most bridge equipment, because it offers a wide range of smoothly variable current changes within the measuring circuit.
The third arm of the bridge is the detector circuit. The detector circuit may use a galvanometer for sensitive measurements that require high accuracy. In the case of bridges using ac as the power source, the galvanometer must be adapted for use in an ac circuit. In many practical bridge circuits using ac to operate the bridge, an electron-ray indicating tube is used to indicate the balanced condition by opening and closing the shadow area of the tube. Headsets are also used for audible balance detection, but this method reduces the accuracy obtainable with the bridge.
Switches are used in bridge circuits to control the application of operating power to the bridge and to complete the detector circuit. Frequently, the two switching functions are combined into a single key, called a bridge key, so that the operating power is applied to the bridge prior to the detector circuit. This sequence reduces the effects of inductance and capacitance during the process of measurement.
The most unfavorable condition for making a measurement occurs when the resistance, capacitance, or inductance to be measured is completely unknown. In these cases, the galvanometer cannot be protected by setting the bridge arms for approximate balance. To reduce the possibility of damage to the galvanometer, you should use an adjustable shunt circuit across the meter terminals. As the bridge is brought closer to the balanced condition, the resistance of the shunt can be increased; when the bridge is in balance, the meter shunt can be removed to obtain maximum detector sensitivity.
Bridges designed specifically for capacitance measurements provide a dc source of potential for electrolytic capacitors. The electrolytic capacitors often require the application of dc polarizing voltages in order for them to exhibit the same capacitance values and dissipation factors that would be obtained in actual circuit operation. The dc power supply and meter circuits used for this purpose are connected so that there is no interference with the normal operation of the capacitance-measuring bridge circuit. The dissipation factor of the capacitor may be obtained while the capacitor is polarized. In figure 3-2, the signal voltage in the A and B branches of the bridge will be divided in proportion to the resistance ratios of its component members, RA and RB, for the range of values selected. The same signal voltage is impressed across the branches S and X of the bridge. The variable control, RS, is rotated to change the current flowing through the S and X branches of the bridge. When the voltage drop across branch S is equal to the voltage drop across branch A, the voltage drop across branch X is equal to the voltage drop across branch B. At this time the potentials across the detector circuit are the same, resulting in no current flow through the detector circuit and an indication of zero-current flow. The bridge is balanced at these settings of its operating controls, and they cannot be placed at any other setting and still maintain this balanced condition.
The ability of the bridge circuit to detect a balanced condition is not impaired by the length or the leads connecting the bridge to the electronic part to be measured. However, the accuracy of the measurement is not always acceptable, because the connecting leads exhibit capacitive and inductive
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characteristics, which must be subtracted from the total measurement. Hence, the most serious errors affecting accuracy of a measurement are because of the connecting leads.
Stray wiring capacitance and inductance, called residuals, that exist between the branches of the bridge also cause errors. The resistance-ratio bridge, for example, is redrawn in figure 3-3 to show the interfering residuals that must be eliminated or taken into consideration. Fortunately, these residuals can be reduced to negligible proportions by shielding and grounding. A method of shielding and grounding a bridge circuit to reduce the effects of interfering residuals is through the use of a Wagner ground, as shown in figure 3-4. Observe that with switch S in position Y, the balanced condition can be obtained by adjusting Z1 and Z2. With switch S in position X, the normal method of balancing the bridge applies. You should be able to reach a point where there is no deflection of the meter movement for either switch position (X or Y) by alternately adjusting Z1 and Z2 when the switch is at position Y and by adjusting RS when the switch is at position X. Under these conditions, point 1 is at ground potential; and the residuals at points 2, 3, and 4 are effectively eliminated from the bridge. The main disadvantage of the Wagner ground is that two balances must be made for each measurement. One is to balance the bridge, and the other is to balance the Wagner ground. Both adjustments are interacting because RA and RB are common to both switch positions X and Y.
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Many bridge instruments provide terminals for external excitation potentials; however, do not use a voltage in excess of that needed to obtain reliable indicator deflection because the resistivity of electronic parts varies with heat, which is a function of the power applied.
Q-1. What conditions must be met in order to balance a bridge circuit?
Q-2. When you are measuring a component using a bridge, what is the most common cause of inaccurate measurements?
The Wheatstone bridge, shown in figure 3-1, is often used to measure resistance. These instruments are usually portable because they require only a small, dc source to power the bridge, which is easily obtained from flashlight batteries. In those cases where an external supply voltage is desirable for the operation of the bridge, use the minimum voltage that will give a reliable indication by the galvanometer. Increasing the supply voltage any further results in uncompensated thermal variations and decreased bridge accuracy. If greater bridge sensitivity is needed, use a galvanometer with greater sensitivity.
A number of other considerations are involved in the choice of a galvanometer. For example, the galvanometer should not be subjected to false or erratic indications because of external magnetic fields.  It is also desirable to use a critically dampened meter movement to ensure decisive movement of the meter pointer during conditions of bridge unbalance. Thermal agitation sometimes produces voltages that interfere with the balancing of the bridge. For this reason, the Wheatstone bridge usually includes a polarity-reversing switch in the detector circuit. When a measurement is required, note the reading for both positive and negative indications, and figure the average of both readings. With the exception of inaccuracies introduced by thermal variations (caused by excessive supply voltages), the accuracy of the Wheatstone bridge is, otherwise, independent of the value of supply voltages. The units used in calibrating the galvanometer are unimportant to the accuracy of the bridge, since a 0 indication is desired at the balanced condition.
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Resistance values ranging from 1 ohm to 1 megohm can be measured with an accuracy of approximately 0.1%. However, difficulties are encountered when very high and very low resistances are measured. Resistances less than 1 ohm are difficult to measure accurately because of uncertainty arising from the contact resistance present between the resistor to be measured and the binding posts of the bridge. Measurement of resistances greater than 1 megohm becomes difficult because of two factors: (1) The ratio of standard resistances RA and RB involve a ratio on the order of 1,000 to 1, and (2) the voltage applied to the bridge must be substantially increased to obtain definite galvanometer action. The result is that an increase in the supply voltage increases the power dissipation (heat) of the bridge resistors. The change in resistance RB, because of the heat, is sufficient to produce an appreciable error. A Kelvin bridge is recommended for measuring resistances lower than 1 ohm. An electronic multimeter is recommended for the indicating device in bridges used for the measurement of very high resistances.
One of the most elementary precautions concerning the use of a bridge, when measuring low resistance, is to tighten the binding posts securely so that the contact resistance between the binding posts and the resistance to be measured is minimum. Leakage paths between the resistor leads along the outside surface of the resistor body must be avoided when resistances greater than 0.1 megohm are measured. Search for defective solder joints or broken strands in stranded wire leads; these defects can cause erratic galvanometer indications. In those cases where wire leads must be used to reach from the resistance under test to the bridge terminals, measure the ohmic value of those leads prior to further measurements.
Q-3. How does the supply voltage affect the accuracy of Wheatstone bridge measurements?
It is often necessary to make rapid measurements of low resistances, such as samples of wire or low values of meter shunt resistors. A frequently used instrument that is capable of good precision is the Kelvin bridge, shown in figure 3-1. Note the similarity between this and the Wheatstone bridge. Two additional resistances, R1 and R2, are connected in series and shunted across resistance R, which is the circuit resistance existing between the standard and unknown resistances, RS and R X, respectively. In performing the adjustment for balance, you must make the ratio of R1 to R2 equal to the ratio of RA to R B. When this is done, the unknown resistance can be computed in the same manner as that for the Wheatstone bridge, because resistance R is effectively eliminated.
In using a Kelvin bridge, you must follow precautions similar to those given for the Wheatstone bridge. A rheostat is usually placed in series with the battery so that bridge current can be conveniently limited to the maximum current allowable. This value of current, which affects the sensitivity of the bridge, is determined by the largest amount of heat that can be sustained by the bridge resistances without causing a change in their values. All connections must be firm and electrically perfect so that contact resistances are held to a minimum. The use of point and knife-edge clamps is recommended. Commercially manufactured Kelvin bridges have accuracies of approximately 2% for resistance ranges from 0.001 ohm to 25 ohms.
Q-4. Kelvin bridges are well suited for what type of measurements?
The resistance-ratio bridge, shown in figure 3-1, may be used to measure capacitance, inductance, or resistance so long as the electronic part to be measured is compared with a similar standard. The measurement of the value of a capacitor must be made in terms of another capacitor of known characteristics, termed the STANDARD CAPACITOR. The same requirement is necessary for an inductance measurement. The standard of comparison is designated as XX, and the losses of the standard are represented as R X. If you experience difficulty in obtaining a balanced bridge condition, insert
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additional resistance in series with branch S of the bridge. This adjustment becomes necessary because the Q of the unknown capacitor or inductor in branch X is higher than the comparable Q of the standard in branch S.
The Schering bridge, shown in figure 3-1, is a commonly used type of bridge for the measurement of capacitors and dielectric losses. The Q of a capacitor is defined as the reciprocal of the dissipation factor, which is the ratio of the capacitor's dielectric constant to its conductivity at a given frequency. Accordingly, capacitor Q is determined by the frequency used to conduct the measurement and the value of the capacitor, CB, required to obtain bridge balance. The accuracy of this type of bridge is excellent, about 2% for dissipation factors ranging from 0.00002 to 0.6. Typical accuracies for capacitive reactances in the range of 100 picofarads to 1 microfarad are 0.2%.
The Hay bridge, shown in figure 3-1, is used for the measurement of inductance and the Q of the inductor. It is interesting to note that this type of bridge measures inductance by comparing it with a standard capacitor of known characteristics. This arrangement provides the advantage of a wide measurement range with the minimum use of electronic parts as comparison standards. A typical range of values that can be measured with the Hay bridge is from 1 microhenry to 100 henries. The accuracy of the measurements made with this bridge is about 2%. The frequency used in conducting the inductance measurement must be taken into account because of the series reactance of capacitor CB. The loss factor of the inductor under test is balanced in terms of the Q of the inductor. The Hay bridge, then, is used for measurement of inductances having a Q greater than 10. For instance, a Q of 10 gives a calibration error of 1%, whereas a Q of 30 gives a calibration error of 0.1%.
Q-5. When you are testing an inductor with a Hay bridge, the characteristics of the inductor are compared with what type of device?
The Maxwell bridge, shown in figure 3-1, is used for the measurement of inductance and inductive Q. This bridge is similar to the Hay bridge because it also measures inductance by comparison with a standard capacitor of known characteristics. Notice, in particular, that capacitor C B is connected in parallel with resistor R B. In connection with this difference, the requirement of an accurately known frequency is removed. This bridge circuit is employed for measuring the inductance of inductors having large losses; i.e., low Q. The range of this type of instrument is much greater than that of the Hay bridge; values ranging from 1 microhenry to 1,000 henries are measurable, with an error of only 2%.
The basic bridges described up to now determined the resistive and reactive components of the unknown impedance; however, the vector bridge indicates the magnitude and phase angle. Typically, vector bridges require two null readings. Consider the basic bridge circuit of figure 3-5. The magnitude of the unknown impedance (Z X) is determined by the voltages applied across R and ZX and to the bases of emitter followers Q1 and Q2, which bias the balanced rectifiers, CR1 and CR2. Resistors A and B are equal in value. When R is adjusted to equal ZX, the voltages between points 1 and 2 and between points 1 and 4 are equal in magnitude, and the vtvm will indicate 0 volts.
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The absolute value of Z X is determined from the dial calibration of R. Without altering the amplitude balance, you reconnect the external circuits as shown in figure 3-6. Note that the voltage between points 1 and 3 is being compared to the voltage between points 1 and 2. Potentiometer R, calibrated in degrees, is adjusted for a null indication on the vtvm; and the phase angle is read directly. If Z X is purely resistive, the voltage between points 1 and 3 will be zero and the setting of R will be 0 volts. If ZX is purely reactive (capacitive or inductive), the setting of R will be at maximum voltage. For phase angles between 0º and 90º, the scale of R may be calibrated directly in degrees. The sign of the phase angle can be determined by changing the signal frequency slightly and observing the change in impedance. The presence of harmonics in the signal input will severely hamper the measurements. If a pure frequency source is not available, suitable low-pass filters will have to be employed in the output leads from the bridge.
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This technique employs an oscillator circuit and a vtvm, as shown in figure 3-7.
A large value of resistance, R, is selected so that IC is virtually independent of the range of Z X to be measured. Thus, ICZ X represents the value of voltage measured by the vtvm. If R is chosen so that the voltage drop across ZX corresponds to a full-scale reading on the vtvm, a direct reading impedance meter is realized. For example, assume that the audio oscillator open-circuit voltage is 10 volts (rms) and that the full-scale reading of the vtvm is 0.05 volt. If you want to measure ZX values ranging up to a maximum of 5,000 ohms, you should use a 1-megohm resistor for R. This will result in a full-scale, 0.05-volt deflection. An oscillator that does not produce harmonics should be used.
Like vector bridges, impedance-angle meters determine an unknown impedance in terms of magnitude and phase angle. However, a non-bridge technique is used. The simplified circuit of a commercial instrument is shown in figure 3-8. With switches S1 and S2 at the BAL position, the variable
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standard resistor, R, is adjusted until the balanced rectifier outputs of Q1 and Q2 are equal (indicated by a null in the deflection of the voltmeter connected between the emitters of Q3 and Q4). The dial setting of R gives the value of ZX. For phase angle determination, the circuit is switched to CAL and the input voltage is adjusted for full-scale voltmeter deflection. The circuit is then switched to PHASE; thus, the paralleled outputs of Q1 and Q2 are applied to rectifier CR1 only. With S2 in the phase position, there is no input to the base of Q4. If Z is purely resistive, the outputs of Q1 and Q2 cancel, and the voltmeter indicates zero deflection. For a complex impedance, the base of Q3 will be unbalanced with respect to the base of Q4; and the voltmeter deflection, calibrated in degrees, determines the phase angle of the unknown impedance. Typical commercial impedance angle meters, operating at 2 MHz, are accurate to within 4% for impedances of from 10 to 500 ohms.
Q-6. What do impedance-angle meters and vector bridges have in common?
The amount of current that flows in an antenna is one of the most important factors affecting the performance of transmitter equipment. As much of the rf energy generated as possible must be efficiently transferred to the antennas to secure the maximum radiated power from a transmitter. Also, for best reception, maximum transfer of energy from the antenna to the receiver must occur. Efficient transmission and reception conditions prevail whenever the transmitter (or receiver) is properly matched to the transmission line and the transmission line is properly matched to the antenna. Normally, performance tests concerning impedance match consist primarily of taking standing-wave measurements. In certain instances, it may be found that a change in antenna impedance has resulted in an undesirably high standing-wave ratio. This could be the result of a new antenna installation or an interfering structure near the antenna that influences antenna characteristics.
In practice, the antenna-matching network is varied to match the new antenna characteristics, since the transmission line is designed to match equipment impedance. This can best be done by making a series of standing-wave-ratio checks and antenna-matching adjustments until an acceptable standing-wave
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ratio is reached. It must be understood, however, that the antenna does have a specific impedance at a given frequency and that, when necessary, this impedance may be determined by use of an rf impedance bridge.
A typical rf impedance bridge circuit is shown in figure 3-9. Rf impedance bridge measurements require an rf signal generator, a detector, and a calibrated rf bridge to determine transmission-line impedance. The bridge compares the parallel resistive-reactive combination with the series combination and can typically measure impedance over a frequency range of 500 kHz to 60 MHz.
Basically, the bridge is balanced with a known capacitance under short-circuit conditions. The unknown impedance is then inserted in lieu of the short bus, and the bridge is rebalanced. The difference between the known impedance under short-circuit conditions and the balance measurements obtained with the unknown impedance inserted in lieu of the short is the value of the unknown impedance.
Q-7. What is the result of an impedance mismatch between a receiver or transmitter and its transmission line or antenna?
It is often necessary to check the input and output signal power levels of electronic equipment. The determination of dc power is computed by using a derivative of Ohm's law (P = IE = I2R = E 2/R). However, the presence of a reactive component in ac circuits means that apparent power is being measured or calculated unless the rms voltage-current value is multiplied by a power factor to obtain true lower. The measurement of ac power is further complicated by the frequency limitations of various power meters. If there is no phase difference, ac power may be computed in the same manner as dc power by determining the average value of the product of the voltage and current. In practical ac circuits, the apparent power must be multiplied by the cosine of the phase angle between the voltage and current in order to compute true power.
In the repeated measurement of audio-frequency (af) power, you may use a normal power meter calibrated directly in watts. However, when reactive components of dissipative impedance introduce a
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phase angle, a device that is proportional to both the power factor and the apparent power must be used. Because power-level measurements are concerned with decibel units, a working knowledge of decibels is required for proper interpretation of power tests. The decibel is used to determine the ratio of power changes or to indicate the power level in a circuit with respect to either 0 or a standard reference level.
In the electrical transmission of speech or music, rapidly fluctuating amplitudes and frequencies are involved. The average power-level measurement and its variation rate depend on the signal characteristics and time interval over which this average is taken. Power measurements for af circuits are usually indicated in terms of decibels (dB), decibels referenced to 1 milliwatt (dBm), or volume units (vu). For example, the power gain of an amplifier can be expressed in dB; the power level of a sinusoidal signal compared to a 1-milliwatt reference is indicated in dBm; and the power level of a complex signal, such as voice, music, or multiplexed information, compared to a reference level of 1 milliwatt, is indicated in vu.
Q-8. What are the three units of measure most commonly used when referring to af power measurements?
A dB meter is a form of ac electronic voltmeter calibrated in dB's. These meters are useful for making measurements where direct indication in decibels is desired. However, remember that these are voltmeters, and power measurements are not meaningful unless the circuit impedance is known. When the dB meter is calibrated, a reference point, based on a specific power or value of voltage across a specified resistance, is selected to represent 0 dB. Many electronic voltmeters use a single dB scale based on 1 milliwatt into a 600-ohm load to represent 0 dBm. Based on this reference point, various voltage readings could be made on the low ac-voltage scale. The +dB numbers corresponding to voltage ratios that exist between successive ranges and the low ac range have been computed for each range. These numbers, shown on the front panel of the instrument, are added algebraically to each successive range reading to produce the correct value for the range. The term decibel does not, in itself, indicate power. It indicates a ratio or comparison between two power levels that permits you to calculate the power. Often, it is more desirable to express performance measurements in terms of decibels using a fixed power level as a reference. The original standard reference level was 6 milliwatts, but to simplify calculations a standard reference level of 1 milliwatt has been adopted.
Q-9. In reference to dB meters, 0 dBm represents 1 milliwatt into what value of load?
The volume unit (vu) meter is used in audio equipment to indicate input power to a transmitter or to a transmission line. This type of meter has special characteristics, such as a standardized speed of pointer movement, speed of return, and calibration. The measurement of the average power level and its rate of variation with respect to time depends not only on the signal characteristics, but also on the time interval over which the average is being taken. Accordingly, the speed of response of the instrument used to measure average power is of particular concern. The unit of measurement is the volume unit (vu), which is numerically equal to the number of dB above or below the reference level of 1 milliwatt into a 600-ohm load (provided the standard instrument was calibrated under constant-amplitude, sine-wave conditions). A change of one vu is the same as a change of one decibel. Therefore, the vu value obtained represents averages of instantaneous power of speech or music obtained by an instrument having particular dynamic characteristics. The vu readings are equivalent to the power level in decibels only if the sinusoidal waveform is of constant amplitude.
Q-10. What is the main difference between a vu and a dB meter?
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The electrodynamic wattmeter is used to measure power taken from ac or dc power sources. The electrodynamic wattmeter, shown in figure 3-10, uses the reaction between the magnetic fields of two current-carrying coils (or sets of coils), one fixed and the other movable. When the current through the fixed-position field winding(s) is the same as current through the load and the current through the moving coil is proportional to the load voltage, then the instantaneous pointer deflection is proportional to the instantaneous power. Since the moving pointer cannot follow the rapid variations in torque because of its momentum, it assumes a deflection proportional to the average power. The dynamometer-type wattmeter automatically compensates for the power factor error of the circuit under test. It indicates only the instantaneous power resulting from in-phase values of current and voltage. With out-of-phase relationships, a current peak through the moving coil never occurs at the same instant as the voltage peak across the load, resulting in less pointer deflection than when the current and voltage are in phase. The simple meter shown in figure 3-10 is not compensated. When the load is disconnected, this meter will still indicate that power is being consumed in the circuit. This difficulty can be eliminated by incorporating two compensating windings, mounted with the primary fixed-coil current windings, as shown in figure 3- 11. These stationary windings are used to produce a magnetic flux proportional to the current through the movable coil. As shown by the arrows, the currents through the primary movable coil and the compensating coil flow in opposite directions, producing a torque caused by the opposing magnetic fields. These opposing fields cancel. Hence, with the load removed from the circuit, the meter will indicate zero power through the load.
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Electrodynamic wattmeters are subject to errors arising from various factors, such as temperature and frequency characteristics and vibration. Heat through the control mechanism can cause the springs to lengthen and lose tension; as a result, deflection errors are produced. Figure 3-12 illustrates the mechanical equivalent of the electrodynamic wattmeter. Large currents within the circuit will also produce errors. Therefore, the maximum current range of electrodynamic wattmeters is normally restricted to about 20 amperes. When larger load currents are involved, a current transformer of suitable range is used in conjunction with the wattmeter. However, a current transformer cannot be used if the ac circuit under test contains a dc component.
The voltage range of wattmeters is generally limited to several hundred volts because of heat dissipation within the voltage circuit. However, the voltage range can be extended by using external voltage dividers. Wattmeters used as laboratory standards have an accuracy of 0.1%, high-grade portable wattmeters an accuracy of 0.2% to 0.25%, and high-grade switchboard wattmeters an accuracy of 1% of
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full-scale value. Because electrodynamic wattmeter errors increase with frequency, they are used primarily for measuring 60-hertz line power. Unshielded electrodynamic wattmeters should not be placed in the vicinity of stray magnetic fields. A wattmeter has current, voltage, and power ratings; therefore, damage may result when any of these ratings is exceeded.
The electrodynamic wattmeter may be converted into an instrument for measuring reactive power by replacing the resistance normally in series with the voltage coil with a large inductance. A 90-degree current lag within the voltage coil provides a direct reading proportional to the reactive power in the circuit. Compensating networks must be used to cause the phase shift to be exactly 90º.
Q-11. What type of device is used to extend the current-measuring capability of electrodynamic wattmeters?
Iron-core wattmeters are primarily used as switchboard instruments and employ the induction principle. Voltage and current coils are wound around a laminated iron core shaped to produce a mutually perpendicular magnetic field across an air gap. Eddy currents induced in a thin metal cylinder rotating in this air gap interact with the magnetic field to produce a torque proportional to the instantaneous power. This type of construction provides the advantages of increased operating torque, larger angles of rotation, ruggedness, compactness, and freedom from errors caused by stray fields. It has the disadvantage of a very narrow frequency range.
The composite-coil wattmeter uses the upscale torque, produced by the ac power being measured, in opposition to the torque produced by an adjustable dc current in a set of windings intermingled or wound within the ac windings. Greater reading precision is obtained with this method than is possible with straightforward wattmeters, and errors caused by elasticity of the spring suspension carrying the moving- coil system are avoided. The torsion-head wattmeter is used to restore the movable coil to its original position after deflection and to remove the mutual inductance error.
Electronic wattmeters are used for direct, small power measurements or for power measurements at frequencies beyond the range of electrodynamometer-type instruments. A simplified electronic wattmeter circuit is shown in figure 3-13. The matched triodes are operated in the nonlinear portion of their characteristic grid-voltage, plate-current curves. The symmetrical resistive T network between the generator and load will provide V1 and V2 voltages proportional to, and in phase with, the load current and voltage, respectively. A source of ac power is connected to the load through the series resistors R1 and R2. These two resistors are of equal value and are made small to prevent the voltage drop across them from reducing the load voltage appreciably.  Therefore, the R3 voltage is equal to the load voltage, and the voltage across either series resistor is proportional to the difference in the output currents of the tubes. The average value of the difference could be measured by a dc meter connected to read the voltage potential between the grids of V1 and V2. This method is adequate only at low frequencies. As the frequency increases, the stray capacitances and inductances also increase. The frequency range of the electronic wattmeter can be extended up to 20 megahertz by using pentodes instead of triode tubes. The operating conditions in a pentode are adjusted so that plate current is proportional to the product of a linear function of plate voltage and an exponential function of grid voltage.
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Q-12. For power measurements, what advantage does an electronic wattmeter have over an electrodynamic wattmeter?
Absorption power meters absorb either all or part of the source power. They require means of dissipating the absorbed power, sensing the power thus dissipated, and indicating the amount of power absorbed by the sensing network. Output power meters, in-line wattmeters, and meters employing bolometers are examples of absorption power meters used by the Navy.
Figure 3-14 shows a common output power meter used in vhf-uhf applications. It has a 0- to 150- watt range covered in two steps: 0-50 watts and 0-150 watts. Attenuator AT1 provides a 50-ohm nominal resistive (dummy) load and uses metal film on glass construction. This dummy load is tapped to provide the proper operating voltage to the meter. Resistors R3 and R5 form a calibration network at 50 watts; R7 and R8 form a calibration network at 150 watts. Accuracy, at approximately 20º C, is ±5% for frequencies between 30 MHz and 600 MHz, ±10% for frequencies between 0.6 GHz and 0.8 GHz, and ±20% for frequencies between 0.8 and 1.0 GHz. When radio-frequency (rf) power is applied to AT1, this attenuator minimizes the effects of power factors generated by any reactive components. The rf energy is then detected and filtered by CR1 and C1, respectively. The resultant dc voltage, which is proportional to the input power, is applied to a sensitive microammeter via one of the calibration networks. This meter has a scale provided with two ranges: 0-50 watts and 0-150 watts. To protect the meter, you should always try the higher range first. If the value proves to be under 50 watts, a shift to the lower scale would provide improved accuracy.
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The AN/URM-120 in-line wattmeter, shown in figure 3-15, measures power applied to a 50-ohm impedance load and the power reflected from that load. The internal directional coupler is oriented such that it responds only to a wave traveling in one direction on the transmission line. The coupler can be rotated to accommodate either incidental or reflected power. The rf is then rectified, filtered, and applied to the meter, which is scaled in watts. The rf power of 50 to 1,000 watts can be measured between the frequencies of 2 MHz to 30 MHz; and 10 to 500 watts, between the frequencies of 30 MHz to 1,000 MHz.
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Q-13. What is the advantage of using in-line wattmeters over output power meters?
A bolometer features a specially constructed element of temperature-sensitive material. The active material is a semiconductor bead supported between two pigtail leads. When rf power is applied to a bolometer element, the power absorption by the element heats the element and causes a change in its electrical resistance. Thus, a bolometer can be used in a bridge circuit so that small resistance changes can be easily detected and power measurement can be accomplished by the substitution method (that is, substitution of dc or low-frequency power to produce an equivalent heating effect). A D'Arsonval meter movement is usually employed as the null indicator.
According to one principle of measurement (the principle used in the balanced bridge), the bridge is initially balanced with low-frequency bias power. Rf power is then applied to the bolometer and the bias power is gradually removed until the bridge is again balanced. The actual rf power is then equal to the bias power removed.
According to another principle of measurement (the principle used in the unbalanced bridge), the bridge is not rebalanced after the rf power is applied. Rather, the indicator reading is converted directly into power by calibration previously performed.
Figure 3-16 illustrates the basic bolometer bridge circuit. The bolometer element must be physically small to be highly sensitive; it must be equally responsive to low-frequency and rf power; and it must be matched to the rf-input power line. The cross-sectional dimension of the bolometer element is approximately equal to the skin depth of rf current penetration at the highest frequency of operation. This condition permits the dc and rf resistivities to be essentially equal with the reactive component of the bolometer impedance at a minimum. Thermistors, which are a type of bolometer, use semiconductor material shaped like a bead, with a thicker skin depth and shorter length to minimize standing-wave effects. These physical properties assure correspondence between lengthwise low-frequency and rf power distribution to provide the necessary inherent accuracy of the bolometer.
An air-mounted bolometer provides a power sensitivity 100 or more times greater than that provided by static calorimetric devices. Additional sensitivity may be obtained by mounting the element within an evacuated envelope to eliminate convective heat loss. The small size of bolometer elements is associated with small thermal mass and short thermal time constants. The thermal time constant varies directly with the volume-to-area ratio of the element for a particular shape and composition. Typical time is up to 0.1
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second for thermistor beads. The thermistor type of bolometer element is usually composed of a ceramic- like mixture of metallic oxides having a large negative temperature coefficient of resistance. Two fine platinum-alloy wires are embedded in the bead, after which the bead is heated and coated with a glass film. Typical dimensions of a thermistor bead used for microwave measurements are 0.015 inch along its major axis and 0.010 inch along its minor axis. The thermistor bead may be operated at high temperatures; it is rugged, both electrically and mechanically; it has high resistance-power sensitivity; and it has a good temperature-power sensitivity. In addition, it can endure large pulse energies; it has a sluggish thermal response; and it has negligible pulsed-power measurement errors. The more sensitive thermistor requires thermal shielding or heat compensation for best operation.
Q-14. What type of material is used in the construction of bolometers and thermistors?
The standard power meter used in the Navy (Hewlett-Packard 431 C) is an automatic self-balancing instrument employing dual-bridge circuits. It is designed to operate with temperature-compensated thermistor mounts that enable you to measure power in a 50-ohm coaxial system from 10 MHz to 18 GHz and in a waveguide system from 2.6 GHz to 40 GHz. This power meter can be operated from either an ac or a dc primary power source. The ac source can be either 115 or 230 volts at 50 to 400 hertz. The dc source is a 24-volt rechargeable battery. A seven-position range switch allows full-scale power measurements of 10 microwatts to 10 milliwatts or of −20 dBm to +10 dBm. These ranges can be further extended with the aid of attenuators. The thermistor mount (as shown in fig. 3-17) contains two thermistors: one in the detection bridge, which absorbs the microwave power to be measured, and the other in the compensation and metering bridge, which supplies temperature compensation and converts the measured rf power to a meter indication. Each bridge includes its respective thermistor element as a bridge arm.
3-20
Basically, the power meter circuit consists of two bridges; each bridge includes one of the thermistor elements as a bridge arm. The bridges are made self-balancing through the use of feedback loops. Positive or regenerative feedback is used in feedback loop 1; degenerative (negative) feedback is used in feedback
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loop 2. Both bridges are excited by a common 10-kHz source. The 10-kHz amplifier-oscillator supplies 10-kHz power to bias the thermistor in feedback loop 1 to produce the resistance required to balance the rf bridge. An equal amount of 10-kHz power is supplied by the same oscillator to the second thermistor in feedback loop 2 through two series-connected transformers. Feedback loop 2 balances the meter bridge. When rf is applied to the thermistor in the detection bridge (but not to the compensation and metering bridge), an amount of 10-kHz power is present, equal to the rf power being removed from the detection bridge by the self-balancing action of the bridge. Since the rf power replaced the 10-kHz power, the detection bridge is in balance; however, the metering bridge must be balanced by its separate feedback loop. Sufficient dc power to equal the 10-kHz power lost by the metering bridge is automatically replaced, balancing this loop. Hence the dc power applied to the metering bridge thermistor is equal to the microwave power applied to the detection bridge. The meter circuit senses the magnitude of the feedback current. The resultant meter current passes through a differential amplifier to the indicating meter. The two thermistors are matched with respect to their temperature characteristics; therefore, there is only a very small amount of drift of the zero point with ambient temperature changes. When there is a change in temperature, there is a change in the electrical power needed by the thermistors to maintain constant operating resistances. This change is automatically performed by feedback loop 1, which changes the amount of 10-kHz power for both thermistors by the proper amount. The dc power in feedback loop 2 is not changed; and since it is this dc power that is metered, the temperature change has not affected the meter indication.
The calorimeters are the most accurate of all instruments for measuring high power. Calorimeters depend on the complete conversion of the input electromagnetic energy into heat. Direct heating requires the measurement of the heating effect on the medium, or load, terminating the line. Indirect heating requires the measurement of the heating effect on a medium or body other than the original power- absorbing material. Power measurement with true calorimeter methods is based solely on temperature, mass, and time. Substitution methods use a known, low-frequency power to produce the same physical effect as an unknown rf power being measured. Calorimeters are classified as STATIC (nonflow) types and CIRCULATING (flow) types.
Q-15. Power measurements performed with calorimeters are based on what three variables?
The static calorimeter uses a thermally shielded body. Since an isolated body loses little heat to a surrounding medium, the temperature increase of the body is in direct proportion to the time of applied power. The product of the rate of temperature rise in the calorimetric body and its heat capacity equals applied power. Figure 3-18 illustrates a static-type calorimeter.
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The most common type of static calorimeter is the ADIABATIC calorimeter. In the adiabatic meter, power is applied directly to a thermally isolated body; and the rate of temperature rise is determined from a temperature change measurement during a sufficiently long, known time interval. Figure 3-19 illustrates an adiabatic calorimeter using water as the body contained in a covered Dewar flask.  Thorough mixing of the water is accomplished with a stirrer, and a sensitive thermometer measures the temperature rise. A heating coil is wound around the waveguide inside the calorimeter and is used for calibrating purposes when low-frequency power is applied. This type of meter can be used for accurate measurement of several hundred watts of average power and can withstand 50 kilowatts of peak power.
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The NONADIABATIC calorimeter uses an rf termination with a resistive film strip or LOSSY dielectric materials (solids or liquids that are designed to efficiently dissipate the applied power) as a load. Temperature indication can be accomplished with thermocouples, thermopiles, thermistors, thermometers, bimetallic strips, and manometers. Calibration is against a power standard or known low- frequency power.
Based on the above principle, a coaxial calorimeter of good sensitivity with a short, 50-ohm resistive film on a lava (dielectric) center conductor, enclosed within a tapered, thin-walled outer conductor, is used for frequencies between 0 and 1.2 GHz. The rf termination is electrically connected to, but thermally isolated from, a massive mounting plate by a short section of silvered-lava coaxial line with a high thermal resistance. The steady-state temperature rise of the outer casing of the load with respect to the mounting plate is measured by a differential platinum-resistance thermometer in a Wheatstone bridge. Low-frequency power applied to the termination provides a method of calibration. Power in the range of 0 to 2.5 watts may be measured. A 70-second time constant and steady-state temperatures are attained in about 6 minutes. The small physical size of termination (to keep convective and radiative heat losses low) provides high sensitivity. Calibration with lower frequency power is extremely accurate, because the termination is broadband and should exhibit the same power distribution from dc to 10 gigahertz.
A twin calorimeter provides a method of using two calorimetric bodies thermally shielded against ambient temperature variations and improves sensitivity. Figure 3-20 illustrates this type of calorimetric device. The power to be measured is applied to one calorimetric body; the other calorimetric body acts as a temperature reference. The steady-state temperature difference between the two calorimeters is used as a measure of rf power. Calibration is performed by applying low-frequency power. A differential-air, thermometer-type temperature difference indicator, shown in figure 3-21, is used with a twin calorimeter to measure microwave power in the 0.1-mW range. This instrument consists of two similar glass cells connected by a capillary tube containing a liquid pellet. Each glass cell contains a tapered, carbon-coated strip; and the entire assembly is mounted in a rectangular waveguide. Balancing dc power heats one strip; the other strip is heated by rf power. The liquid pellet, which indicates the differential expansion of the air within the two cells, is viewed through an aperture in the waveguide wall, preferably with a microscopy for highest sensitivity. This procedure permits a 2% accuracy at 10 mW.
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Flow calorimeters are classified by the type of circulating method used (open or closed), the type of heating used (direct or indirect), and the type of measurement performed (true calorimetric or substitution). Water or other calorimetric fluid is used only once in an open system. An overflow system is used to maintain a constant rate of flow. Closed systems recirculate the fluid continuously by means of a pump, and a cooling system restores the fluid to ambient temperatures prior to its return to the calorimeter. Closed systems are more elaborate and permit the use of fluids other than water.
Flow calorimeters provide the primary standards for the measurement of high power levels; and, in conjunction with calibrated directional couplers, attenuators, power dividers, or other similar devices serve to standardize medium- and low-power measuring instruments. The measurement time depends on the required time for the entering fluid to reach the outlet, where the rise in temperature is measured. The circulating fluid may serve in a dual capacity as the dissipative medium and coolant, using the direct heating method, or solely as a coolant, using the indirect heating method. Because of its excellent thermal properties and high dielectric losses at 1 GHz or higher, water is normally used in both heating methods. Water is rarely used as the fluid at frequencies lower than 100 MHz, because of insufficient dielectric losses. The indirect heating method offers a wider frequency and power-range coverage and can be used in substitution-type measurements.
True calorimetric measurements contain appreciable error, because of nonuniformity of flow rate, air bubbles, flow-rate measurement inaccuracies, and temperature rise. Flow regulators, bubble traps, and good thermal insulation are required to eliminate the majority of these errors. Substitution methods do not involve direct heat dissipation measurement of moving fluid. Greater accuracy is obtained because known low-frequency power is substituted for the unknown rf power, with all other measurement parameters remaining constant. The accuracy depends on the exactness of the low-frequency power determination and the degree to which factors remain fixed during the substitution of one type of power with another.
Figure 3-22 illustrates a flow calorimeter using low-frequency power substitution. Two different measurement techniques are possible with this type of meter: the calibration technique and the balance technique. The CALIBRATION TECHNIQUE uses an adjustable known power to exactly reproduce the same temperature indication originally obtained by the unknown rf power measurement. The BALANCE TECHNIQUE uses an initial low-frequency power (P1) to provide a steady-state temperature rise in the calorimetric fluid. When unknown rf power is applied, the original power (P 1) is reduced to a new power (P2) to maintain the same temperature indication. Therefore, the actual power equals P1 minus P 2. Figure 3-23 illustrates a widely used method of power measurement using a balanced-flow calorimeter. Temperature-sensitive resistors are bridge-connected as the thermometric elements and are balanced at ambient temperature prior to the application of power. Low-frequency balancing power and the unknown
3-25
rf power are applied to maintain the bridge at null. This occurs when the temperature rise caused by the unknown rf power equals the temperature rise caused by the known low-frequency power.
Q-16. What is the result of applying power to a calorimeter?
3-26
Frequency measurements are an essential part of preventive and corrective maintenance for communication and electronic equipment. Rotation frequencies of some mechanical devices must be determined; the output frequency of electric power generators is checked when the engine is started and during preventive maintenance routines; carrier equipment that operates in the audio-frequency range must be adjusted to operate at the correct frequencies; and radio transmitters must be accurately tuned to the assigned frequencies to provide reliable communications and to avoid interfering with radio circuits operating on other frequencies. These are only a few of the applications for making frequency measurements.
Frequency-measuring equipment and devices, particularly those used to determine radio frequencies, constitute a distinct class of test equipment, because of the important and critical nature of such measurements. The requirement of precise calibration is extremely important in all frequency-measuring work. To provide accurate measurements, every type of frequency-measuring device must be calibrated against some frequency standard.
Of considerable importance in the measurements of frequency or wavelength are the standards against which frequency-measuring devices are compared and calibrated. Frequency standards belong to two general categories: primary and secondary standards. The PRIMARY FREQUENCY STANDARD maintained by the U.S. National Bureau of Standards has long-term stability and an accuracy of 1 part in 1012, using an atomic clock. A SECONDARY FREQUENCY STANDARD is a highly stable and accurate standard that has been calibrated against the primary standard. Secondary standards are maintained by calibration laboratories that service your test equipment.
The National Bureau of Standards provides time and frequency standards from station WWV at Fort Collins, Colorado, and from station WWVH at Kekaha, Kauai, Hawaii. The following technical radio services are given continuously by these stations:
The UTC scale uses the ATOMIC SECOND as a time interval. UT 1 is based on the earth's uniform rate of rotation. Since the earth's rotation is not precisely uniform, UT1 is an adjustable interval.
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To ensure reliable coverage of the United States and extensive coverage of other parts of the world, radio stations WWV and WWVH provide the primary standard radio frequencies listed in table 3-1. The transmission of WWV and WWVH are interrupted for 5 minutes of each hour. The silent period begins at 15 minutes past the hour for station WWVH and 45 minutes past the hour for station WWV. These silent periods are provided to eliminate errors caused by interference.
Table 3-1.—NBS Frequency Standards and Time Transmission
RF Signal Frequency MHz 5, 10, and 15 5, 10, and 15 Frequency Stability 1 part in 1011 1 part in 1011 Frequency Deviation 1 part in 1012 per day 1 part in 1012 per day Seconds Frequency and Duration 5 cycles of 1000Hz for .005
seconds 6 cycles of 1200Hz for .005 seconds
Frequency Accuracy 1 part in 1012 1 part in 1012 Propagation Forecast 14 min. past the hour (in voice) None
Two primary standard audio-frequency tones (440 Hz and 600 Hz) are broadcast on all WWV and WWVH carrier frequencies. In the absence of a message, a 500-Hz tone is broadcast during the message interval. The 440-Hz signal that denotes the 1-hour mark is the standard musical pitch, A above middle C. The 600-Hz tone provides a frequency standard for checking the 60-Hz power-line frequency.
The standard time pulse marking interval of 1 second consists of five cycles of a 1,000-Hz tone at WWV and six cycles of a 1,200-Hz tone at WWVH. These marker pulses are heard as clock ticks. Intervals of 1 minute are marked by a 0.8-second, 100-Hz tone for WWV and a 0.8-second, 1,200-Hz tone for WWVH. Each hour is marked by a 0.8-second, 1,500-Hz tone on both stations. Universal Time Coordinated (UTC) is announced on WWVH between the 45 and 52.5 seconds of each minute and on WWV between the 52.5 and 60 seconds of each minute.
An announcement of radio propagation conditions (geophysical alert) for the North Atlantic area is broadcast by station WWV in voice at 18 minutes after each hour. For example, these short-term announcements might state, "The radio propagation quality forecast at ... (normal, unsettled, disturbed)." The propagation format is repeated phonetically and in numerical code to ensure clarity. The letter designations N, U, and W, signifying "normal," unsettled," and "disturbed," respectively, classify the radio propagation conditions at the time of the broadcast. The digits from 1 to 9 indicate the expected radio propagation conditions during the next 6 hours; refer to table 3-2 for code interpretations. The National Bureau of Standards forecasts are based on information obtained from a worldwide network of geophysical and solar observations.
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Table 3-2.—NBS Radio Propagation Coding
Q-17. What government agency is responsible for monitoring our primary frequency standards?
There are many instances when you are very much concerned with the question of rotational or vibratory speeds. Knowledge of rotational speeds is necessary where the output of a direct current generator has fallen below a minimum desired output or where the speed of a motor (such as the motor in a teletypewriter or radar antenna) must be maintained at a constant value. There are many instruments that you can use for this purpose, such as tuning forks, stroboscopes, vibrating-reed meters, and electromechanical counters. The oscilloscope and the frequency counter are two of the other devices which may be used, but their use may require the employment of accessory equipment.
A tuning fork is generally used in conjunction with the measurement of the rotational speed of a teletypewriter or facsimile motor but is not limited to this application. However, you must remember that the tuning fork can be used at only one frequency, the frequency of vibration for which it was manufactured, and therefore cannot be used on variable-speed motors. To use the tuning fork, you direct a source of light upon the point to be observed. In the case of a teletypewriter, a black-and-white segmented target is painted on the outer circumference of the motor governor. Radial spokes in a flywheel could be used equally well. Permit the motor to reach operational speed under normal load conditions; otherwise, the motor will slow down considerably when the normal load is applied. Strike the tuning fork against the side of your hand to set it into vibration. Then observe the target through the slots in the plates attached to the tines of the fork. The correct speed is obtained when the segments of the target appear to be stationary. If the segments seem to move backward, apparently against the known motor rotational direction, the speed is too low. If the segments seem to move forward, the speed is too high. There is also the possibility that the target segments will appear to jump back and forth or to disappear suddenly. Such erratic action is often because of governor malfunctioning. The correct speed adjustment is reached when the targets appear to be stationary.
Q-18. What is the primary measurement application for tuning forks?
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When using a stroboscope to measure the speed of rotating or reciprocating mechanisms, hold the instrument so that the light from the stroboscope lamp falls directly on the part to be observed. If the part is uniform, or symmetrical, place an identification mark with chalk or a grease pencil on the portion to be observed. This method provides a positive means of identification, because if only one reference mark is observed during measurement, you can be sure that either the fundamental synchronization or a submultiple thereof has been obtained. If the approximate speed of rotation is known, the stroboscope controls may be set to the appropriate positions prior to actual measurement. The main frequency control that determines the rate of the flashing light is then varied until the reference mark on the moving part appears to be standing still. The calibrated scale of the stroboscope will then show the speed directly in revolutions per minute (rpm).
If you have no idea of the speed of the moving part, it is best to start the measurement procedure at the highest frequency that the stroboscope can deliver. The flashing rate of the stroboscope can then be gradually reduced until a single stationary image of the reference mark is obtained. This is the point of fundamental synchronism that corresponds to the speed of the moving part. Do not continue to reduce the flashing rate of the instrument beyond this point without a valid reason for doing so. If you do continue the reduction, a stationary image will still be observed, but the stroboscope will indicate a submultiple of the true rotational speed; thus, a measurement error will be introduced.
Stroboscopes generally have a high- and low-range switch. The typical low range is from 600 to 3,600 rpm, and the upper range is from 3,600 to 15,000 rpm; there is a slight overlap in ranges to ensure reliable frequency coverage. In view of the limitation imposed by flasher tube life, the stroboscope should always be operated at a flashing rate that is as low as possible, consistent with the rotational speed of the observed part. If you should be required to operate this instrument over a long period of time, use a submultiple of the fundamental synchronous speed. The pattern will remain just as stationary, and the tube life will be greatly extended. In addition, the quality of the light is better at the lower ranges than at the upper end of the scale. Sometimes you will encounter a rotating or vibrating device that is moving faster (or slower) than the measuring range of the stroboscope will accommodate. Although such speeds can still be measured, you must use the multiple or submultiple synchronism points.
There are two methods of measuring high speeds. The first method is to obtain a single stationary image of the rotating object at a subharmonic speed relationship and to record that value as A. Then obtain a second single stationary image at the next lower subharmonic speed relationship, and record this value as B. The unknown speed may then be computed from the following formula:
For example, assume reading A was 4,000 rpm and reading B was 3,500 rpm. The computation would be as follows:
3-30
The second method is used where the value of A × B becomes progressively smaller. The A reading is obtained as in the previous example (for the sake of easier computation, suppose that the A reading is still 4,000 rpm). Then obtain another submultiple reading for B, keeping in mind the number of times a stationary single image was observed. If a stationary single image was observed seven different times and the final B reading was 2,000 rpm, the calculation would become as follows:
At speeds lower than the lowest range of the stroboscope, multiple images will be observed. For example, assume a dial reading of 900 rpm was obtained when two stationary images were observed. Then dividing the rpm by the number of images will give the unknown shaft speed, as shown below:
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Exercise caution in using a stroboscope. The illusion of stopped motion is very convincing. Do not attempt to touch the moving equipment.
Q-19. If you are required to monitor the speed of a device with a stroboscope over an extended period of time, what step should be taken to prolong the life of the flasher tube?
Various frequency counters have found application as an ELECTRONIC TACHOMETER to obtain accurate measurements of high-speed rotating machinery. A tachometer pickup may be used to produce signals that are fed directly to the frequency counter. If the tachometer pickup is designed to generate 1 signal per revolution, the counter will indicate directly in revolutions per second; if the pickup is designed to produce 60 signals per revolution, the counter will indicate directly in revolutions per minute.
Audio-frequencies can be measured with a variety of nonelectronic and electronic devices.
Examples of nonelectronic measuring devices are the vibrating-reed meter and the moving-disk frequency meter. (Both of these devices were discussed in NEETS, module 3.) They are used primarily to measure the frequency of ac power, 60 Hz. However, such instruments do not have a wide frequency range. The most common instruments available for the measurement of audio frequencies are oscilloscopes and frequency counters.
The frequency of a waveform can readily be determined by using an oscilloscope. The most common oscilloscope method of measuring a frequency is accomplished by first measuring the time duration of the waveform. Frequency is the reciprocal of time
and may be easily computed, as shown in figure 3-24.
3-32
Another common method of determining the frequency of a waveform is by using Lissajous patterns. This method was discussed in NEETS, module 19.
While oscilloscopes can be used to compare rectangular waveforms for the purpose of measuring the frequency of a signal, frequency counters, as shown in figure 3-25, are much more useful for this purpose. The fundamental measurement of frequency is accomplished by totaling the number of cycles into the counter for a precise period of time. The result is then displayed as an exact digital readout. The audio- frequency signal must be of sufficient amplitude to trigger the counter. The AUTO-MANUAL switch provides two methods of frequency counter operation. One method is to initiate the count simultaneously with the initiation of the signal to be measured. With this method, the AUTO-MANUAL switch should be set to the MANUAL position. The second method assumes that the signal to be measured has been operating over some indefinite period of time and that it will continue to do so after a measurement has been taken (hence, only that segment of the signal required to make the frequency measurement is important). With this method, the AUTO-MANUAL switch is to be set to the AUTO position.
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Radio-frequency measurements are primarily made with frequency counters. Most oscilloscopes are limited in use to approximately 100 MHz. Frequency meters, such as the Hewlett-Packard 530 series, are widely used but lack the accuracy of frequency counters.
Prior to the invention of the frequency counter, most frequency measurements above the af range were made primarily with frequency meters.
This process involved heterodyning the frequency to be measured against the calibrated output of the frequency meter to obtain a zero beat from which the measured frequency was then read. This method proved inaccurate because of reading errors.
Frequency meters as we know them today are entirely different from their predecessors. Today's frequency meters (fig. 3-26) contain waveguide or coaxial lines coupled to quarter-wavelength resonant cavities. The meter is adjusted until the cavity is tuned to the resonant frequency of the signal being measured. At resonance, power is absorbed by the cavity and produces a dip in the output-power level, as measured at the frequency meter's output connector. The resonant frequency is read directly from the frequency meter dial and is accurate, in most cases, to approximately ±0.2%. Frequency meters are capable of measuring frequencies in the range of 1 to 40 gigahertz, far exceeding the frequency limitations of the average frequency counter.
Q-20. What happens when a frequency meter is adjusted to the frequency of the signal being measured?
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In the early 1950s, the frequency counter was developed. The device could measure and accurately indicate frequencies up to 10 MHz. Present-day frequency counters can accurately read frequencies as high as 40 GHz. In addition to direct frequency measurement indication, some types of frequency counters can measure the WAVE PERIOD, which is the inverse of frequency; RATIO, which compares one frequency against another; and TIME INTERVAL, the time between two events or the time between two functions of an event. In addition, frequency counters can totalize event indications. This is similar to measuring the frequency except that a manual or an electronic start-stop gate controls the time over which the measurement is taken. Frequency counters can also provide scaling in the form of a digital output signal from the frequency counter that represents a frequency-related division of the input frequency.
All of the above functions have useful applications. For pulse timing, the period function is used; totalizing is used in digital applications; and ratio is used in comparing harmonic-related signals. Scaling is used for triggering other test equipment used in conjunction with the frequency counter; and time- interval capability is used in measuring the interval between two pulses or between two sets of pulses. Because of the wide variety of frequency counters in use, the technical manual for a specific frequency counter should be consulted to determine the instrument's full capabilities.
All frequency counter measurements are measured with 1 part in 108 of accuracy. However, frequency counters have provisions for input from external frequency standards. This extends the accuracy of the frequency to that of the standard. A frequency self-check capability is provided to determine if the counting and lighting circuits are operating properly.
3-35
Wavemeters are calibrated resonant circuits used to measure frequency. Although the accuracy of wavemeters is not as high as that of heterodyne frequency meters, they have the advantage of being comparatively simple and can be easily carried about.
Any type of resonant circuit may be used in wavemeter applications. The exact kind of circuit employed depends on the frequency range for which the meter is intended. Resonant circuits consisting of coils and capacitors are used for low-frequency wavemeters. Butterfly circuits, adjustable transmission line sections, and resonant cavities are used in vhf and microwave instruments.
There are three basic kinds of wavemeters: the absorption, the reaction, and the transmission types. Absorption wavemeters are composed of the basic resonant circuit, a rectifier, and a meter for indicating the amount of current induced into the wavemeter. In use, this type of wavemeter is loosely coupled to the circuit to be measured. The resonant circuit of the wavemeter is then adjusted until the current meter shows a maximum deflection. The frequency of the circuit under test is then determined from the calibrated dial of the wavemeter.
The reaction type derives its name from the fact that it is adjusted until a marked reaction occurs in the circuit being measured. For example, the wavemeter is loosely coupled to an oscillator, and the resonant circuit of the meter is adjusted until it is in resonance with the oscillator frequency. The setting of the wavemeter dial is made by observing the output current of the oscillator. At resonance, the wavemeter circuit takes energy from the oscillator, causing the current to dip sharply. The frequency of the oscillator is then determined from the calibrated dial of the wavemeter.
The transmission wavemeter is an adjustable coupling link. When it is inserted between a source of rf energy and an indicator, energy is transmitted to the indicator only when the wavemeter is tuned to the frequency of the source. Transmission wavemeters are widely used in measuring microwave frequencies.
In figure 3-27, a typical cavity wavemeter is illustrated.
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The wavemeter illustrated is of the type commonly used for the measurement of microwave frequencies. The device employs a resonant cavity, which effectively acts as a high-Q LC tank circuit. The resonant frequency of the cavity is varied by means of a plunger that is mechanically connected to a micrometer mechanism. Movement of the plunger into the cavity reduces the cavity size and increases the resonant frequency. Conversely, an increase in the size of the cavity (made by withdrawing the plunger) lowers the resonant frequency. The microwave energy from the equipment under test is fed into the wavemeter through one of two inputs, A or D. A crystal rectifier then detects or rectifies the signal, and the rectified current is indicated on the current meter, M.
The instrument can be used as either a transmission type or an absorption type of wavemeter. When used as a transmission wavemeter, the unknown signal is coupled into the circuit by means of input A. When the cavity is tuned to the resonant frequency of the signal, energy is coupled through coupling loop B into the cavity and out through loop C to the crystal rectifier where it is rectified and indicated on the meter. At frequencies off resonance little or no current flows in the detector and the meter reading is small. Therefore, the micrometer and attached plunger are varied until a maximum meter reading is obtained. The micrometer setting is then compared with a calibration chart supplied with the wavemeter to determine the unknown frequency.
When the unknown signal is relatively weak, such as the signal from a klystron oscillator, the wavemeter is usually used as an absorption type of device. Connection is made to the instrument at input D. Rf loop C then acts as an injection loop to the cavity. When the cavity is tuned to the resonant frequency of the klystron, maximum energy is absorbed by the cavity, and the current indicated on the meter dips. When the cavity is not tuned to the frequency of the klystron, high current is indicated on the current meter. Therefore, the cavity is tuned for a minimum reading, or dip, in the meter; and the resonant frequency is determined from the micrometer setting and the calibration chart.
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The potentiometer, R1, is used to adjust the sensitivity of the meter from the front panel of the instrument. J1 is a video jack and is provided for observing video waveforms with a test oscilloscope.
The following is a brief summary of the important points of this chapter.
All IMPEDANCE BRIDGES have several things in common. Each type of bridge has a comparing circuit and a measuring circuit. They measure an unknown impedance by comparing the characteristics of the device under test with the characteristics of components within the test set.
POWER METERS that are designed to measure af power can be separated into two distinct groups. Power meters that are designed for measuring sine waves are basically electronic voltmeters calibrated in dB or dBm. VU METERS are designed to measure the average value of complex waveforms, such as a voice.
The most common type of test equipment used to measure rf power is the ABSORPTION POWER METER. Absorption power meters are designed to absorb all or part of the signal being measured. Examples of absorption power meters are output power meters, in-line wattmeters, and meters employing bolometers.
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CALORIMETERS are the most accurate type of test equipment used for measuring high power. As power is applied to a calorimeter, its medium (either liquid or solid) is heated. The heat that is produced is directly proportional to the amount of applied power. The amount of applied power is determined by measuring the change in temperature of the medium.
Today's ELECTRONIC FREQUENCY COUNTERS are capable of measuring frequencies from dc to 40 GHz. Most have added features that enable period averaging, time-interval measurements, and scaling. Frequency counter accuracy can be extended by using an external frequency standard in lieu of its internal frequency standard.
Coaxial Frequency Meter, NAVSHIPS 0969-092-3010, Naval Ships Systems Command, Washington, D.C., 1978.
EIMB, Test Methods and Practices, NAVSEA 08967-LP-000-0130, Naval Sea Systems Command, Washington, D.C., 1980.
Fire Control Technician (M) 3 & 2, NAVEDTRA 10209-A, Naval Education Training and Program Development Center, Pensacola, Fla., 1974.
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NEETS, Module 16, Introduction to Test Equipment, NAVEDTRA 172-16-00-84, Naval Education and Training Professional Development and Technology Center, Pensacola, Fla., 1984.
ANSWERS TO QUESTIONS Q1 THROUGH Q20.
A-1. A bridge circuit is balanced when the opposite legs of the comparing and measuring circuits exhibit the same voltage drop.
A-2. The capacitive and inductive characteristics of the test leads.
A-3. As the supply voltage increases, bridge components may heat up and become less accurate.
A-4. Small values of resistances.
A-5. A standard capacitor.
A-6. Both measure phase angle and magnitude in determining impedance.
A-7. High vswr, which equates to poor reception or a loss of power output.
A-8. DB, dBm, and vu.
A-9. 600-ohm load.
A-10. DB meters are used for measuring sine waves. Vu meters are used to measure the average value of complex waveforms.
A-11. Current transformers.
A-12. Electronic wattmeters are capable of measuring high-fequency signals.
A-13. Most in-line wattmeters are capable of measuring both forward and reflected power.
A-14. Temperature-sensitive material that exhibits a large negative temperature coefficient.
A-15. Temperature, mass, and time.
A-16. As power is applied, the medium heats up in proportion to the applied power.
A-17. The National Bureau of Standards.
A-18. They are used to monitor fixed motor speeds.
A-19. Monitor a submultiple frequency to prolong the flasher-tube life.
A-20. Power is absorbed by the frequency meter cavity; and a pronounced dip in power, at the output, will be observed.
4-1
Upon completion of this chapter, you will be able to do the following:
1. Identify the various methods of measuring standing-wave ratios.
2. Identify the various methods of determining electrical losses caused by deterioration of transmission lines.
3. Identify the methods of measuring intermodulation distortion.
INTRODUCTION TO QUALITATIVE MEASUREMENTS As a technician, you are responsible for repairing and maintaining complex electronic systems. The
basic ability to repair a specific piece of equipment is only the first step in becoming a qualified technician. Your ultimate goal should be to become proficient at systems fault isolation — in other words, to know the entire system like the back of your hand. To reach this goal you will need to be familiar with all parts of the system and know how they are interconnected and interact with each other. There are numerous shortcuts or tricks of the trade that can only be learned through experience on any system, but the most practical thing for you to remember is to approach all problems in a logical manner.
Various combinations of electronic equipment are interconnected to form a system capable of performing specific functions. You must be able to apply general test methods and practices to installation, tuning, maintenance, and repair of the system. This requires you to have a thorough knowledge of many types of electronic equipment. When radar, communication, and digital computers are interconnected, they require different maintenance procedures than when they are operated separately. Revised test procedures may be necessary. Detrimental interactions between equipment or facilities must be corrected and effective preventive maintenance procedures must be planned for all equipment within the system. System quality figures, such as sensitivity and coverage, must be determined and measured during equipment preventive maintenance checks to assure efficient operation. System monitoring at specific test points is often used to help localize a problem.
System testing and monitoring are frequently accomplished by using an external piece of electronic equipment, which is designed specifically for testing a particular system. Some computers and computer systems build in their own monitoring and testing devices and will inform the operator when and where failure has occurred. You must realize that any equipment designed to test, monitor, or repair another system is itself subject to malfunction and will require periodic checks and preventive maintenance. This chapter will cover some of the basic test methods and practices associated with system-level troubleshooting.
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current at any point along a transmission line. Swr measurements are used to determine the matching quality of the termination of the line.
A variety of methods and test equipments may be used to measure the voltage or current distribution along a transmission line. An open transmission line is accessible for coupling to many types of voltage- measuring devices, such as a wavemeter or a grid-dip meter. However, at higher frequencies where coaxial cables or waveguides are used to minimize skin effect losses, (discussed in NEETS, module 10) access is more complicated. Access to the interior of the waveguide or center conductor of the coaxial cable must be gained by using a unidirectional or bidirectional coupler, which is inserted into the transmission line. The coupler contains a slot into which an rf probe is inserted and positioned with respect to directivity.
The conditions that produce standing waves and their adverse effects are discussed in detail in NEETS, module 10. The different methods of detecting and measuring standing waves are discussed in the following paragraphs.
A magnetic or electric probe can be used to observe the standing wave on a short-circuited, terminated line. The wavelength is obtained by measuring the distance between alternate maximum or minimum current points along the line. A typical setup operating at 300 megahertz might use two 10-foot lengths of number 14 phosphor-bronze wires, which are spaced 1 inch apart and supported parallel to a set of probe guide rails. The line should be partially matched to the source generator by means of a parallel- wire shorting stub connected in parallel with the transmission line and the oscillator output line. Figure 4- 1, view A and view B, illustrates the types of probes required for this method of measurement.
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In this method of measurement, a neon bulb or milliammeter is moved along the two-wire parallel transmission line. Points of maximum voltage (standing-wave voltage peaks) with the lamp or points of maximum current (standing-wave current peaks) with the indicator will have maximum brilliance or indication, respectively.
Q-1. At what points along a transmission line will a neon lamp glow the brightest? BRIDGE METHODS
The bridge method permits measurement of the standing-wave ratio without actually measuring the standing waves. The bridge method is applicable because the input impedance of a line terminated in its characteristic impedance is a pure resistance equal to the characteristic impedance. A line terminated in this way can be used as the unknown resistance in a bridge circuit and a null can be obtained in the indicating device when the other resistance arms of the bridge are properly adjusted.
Many types of bridges can be used. For example, an ac bridge that is independent of the applied frequency can be used. The bridge will become unbalanced when the line is no longer properly terminated. Improper termination will produce a reactive component as well as a resistive component in the input impedance of the line and result in a standing wave. The reading of the indicating device depends on the degree of imbalance, which becomes more severe as the mismatch caused by the termination becomes worse. The indicating device can be calibrated directly to indicate the standing-wave ratio. The most common indicator consists of a crystal rectifier, a filtering circuit, and a sensitive dc meter movement in series with a high resistance.
A resistance-capacitance bridge circuit is shown in view A of figure 4-2. The bridge is theoretically independent of the applied frequency.
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However, the applied frequency must be low enough to avoid skin effect, stray inductance, capacitance, and coupling between circuit elements and wiring. The leads must be kept short to eliminate stray reactance, which causes bridge imbalance. The rectifier circuit wiring must be isolated from other bridge component fields so that induced voltages do not cause an erroneous indication. You should only use resistors having negligible capacitance and inductance effects.
Before you calibrate a newly constructed bridge, the following procedure must be followed if residual readings caused by stray effects are to be held to a minimum:
1. Connect a noninductive resistor (RL in view B) that is equal to the characteristic impedance of the line to the output terminals of the bridge.
2. Apply an rf voltage to the input terminals and adjust the variable capacitor for a minimum reading on the meter.
3. Reconnect the resistor (R L) to the input terminals and connect the rf power source to the output
terminals.
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4. Adjust the rf voltage amplitude applied to the bridge until a full-scale meter reading is obtained. 5. Reconnect the bridge in the normal manner (resistor RL to the output terminals, etc.). If the meter
reading is now more than 1% or 2% of the full-scale reading, different arrangements (lead dress) of the internal wiring must be tried until the null is reduced to 0 or as close as possible to the 0 point.
The bridge can be calibrated after completion of the preceding check. Connect the transmission line under investigation to the output terminals of the bridge and connect a succession of noninductive resistors (RO in view C) to the load end of the transmission line until the bridge is balanced. Assuming that the bridge was originally balanced for the characteristic impedance of the line, the standing-wave ratio can be computed from the following equation:
Select the formula that yields a ratio greater than unity. The swr calibration can be recorded on the meter scale directly, recorded on a chart in terms of the meter deflection, or plotted on a graph against the meter deflection. The variable capacitor, in turn, can be calibrated for various characteristic impedances. This is accomplished by applying suitable resistors (RO) across the output terminals and noting the capacitor settings at the respective balance points. A range of 50 to 300 ohms should prove attainable.
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To assure accurate measurements, the rf signal applied to the bridge must be properly adjusted each time a calibrated instrument is used. Essentially, this adjustment is a repetition of the previously described reversed-bridge procedure. The following steps are to be performed:
1. Connect the line to the input terminals of the bridge and connect the transmitter to the output terminals.
2. Adjust the transmitter coupling until full-scale deflection is obtained. From this point on, the coupling must be left untouched.
3. Reconnect the bridge in the usual way and proceed with the measurement.
For maximum transfer of the power out of an rf source, with minimum heating from reflected power, the total output impedance sensed by the rf source must be equal to the internal impedance of that source. A perfect impedance match between transmitter and load would exist if the swr were 1 to 1. As discussed in NEETS, module 10, test equipment designed to measure the instantaneous voltage of a standing wave will give you a voltage standing-wave ratio (vswr). Test equipment designed to measure the instantaneous current component of a standing wave will give you the current standing-wave ratio (iswr). Regardless of the type of test equipment selected, both ratios will be the same.
Q-2. What vswr is a perfect match between a transmitter and its load? SWR METERS
The Hewlett-Packard Model 415E swr meter, shown in figure 4-3, is a commonly used swr meter. It is extremely accurate, sensitive, lightweight, easy to use, and portable. It is essentially a high-gain, tuned audio amplifier with a square-law meter that is calibrated to read swr directly. The meter is designed to be operated at a mean center frequency of 1,000 hertz.
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Figure 4-4 shows a typical swr measurement setup using the swr meter. The signal source is usually a sinusoidal wave that is square-wave modulated at 1,000 hertz.
The swr meter usually gets its input from a detector, either a barretter or a crystal diode. This detector must be a square-law device (its output voltage is proportional to the applied rf power) to ensure
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the accuracy of the meter. The input is amplified and applied directly to the meter. To perform the measurement as shown in figure 4-4, you move the detector along the slotted line so that its probe is at a voltage maximum and adjust the gain of the meter with the RANGE-DB, GAIN, and VERNIER controls (EXPAND switch to NORM) for full-scale deflection (1.0 on the 1.0 to 4 SWR scale). Then move the probe toward a minimum. If the meter drops below 3.2, rotate the RANGE-DB switch one position clockwise and read on the 3.2 to 10 SWR scale. If the pointer drops below this scale, rotate the RANGE- DB switch one more position clockwise and read on the 1.0 to 4 scale and multiply by 10. This pattern continues for still higher swr readings.
The dB scales can be used for a standing-wave-ratio measurement by setting the meter to full scale at a voltage maximum, then turning the RANGE-DB switch clockwise for an on-scale reading at a voltage minimum and noting the difference in dB reading at the maximum and minimum. A dB reading is obtained by adding the RANGE-DB switch setting and meter indication. The swr meter may also be used for high resolution insertion loss measurements.
The setup for performing insertion loss or attenuation measurements is shown in figure 4-5. It requires that you initially establish a convenient reference on the DB scale of the meter. This is accomplished by connecting the signal source directly to the detector and using the GAIN and VERNIER controls to adjust the meter pointer to a convenient reference. Then you can insert the device to be measured between the signal source and the detector and note the change in dB, as shown on the meter.
Transmission lines are sometimes subjected to extremes of weather and the corrosive effects of salt water. You should be aware of the adverse effects of this environment on transmission lines and how to determine electrical losses caused by transmission-line deterioration.
Q-3. What are the two common causes of transmission-line deterioration? LOSS MEASUREMENT
Insertion loss measurement of transmission lines requires the use of a good signal generator and an accurate power meter. The method is identical to the insertion loss measurements used on most couplers. When a known frequency, at a predetermined level of power, is inserted into one end of a transmission
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line, then the same frequency and the same level of power should be transmitted to the other end of a transmission line. Because all transmission lines contain some degree of resistance, some loss of power will occur during the test.
Exposure to the elements over a period of time causes transmission-line deterioration. To determine the accuracy of this test, you should use the power meter to measure the output of the signal generator at the end of the test cable to be attached to the transmission line. Any power loss associated with the test cables should be recorded and subtracted from the measurement taken with the transmission line connected.
You should note that transmission lines, like all other electronic components, are designed to operate over a specific range of frequencies. It is not uncommon for a transmission line to operate improperly at one frequency, yet operate properly over the remainder of its frequency spectrum. You should check transmission-line losses over their entire frequency range. Insertion loss measurements are normally taken when a system is first installed or the transmission line is replaced. Periodic measurements should be performed to enable you to determine if system performance is being degraded by transmission-line deterioration.
Q-4. Is it possible for a transmission line to operate improperly at certain frequencies and properly at others?
Transmission lines are engineered and manufactured to meet certain specifications. The most important of these specifications relates to frequency, power-handling capabilities, and characteristic impedance. The dielectric constant (K) of the insulating material is probably the manufacturer’s most important consideration and is the primary factor that affects the size of the coaxial cable. The formulas in the following sections discuss some aspects of coaxial transmission-line engineering.
A cross section of a coaxial line is shown in figure 4-6. The characteristic impedance of a coaxial line can be determined by the following formula:
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Table 4-1.—Dielectric Constants of Materials