DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.
DISTRIBUTION STATEMENT A: Approved for public release; distribution is unlimited.
Although the words “he,” “him,” and “his” are used sparingly in this course to enhance communication, they are not intended to be gender driven or to affront or discriminate against anyone.
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PREFACE By enrolling in this self-study course, you have demonstrated a desire to improve yourself and the Navy. Remember, however, this self-study course is only one part of the total Navy training program. Practical experience, schools, selected reading, and your desire to succeed are also necessary to successfully round out a fully meaningful training program.
COURSE OVERVIEW: To introduce the student to the subject of Wave-Generation and Wave-Shaping Circuits who needs such a background in accomplishing daily work and/or in preparing for further study.
THE COURSE: This self-study course is organized into subject matter areas, each containing learning objectives to help you determine what you should learn along with text and illustrations to help you understand the information. The subject matter reflects day-to-day requirements and experiences of personnel in the rating or skill area. It also reflects guidance provided by Enlisted Community Managers (ECMs) and other senior personnel, technical references, instructions, etc., and either the occupational or naval standards, which are listed in the Manual of Navy Enlisted Manpower Personnel Classifications and Occupational Standards, NAVPERS 18068.
THE QUESTIONS: The questions that appear in this course are designed to help you understand the material in the text.
VALUE: In completing this course, you will improve your military and professional knowledge. Importantly, it can also help you study for the Navy-wide advancement in rate examination. If you are studying and discover a reference in the text to another publication for further information, look it up.
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“I am a United States Sailor.
I will support and defend the Constitution of the United States of America and I will obey the orders of those appointed over me.
I represent the fighting spirit of the Navy and those who have gone before me to defend freedom and democracy around the world.
I proudly serve my country’s Navy combat team with honor, courage and commitment.
I am committed to excellence and the fair treatment of all.”
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1. Tuned Circuits .......................................................................................................... 1-1
2. Oscillators................................................................................................................. 2-1
3. Waveforms and Wave Generators............................................................................ 3-1
4. Wave Shaping........................................................................................................... 4-1
I. Glossary.................................................................................................................. AI-1
II. Square and Square Roots Table.............................................................................. AII-1
INDEX ......................................................................................................................... INDEX-1
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The Navy Electricity and Electronics Training Series (NEETS) was developed for use by personnel in many electrical- and electronic-related Navy ratings. Written by, and with the advice of, senior technicians in these ratings, this series provides beginners with fundamental electrical and electronic concepts through self-study. The presentation of this series is not oriented to any specific rating structure, but is divided into modules containing related information organized into traditional paths of instruction.
The series is designed to give small amounts of information that can be easily digested before advancing further into the more complex material. For a student just becoming acquainted with electricity or electronics, it is highly recommended that the modules be studied in their suggested sequence. While there is a listing of NEETS by module title, the following brief descriptions give a quick overview of how the individual modules flow together.
Module 1, Introduction to Matter, Energy, and Direct Current, introduces the course with a short history of electricity and electronics and proceeds into the characteristics of matter, energy, and direct current (dc). It also describes some of the general safety precautions and first-aid procedures that should be common knowledge for a person working in the field of electricity. Related safety hints are located throughout the rest of the series, as well.
Module 2, Introduction to Alternating Current and Transformers, is an introduction to alternating current (ac) and transformers, including basic ac theory and fundamentals of electromagnetism, inductance, capacitance, impedance, and transformers.
Module 3, Introduction to Circuit Protection, Control, and Measurement, encompasses circuit breakers, fuses, and current limiters used in circuit protection, as well as the theory and use of meters as electrical measuring devices.
Module 4, Introduction to Electrical Conductors, Wiring Techniques, and Schematic Reading, presents conductor usage, insulation used as wire covering, splicing, termination of wiring, soldering, and reading electrical wiring diagrams.
Module 5, Introduction to Generators and Motors, is an introduction to generators and motors, and covers the uses of ac and dc generators and motors in the conversion of electrical and mechanical energies.
Module 6, Introduction to Electronic Emission, Tubes, and Power Supplies, ties the first five modules together in an introduction to vacuum tubes and vacuum-tube power supplies.
Module 7, Introduction to Solid-State Devices and Power Supplies, is similar to module 6, but it is in reference to solid-state devices.
Module 8, Introduction to Amplifiers, covers amplifiers. Module 9, Introduction to Wave-Generation and Wave-Shaping Circuits, discusses wave generation and wave-shaping circuits.
Module 10, Introduction to Wave Propagation, Transmission Lines, and Antennas, presents the characteristics of wave propagation, transmission lines, and antennas.
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Module 11,Microwave Principles, explains microwave oscillators, amplifiers, and waveguides.
Module 12,Modulation Principles, discusses the principles of modulation.
Module 13, Introduction to Number Systems and Logic Circuits, presents the fundamental concepts of number systems, Boolean algebra, and logic circuits, all of which pertain to digital computers.
Module 14, Introduction to Microelectronics, covers microelectronics technology and miniature and microminiature circuit repair.
Module 15, Principles of Synchros, Servos, and Gyros, provides the basic principles, operations, functions, and applications of synchro, servo, and gyro mechanisms.
Module 16, Introduction to Test Equipment, is an introduction to some of the more commonly used test equipments and their applications.
Module 17, Radio-Frequency Communications Principles, presents the fundamentals of a radio- frequency communications system.
Module 18, Radar Principles, covers the fundamentals of a radar system.
Module 19, The Technician's Handbook, is a handy reference of commonly used general information, such as electrical and electronic formulas, color coding, and naval supply system data.
Module 20,Master Glossary, is the glossary of terms for the series.
Module 21, Test Methods and Practices, describes basic test methods and practices.
Module 22, Introduction to Digital Computers, is an introduction to digital computers.
Module 23,Magnetic Recording, is an introduction to the use and maintenance of magnetic recorders and the concepts of recording on magnetic tape and disks.
Module 24, Introduction to Fiber Optics, is an introduction to fiber optics.
Embedded questions are inserted throughout each module, except for modules 19 and 20, which are reference books. If you have any difficulty in answering any of the questions, restudy the applicable section.
Although an attempt has been made to use simple language, various technical words and phrases have necessarily been included. Specific terms are defined in Module 20,Master Glossary.
Considerable emphasis has been placed on illustrations to provide a maximum amount of information. In some instances, a knowledge of basic algebra may be required.
Assignments are provided for each module, with the exceptions of Module 19, The Technician's Handbook; and Module 20, Master Glossary. Course descriptions and ordering information are in NAVEDTRA 12061, Catalog of Nonresident Training Courses.
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Throughout the text of this course and while using technical manuals associated with the equipment you will be working on, you will find the below notations at the end of some paragraphs. The notations are used to emphasize that safety hazards exist and care must be taken or observed.
AN OPERATING PROCEDURE, PRACTICE, OR CONDITION, ETC., WHICH MAY RESULT IN INJURY OR DEATH IF NOT CAREFULLY OBSERVED OR FOLLOWED.
AN OPERATING PROCEDURE, PRACTICE, OR CONDITION, ETC., WHICH MAY RESULT IN DAMAGE TO EQUIPMENT IF NOT CAREFULLY OBSERVED OR FOLLOWED.
An operating procedure, practice, or condition, etc., which is essential to emphasize.
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The text pages that you are to study are listed at the beginning of each assignment. Study these pages carefully before attempting to answer the questions. Pay close attention to tables and illustrations and read the learning objectives. The learning objectives state what you should be able to do after studying the material. Answering the questions correctly helps you accomplish the objectives.
Read each question carefully, then select the BEST answer. You may refer freely to the text. The answers must be the result of your own work and decisions. You are prohibited from referring to or copying the answers of others and from giving answers to anyone else taking the course.
To have your assignments graded, you must be enrolled in the course with the Nonresident Training Course Administration Branch at the Naval Education and Training Professional Development and Technology Center (NETPDTC). Following enrollment, there are two ways of having your assignments graded: (1) use the Internet to submit your assignments as you complete them, or (2) send all the assignments at one time by mail to NETPDTC.
Grading on the Internet: Advantages to Internet grading are:
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Follow the instructions for marking your answers on the answer sheet. Be sure that blocks 1, 2, and 3 are filled in correctly. This information is necessary for your course to be properly processed and for you to receive credit for your work.
Courses must be completed within 12 months from the date of enrollment. This includes time required to resubmit failed assignments.
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If your overall course score is 3.2 or higher, you will pass the course and will not be required to resubmit assignments. Once your assignments have been graded you will receive course completion confirmation.
If you receive less than a 3.2 on any assignment and your overall course score is below 3.2, you will be given the opportunity to resubmit failed assignments. You may resubmit failed assignments only once. Internet students will receive notification when they have failed an assignment--they may then resubmit failed assignments on the web site. Internet students may view and print results for failed assignments from the web site. Students who submit by mail will receive a failing result letter and a new answer sheet for resubmission of each failed assignment.
After successfully completing this course, you will receive a letter of completion.
Errata are used to correct minor errors or delete obsolete information in a course. Errata may also be used to provide instructions to the student. If a course has an errata, it will be included as the first page(s) after the front cover. Errata for all courses can be accessed and viewed/downloaded at:
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If you are a member of the Naval Reserve, you will receive retirement points if you are authorized to receive them under current directives governing retirement of Naval Reserve personnel. For Naval Reserve retirement, this course is evaluated at 6 points. (Refer to Administrative Procedures for Naval Reservists on Inactive Duty, BUPERSINST 1001.39, for more information about retirement points.)
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Learning objectives are stated at the beginning of each chapter. These learning objectives serve as a preview of the information you are expected to learn in the chapter. The comprehensive check questions are based on the objectives. By successfully completing the OCC/ECC, you indicate that you have met the objectives and have learned the information. The learning objectives are listed below.
Upon completion of this chapter, you will be able to:
1. State the applications of a resonant circuit.
2. Identify the conditions that exist in a resonant circuit.
3. State and apply the formula for resonant frequency of an a.c. circuit.
4. State the effect of changes in inductance (L) and capacitance (C) on resonant frequency (fr).
5. Identify the characteristics peculiar to a series resonant circuit.
6. Identify the characteristics peculiar to a parallel resonant circuit.
7. State and apply the formula for Q.
8. State what is meant by the bandwidth of a resonant circuit and compute the bandwidth for a given circuit.
9. Identify the four general types of filters.
10. Identify how the series- and parallel-resonant circuit can be used as a bandpass or a band-reject filter.
When your radio or television set is turned on, many events take place within the "receiver" before you hear the sound or see the picture being sent by the transmitting station.
Many different signals reach the antenna of a radio receiver at the same time. To select a station, the listener adjusts the tuning dial on the radio receiver until the desired station is heard. Within the radio or TV receiver, the actual "selecting" of the desired signal and the rejecting of the unwanted signals are accomplished by what is called a TUNED CIRCUIT. A tuned circuit consists of a coil and a capacitor connected in series or parallel. Later in this chapter you will see the application and advantages of both series- and parallel-tuned circuits. Whenever the characteristics of inductance and capacitance are found in a tuned circuit, the phenomenon as RESONANCE takes place.
You learned earlier in the Navy Electricity and Electronics Training Series, Module 2, chapter 4, that inductive reactance (XL) and capacitive reactance (XC) have opposite effects on circuit impedance (Z).
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You also learned that if the frequency applied to an LCR circuit causes XL and XC to be equal, the circuit is RESONANT.
If you realize that XL and XC can be equal ONLY at ONE FREQUENCY (the resonant frequency), then you will have learned the most important single fact about resonant circuits. This fact is the principle that enables tuned circuits in the radio receiver to select one particular frequency and reject all others. This is the reason why so much emphasis is placed on XL and X C in the discussions that follow.
Examine figure 1-1. Notice that a basic tuned circuit consists of a coil and a capacitor, connected either in series, view (A), or in parallel, view (B). The resistance (R) in the circuit is usually limited to the inherent resistance of the components (particularly the resistance of the coil). For our purposes we are going to disregard this small resistance in future diagrams and explanations.
You have already learned how a coil and a capacitor in an a.c. circuit perform. This action will be the basis of the following discussion about tuned circuits.
Why should you study tuned circuits? Because the tuned circuit that has been described above is used in just about every electronic device, from remote-controlled model airplanes to the most sophisticated space satellite.
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You can assume, if you are going to be involved in electricity or electronics, that you will need to have a good working knowledge of tuned circuits and how they are used in electronic and electrical circuits.
REVIEW OF SERIES/PARALLEL A.C. CIRCUITS
First we will review the effects of frequency on a circuit which contains resistance, inductance, and capacitance. This review recaps what you previously learned in the Inductive and Capacitive Reactance chapter in module 2 of the NEETS.
Perhaps the most often used control of a radio or television set is the station or channel selector. Of course, the volume, tone, and picture quality controls are adjusted to suit the individual's taste, but very often they are not adjusted when the station is changed. What goes on behind this station selecting? In this chapter, you will learn the basic principles that account for the ability of circuits to "tune" to the desired station.
In an a.c. circuit, an inductor produces inductive reactance which causes the current to lag the voltage by 90 degrees. Because the inductor "reacts" to a changing current, it is known as a reactive component. The opposition that an inductor presents to a.c. is called inductive reactance (X L). This opposition is caused by the inductor "reacting" to the changing current of the a.c. source. Both the inductance and the frequency determine the magnitude of this reactance. This relationship is stated by the formula:
As shown in the equation, any increase in frequency, or "f," will cause a corresponding increase of inductive reactance, or "XL." Therefore, the INDUCTIVE REACTANCE VARIES DIRECTLY WITH THE FREQUENCY. As you can see, the higher the frequency, the greater the inductive reactance; the lower the frequency, the less the inductive reactance for a given inductor. This relationship is illustrated in figure 1-2. Increasing values of XL are plotted in terms of increasing frequency. Starting at the lower left corner with zero frequency, the inductive reactance is zero. As the frequency is increased (reading to the right), the inductive reactance is shown to increase in direct proportion.
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In an a.c. circuit, a capacitor produces a reactance which causes the current to lead the voltage by 90 degrees. Because the capacitor "reacts" to a changing voltage, it is known as a reactive component. The opposition a capacitor presents to a.c. is called capacitive reactance (XC). The opposition is caused by the capacitor "reacting" to the changing voltage of the a.c. source. The formula for capacitive reactance is:
In contrast to the inductive reactance, this equation indicates that the CAPACITIVE REACTANCE VARIES INVERSELY WITH THE FREQUENCY. When f = 0, XC is infinite (∞) and decreases as frequency increases. That is, the lower the frequency, the greater the capacitive reactance; the higher the frequency, the less the reactance for a given capacitor.
As shown in figure 1-3, the effect of capacitance is opposite to that of inductance. Remember, capacitance causes the current to lead the voltage by 90 degrees, while inductance causes the current to lag the voltage by 90 degrees.
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both contain "f" (frequency). Any change of frequency changes the reactance of the circuit components as already explained. So far, nothing has been said about the effect of frequency on resistance. In an Ohm's law relationship, such as R = E/I no "f" is involved. Thus, for all practical purposes, a change of frequency does not affect the resistance of the circuit. If a 60-hertz a.c. voltage causes 20 milliamperes of current in a resistive circuit, then the same voltage at 2000 hertz, for example, would still cause 20 milliamperes to flow.
NOTE: Remember that the total opposition to a.c. is called impedance (Z). Impedance is the combination of inductive reactance (XL), capacitive reactance (XC), and resistance (R). When dealing with a.c. circuits, the impedance is the factor with which you will ultimately be concerned. But, as you have just been shown, the resistance (R) is not affected by frequency. Therefore, the remainder of the discussion of a.c. circuits will only be concerned with the reactance of inductors and capacitors and will ignore resistance.
A.c. Circuits Containing Both Inductive and Capacitive Reactances
A.c. circuits that contain both an inductor and a capacitor have interesting characteristics because of the opposing effects of L and C. X L and XC may be treated as reactors which are 180 degrees out of phase. As shown in figure 1-2, the vector for XL should be plotted above the baseline; vector for XC, figure 1-3, should be plotted below the baseline. In a series circuit, the effective reactance, or what is termed the RESULTANT REACTANCE, is the difference between the individual reactances. As an equation, the resultant reactance is:
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Suppose an a.c. circuit contains an XL of 300 ohms and an XC of 250 ohms. The resultant reactance is:
In some cases, the XC may be larger than the X L. If XL = 1200 ohms and X C = 4000 ohms, the difference is: X = XL − XC = 1200 − 4000 = −2800 ohms (capacitive). The total carries the sign (+ or −) of the greater number (factor).
Q-1. What is the relationship between frequency and the values of (a) XL, (b) XC, and (c) R?
Q-2. In an a.c. circuit that contains both an inductor and a capacitor, what term is used for the difference between the individual reactances?
For every combination of L and C, there is only ONE frequency (in both series and parallel circuits) that causes XL to exactly equal XC; this frequency is known as the RESONANT FREQUENCY. When the resonant frequency is fed to a series or parallel circuit, X L becomes equal to XC, and the circuit is said to be RESONANT to that frequency. The circuit is now called a RESONANT CIRCUIT; resonant circuits are tuned circuits. The circuit condition wherein XL becomes equal to XC is known as RESONANCE.
Each LCR circuit responds to resonant frequency differently than it does to any other frequency. Because of this, an LCR circuit has the ability to separate frequencies. For example, suppose the TV or radio station you want to see or hear is broadcasting at the resonant frequency. The LC "tuner" in your set can divide the frequencies, picking out the resonant frequency and rejecting the other frequencies. Thus, the tuner selects the station you want and rejects all other stations. If you decide to select another station, you can change the frequency by tuning the resonant circuit to the desired frequency.
As stated before, the frequency at which XL equals XC (in a given circuit) is known as the resonant frequency of that circuit. Based on this, the following formula has been derived to find the exact resonant frequency when the values of circuit components are known:
There are two important points to remember about this formula. First, the resonant frequency found when using the formula will cause the reactances (XL and XC) of the L and C components to be equal. Second, any change in the value of either L or C will cause a change in the resonant frequency.
An increase in the value of either L or C, or both L and C, will lower the resonant frequency of a given circuit. A decrease in the value of L or C, or both L and C, will raise the resonant frequency of a given circuit.
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The symbol for resonant frequency used in this text is f. Different texts and references may use other symbols for resonant frequency, such as fo, Fr, and fR. The symbols for many circuit parameters have been standardized while others have been left to the discretion of the writer. When you study, apply the rules given by the writer of the text or reference; by doing so, you should have no trouble with nonstandard symbols and designations.
The resonant frequency formula in this text is:
By substituting the constant .159 for the quantity
the formula can be simplified to the following:
Let's use this formula to figure the resonant frequency (fr). The circuit is shown in the practice tank circuit of figure 1-4.
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The important point here is not the formula nor the mathematics. In fact, you may never have to compute a resonant frequency. The important point is for you to see that any given combination of L and C can be resonant at only one frequency; in this case, 205 kHz.
The universal reactance curves of figures 1-2 and 1-3 are joined in figure 1-5 to show the relative values of XL and XL at resonance, below resonance, and above resonance.
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First, note that fr, (the resonant frequency) is that frequency (or point) where the two curves cross. At this point, and ONLY this point, XL equals XC. Therefore, the frequency indicated by fr is the one and only frequency of resonance. Note the resistance symbol which indicates that at resonance all reactance is cancelled and the circuit impedance is effectively purely resistive. Remember, a.c. circuits that are resistive have no phase shift between voltage and current. Therefore, at resonance, phase shift is cancelled. The phase angle is effectively zero.
Second, look at the area of the curves to the left of fr. This area shows the relative reactances of the circuit at frequencies BELOW resonance. To these LOWER frequencies, XC will always be greater than XL. There will always be some capacitive reactance left in the circuit after all inductive reactance has been cancelled. Because the impedance has a reactive component, there will be a phase shift. We can also state that below fr the circuit will appear capacitive.
Lastly, look at the area of the curves to the right of f. This area shows the relative reactances of the circuit at frequencies ABOVE resonance. To these HIGHER frequencies, XL will always be greater than XC. There will always be some inductive reactance left in the circuit after all capacitive reactance has been cancelled. The inductor symbol shows that to these higher frequencies, the circuit will always appear to have some inductance. Because of this, there will be a phase shift.
Resonant circuits may be designed as series resonant or parallel resonant. Each has the ability to discriminate between its resonant frequency and all other frequencies. How this is accomplished by both series- and parallel-LC circuits is the subject of the next section.
NOTE: Practical circuits are often more complex and difficult to understand than simplified versions. Simplified versions contain all of the basic features of a practical circuit, but leave out the nonessential features. For this reason, we will first look at the IDEAL SERIES-RESONANT CIRCUIT— a circuit that really doesn't exist except for our purposes here.
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The ideal series-resonant circuit contains no resistance; it consists of only inductance and capacitance in series with each other and with the source voltage. In this respect, it has the same characteristics of the series circuits you have studied previously. Remember that current is the same in all parts of a series circuit because there is only one path for current.
Each LC circuit responds differently to different input frequencies. In the following paragraphs, we will analyze what happens internally in a series-LC circuit when frequencies at resonance, below resonance, and above resonance are applied. The L and C values in the circuit are those used in the problem just studied under resonant-frequency. The frequencies applied are the three inputs from figure 1-6. Note that the resonant frequency of each of these components is 205 kHz, as figured in the problem.
Note: You are given the values of XL, X C, and fr but you can apply the formulas to figure them. The values given are rounded off to make it easier to analyze the circuit.
First, note that XL and XC are equal. This shows that the circuit is resonant to the applied frequency of 205 kHz. XL and XC are opposite in effect; therefore, they subtract to zero. (2580 ohms − 2580 ohms = zero.) At resonance, then, X = zero. In our theoretically perfect circuit with zero resistance and zero reactance, the total opposition to current (Z) must also be zero.
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Now, apply Ohm's law for a.c. circuits:
Don't be confused by this high value of current. Our perfect, but impossible, circuit has no opposition to current. Therefore, current flow will be extremely high. The important points here are that AT RESONANCE, impedance is VERY LOW, and the resulting current will be comparatively HIGH.
If we apply Ohm's law to the individual reactances, we can figure relative values of voltage across each reactance.
These are reactive voltages that you have studied previously. The voltage across each reactance will be comparatively high. A comparatively high current times 2580 ohms yields a high voltage. At any given instant, this voltage will be of opposite polarity because the reactances are opposite in effect. EL + EC = zero volts
THE INDIVIDUAL VOLTAGES MAY REACH QUITE HIGH VALUES.
Let's summarize our findings so far. In a series-LC circuit with a resonant-frequency voltage applied, the following conditions exist:
• XL and XC are equal and subtract to zero.
• Resultant reactance is zero ohms.
• Impedance (Z) is reduced to a MINIMUM value.
• With minimum Z, current is MAXIMUM for a given voltage.
• Maximum current causes maximum voltage drops across the individual reactances.
All of the above follow in sequence from the fact that X L = XC at the resonant frequency.
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Given:
First, note that XL and XC are no longer equal. XC is larger than it was at resonance; XL is smaller. By applying the formulas you have learned, you know that a lower frequency produces a higher capacitive reactance and a lower inductive reactance. The reactances subtract but do not cancel (X L − XC = 1260 − 5300 = 4040 ohms (capacitive)). At an input frequency of 100 kHz, the circuit (still resonant to 205 kHz) has a net reactance of 4040 ohms. In our theoretically perfect circuit, the total opposition (Z) is equal to X, or 4040 ohms.
As before, let's apply Ohm's law to the new conditions.
The voltage drops across the reactances are as follows:
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In summary, in a series-LC circuit with a source voltage that is below the resonant frequency (100 kHz in the example), the resultant reactance (X), and therefore impedance, is higher than at resonance. In addition current is lower, and the voltage drops across the reactances are lower. All of the above follow in sequence due to the fact that XC is greater than XL at any frequency lower than the resonant frequency.
Given:
Again, XL and XC are not equal. This time, XL is larger than XC. (If you don't know why, apply the formulas and review the past several pages.) The resultant reactance is 2000 ohms (XL − X C = 3770 − 1770 = 2000 ohms.) Therefore, the resultant reactance (X), or the impedance of our perfect circuit at 300 kHz, is 2000 ohms.
By applying Ohm's law as before:
In summary, in a series-LC circuit with a source voltage that is above the resonant frequency (300 kHz in this example), impedance is higher than at resonance, current is lower, and the voltage drops across the reactances are lower. All of the above follow in sequence from the fact that X L is greater than XC at any frequency higher than the resonant frequency.
The ideal series-resonant circuit has zero impedance. The impedance increases for frequencies higher and lower than the resonant frequency. The impedance characteristic of the ideal series-resonant circuit results because resultant reactance is zero ohms at resonance and ONLY at resonance. All other frequencies provide a resultant reactance greater than zero.
Zero impedance at resonance allows maximum current. All other frequencies have a reduced current because of the increased impedance. The voltage across the reactance is greatest at resonance because voltage drop is directly proportional to current. All discrimination between frequencies results from the fact that XL and XC completely counteract ONLY at the resonant frequency.
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As you learned much earlier in this series, resistance is always present in practical electrical circuits; it is impossible to eliminate. A typical series-LC circuit, then, has R as well as L and C.
If our perfect (ideal) circuit has zero resistance, and a typical circuit has "some" resistance, then a circuit with a very small resistance is closer to being perfect than one that has a large resistance. Let's list what happens in a series-resonant circuit because resistance is present. This is not new to you - just a review of what you have learned previously.
In a series-resonant circuit that is basically L and C, but that contains "some" R, the following statements are true:
• XL, XC, and R components are all present and can be shown on a vector diagram, each at right angles with the resistance vector (baseline).
• At resonance, the resultant reactance is zero ohms. Thus, at resonance, The circuit impedance equals only the resistance (R). The circuit impedance can never be less than R because the original resistance will always be present in the circuit.
• At resonance, a practical series-RLC circuit ALWAYS has MINIMUM impedance. The actual value of impedance is that of the resistance present in the circuit (Z = R).
Now, if the designers do their very best (and they do) to keep the value of resistance in a practical series-RLC circuit LOW, then we can still get a fairly high current at resonance. The current is NOT "infinitely" high as in our ideal circuit, but is still higher than at any other frequency. The curve and vector relationships for the practical circuit are shown in figure 1-7.
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Note that the impedance curve does not reach zero at its minimum point. The vectors above and below resonance show that the phase shift of the circuit at these frequencies is less than 90 degrees because of the resistance.
The horizontal width of the curve is a measure of how well the circuit will pick out (discriminate) the one desired frequency. The width is called BANDWIDTH, and the ability to discriminate between frequencies is known as SELECTIVITY. Both of these characteristics are affected by resistance. Lower resistance allows narrower bandwidth, which is the same as saying the circuit has better selectivity. Resistance, then, is an unwanted quantity that cannot be eliminated but can be kept to a minimum by the circuit designers.
More on bandwidth, selectivity, and measuring the effects of resistance in resonant circuits will follow the discussion of parallel resonance.
Q-3. State the formula for resonant frequency.
Q-4. If the inductor and capacitor values are increased, what happens to the resonant frequency?
Q-5. In an "ideal" resonant circuit, what is the relationship between impedance and current?
Q-6. In a series-RLC circuit, what is the condition of the circuit if there is high impedance, low current, and low reactance voltages?
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A parallel-LC circuit is often called a TANK CIRCUIT because it can store energy much as a tank stores liquid. It has the ability to take energy fed to it from a power source, store this energy alternately in the inductor and capacitor, and produce an output which is a continuous a.c. wave. You can understand how this is accomplished by carefully studying the sequence of events shown in figure 1-8. You must thoroughly understand the capacitor and inductor action in this figure before you proceed further in the study of parallel-resonant circuits.
In each view of figure 1-8, the waveform is of the charging and discharging CAPACITOR VOLTAGE. In view (A), the switch has been moved to position C. The d.c. voltage is applied across the capacitor, and the capacitor charges to the potential of the battery.
In view (B), moving the switch to the right completes the circuit from the capacitor to the inductor and places the inductor in series with the capacitor. This furnishes a path for the excess electrons on the upper plate of the capacitor to flow to the lower plate, and thus starts neutralizing the capacitor charge. As these electrons flow through the coil, a magnetic field is built up around the coil. The energy which was first stored by the electrostatic field of the capacitor is now stored in the electromagnetic field of the inductor.
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View (C) shows the capacitor discharged and a maximum magnetic field around the coil. The energy originally stored in the capacitor is now stored entirely in the magnetic field of the coil.
Since the capacitor is now completely discharged, the magnetic field surrounding the coil starts to collapse. This induces a voltage in the coil which causes the current to continue flowing in the same direction and charges the capacitor again. This time the capacitor charges to the opposite polarity, view (D).
In view (E), the magnetic field has completely collapsed, and the capacitor has become charged with the opposite polarity. All of the energy is again stored in the capacitor.
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In view (F), the capacitor now discharges back through the coil. This discharge current causes the magnetic field to build up again around the coil.
In view (G), the capacitor is completely discharged. The magnetic field is again at maximum.
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In view (H), with the capacitor completely discharged, the magnetic field again starts collapsing. The induced voltage from the coil maintains current flowing toward the upper plate of the capacitor.
In view (I), by the time the magnetic field has completely collapsed, the capacitor is again charged with the same polarity as it had in view (A). The energy is again stored in the capacitor, and the cycle is ready to start again.
The number of times per second that these events in figure 1-8 take place is called NATURAL FREQUENCY or RESONANT FREQUENCY of the circuit. Such a circuit is said to oscillate at its resonant frequency.
It might seem that these oscillations could go on forever. You know better, however, if you apply what you have already learned about electric circuits.
This circuit, as all others, has some resistance. Even the relatively small resistance of the coil and the connecting wires cause energy to be dissipated in the form of heat (I2R loss). The heat loss in the circuit resistance causes the charge on the capacitor to be less for each subsequent cycle. The result is a DAMPED WAVE, as shown in figure 1-9. The charging and discharging action will continue until all of the energy has been radiated or dissipated as heat.
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If it were possible to have a circuit with absolutely no resistance, there would be no heat loss, and the oscillations would tend to continue indefinitely. You have already learned that tuned circuits are designed to have very little resistance. Reducing I2R losses is still another reason for having low resistance.
A "perfect" tuned circuit would produce the continuous sine wave shown in figure 1-10. Its frequency would be that of the circuit.
Because we don't have perfection, another way of causing a circuit to oscillate indefinitely would be to apply a continuous a.c. or pulsing source to the circuit. If the source is at the resonant frequency of the circuit, the circuit will oscillate as long as the source is applied.
The reasons why the circuit in figure 1-8 oscillates at the resonant frequency have to do with the characteristics of resonant circuits. The discussion of parallel resonance will not be as detailed as that for series resonance because the idea of resonance is the same for both circuits. Certain characteristics differ as a result of L and C being in parallel rather than in series. These differences will be emphasized.
Q-7. When the capacitor is completely discharged, where is the energy of the tank circuit stored?
Q-8. When the magnetic field of the inductor is completely collapsed, where is the energy of the tank circuit stored?
Much of what you have learned about resonance and series-LC circuits can be applied directly to parallel-LC circuits. The purpose of the two circuits is the same — to select a specific frequency and reject all others. XL still equals XC at resonance. Because the inductor and capacitor are in parallel, however, the circuit has the basic characteristics of an a.c. parallel circuit. The parallel hookup causes
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frequency selection to be accomplished in a different manner. It gives the circuit different characteristics. The first of these characteristics is the ability to store energy.
Look at figure 1-11. In this circuit, as in other parallel circuits, the voltage is the same across the inductor and capacitor. The currents through the components vary inversely with their reactances in accordance with Ohm's law. The total current drawn by the circuit is the vector sum of the two individual component currents. Finally, these two currents, IL and IC, are 180 degrees out of phase because the effects of L and C are opposite. There is not a single fact new to you in the above. It is all based on what you have learned previously about parallel a.c. circuits that contain L and C.
Now, at resonance, XL is still equal to X C. Therefore, IL must equal IC. Remember, the voltage is the same; the reactances are equal; therefore, according to Ohm's law, the currents must be equal. But, don't forget, even though the currents are equal, they are still opposites. That is, if the current is flowing "up" in the capacitor, it is flowing "down" in the coil, and vice versa. In effect, while the one component draws current, the other returns it to the source. The net effect of this "give and take action" is that zero current is drawn from the source at resonance. The two currents yield a total current of zero amperes because they are exactly equal and opposite at resonance.
A circuit that is completed and has a voltage applied, but has zero current, must have an INFINITE IMPEDANCE (apply Ohm's law — any voltage divided by zero yields infinity).
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By now you know that we have just ignored our old friend resistance from previous discussions. In an actual circuit, at resonance, the currents will not quite counteract each other because each component will have different resistance. This resistance is kept extremely low, but it is still there. The result is that a relatively small current flows from the source at resonance instead of zero current. Therefore, a basic characteristic of a practical parallel-LC circuit is that, at resonance, the circuit has MAXIMUM impedance which results in MINIMUM current from the source. This current is often called line current. This is shown by the peak of the waveform for impedance and the valley for the line current, both occurring at fr the frequency of resonance in figure 1-11.
There is little difference between the circuit pulsed by the battery in figure 1-8 that oscillated at its resonant (or natural) frequency, and the circuit we have just discussed. The equal and opposite currents in the two components are the same as the currents that charged and discharged the capacitor through the coil.
For a given source voltage, the current oscillating between the reactive parts will be stronger at the resonant frequency of the circuit than at any other frequency. At frequencies below resonance, capacitive current will decrease; above the resonant frequency, inductive current will decrease. Therefore, the oscillating current (or circulating current, as it is sometimes called), being the lesser of the two reactive currents, will be maximum at resonance.
If you remember, the basic resonant circuit produced a "damped" wave. A steady amplitude wave was produced by giving the circuit energy that would keep it going. To do this, the energy had to be at the same frequency as the resonant frequency of the circuit.
So, if the resonant frequency is "timed" right, then all other frequencies are "out of time" and produce waves that tend to buck each other. Such frequencies cannot produce strong oscillating currents.
In our typical parallel-resonant (LC) circuit, the line current is minimum (because the impedance is maximum). At the same time, the internal oscillating current in the tank is maximum. Oscillating current may be several hundred times as great as line current at resonance.
In any case, this circuit reacts differently to the resonant frequency than it does to all other frequencies. This makes it an effective frequency selector.
Both series- and parallel-LC circuits discriminate between the resonant frequency and all other frequencies by balancing an inductive reactance against an equal capacitive reactance.
In series, these reactances create a very low impedance. In parallel, they create a very high impedance. These characteristics govern how and where designers use resonant circuits. A low- impedance requirement would require a series-resonant circuit. A high-impedance requirement would require the designer to use a parallel-resonant circuit.
Our resonant circuits so far have been tuned to a single frequency - the resonant frequency. This is fine if only one frequency is required. However, there are hundreds of stations on many different frequencies.
Therefore, if we go back to our original application, that of tuning to different radio stations, our resonant circuits are not practical. The reason is because a tuner for each frequency would be required and this is not practical.
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What is a practical solution to this problem? The answer is simple. Make either the capacitor or the inductor variable. Remember, changing either L or C changes the resonant frequency.
Now you know what has been happening all of these years when you "pushed" the button or "turned" the dial. You have been changing the L or C in the tuned circuits by the amount necessary to adjust the tuner to resonate at the desired frequency. No matter how complex a unit, if it has LC tuners, the tuners obey these basic laws.
Q-9. What is the term for the number of times per second that tank circuit energy is either stored in the inductor or capacitor?
Q-10. In a parallel-resonant circuit, what is the relationship between impedance and current?
Q-11. When is line current minimum in a parallel-LC circuit?
The principle of series- or parallel-resonant circuits have many applications in radio, television, communications, and the various other electronic fields throughout the Navy. As you have seen, by making the capacitance or inductance variable, the frequency at which a circuit will resonate can be controlled.
In addition to station selecting or tuning, resonant circuits can separate currents of certain frequencies from those of other frequencies.
Circuits in which resonant circuits are used to do this are called FILTER CIRCUITS.
If we can select the proper values of resistors, inductors, or capacitors, a FILTER NETWORK, or "frequency selector," can be produced which offers little opposition to one frequency, while BLOCKING or ATTENUATING other frequencies. A filter network can also be designed that will "pass" a band of frequencies and "reject" all other frequencies.
Most electronic circuits require the use of filters in one form or another. You have already studied several in modules 6, 7, and 8 of the NEETS.
One example of a filter being applied is in a rectifier circuit. As you know, an alternating voltage is changed by the rectifier to a direct current. However, the d.c. voltage is not pure; it is still pulsating and fluctuating. In other words, the signal still has an a.c. component in addition to the d.c. voltage. By feeding the signal through simple filter networks, the a.c. component is reduced. The remaining d.c. is as pure as the designers require.
Bypass capacitors, which you have already studied, are part of filter networks that, in effect, bypass, or shunt, unwanted a.c. components to ground.
Several times in this chapter, we have discussed "ideal" or theoretically perfect circuits. In each case, you found that resistance kept our circuits from being perfect. You also found that low resistance in tuners was better than high resistance. Now you will learn about a factor that, in effect, measures just how close to perfect a tuner or tuner component can be. This same factor affects BANDWIDTH and SELECTIVITY. It can be used in figuring voltage across a coil or capacitor in a series-resonant circuit and the amount of circulating (tank) current in a parallel-resonant circuit. This factor is very important
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and useful to designers. Technicians should have some knowledge of the factor because it affects so many things. The factor is known as Q. Some say it stands for quality (or merit). The higher the Q, the better the circuit; the lower the losses (I2R), the closer the circuit is to being perfect.
Having studied the first part of this chapter, you should not be surprised to learn that resistance (R) has a great effect on this figure of merit or quality.
Q is really very simple to understand if you think back to the tuned-circuit principles just covered. Inductance and capacitance are in all tuners. Resistance is an impurity that causes losses. Therefore, components that provide the reactance with a minimum of resistance are "purer" (more perfect) than those with higher resistance. The actual measure of this purity, merit, or quality must include the two basic quantities, X and R.
does the job for us. Let's take a look at it and see just why it measures quality.
First, if a perfect circuit has zero resistance, then our ratio should give a very high value of Q to reflect the high quality of the circuit. Does it?
Assume any value for X and a zero value for R.
Then:
Remember, any value divided by zero equals infinity. Thus, our ratio is infinitely high for a theoretically perfect circuit.
With components of higher resistance, the Q is reduced. Dividing by a larger number always yields a smaller quantity. Thus, lower quality components produce a lower Q. Q, then, is a direct and accurate measure of the quality of an LC circuit.
Q is just a ratio. It is always just a number — no units. The higher the number, the "better" the circuit. Later as you get into more practical circuits, you may find that low Q may be desirable to provide certain characteristics. For now, consider that higher is better.
Because capacitors have much, much less resistance in them than inductors, the Q of a circuit is very often expressed as the Q of the coil or:
The answer you get from using this formula is very near correct for most purposes. Basically, the Q of a capacitor is so high that it does not limit the Q of the circuit in any practical way. For that reason, the technician may ignore it.
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Q is a feature that is designed into a coil. When the coil is used within the frequency range for which it is designed, Q is relatively constant. In this sense, it is a physical characteristic.
Inductance is a result of the physical makeup of a coil - number of turns, core, type of winding, etc. Inductance governs reactance at a given frequency. Resistance is inherent in the length, size, and material of the wire. Therefore, the Q of a coil is mostly dependent on physical characteristics.
Values of Q that are in the hundreds are very practical and often found in typical equipment.
For the most part, Q is the concern of designers, not technicians. Therefore, the chances of you having to figure the Q of a coil are remote. However, it is important for you to know some circuit relationships that are affected by Q.
Q can be used to determine the "gain" of series-resonant circuits. Gain refers to the fact that at resonance, the voltage drop across the reactances are greater than the applied voltage. Remember, when we applied Ohm's law in a series-resonant circuit, it gave us the following characteristics:
• Low impedance, high current.
• High current; high voltage across the comparatively high reactances.
This high voltage is usable where little power is required, such as in driving the grid of a vacuum tube or the gate of a field effect transistor (F.E.T.). The gain of a properly designed series-resonant circuit may be as great or greater than the amplification within the amplifier itself. The gain is a function of Q, as shown in the following example:
If the Q of the coil were 100, then the gain would be 100; that is, the voltage of the coil would be 100 times that of the input voltage to the series circuit.
Resistance affects the resonance curve of a series circuit in two ways — the lower the resistance, the higher the current; also, the lower the resistance, the sharper the curve. Because low resistance causes high Q, these two facts are usually expressed as functions of Q. That is, the higher the Q, the higher and sharper the curve and the more selective the circuit.
The lower the Q (because of higher resistance), the lower the current curve; therefore, the broader the curve, the less selective the circuit. A summary of the major characteristics of series RLC-circuits at resonance is given in table 1-1.
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Table 1-1.—Major Characteristics of Series RLC Circuits at Resonance
There is no voltage gain in a parallel-resonant circuit because voltage is the same across all parts of a parallel circuit. However, Q helps give us a measure of the current that circulates in the tank.
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Given:
Again, if the Q were 100, the circulating current would be 100 times the value of the line current. This may help explain why some of the wire sizes are very large in high-power amplifying circuits.
The impedance curve of a parallel-resonant circuit is also affected by the Q of the circuit in a manner similar to the current curve of a series circuit. The Q of the circuit determines how much the impedance is increased across the parallel-LC circuit. (Z = Q × XL)
The higher the Q, the greater the impedance at resonance and the sharper the curve. The lower the Q, the lower impedance at resonance; therefore, the broader the curve, the less selective the circuit. The major characteristics of parallel-RLC circuits at resonance are given in table 1-2.
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Table 1-2.—Major Characteristics of Parallel RLC Circuits at
The ratio that is called Q is a measure of the quality of resonant circuits and circuit components. Basically, the value of Q is an inverse function of electrical power dissipated through circuit resistance. Q is the ratio of the power stored in the reactive components to the power dissipated in the resistance. That is, high power loss is low Q; low power loss is high Q.
Circuit designers provide the proper Q. As a technician, you should know what can change Q and what quantities in a circuit are affected by such a change.
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If circuit Q is low, the gain of the circuit at resonance is relatively small. The circuit does not discriminate sharply (reject the unwanted frequencies) between the resonant frequency and the frequencies on either side of resonance, as shown by the curve in figure 1-12, view (A). The range of frequencies included between the two frequencies (426.4 kHz and 483.6 kHz in this example) at which the current drops to 70 percent of its maximum value at resonance is called the BANDWIDTH of the circuit.
It is often necessary to state the band of frequencies that a circuit will pass. The following standard has been set up: the limiting frequencies are those at either side of resonance at which the curve falls to a point of .707 (approximately 70 percent) of the maximum value. This point is called the HALF-POWER point. Note that in figure 1-12, the series-resonant circuit has two half-power points, one above and one
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below the resonant frequency point. The two points are designated upper frequency cutoff (fco) and lower frequency cutoff (fco) or simply f1 and f2. The range of frequencies between these two points comprises the bandwidth. Views (A) and (B) of figure 1-12 illustrate the bandwidths for low- and high-Q resonant circuits. The bandwidth may be determined by use of the following formulas:
For example, by applying the formula we can determine the bandwidth for the curve shown in figure 1-12, view (A).
If the Q of the circuit represented by the curve in figure 1-12, view (B), is 45.5, what would be the bandwidth?
If Q equals 7.95 for the low-Q circuit as in view (A) of figure 1-12, we can check our original calculation of the bandwidth.
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The Q of the circuit can be determined by transposing the formula for bandwidth to:
To find the Q of the circuit using the information found in the last example problem:
Q-12. What is the relationship of the coil to the resistance of a circuit with high "Q"?
Q-13. What is the band of frequencies called that is included between the two points at which current falls to 70 percent of its maximum value in a resonant circuit?
In many practical applications of complex circuits, various combinations of direct, low-frequency, audio-frequency, and radio-frequency currents may exist. It is frequently necessary to have a means for separating these component currents at any desired point. An electrical device for accomplishing this separation is called a FILTER.
A filter circuit consists of inductance, capacitance, and resistance used singularly or in combination, depending upon the purpose. It may be designed so that it will separate alternating current from direct current, or so that it will separate alternating current of one frequency (or a band of frequencies) from other alternating currents of different frequencies.
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The use of resistance by itself in filter circuits does not provide any filtering action, because it opposes the flow of any current regardless of its frequency. What it does, when connected in series or parallel with an inductor or capacitor, is to decrease the "sharpness," or selectivity, of the filter. Hence, in some particular application, resistance might be used in conjunction with inductance or capacitance to provide filtering action over a wider band of frequencies.
Filter circuits may be divided into four general types: LOW-PASS, HIGH-PASS, BANDPASS, AND BAND-REJECT filters.
Electronic circuits often have currents of different frequencies. The reason is that a source produces current with the same frequency as the applied voltage. As an example, the a.c. signal input to an audio amplifier can have high- and low-audio frequencies; the input to an rf amplifier can have a wide range of radio frequencies.
In such applications where the current has different frequency components, it is usually necessary for the filter either to accept or reject one frequency or a group of frequencies. The electronic filter that can pass on the higher-frequency components to a load or to the next circuit is known as a HIGH-PASS filter. A LOW-PASS filter can be used to pass on lower-frequency components.
Before discussing filters further, we will review and apply some basic principles of the frequency- response characteristics of the capacitor and the inductor. Recall the basic formula for capacitive reactance and inductive reactance:
Assume any given value of L and C. If we increase the applied frequency, XC decreases and XL increases. If we increase the frequency enough, the capacitor acts as a short and the inductor acts as an open. Of course, the opposite is also true. Decreasing frequency causes XC to increase and XL to decrease. Here again, if we make a large enough change, XC acts as an open and XL acts as a short. Figure 1-13 gives a pictorial representation of these two basic components and how they respond to low and high frequencies.
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If we apply these same principles to simple circuits, such as the ones in figure 1-14, they affect input signals as shown. For example, in view (A) of the figure, a low frequency is blocked by the capacitor which acts as an open and at a high frequency the capacitor acts as a short. By studying the figure, it is easy to see how the various components will react in different configurations with a change in frequency.
As mentioned before, high-pass and low-pass filters pass the specific frequencies for which circuits are designed.
There can be a great deal of confusion when talking about high-pass, low-pass, discrimination, attenuation, and frequency cutoff, unless the terms are clearly understood. Since these terms are used widely throughout electronics texts and references, you should have a clear understanding before proceeding further.
• HIGH-PASS FILTER. A high-pass filter passes on a majority of the high frequencies to the next circuit and rejects or attenuates the lower frequencies. Sometimes it is called a low-frequency discriminator or low-frequency attenuator.
• LOW-PASS FILTER. A low-pass filter passes on a majority of the low frequencies to the next circuit and rejects or attenuates the higher frequencies. Sometimes it is called a high-frequency discriminator or high-frequency attenuator.
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• DISCRIMINATION. The ability of the filter circuit to distinguish between high and low frequencies and to eliminate or reject the unwanted frequencies.
• ATTENUATION. The ability of the filter circuit to reduce the amplitude of the unwanted frequencies below the level of the desired output frequency.
• FREQUENCY CUTOFF (fco). The frequency at which the filter circuit changes from the point of rejecting the unwanted frequencies to the point of passing the desired frequency; OR the point at which the filter circuit changes from the point of passing the desired frequency to the point of rejecting the undesired frequencies.
A low-pass filter passes all currents having a frequency below a specified frequency, while opposing all currents having a frequency above this specified frequency. This action is illustrated in its ideal form in view (A) of figure 1-15. At frequency cutoff, known as fc the current decreases from maximum to zero. At all frequencies above fc the filter presents infinite opposition and there is no current. However, this sharp division between no opposition and full opposition is impossible to attain. A more practical graph of the current is shown in view (B), where the filter gradually builds up opposition as the cutoff frequency (f) is approached. Notice that the filter cannot completely block current above the cutoff frequency.
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View (A) of figure 1-16 shows the electrical construction of a low-pass filter with an inductor inserted in series with one side of a line carrying both low and high frequencies. The opposition offered by the reactance will be small at the lower frequencies and great at the higher frequencies. In order to divert the undesired high frequencies back to the source, a capacitor must be added across the line to bypass the higher frequencies around the load, as shown in view (B).
The capacitance of the capacitor must be such that its reactance will offer little opposition to frequencies above a definite value, and great opposition to frequencies below this value. By combining the series inductance and bypass capacitance, as shown in view (C), the simplest type of low-pass filter is obtained. At point P, a much higher opposition is offered to the low frequencies by the capacitor than by the inductor, and most of the low-frequency current takes the path of least opposition. On the other hand,
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the least amount of opposition is offered to the high frequencies by the capacitor, and most of the high- frequency energy returns to the source through the capacitor.
A high-pass filter circuit passes all currents having a frequency higher than a specified frequency, while opposing all currents having a frequency lower than its specified frequency. This is illustrated in figure 1-17. A capacitor that is used in series with the source of both high and low frequencies, as shown in view (A) of figure 1-18, will respond differently to high-frequency, low-frequency, and direct currents. It will offer little opposition to the passage of high-frequency currents, great opposition to the passage of low-frequency currents, and completely block direct currents. The value of the capacitor must be chosen so that it allows the passage of all currents having frequencies above the desired value, and opposes those having frequencies below the desired value. Then, in order to shunt the undesired low-frequency currents back to the source, an inductor is used, as shown in view (B). This inductor must have a value that will allow it to pass currents having frequencies below the frequency cutoff point, and reject currents having frequencies above the frequency cutoff point, thus forcing them to pass through the capacitor. By combining inductance and capacitance, as shown in view (C), you obtain the simplest type of high-pass filter. At point P most of the high-frequency energy is passed on to the load by the capacitor, and most of the low-frequency energy is shunted back to the source through the inductor.
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Resonant circuits can be made to serve as filters in a manner similar to the action of individual capacitors and inductors. As you know, the series-LC circuit offers minimum opposition to currents that have frequencies at or near the resonant frequency, and maximum opposition to currents of all other frequencies.
You also know that a parallel-LC circuit offers a very high impedance to currents that have frequencies at or near the resonant frequency, and a relatively low impedance to currents of all other frequencies.
If you use these two basic concepts, the BANDPASS and BAND-REJECT filters can be constructed. The bandpass filter and the band-reject filter are two common types of filters that use resonant circuits.
A bandpass filter passes a narrow band of frequencies through a circuit and attenuates all other frequencies that are higher or lower than the desired band of frequencies. This is shown in figure 1-19 where the greatest current exists at the center frequency (fr). Frequencies below resonance (f1) and frequencies above resonance (f2) drop off rapidly and are rejected.
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In the circuit of figure 1-20, view (A), the series-LC circuit replaces the inductor of figure 1-16, view (A), and acts as a BANDPASS filter. It passes currents having frequencies at or near its resonant frequency, and opposes the passage of all currents having frequencies outside this band.
Thus, in the circuit of figure 1-20, view (B), the parallel-LC circuit replaces the capacitor of figure 1- 16, view (B). If this circuit is tuned to the same frequency as the series-LC circuit, it will provide a path for all currents having frequencies outside the limits of the frequency band passed by the series-resonant circuit. The simplest type of bandpass filter is formed by connecting the two LC circuits as shown in figure 1-20, view (C). The upper and lower frequency limits of the filter action are filter cutoff points.
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A band-reject filter circuit is used to block the passage of current for a narrow band of frequencies, while allowing current to flow at all frequencies above or below this band. This type of filter is also known as a BAND-SUPPRESSION or BAND-STOP filter. The way it responds is shown by the response curve of figure 1-21. Since the purpose of the band-reject filter is directly opposite to that of a bandpass filter, the relative positions of the resonant circuits in the filter are interchanged. The parallel-LC circuit shown in figure 1-22, view (A), replaces the capacitor of figure 1-18, view (A). It acts as a band-reject filter, blocking the passage of currents having frequencies at or near resonant frequency and passing all currents having frequencies outside this band. The series-LC circuit shown in figure 1-22, view (B), replaces the inductor of figure 1-18, view (B). If this series circuit is tuned, to the same frequency as the parallel circuit, it acts as a bypass for the band of rejected frequencies. Then, the simplest type of band- reject filter is obtained by connecting the two circuits as shown in figure 1-22, view (C).
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Q-14. What is the device called that will separate alternating current from direct current, or that will separate alternating current of one frequency from other alternating currents of different frequencies?
Q-15. What are the four general types of filters?
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Q-16. What is the filter called in which the low frequencies do not produce a useful voltage?
Q-17. What is the filter called that passes low frequencies but rejects or attenuates high frequencies?
Q-18. How does a capacitor and an inductor react to (a) low frequency and (b) high frequency?
Q-19. What term is used to describe the frequency at which the filter circuit changes from the point of rejecting the unwanted frequencies to the point of passing the desired frequencies?
Q-20. What type filter is used to allow a narrow band of frequencies to pass through a circuit and attenuate all other frequencies above or below the desired band?
Q-21. What type filter is used to block the passage of current for a narrow band of frequencies, while allowing current to flow at all frequencies above or below this band?
All of the various types of filters we have discussed so far have had only one section. In many cases, the use of such simple filter circuits does not provide sufficiently sharp cutoff points. But by adding a capacitor, an inductor, or a resonant circuit in series or in parallel (depending upon the type of filter action required), the ideal effect is more nearly approached. When such additional units are added to a filter circuit, the form of the resulting circuit will resemble the letter T, or the Greek letter pi (pi). They are, therefore, called T- or pi-type filters, depending upon which symbol they resemble. Two or more T- or pi−type filters may be connected together to produce a still sharper cutoff point.
Figure 1-23, (view A) (view B) and (view C), and figure 1-24, (view A) (view B) and (view C) depict some of the common configurations of the T- and pi-type filters. Further discussion about the theory of operation of these circuits is beyond the intended scope of this module. If you are interested in learning more about filters, a good source of information to study is the Electronics Installation and Maintenance Handbook (EIMB), section 4 (Electronics Circuits), NAVSEA 0967-LP-000-0120.
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When working with resonant circuits, or electrical circuits, you must be aware of the potentially high voltages. Look at figure 1-25. With the series circuit at resonance, the total impedance of the circuit is 5 ohms.
Remember, the impedance of a series-RLC circuit at resonance depends on the resistive element. At resonance, the impedance (Z) equals the resistance (R). Resistance is minimum and current is maximum. Therefore, the current at resonance is:
The voltage drops around the circuit with 2 amperes of current flow are:
EC = 40 volts a.c.
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EL = 40 volts a.c.
ER = 10 volts a.c.
You can see that there is a voltage gain across the reactive components at resonance.
If the frequency was such that XL and X C were equal to 1000 ohms at the resonant frequency, the reactance voltage across the inductor or capacitor would increase to 2000 volts a.c. with 10 volts a.c. applied. Be aware that potentially high voltage can exist in series-resonant circuits.
This chapter introduced you to the principles of tuned circuits. The following is a summary of the major subjects of this chapter.
THE EFFECT OF FREQUENCY on an INDUCTOR is such that an increase in frequency will cause an increase in inductive reactance. Remember that XL = 2pifL; therefore, XL varies directly with frequency.
THE EFFECT OF FREQUENCY on a CAPACITOR is such that an increase in frequency will cause a decrease in capacitive reactance. Remember that
therefore, the relationship between XC and frequency is that XC varies inversely with frequency.
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RESULTANT REACTANCE X = (XL − X C) or X = (XC − XL). XL is usually plotted above the reference line and X C below the reference line. Inductance and capacitance have opposite effects on the current in respect to the voltage in a.c. circuits. Below resonance, XC is larger than XL, and the series circuit appears capacitive. Above resonance, XL is larger than XC, and the series circuit appears inductive. At resonance, XL = XC, and the total impedance of the circuit is resistive.
A RESONANT CIRCUIT is often called a TANK CIRCUIT. It has the ability to take energy fed from a power source, store the energy alternately in the inductor and capacitor, and produce an output which is a continuous a.c. wave. The number of times this set of events occurs per second is called the resonant frequency of the circuit. The actual frequency at which a tank circuit will oscillate is determined by the formula:
IN A SERIES-LC CIRCUIT impedance is minimum and current is maximum. Voltage is the variable, and voltage across the inductor and capacitor will be equal but of opposite phases at resonance. Above resonance it acts inductively, and below resonance it acts capacitively.
1-46
IN A PARALLEL-LC CIRCUIT impedance is maximum and current is minimum. Current is the variable and at resonance the two currents are 180 degrees out of phase with each other. Above resonance the current acts capacitively, and below resonance the current acts inductively.
1-47
THE "Q" OR FIGURE OF MERIT of a circuit is the ratio of XL to R. Since the capacitor has negligible losses, the circuit Q becomes equivalent to the Q of the coil.
THE BANDWIDTH of a circuit is the range of frequencies between the half-power points. The limiting frequencies are those at either side of resonance at which the curve falls to .707 of the maximum value. If circuit Q is low, you will have a wide bandpass. If circuit Q is high, you will have a narrow bandpass.
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A FILTER CIRCUIT consists of a combination of capacitors, inductors, and resistors connected so that the filter will either permit or prevent passage of a certain band of frequencies.
A LOW-PASS FILTER passes low frequencies and attenuates high frequencies.
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A HIGH-PASS FILTER passes high frequencies and attenuates low frequencies.
A BANDPASS FILTER will permit a certain band of frequencies to be passed.
1-50
A BAND-REJECT FILTER will reject a certain band of frequencies and pass all others.
A SAFETY PRECAUTION concerning series resonance: Very high reactive voltage can appear across L and C. Care must be taken against possible shock hazard.
1-51
ANSWERS TO QUESTIONS Q1. THROUGH Q21.
A-1.
a. XL varies directly with frequency.
b. XC varies inversely with frequency.
c. Frequency has no affect on resistance.
A-2. Resultant reactance.
A-3.
A-4. Decreases.
A-5. Impedance low Current high.
A-6. Nonresonant (circuit is either above or below resonance).
A-7. Inductor magnetic field.
A-8. Capacitor.
A-9. Natural frequency or resonant frequency (f r).
A-10. Maximum impedance, minimum current.
A-11. At the resonant frequency.
A-12.
A-13. Bandwidth of the circuit.
A-14. A filter.
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A-15.
a. Low-pass.
b. High-pass
c. Bandpass.
d. Band-reject.
A-16. High-pass filter, low-frequency discriminator, or low-frequency attenuator.
A-17. Low-pass filter, high-frequency discriminator or high-frequency attenuator.
A-18. At low-frequency, a capacitor acts as an open and an inductor acts as a short. At high-frequency, a capacitor acts as a short and an inductor acts as an open.
A-19. Frequency cutoff (fco).
A-20. Bandpass.
A-21. Band-reject.
2-1
Upon completion of this chapter you will be able to:
1. List the two broad classifications of oscillators (wave generators).
2. Identify the three frequency-determining devices for sine-wave oscillators.
3. Describe the differences between series-fed and shunt-fed oscillators.
4. Explain how the crystal is equivalent to the series and parallel LC circuit.
5. Identify the Armstrong oscillator.
6. Identify the Hartley oscillator.
7. Identify the Colpitts oscillator.
8. Identify the resistive-capacitive oscillator.
9. Determine the frequency of a resistive-capacitive oscillator.
10. Explain the operation of a pulsed oscillator.
11. Determine how many cycles are present in the output of a pulsed oscillator.
12. Explain how frequency multiplication takes place.
WAVE GENERATORS play a prominent role in the field of electronics. They generate signals from a few hertz to several gigahertz (109 hertz). Modern wave generators use many different circuits and generate such outputs as SINUSOIDAL, SQUARE, RECTANGULAR, SAWTOOTH, and TRAPEZOIDAL waveshapes. These waveshapes serve many useful purposes in the electronic circuits you will be studying. For example, they are used extensively throughout the television receiver to reproduce both picture and sound.
One type of wave generator is known as an OSCILLATOR. An oscillator can be regarded as an amplifier which provides its own input signal. Oscillators are classified according to the waveshapes they produce and the requirements needed for them to produce oscillations.
Wave generators can be classified into two broad categories according to their output waveshapes, SINUSOIDAL and NONSINUSOIDAL.
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A sinusoidal oscillator produces a sine-wave output signal. Ideally, the output signal is of constant amplitude with no variation in frequency. Actually, something less than this is usually obtained. The degree to which the ideal is approached depends upon such factors as class of amplifier operation, amplifier characteristics, frequency stability, and amplitude stability.
Sine-wave generators produce signals ranging from low audio frequencies to ultrahigh radio and microwave frequencies. Many low-frequency generators use resistors and capacitors to form their frequency-determining networks and are referred to as RC OSCILLATORS. They are widely used in the audio-frequency range.
Another type of sine-wave generator uses inductors and capacitors for its frequency-determining network. This type is known as the LC OSCILLATOR. LC oscillators, which use tank circuits, are commonly used for the higher radio frequencies. They are not suitable for use as extremely low-frequency oscillators because the inductors and capacitors would be large in size, heavy, and costly to manufacture.
A third type of sine-wave generator is the CRYSTAL-CONTROLLED OSCILLATOR. The crystal- controlled oscillator provides excellent frequency stability and is used from the middle of the audio range through the radio frequency range.
Nonsinusoidal oscillators generate complex waveforms, such as square, rectangular, trigger, sawtooth, or trapezoidal. Because their outputs are generally characterized by a sudden change, or relaxation, they are often referred to as RELAXATION OSCILLATORS. The signal frequency of these oscillators is usually governed by the charge or discharge time of a capacitor in series with a resistor. Some types, however, contain inductors that affect the output frequency. Thus, like sinusoidal oscillators, both RC and LC networks are used for determining the frequency of oscillation. Within this category of nonsinusoidal oscillators are MULTIVIBRATORS, BLOCKING OSCILLATORS, SAWTOOTH GENERATORS, and TRAPEZOIDAL GENERATORS.
An oscillator can be thought of as an amplifier that provides itself (through feedback) with an input signal. By definition, it is a nonrotating device for producing alternating current, the output frequency of which is determined by the characteristics of the device. The primary purpose of an oscillator is to generate a given waveform at a constant peak amplitude and specific frequency and to maintain this waveform within certain limits of amplitude and frequency.
An oscillator must provide amplification. Amplification of signal power occurs from input to output. In an oscillator, a portion of the output is fed back to sustain the input, as shown in figure 2-1. Enough power must be fed back to the input circuit for the oscillator to drive itself as does a signal generator. To cause the oscillator to be self-driven, the feedback signal must also be
2-3
REGENERATIVE (positive). Regenerative signals must have enough power to compensate for circuit losses and to maintain oscillations.
Since a practical oscillator must oscillate at a predetermined frequency, a FREQUENCY- DETERMINING DEVICE (fdd), sometimes referred to as a FREQUENCY-DETERMINING NETWORK (fdn), is needed. This device acts as a filter, allowing only the desired frequency to pass. Without a frequency-determining device, the stage will oscillate in a random manner, and a constant frequency will not be maintained.
Before discussing oscillators further, let's review the requirements for an oscillator. First, amplification is required to provide the necessary gain for the signal. Second, sufficient regenerative feedback is required to sustain oscillations. Third, a frequency-determining device is needed to maintain the desired output frequency.
The basic oscillator requirements, in addition to the application, determine the type of oscillator to be used. Let's consider some factors that account for the complexity and unique characteristics of oscillators.
Virtually every piece of equipment that uses an oscillator has two stability requirements, AMPLITUDE STABILITY and FREQUENCY STABILITY. Amplitude stability refers to the ability of the oscillator to maintain a constant amplitude in the output waveform. The more constant the amplitude of the output waveform, the better the amplitude stability. Frequency stability refers to the ability of the oscillator to maintain its operating frequency. The less the oscillator varies from its operating frequency, the better the frequency stability.
A constant frequency and amplitude can be achieved by taking extreme care to prevent variations in LOAD, BIAS, and COMPONENT CHARACTERISTICS. Load variations can greatly affect the amplitude and frequency stability of the output of an oscillator. Therefore, maintaining the load as constant as possible is necessary to ensure a stable output.
As you should know from your study of transistor biasing, bias variations affect the operating point of the transistor. These variations may alter the amplification capabilities of the oscillator circuits as well. A well-regulated power supply and a bias-stabilizing circuit are required to ensure a constant, uniform signal output.
As a result of changing temperature and humidity conditions, the value or characteristics of components such as capacitors, resistors, and transistors can change. The changes in these components also cause changes in amplitude and frequency.
Output power is another consideration in the use of oscillators. Generally speaking, high power is obtained at some sacrifice to stability. When both requirements are to be met, a low-power, stable oscillator can be followed by a higher-power BUFFER AMPLIFIER. The buffer provides isolation between the oscillator and the load to prevent changes in the load from affecting the oscillator.
If the oscillator stage must develop high power, efficiency becomes important. Many oscillators use class C bias to increase efficiency. Other types of oscillators may use class A bias when a high efficiency is not required but distortion must be kept at a minimum. Other classes of bias may also be used with certain oscillators.
RC networks, LC tanks, and crystals may appear in sine-wave oscillator circuits. An amplifier can be made into a sine-wave oscillator by providing regenerative feedback through an RC network.
2-4
Figure 2-2, view (A), shows the block diagram of an amplifier with an RC network through which regenerative feedback is provided. The RC network also acts as the frequency-determining device. View (B) shows a vector analysis of the signal E at various points in the circuit.
To analyze the operation of the circuit in view (A), assume that the amplifier is a common-emitter configuration. The signal on the collector (M) is 180 degrees out of phase with the signal (input) on the base (R). For the circuit to produce regenerative feedback, the RC network must provide a 180-degree phase shift of the collector signal. When power is applied to the circuit, a noise voltage (noise contains many different frequencies) will appear on the collector. This noise signal is represented by vector LM in view (B). As the signal couples through C1 and across R1 (view (A)), a phase shift occurs. The voltage across R1 (E R1), represented by vector LN, has been shifted in phase (about 60 degrees) and reduced in amplitude. The signal at point N (view (A)) is then coupled to the next RC section (R2 and C2). Using the same size resistor and capacitor as before will cause another 60-degree phase shift to take place. The signal at point P is the voltage across R2, represented by vector LP. Now the signal at point P has been shifted about 120 degrees and its amplitude is reduced still further. The same actions occur for the last section (R3 and C3). This signal experiences another 60-degree phase shift and has further amplitude reduction. The signal at point R (ER3) has been shifted 180 degrees and is represented by vector LR.
Notice that point R is the input to the base of the common-emitter amplifier. Also, vector LR shows that the signal on the base is regenerative (aiding the circuit operation). This meets the regenerative feedback requirement. An exact 60-degree phase shift per stage is not required, but the sum of the three phase shifts must equal 180 degrees.
2-5
For a given RC network, only one frequency of the initial noise signal will be shifted exactly 180 degrees. In other words, the network is frequency selective. Therefore, the RC network is the frequency- determining device since the lengths of the vectors and their phase relationships depend on frequency. The frequency of oscillations is governed by the values of resistance and capacitance in these sections. Variable resistors and capacitors may be used to provide tuning in the feedback network to allow for minor variations in phase shift. For an RC phase-shift oscillator, the amplifier is biased for class A operation to minimize distortion of the wave or signal.
Some sine-wave oscillators use resonant circuits consisting of inductance and capacitance. For example, recall the tank circuit in which a resonant circuit stores energy alternately in the inductor and capacitor, producing a sine wave. You studied this action of the tank circuit in chapter 1.
If there were absolutely no internal resistances in a tank circuit, oscillations would continue indefinitely, as shown in figure 2-3, view (A). Each resonant circuit does, however, contain some resistance which dissipates power. This power loss causes the amplitude to decrease, as shown in views (B) and (C). The reduction of amplitude in an oscillator circuit is referred to as DAMPING. Damping is caused by both tank and load resistances. The larger the tank resistance, the greater the amount of damping. Loading the tank causes the same effect as increasing the internal resistance of the tank. The effect of this damping can be overcome by applying regenerative feedback.
2-6
Figure 2-4 shows a block diagram of a typical LC oscillator. Notice that the oscillator contains the three basic requirements for sustained oscillations: amplification, a frequency-determining device, and regenerative feedback.
The amplifier supplies energy to begin what is known as the FLYWHEEL EFFECT. The flywheel effect is the maintenance of oscillations in a circuit in the intervals between pulses of excitation energy. Recall that in chapter 1 the tank circuit alternately stored energy in the inductor and capacitor. The LC network provides initial oscillations. A portion of the output of the LC network is then returned to the input of the amplifier through the regenerative-feedback network to sustain the oscillations.
When a tank circuit is used to develop oscillations in an oscillator, the output frequency of the oscillator is primarily the resonant frequency of the tank circuit and can be found by the formula:
Another frequency-determining device is the CRYSTAL. The crystal may be used with a tank circuit, or it may perform alone. Crystals exhibit a characteristic known as the PIEZOELECTRIC EFFECT. The piezoelectric effect is the property of a crystal by which mechanical forces produce electrical charges and, conversely, electrical charges produce mechanical forces. This effect is a form of oscillation similar to the flywheel effect of a tank circuit.
The piezoelectric effect can be seen in a number of crystal substances. The most important of these are the minerals quartz and Rochelle salt. Although quartz does not exhibit the piezoelectric effect to the degree that Rochelle salt does, quartz is used for frequency control in oscillators because of its greater mechanical strength. Another mineral, tourmaline, is physically strong like quartz; but because it is more expensive, it is not used extensively as an fdd. This discussion will deal only with the quartz crystal.
The crystals used in oscillator circuits are thin sheets, or wafers, cut from natural or synthetic quartz and ground to a specific thickness to obtain the desired resonant frequency. The crystals are mounted in holders, which support them physically and provide electrodes by which voltage is applied. The holder must allow the crystals freedom for vibration. There are many different types of holders. One type is shown in figure 2-5.
2-7
The frequency for which a crystal is ground is referred to as the NATURAL RESONANT FREQUENCY of the crystal. Voltage applied to the crystal produces mechanical vibrations which, in turn, produce an output voltage at the natural resonant frequency of the crystal. A vibrating crystal can be represented by an equivalent electrical circuit composed of capacitance, inductance, and resistance.
Figure 2-6, view (A), illustrates the symbol of a crystal; view (B) shows an equivalent circuit for the crystal. View (C) shows an equivalent circuit for the crystal and the holder; C1 represents the capacitance between the metal plates of the holder.
2-8
The Q (discussed in chapter 1) of a crystal is many times greater than that of an LC tank circuit. The high Q is present because the resistance in the crystal is extremely small. Commercially produced crystals range in Q from 5,000 to 30,000. The high Q causes the frequency stability to be much greater than that of an ordinary LC tank circuit. This is the reason a crystal is used in many sine-wave generator circuits.
Q-1. What are the two classifications of wave generators according to their output waveshapes?
Q-2. What are the three networks used for frequency-determining devices?
Q-3. What is another name for nonsinusoidal oscillators?
Q-4. What is a nonrotating device that produces alternating current?
Q-5. What are the three requirements necessary for oscillations to exist in a circuit?
As you have just studied, a basic oscillator can be broken down into three main sections: a frequency-determining device, an amplifier, and a feedback circuit. The frequency-determining device in an LC oscillator is usually an LC tank circuit. Although the tank circuit is normally found in the input circuit of an oscillator (both electron tube and transistor), it sometimes appears in the output circuit. The differences in magnitude of plate and collector currents and shunting impedances are considerations in the designed locations of such tank circuits. In both solid-state and electron tube circuits, oscillations take place in the tuned circuit. Both the electron tube and the transistor function primarily as electrical valves that amplify and automatically deliver to the input circuit the proper amount of energy to sustain oscillations. In both tube and transistor oscillators, the feedback circuit couples energy of the proper amount and of the correct phase from the output to the input circuit to sustain oscillations.
Let's review what you have studied up to this point concerning feedback. Feedback is the process of transferring energy from a high-level point in a system to a low-level point in a system. This means transferring energy from the output of an amplifier back to its input. If the output feedback signal opposes the input signal, the signal is DEGENERATIVE or NEGATIVE FEEDBACK. However, if the feedback aids the input signal, the feedback is REGENERATIVE or POSITIVE FEEDBACK. Regenerative or
2-9
positive feedback is one of the requirements to sustain oscillations in an oscillator. This feedback can be applied in any of several ways to produce a practical oscillator circuit.
Chapter 1 described the resonant or tank circuit and how a sinusoidal signal is generated by the action of an inductor and a capacitor. The feedback signal is coupled from this circuit by either of two means. The first method is to take some of the energy from the inductor. This can be done by any one of the three ways shown in figure 2-7, views (A), (B), and (C). When an oscillator uses a TICKLER COIL, as shown in view (A), it is referred to as an ARMSTRONG OSCILLATOR. When an oscillator uses a tapped coil (view (B)) or a split coil (view (C)), it is referred to as a HARTLEY OSCILLATOR. The second method of coupling the feedback signal is to use two capacitors in the tank circuit and tap the feedback signal between them. This is shown in view (D). An oscillator using this method is referred to as a COLPITTS OSCILLATOR. Each of these particular oscillators is named after the person who originally designed them.
Any of the three basic amplifier configurations (common collector, common base, or common emitter) described in NEETS, Module 7, Introduction to Solid-State Devices and Power Supplies, Chapter 2, may be used for the oscillator circuit. However, certain considerations in the application of the circuit, such as the operating frequency and output power required, usually determine which of the three configurations is to be used. The three basic configurations are shown in figure 2-8, views (A), (B), and (C).
2-10
Since there is no phase reversal between the input and output circuits of a common-collector configuration, the feedback network does not need to provide a phase shift. However, since the voltage gain is less than unity and the power gain is low, the common-collector configuration is very seldom used in oscillator circuits.
The power gain and voltage gain of the common-base configuration are high enough to give satisfactory operation in an oscillator circuit. The wide range between the input resistance and the output resistance make impedance matching slightly harder to achieve in the common-base circuit than in the common-emitter circuit. An advantage of the common-base configuration is that it exhibits better high- frequency response than does the common-emitter configuration.
The common-emitter configuration has high power gain and is used in low-frequency applications. For the energy which is fed back from the output to be in phase with the energy at the input, the feedback network of a common-emitter oscillator must provide a phase shift of approximately 180 degrees. An
2-11
advantage of the common-emitter configuration is that the medium resistance range of the input and output simplifies the job of impedance matching.
Q-6. What type of feedback aids an input signal?
Q-7. What are the two methods used for feedback coupling?
Q-8. Which oscillator uses a tickler coil for feedback?
Q-9. Which oscillator uses a tapped inductor for feedback?
Q-10. Which oscillator uses tapped capacitors for feedback?
Q-11. What are the three basic configurations of transistor oscillators?
Oscillators may be classified by name, such as Armstrong, Hartley, Colpitts, or by the manner in which dc power is applied. An oscillator in which dc power is supplied to the transistor through the tank circuit, or a portion of the tank circuit, is said to be SERIES FED. An oscillator which receives its dc power for the transistor through a path separate and parallel to the tank circuit is said to be PARALLEL FED OR SHUNT FED. All the oscillators in this chapter can be constructed either way, series or shunt fed. The construction depends on the characteristics of the oscillator circuit the designer is interested in.
A SERIES-FED, TUNED-COLLECTOR ARMSTRONG OSCILLATOR is illustrated in figure 2-9, view (A). The dc path is from the negative side (ground) of VCC through RE, Q1, T1, and back to the positive side of VCC. The figure clearly illustrates that both the ac and dc components flow through the tank circuit.
2-12
By modifying the circuit slightly, it becomes a SHUNT-FED, TUNED-COLLECTOR ARMSTRONG OSCILLATOR as shown in view (B). The dc component flows from ground through RE to Q1 to positive VCC. The dc is blocked from the tank circuit by capacitor C2. Only the ac component flows in the tank circuit.
The function of an oscillator is to produce a sinusoidal waveshape of a specific frequency and amplitude. In doing so, the stability of an oscillator is very important. Depending on its application, an oscillator may be required to have either good frequency stability or amplitude stability; in many circumstances, both are required. Of the two, good frequency stability is usually considered more important.
The FREQUENCY STABILITY of an oscillator is a measure of the degree to which a constant frequency output is approached. The better the frequency stability, the closer the output will be to a constant frequency.
Frequency INSTABILITY (variations above and below the desired output frequency) may be caused by transistor characteristics or by variations in the external circuit elements.
As stated before, when output power is not of prime importance, transistor oscillators may be biased class A to ensure stability and minimize distortion. When this is done, the dc operating point established by the power supply is chosen so that the operation of the transistor oscillator occurs over the most linear portion of the transistor's characteristic curve. When the operation of the circuit falls into the nonlinear portion of the characteristic curve, the transistor's parameters (voltages and currents) vary. These parameters are basic to the stable frequency of the transistor oscillator. Operating frequency variations may occur with changes in these bias voltages. Thus, a constant supply voltage is a prime requirement for good frequency stability.
The use of a common bias source for both collector and emitter electrodes results in a relatively constant ratio of the two voltages. In effect, a change in one voltage is somewhat counteracted by the change in the other. This counteraction takes place because an increase in collector voltage causes an
2-13
increase in the oscillating frequency, and an increase in emitter voltage causes a decrease in the oscillating frequency. This is a result of the change in capacitance between the junctions of the transistor. However, a common bias source does not completely compensate since the effects on other circuit parameters of each bias voltage differ.
Just as in any transistor circuit, changes in the transistor operating point and changes in temperature are encountered in the transistor oscillator. The effects of changes in temperature are to cause collector current to increase if the transistor is not stabilized. The increase in collector current can be prevented by reducing the forward bias.
The AMPLITUDE STABILITY of a transistor oscillator indicates the amount by which the actual output amplitude varies from the desired output amplitude.
The same parameters (voltages and currents) that affect frequency stability also affect amplitude stability. Output amplitude may be kept relatively constant by ensuring that the feedback is large enough that the collector current is maintained at the proper level. Feedback used in this manner makes the output voltage directly proportional to the supply voltage. Thus, regulation of the supply voltage ensures good amplitude stability.
The ARMSTRONG OSCILLATOR is used to produce a sine-wave output of constant amplitude and of fairly constant frequency within the rf range. It is generally used as a local oscillator in receivers, as a source in signal generators, and as a radio-frequency oscillator in the medium- and high-frequency range.
The identifying characteristics of the Armstrong oscillator are that (1) it uses an LC tuned circuit to establish the frequency of oscillation, (2) feedback is accomplished by mutual inductive coupling between the tickler coil and the LC tuned circuit, and (3) it uses a class C amplifier with self-bias. Its frequency is fairly stable, and the output amplitude is relatively constant.
Views (A), (B), and (C) shown in figure 2-10 can be used to build the basic Armstrong oscillator. View (A) shows a conventional amplifier. R2 provides the forward bias for Q1, C2 is a coupling capacitor, and L1 and R1 form the collector load impedance. This is a common-emitter configuration which provides the 180-degree phase shift between the base and collector.
2-14
View (B) shows the frequency-determining device composed of inductor L2 and capacitor C1. C1 is a variable tuning capacitor which is used to adjust the resonant frequency to the desired value.
View (C) is the feedback network which uses L1 (the collector load) as the primary and L2 as the secondary winding of a coupling transformer to provide a 180-degree phase shift. Variable resistor R1 controls the amount of current through L1. When R1 is adjusted for maximum resistance, most of the current flows through L1. The transformer now couples a maximum signal which represents a large feedback amplitude into the tank circuit (L2, C1). If R1 is adjusted for a smaller resistance, less current
2-15
flows through L1, and less energy is coupled to the tank circuit; therefore, feedback amplitude decreases. R1 is normally adjusted so that the L1 current is adequate to sustain tank oscillations.
View (D) shows the complete oscillator circuit. Connecting the feedback network through coupling capacitor C2 to the base of Q1 forms a "closed loop" for feedback (shown by the solid arrows). Let's verify that the feedback is regenerative. Assume a positive signal on the base of Q1. The transistor conducts heavily when forward biased. This current flow through L1 and R1 causes the voltage across L1 to increase. The voltage increase is inductively coupled to L2 and inverted. This action ensures that the voltage is positive at the base end of L2 and C1 and in phase with the base voltage. The positive signal is now coupled through C2 to the base of Q1. The regenerative feedback offsets the damping in the frequency-determining network and has sufficient amplitude to provide unity circuit gain.
The circuit in view (D) has all three requirements for an oscillator: (1) amplification, (2) a frequency- determining device, and (3) regenerative feedback. The oscillator in this schematic drawing is a tuned- base oscillator, because the fdd is in the base circuit. If the fdd were in the collector circuit, it would be a tuned-collector oscillator. The circuit in view (D) is basically an Armstrong oscillator.
Refer to figure 2-10, view (D), for the following discussion of the circuit operation of the Armstrong oscillator. When VCC is applied to the circuit. a small amount of base current flows through R2 which sets the forward bias on Q1. This forward bias causes collector current to flow from ground through Q1, R1, and L1 to +VCC. The current through L1 develops a magnetic field which induces a voltage into the tank circuit. The voltage is positive at the top of L2 and C1. At this time, two actions occur. First, resonant tank capacitor C1 charges to this voltage; the tank circuit now has stored energy. Second, coupling capacitor C2 couples the positive signal to the base of Q1. With a positive signal on its base, Q1 conducts harder. With Q1 conducting harder, more current flows through L1, a larger voltage is induced into L2, and a larger positive signal is coupled back to the base of Q1. While this is taking place, the frequency- determining device is storing more energy and C1 is charging to the voltage induced into L2.
The transistor will continue to increase in conduction until it reaches saturation. At saturation, the collector current of Q1 is at a maximum value and cannot increase any further. With a steady current through L1, the magnetic fields are not moving and no voltage is induced into the secondary.
With no external voltage applied, C1 acts as a voltage source and discharges. As the voltage across C1 decreases, its energy is transferred to the magnetic field of L2. Now, let's look at C2.
The coupling capacitor, C2, has charged to approximately the same voltage as C1. As C1 discharges, C2 discharges. The primary discharge path for C2 is through R2 (shown by the dashed arrow). As C2 discharges, the voltage drop across R2 opposes the forward bias on Q1 and collector current begins to decrease. This is caused by the decreasing positive potential at the base of Q1.
A decrease in collector current allows the magnetic field of L1 to collapse. The collapsing field of L1 induces a negative voltage into the secondary which is coupled through C2 and makes the base of Q1 more negative. This, again, is regenerative action; it continues until Q1 is driven into cutoff.
When Q1 is cut off, the tank circuit continues to flywheel, or oscillate.  Without feedback, the oscillations of L2 and C1 would dampen out after several cycles.
To ensure that the amplitude of the signal remains constant, regenerative feedback is supplied to the tank once each cycle, as follows: As the voltage across C1 reaches maximum negative, C1 begins discharging toward 0 volts. Q1 is still below cutoff. C1 continues to discharge through 0 volts and becomes positively charged. The tank circuit voltage is again coupled to the base of Q1, so the base voltage becomes positive and allows collector current to flow. The collector current creates a magnetic
2-16
field in L1, which is coupled into the tank. This feedback action replaces any lost energy in the tank circuit and drives Q1 toward saturation. After saturation is reached, the transistor is again driven into cutoff.
The operation of the Armstrong oscillator is basically this: Power applied to the transistor allows energy to be applied to the tank circuit causing it to oscillate. Once every cycle, the transistor conducts for a short period of time (class C operation) and returns enough energy to the tank to ensure a constant amplitude output signal.
Class C operation has high efficiency and low loading characteristics. The longer Q1 is cut off, the less the loading on the frequency-determining device.
Figure 2-11 shows a tuned-base Armstrong oscillator as you will probably see it. R3 has been added to improve temperature stability. Bypass capacitor C3 prevents degeneration. C4 is an output coupling capacitor, and impedance-matching transformer T2 provides a method of coupling the output signal. T2 is usually a loosely coupled rf transformer which reduces undesired reflected impedance from the load back to the oscillator.
The Armstrong oscillator is an example of how a class C amplifier can produce a sine-wave output that is not distorted. Although class C operation is nonlinear and many harmonic frequencies are generated, only one frequency receives enough gain to cause the circuit to oscillate. This is the frequency of the resonant tank circuit. Thus, high efficiency and an undistorted output signal can be obtained.
The waveforms in figure 2-12 illustrate the relationship between the collector voltage and collector current. Notice that collector current (IC) flows for only a short time during each cycle. While the tank circuit is oscillating (figure 2-11), L2 acts as the primary of the transformer and L1 acts as the secondary. The signal from the tank is, therefore, coupled through T1 to coupling capacitor C4, and the output voltage across L4 is a sine wave.
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The HARTLEY OSCILLATOR is an improvement over the Armstrong oscillator. Although its frequency stability is not the best possible of all the oscillators, the Hartley oscillator can generate a wide range of frequencies and is very easy to tune. The Hartley will operate class C with self-bias for ordinary operation. It will operate class A when the output waveform must be of a constant voltage level or of a linear waveshape. The two versions of this oscillator are the series-fed and the shunt-fed. The main difference between the Armstrong and the Hartley oscillators lies in the design of the feedback (tickler) coil. A separate coil is not used. Instead, in the Hartley oscillator, the coil in the tank circuit is a split inductor. Current flow through one section induces a voltage in the other section to develop a feedback signal.
One version of a SERIES-FED HARTLEY OSCILLATOR is shown in figure 2-13. The tank circuit consists of the tapped coil (L1 and L2) and capacitor C2. The feedback circuit is from the tank circuit to the base of Q1 through the coupling capacitor C1. Coupling capacitor C1 prevents the low dc resistance of L2 from placing a short across the emitter-to-base junction and resistor RE. Capacitor C3 bypasses the sine-wave signal around the battery, and resistor RE is used for temperature stabilization to prevent thermal runaway. Degeneration is prevented by CE in parallel with RE. The amount of bias is determined by the values of RB, the emitter-to-base resistance, the small amount of dc resistance of coil L1, and the resistance of RE.
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When a voltage is applied to the circuit, current from the battery flows through coil L1 and to the emitter through RE. Current then flows from the emitter to the collector and back to the battery. The surge of current through coil L1 induces a voltage in coil L2 to start oscillations within the tank circuit.
When current first starts to flow through coil L1, the bottom of L1 is negative with respect to the top of L2. The voltage induced into coil L2 makes the top of L2 positive. As the top of L2 becomes positive, the positive potential is coupled to the base of Q1 by capacitor C1. A positive potential on the base results in an increase of the forward bias of Q1 and causes collector current to increase. The increased collector current also increases the emitter current flowing through coil L1. Increased current through L1 results in more energy being supplied to the tank circuit, which, in turn, increases the positive potential at the top of the tank (L2) and increases the forward bias of Q1. This action continues until the rate of current change through coil L1 can no longer increase. The current through coil L1 and the transistor cannot continue increasing indefinitely, or the coil and transistor will burn up. The circuit must be designed, by proper selection of the transistor and associated parts, so that some point is reached when the current can no longer continue to increase. At this point C2 has charged to the potential across L1 and L2. This is shown as the heavy dot on the base waveform. As the current through L1 decreases, the voltage induced in L2 decreases. The positive potential across the tank begins to decrease and C2 starts discharging through L1 and L2. This action maintains current flow through the tapped coil and causes a decrease in the forward bias of Q1. In turn, this decrease in the forward bias of Q1 causes the collector and emitter current to decrease. At the instant the potential across the tank circuit decreases to 0, the energy of the tank circuit is contained in the magnetic field of the coil. The oscillator has completed a half cycle of operation.
Next, the magnetic field around L2 collapses as the current from C2 stops. The action of the collapsing magnetic field causes the top of L2 to become negative at this instant. The negative charge causes capacitor C2 to begin to charge in the opposite direction. This negative potential is coupled to the base of Q1, opposing its forward bias. Most transistor oscillators are operated class A; therefore, the positive and negative signals applied to the base of Q1 will not cause it to go into saturation or cutoff. When the tank circuit reaches its maximum negative value, the collector and the emitter currents will still be present but at a minimum value. The magnetic field will have collapsed and the oscillator will have completed 3/4 cycle.
At this point C2 begins to discharge, decreasing the negative potential at the top of L2 (potential will swing in the positive direction). As the negative potential applied to the base of Q1 decreases, the opposition to the forward bias also decreases. This, in effect, causes the forward bias to begin increasing, resulting in increased emitter current flowing through L1. The increase in current through L1 causes additional energy to be fed to the tank circuit to replace lost energy. If the energy lost in the tank is replaced with an equal or larger amount of energy, oscillations will be sustained. The oscillator has now completed 1 cycle and will continue to repeat it over and over again.
A version of a SHUNT-FED HARTLEY OSCILLATOR is shown in figure 2-14. The parts in this circuit perform the same basic functions as do their counterparts in the series-fed Hartley oscillator. The difference between the series-fed and the shunt-fed circuit is that dc does not flow through the tank circuit. The shunt-fed circuit operation is essentially the same as the series-fed Hartley oscillator. When voltage is applied to the circuit, Q1 starts conducting. As the collector current of Q1 increases, the change (increase) is coupled through capacitor C3 to the tank circuit, causing it to oscillate. C3 also acts as an isolation capacitor to prevent dc from flowing through the feedback coil. The oscillations at the collector will be coupled through C3 (feedback) to supply energy lost within the tank.
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Q-12. What is the main difference between the Armstrong oscillator and the Hartley oscillator?
Q-13. What is the difference between the series-fed and the shunt-fed Hartley oscillator?
Both the Armstrong and the Hartley oscillators have a tendency to be unstable in frequency because of junction capacitance. In comparison, the COLPITTS OSCILLATOR has fairly good frequency stability, is easy to tune, and can be used for a wide range of frequencies. The large value of split capacitance is in parallel with the junctions and minimizes the effect on frequency stability.
The Colpitts oscillator is very similar to the shunt-fed Hartley oscillator, except that two capacitors are used in the tank circuit instead of a tapped coil (figure 2-15). The Hartley oscillator has a tap between two coils, while the Colpitts has a tap between two capacitors. You can change the frequency of the Colpitts either by varying the inductance of the coil or by varying the capacitance of the two capacitors in the tank circuit. Notice that no coupling capacitor is used between the tank circuit and the base of Q1. Capacitors C1 and C2 of the tank circuit are in parallel with the input and the output interelement capacitance (capacitance between emitter, base, and collector) of the transistor. Thus the input and the output capacitive effect can be minimized on the tank circuit and better frequency stability can be obtained than with the Armstrong or the Hartley oscillator.
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Figure 2-16 shows a common-base Colpitts oscillator using a pnp transistor as the amplifying device. Notice in this version of the Colpitts oscillator that regenerative feedback is obtained from the tank circuit and applied to the emitter. Base bias is provided by resistor RB and RF. Resistor R C is the collector load resistor. Resistor RE develops the input signal and also acts as the emitter swamping resistor. The tuned circuit consists of C1 and C2 in parallel with the primary winding of transformer T1. The voltage developed across C2 is the feedback voltage. Either or both capacitors may be adjusted to control the frequency. In the common-base configuration there is no phase difference between the signal at the collector and the emitter signal. Therefore, the phase of the feedback signal does not have to be changed. When the emitter swings negative, the collector also swings negative and C2 charges negatively at the junction of C1 and C2. This negative charge across C2 is fed back to the emitter. This increases the reverse bias on Q1. The collector of Q1 becomes more negative and C2 charges to a negative potential. This feedback effect continues until the collector of Q1 is unable to become any more negative. At that time the primary of T1 will act as a source because of normal tank circuit operation. As its field collapses, the tank potential will reverse and C1 and C2 will begin to discharge. As C2 becomes less negative, the reverse bias on Q1 decreases and its collector voltage swings in the positive direction. C1 and C2 will continue to discharge and then charge in a positive direction. This positive-going voltage across C2 will be fed back to the emitter as regenerative feedback. This will continue until the field around the primary of T1 collapses. At that time the collector of Q1 will be at a maximum positive value. C1 and C2 will begin to discharge and the potential at their junction will become less positive. This increases the reverse bias on Q1 and drives the collector negative, causing C1 and C2 to charge in a negative direction and to repeat the cycle.
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Q-14. What is the identifying feature of a Colpitts oscillator?
As mentioned earlier, resistive-capacitive (RC) networks provide regenerative feedback and determine the frequency of operation in RESISTIVE-CAPACITIVE (RC) OSCILLATORS.
The oscillators presented in this chapter have used resonant tank circuits (LC). You should already know how the LC tank circuit stores energy alternately in the inductor and capacitor.
The major difference between the LC and RC oscillator is that the frequency-determining device in the RC oscillator is not a tank circuit. Remember, the LC oscillator can operate with class A or C biasing because of the oscillator action of the resonant tank. The RC oscillator, however, must use class A biasing because the RC frequency-determining device doesn't have the oscillating ability of a tank circuit.
An RC FEEDBACK or PHASE-SHIFT oscillator is shown in figure 2-17. Components C1, R1, C2, R2, C3, and RB are the feedback and frequency-determining network. This RC network also provides the needed phase shift between the collector and base.
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The PHASE-SHIFT OSCILLATOR, shown in figure 2-17, is a sine-wave generator that uses a resistive-capacitive (RC) network as its frequency-determining device.
As discussed earlier in the common-emitter amplifier configuration (figure 2-17), there is a 180-degree phase difference between the base and the collector signal. To obtain the regenerative feedback in the phase-shift oscillator, you need a phase shift of 180 degrees between the output and the input signal. An RC network consisting of three RC sections provides the proper feedback and phase inversion to provide this regenerative feedback. Each section shifts the feedback signal 60 degrees in phase.
Since the impedance of an RC network is capacitive, the current flowing through it leads the applied voltage by a specific phase angle. The phase angle is determined by the amount of resistance and capacitance of the RC section.
If the capacitance is a fixed value, a change in the resistance value will change the phase angle. If the resistance could be changed to zero, we could get a maximum phase angle of 90 degrees. But since a voltage cannot be developed across zero resistance, a 90-degree phase shift is not possible.
With a small value of resistance, however, the phase angle or phase shift is less than 90 degrees. In the phase-shift oscillator, therefore, at least three RC sections are needed to give the required 180-degree phase shift for regenerative feedback. The values of resistance and capacitance are generally chosen so that each section provides about a 60-degree phase shift.
Resistors RB, RF, and RC provide base and collector bias. Capacitor C E bypasses ac variations around the emitter resistor R E. Capacitors C1, C2, and C3 and resistors R1, R2, and R B form the feedback and phase-shifting network. Resistor R2 is variable for fine tuning to compensate for any small changes in value of the other components of the phase-shifting network.
When power is applied to the circuit, oscillations are started by any random noise (random electrical variations generated internally in electronic components). A change in the flow of base current results in an amplified change in collector current which is phase-shifted the 180 degrees. When the signal is returned to the base, it has been shifted 180 degrees by the action of the RC network, making the circuit regenerative. View (A) of figure 2-18 shows the amount of phase shift produced by C1 and R1. View (B) shows the amount of phase shift produced by C2 and R2 (signal received from C1 and R1), and view (C) shows the complete phase shift as the signal leaves the RC network. With the correct amount of resistance and capacitance in the phase-shifting network, the 180-degree phase shift occurs at only one frequency. At any other than the desired frequency, the capacitive reactance increases or decreases and causes an incorrect phase relationship (the feedback becomes degenerative). Thus, the oscillator works at only one frequency. To find the resonant frequency (fr) of an RC phase shift oscillator, use the following formula:
where n is the number of RC sections.
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A high-gain transistor must be used with the three-section RC network because the losses in the network are high. Using more than three RC sections actually reduces the overall signal loss within the network. This is because additional RC sections reduce the phase shift necessary for each section, and the loss for each section is lowered as the phase shift is reduced. In addition, an oscillator that uses four or more RC networks has more stability than one that uses three RC networks. In a four-part RC network,
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each part shifts the phase of the feedback signal by approximately 45 degrees to give the total required 180-degree phase shift.
Q-15. Which components provide the regenerative feedback signal in the phase-shift oscillator?
Q-16. Why is a high-gain transistor used in the phase-shift oscillator?
Q-17. Which RC network provides better frequency stability, three-section or four-section?
Crystal oscillators are those in which a specially-cut crystal controls the frequency. CRYSTAL- CONTROLLED OSCILLATORS are the standard means used for maintaining the frequency of radio transmitting stations within their assigned frequency limits. A crystal-controlled oscillator is usually used to produce an output which is highly stable and at a very precise frequency.
As stated earlier, crystals used in electrical circuits are thin sheets cut from the natural crystal and are ground to the proper thickness for the desired resonant frequency. For any given crystal cut, the thinner the crystal, the higher the resonant frequency. The "cut" (X, Y, AT, and so forth) of the crystal means the precise way in which the usable crystal is cut from the natural crystal. Some typical crystal cuts may be seen in figure 2-19.
Transmitters which require a very high degree of frequency stability, such as a broadcast transmitter, use temperature-controlled ovens to maintain a constant crystal temperature. These ovens are thermostatically controlled containers in which the crystals are placed.
The type of cut also determines the activity of the crystal. Some crystals vibrate at more than one frequency and thus will operate at harmonic frequencies. Crystals which are not of uniform thickness may have two or more resonant frequencies. Usually one resonant frequency is more pronounced than the others. The other less pronounced resonant frequencies are referred to as SPURIOUS frequencies. Sometimes such a crystal oscillates at two frequencies at the same time.
The amount of current that can safely pass through a crystal ranges from 50 to 200 milliamperes. When the rated current is exceeded, the amplitude of mechanical vibration becomes too great, and the
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crystal may crack. Overloading the crystal affects the frequency of vibration because the power dissipation and crystal temperature increase with the amount of load current.
A quartz crystal and its equivalent circuit are shown in figure 2-20, views (A) and (B). Capacitor C2, inductor L1, and resistor R1 in view (B) represent the electrical equivalent of the quartz crystal in view (A). Capacitance C1 in (view B) represents the capacitance between the crystal electrodes in view (A). Depending upon the circuit characteristics, the crystal can act as a capacitor, an inductor, a series-tuned circuit, or a parallel-tuned circuit.
At some frequency, the reactances of equivalent capacitor C1 and inductor L will be equal and the crystal will act as a series-tuned circuit. A series-tuned circuit has a minimum impedance at resonance (figure 2-21). Above resonance the series-tuned circuit acts INDUCTIVELY, and below resonance it acts CAPACITIVELY. In other words, the crystal unit has its lowest impedance at the series-resonance frequency. The impedance increases as the frequency is lowered because the unit acts as a capacitor. The impedance of the crystal unit also increases as the frequency is raised above the series-resonant point because the unit acts as an inductor. Therefore, the crystal unit reacts as a series-tuned circuit.
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