NEETS Module 9 — Introduction to Wave Generation and WaveShapingPages
i  ix, 11 to 110,
111 to 120, 121 to 130,
131 to 140, 141 to 152,
21 to 210, 211 to 220,
221 to 230, 231 to 238,
31 to 310, 311 to 320,
321 to 330, 331 to 340,
341 to 350, 351 to 356,
41 to 410, 411 to 420,
421 to 430, 431 to 440,
441 to 450, 451 to 461, Index
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. The Characteristics of a Typical ParallelResonant Circuit Look at figure 111. 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 AC circuits that contain L and C. Figure 111.—Curves of impedance and current in an RLC parallelresonant circuit. Now, at resonance, X_{L} is still equal to X_{C}. Therefore, I_{L} must equal I_{C}. 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). 121
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 parallelLC 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 f_{r} the frequency of resonance in figure 111. There is little difference between the circuit pulsed by the battery in figure 18 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 parallelresonant (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. Summary of Resonance Both series and parallelLC 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 seriesresonant circuit. A highimpedance requirement would require the designer to use a parallelresonant circuit. Tuning a Band of Frequencies 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. 122
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. Q9. What is the term for the number of times per second that tank circuit energy is either stored in the inductor or capacitor? Q10. In a parallelresonant circuit, what is the relationship between impedance and current? Q11. When is line current minimum in a parallelLC circuit? RESONANT CIRCUITS AS FILTER CIRCUITS The principle of series or parallelresonant 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 DC voltage is not pure; it is still pulsating and fluctuating. In other words, the signal still has an AC component in addition to the DC voltage. By feeding the signal through simple filter networks, the AC component is reduced. The remaining DC 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 AC components to ground. THE IDEA OF "Q" 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 seriesresonant circuit and the amount of circulating (tank) current in a parallelresonant circuit. This factor is very important 123
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 (I^{2}R), 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 a Ratio Q is really very simple to understand if you think back to the tunedcircuit 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. The ratio 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. 124
The Q of a Coil 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. Application of Q 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 Relationships in Series Circuits Q can be used to determine the "gain" of seriesresonant 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 seriesresonant 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 seriesresonant 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: E = the input voltage to the tuned circuit E_{L} = the voltage drop across the coil at resonance Q. Q = the Q of the coil. Then: E_{L} = EQ 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 RLCcircuits at resonance is given in table 11. 125
Table 11.—Major Characteristics of Series RLC Circuits at Resonance Q Relationships in a ParallelResonant Circuit There is no voltage gain in a parallelresonant 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. 126
Given: I_{LINE} = current drawn from the source I_{L} = current through the coil (or circulating current Q = the Q of the coil Then: I_{L} = I_{LINE} Q 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 highpower amplifying circuits. The impedance curve of a parallelresonant 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 parallelLC circuit. (Z = Q x X_{L}) 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 parallelRLC circuits at resonance are given in table 12. 127
Table 12.—Major Characteristics of Parallel RLC Circuits at Resonance Summary of Q 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. 128
BANDWIDTH 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 112, 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. Figure 112A.—Bandwidth for high and lowQ series circuit. LOW Q CURRENT CURVE. Figure 112B.—Bandwidth for high and lowQ series circuit. HIGH Q CURRENT CURVE. 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 HALFPOWER point. Note that in figure 112, the seriesresonant circuit has two halfpower points, one above and one 129
below the resonant frequency point. The two points are designated upper frequency cutoff (fco) and lower frequency cutoff (f_{co}) or simply f_{1} and f_{2}. The range of frequencies between these two points comprises the bandwidth. Views (A) and (B) of figure 112 illustrate the bandwidths for low and highQ resonant circuits. The bandwidth may be determined by use of the following formulas: Where: BW = bandwidth of a circuit in units of frequency f_{r} = resonant frequency f_{2} = the upper cutoff frequency f_{1} = the lower cutoff frequency
For example, by applying the formula we can determine the bandwidth for the curve shown in figure 112, view (A). Solution: BW= f_{2}  f_{1} BW = 483.6 kHz  426.4 kHz BW = 57.2 kHz If the Q of the circuit represented by the curve in figure 112, view (B), is 45.5, what would be the bandwidth? Solution: If Q equals 7.95 for the lowQ circuit as in view (A) of figure 112, we can check our original calculation of the bandwidth. 130
Introduction to Matter, Energy, and Direct Current, Introduction
to Alternating Current and Transformers, Introduction to Circuit Protection,
Control, and Measurement, Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading, Introduction to Generators and Motors,
Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to SolidState Devices and Power Supplies,
Introduction to Amplifiers, Introduction to
WaveGeneration and WaveShaping Circuits, Introduction to Wave Propagation, Transmission
Lines, and Antennas, Microwave Principles,
Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics, Principles of Synchros, Servos, and Gyros,
Introduction to Test Equipment, RadioFrequency
Communications Principles, Radar Principles, The Technician's Handbook,
Master Glossary, Test Methods and Practices, Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics
