Module 9 - Introduction to Wave-Generation and Wave-Shaping
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NEETS Module 9 − Introduction to Wave− Generation and Wave−Shaping Pages i, 1−1, 1−11, 1−21, 1−31, 1−41, 2−1, 2−11, 2−21, 2−31, 3−1, 3−11, 3−21, 3−31, 3−41, 3−51, 4−1, 4−11, 4−21, 4−31, 4−41, 4−51, Index
Q-14. What is the identifying feature of a Colpitts oscillator? Resistive-Capacitive (RC) Feedback Oscillator
Figure 2-16 - Common-base Colpitts oscillator.
Figure 2-17 - Phase-shift 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. Phase-Shift Oscillators 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.
Figure 2-18A. - Three-section, phase-shifting RC network. Phase-SHIFT Network C1 and R1.
Figure 2-18B. - Three-section, phase-shifting RC network. Phase-SHIFT Network C2 and R2.
Figure 2-18C - Three-section, phase-shifting RC network. Phase-SHIFT Network C3 and RB.
Figure 2-19 - Quartz crystal cuts.
Figure 2-20A - Quartz crystal and equivalent circuit.
Figure 2-20B - Quartz crystal and equivalent circuit. Resistors RB, RF, and RC provide base and collector bias. Capacitor CE bypasses ac variations around the emitter resistor RE. Capacitors C1, C2, and C3 and resistors R1, R2, and RB 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:
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, 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 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 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. Crystals as Tuned Circuits 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.
Figure 2-21 - Frequency response of a crystal. Since the series-tuned circuit acts as an inductor above the resonant point, the crystal unit becomes equivalent to an inductor and is parallel with the equivalent capacitor C1 (view (B) of figure 2-20). At some frequency above the series-resonant point, the crystal unit will act as a parallel-tuned circuit. a parallel-tuned circuit has a Maximum impedance at the parallel-resonant frequency and acts inductively below parallel resonance (figure 2-21). Therefore, at some frequency, depending upon the cut of the crystal, the crystal unit will act as a parallel-tuned circuit. The frequency stability of crystal-controlled oscillators depends on the Q of the crystal. The Q of a crystal is very high. It may be more than 100 times greater than that obtained with an equivalent electrical circuit. The Q of the crystal is determined by the cut, the type of holder, and the accuracy of grinding. Commercially produced crystals range in Q from 5,000 to 30,000 while some laboratory experiment crystals range in Q up to 400,000. Crystal-Controlled Armstrong Oscillator
Figure 2-22 - Crystal-controlled Armstrong oscillator. The crystal-controlled Armstrong oscillator (figure 2-22) uses the series-tuned mode of operation. It works much the same as the Hartley oscillator except that frequency stability is improved by the crystal (in the feedback path). To operate the oscillator at different frequencies, you simply change crystals (each crystal operates at a different frequency). Variable capacitor C1 makes the circuit tunable to the selected crystal frequency. C1 is capable of tuning to a wide band of selected crystal frequencies. Regenerative feedback from the collector to base is through the mutual inductance between the transformer windings of T1. This provides the necessary 180-degree phase shift for the feedback signal. Resistors R B, RF, and RC provide the base and collector bias voltage. Capacitor CE bypasses ac variations around emitter resistor RE. At frequencies above and below the series-resonant frequency of the selected crystal, the impedance of the crystal increases and reduces the amount of feedback signal. This, in turn, prevents oscillations at frequencies other than the series-resonant frequency. Crystal-Controlled Pierce Oscillator
Figure 2-23 - Pierce oscillator, common-base configuration.
Figure 2-24 - Pierce oscillator, common-emitter configuration. The crystal-controlled Pierce Oscillator uses a crystal unit as a parallel-resonant circuit. The Pierce oscillator is a modified Colpitts oscillator. They operate in the same way except that the crystal unit replaces the parallel-resonant circuit of the Colpitts. Figure 2-23 shows the common-base configuration of the Pierce oscillator. Feedback is supplied from the collector to the emitter through capacitor C1. Resistors RB, RC, and RF provide the proper bias conditions for the circuit and resistor RE is the emitter resistor. Capacitors C1 and CE form a voltage divider connected across the output. Since no phase shift occurs in the common-base circuit, capacitor C1 feeds back a portion of the output signal to the emitter without a phase shift. The oscillating frequency is determined not only by the crystal but also by the parallel capacitance caused by capacitors C1 and CE. This parallel capacitance affects the oscillator frequency by lowering it. Any change in capacitance of either C1 or CE changes the frequency of the oscillator. Figure 2-24 shows the common-emitter configuration of the Pierce oscillator. The resistors in the circuit provide the proper bias and stabilization conditions. The crystal unit and capacitors C1 and C2 determine the output frequency of the oscillator. The signal developed at the junction between Y1 and C1 is 180 degrees out of phase with the signal at the junction between Y1 and C2. Therefore, the signal at the Y1-C1 junction can be coupled back to the base of Q1 as a regenerative feedback signal to sustain oscillations. Q-18. What is the impedance of a crystal at its resonant frequency when it is used in the parallel mode? Q-19. What is the impedance of a crystal at its resonant frequency when it is used in the series mode? Pulsed Oscillators A sinusoidal (sine-wave) oscillator is one that will produce output pulses at a predetermined frequency for an indefinite period of time; that is, it operates continuously. Many electronic circuits in equipment such as radar require that an oscillator be turned on for a specific period of time and that it remain in an off condition until required at a later time. These circuits are referred to as PULSED Oscillators or RINGING Oscillators. They are nothing more than sine-wave oscillators that are turned on and off at specific times.
Figure 2-25A - Pulsed oscillator.
Figure 2-25B - Pulsed oscillator. Figure 2-25, view (A), shows a pulsed oscillator with the resonant tank in the emitter circuit. a positive input makes Q1 conduct heavily and current flow through L1; therefore no oscillations can take place. a negative-going input pulse (referred to as a gate) cuts off Q1, and the tank oscillates until the gate ends or until the ringing stops, whichever comes first. The waveforms in view (B) show the relationship of the input gate and the output signal from the pulsed oscillator. To see how this circuit operates, assume that the Q of the LC tank circuit is high enough to prevent damping. An output from the circuit is obtained when the input gate goes negative (T0 to T1 and T2 to T3). The remainder of the time (T1 to T2) the transistor conducts heavily and there is no output from the circuit. The width of the input gate controls the time for the output signal. Making the gate wider causes the output to be present (or ring) for a longer time. Frequency of a Pulsed Oscillator The frequency of a pulsed oscillator is determined by both the input gating signal and the resonant frequency of the tank circuit. When a sinusoidal oscillator is resonant at 1 megahertz, the output is 1 million cycles per second. In the case of a pulsed oscillator, the number of cycles present in the output is determined by the gating pulse width. If a 1-megahertz oscillator is cut off for 1/2 second, or 50 percent of the time, then the output is 500,000 cycles at the 1 -megahertz rate. In other words, the frequency of the tank circuit is still 1 megahertz, but the oscillator is only allowed to produce 500,000 cycles each second. The output frequency can be determined by controlling how long the tank circuit will oscillate. For example, suppose a negative input gate of 500 microseconds and a positive input gate of 999,500 microseconds (total of 1 second) are applied. The transistor will be cut off for 500 microseconds and the tank circuit will oscillate for that 500 microseconds, producing an output signal. The transistor will then conduct for 999,500 microseconds and the tank circuit will not oscillate during that time period. The 500 microseconds that the tank circuit is allowed to oscillate will allow only 500 cycles of the 1-megahertz tank frequency. You can easily check this frequency by using the following formula:
One cycle of the 1-megahertz resonant frequency is equal to 1 microsecond.
Then, by dividing the time for 1 cycle (1 microsecond) into gate length (500 microseconds), you will get the number of cycles (500). There are several different varieties of pulsed oscillators for different applications. The schematic diagram shown in figure 2-25, view (A), is an emitter-loaded pulsed oscillator. The tank circuit can be placed in the collector circuit, in which case it is referred to as a collector-loaded pulsed oscillator. The difference between the emitter-loaded and the collector-loaded oscillator is in the output signal. The first alternation of an emitter-loaded npn pulsed oscillator is negative. The first alternation of the collector- loaded pulsed oscillator is positive. If a pnp is used, the oscillator will reverse the first alternation of both the emitter-loaded and the collector-loaded oscillator. You probably have noticed by now that feedback has not been mentioned in this discussion. Remember that regenerative feedback was a requirement for sustained oscillations. In the case of the pulsed oscillator, oscillations are only required for a very short period of time. You should understand, however, that as the width of the input gate (which cuts off the transistor) is increased, the amplitude of the sine wave begins to decrease (dampen) near the end of the gate period because of the lack of feedback. If a long period of oscillation is required for a particular application, a pulsed oscillator with regenerative feedback is used. The principle of operation remains the same except that the feedback network sustains the oscillation period for the desired amount of time. Q-20. Oscillators that are turned on and off at a specific time are known as what type of oscillators? Q-21. What is the polarity of the first alternation of the tank circuit in an emitter-loaded npn pulsed oscillator? Harmonics From your study of oscillators, you should know that the oscillator will oscillate at the resonant frequency of the tank circuit. Although the tank circuit is resonant at a particular frequency, many other frequencies other than the resonant frequency are present in the oscillator. These other frequencies are referred to as Harmonics. a harmonic is defined as a sinusoidal wave having a frequency that is a multiple of the fundamental frequency. In other words, a sine wave that is twice that fundamental frequency is referred to as the SECOND Harmonic. What you must remember is that the current in circuits operating at the resonant frequency is relatively large in amplitude. The harmonic frequency amplitudes are relatively small. For example, the second harmonic of a fundamental frequency has only 20 percent of the amplitude of the resonant frequency. a third harmonic has perhaps 10 percent of the amplitude of the fundamental frequency. One useful purpose of harmonics is that of frequency multiplication. It can be used in circuits to multiply the fundamental frequency to a higher frequency. The need for frequency-multiplier circuits results from the fact that the frequency stability of most oscillators decreases as frequency increases. Relatively good stability can be achieved at the lower frequencies. Thus, to achieve optimum stability, an oscillator is operated at a low frequency, and one or more stages of multiplication are used to raise the signal to the desired operating frequency.
Posted January 5, 2022 |
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, where n is the number
of RC sections. 
