Here is a summary of the material covered in this chapter:
Oscillators are circuits that produce an output waveform without an external signal source. The key to oscillator operation is positive feedback. A positive feedback network produces a feedback voltage () that is in phase with the input signal () as shown in Figure 18-1. The amplifier shown in the figure produces a 180° voltage phase shift, and the feedback network introduces another 180° voltage shift. This results in a combined 360° voltage phase shift, which is the same as a 0° shift. Therefore, is in phase with . (Positive feedback can also be achieved by using an amplifier and a feedback network that both generate a 0° phase shift.)
Figure 18-1 also illustrates the basic principle of how the oscillator produces an output waveform without any input signal. In Figure 18-1a, the switch is momentarily closed, applying an input signal to the circuit. This results in a signal at the output from the amplifier, a portion of which is fed back to the input by the feedback network. In Figure 18-1b, the switch is now open, but the circuit continues to oscillate because the feedback network is supplying the input to the amplifier. The feedback network delivers an input to the amplifier, which in turn generates an input for the feedback network. This circuit action is referred to as regenerative feedback and is the basis for all oscillators.
An oscillator needs a brief trigger signal to start the oscillations. Most oscillators provide their own trigger simply by turning the circuit on. This principle is explained in detail at the end of Section 18.2 of the text. So far, we have established two requirements for oscillator operation:
FIGURE 18-1 Regenerative feedback.
There is one other requirement for oscillator operation. The circuit must fulfill a condition referred to as the Barkhausen criterion.
This relationship is called the Barkhausen criterion. If this criterion is not met, one of the following occurs:
These principles are illustrated in Figure 18-2.
FIGURE 18-2 The effects of on oscillator operation.
If , each oscillation results in a lower-amplitude signal being fed back to the input (as shown in Figure 18-2a). After a few cycles, the signal fades out. This loss of signal amplitude is called damping. If , each oscillation results in a larger and larger signal being fed back to the input (as shown in Figure 18-2b). In this case, the amplifier is quickly driven into clipping. When , each oscillation results in a consistently equal signal being fed back to the input (as shown in Figure 18-2c). One final point: Since there is always some power loss in the resistive components, in practicemust always be just slightly greater than 1.
The phase-shift oscillator contains three RC circuits in its feedback circuit. In your study of basic electronics, you learned that an RC circuit produces a phase shift at a given frequency that can be calculated using:
where = the phase angle of the circuit
= the inverse tangent of the fraction
The phase angle relationship shows that changes with and, therefore, with frequency. This means that an RC circuit can be designed for a specific phase shift at a given frequency.
FIGURE 18-3 Basic phase-shift oscillator.
The three RC networks in the phase-shift oscillator in Figure 18-3 produce a combined phase shift of 180° at a resonant frequency (). The op-amp produces another 180° phase shift, for a total circuit phase shift of 360° . As long as the Barkhausen criterion is met, the circuit oscillates at the frequency that results in the 180° phase shift.
You would think that each RC network in the phase shift oscillator would produce a 60° phase shift (3 × 60° = 180°), but this is not true. Each RC circuit loads the previous RC circuit, so their phase shifts are not equal. However, the total phase shift must equal 180° for the circuit to operate as an oscillator.
In reality, phase-shift oscillators are seldom used because they are extremely unstable (in terms of maintaining a constant frequency and amplitude). It is introduced here simply to help us understand the basic principles of how oscillators work, and because it is easy to build a phase-shift oscillator by mistake. A multistage amplifier can oscillate under certain conditions. Refer to Figure 18.5 of the text.
The Wien-Bridge Oscillator
The Wien-bridge oscillator is a commonly used low-frequency oscillator. This circuit achieves regenerative feedback by introducing no phase shift (0°) in the positive feedback path. As shown in Figure 18-4, there are two RC circuits in the positive feedback path (output to noninverting input).
FIGURE 18-4 Wien-bridge oscillator.
Thecircuit forms a low-pass filter, and the circuit forms a high-pass filter. Both RC filters have the same cutoff frequency (). Combined, they create a band-pass filter. As you know, a band-pass filter has no phase shift in its pass-band. As shown in Figure 18.7 of the text, the circuit oscillates at the intersection of the high-pass and low-pass response curves. It is common to see trimmer potentiometers added in series with and . They are used to fine-tune the circuits operating frequency.
The negative feedback path is from the output to the inverting input of the op-amp. Note the differences from a normal negative feedback circuit. Two diodes have been added in parallel with , as well as the potentiometer labeled . The potentiometer is used to control the of the circuit. The diodes also limit the closed-loop voltage gain of the circuit. If the output signal tries to exceed a predetermined value by more than 0.7 V, then the diodes conduct and limit signal amplitude. The diodes are essentially used as clippers.
Earlier we said that the Wien-bridge oscillator is a common low-frequency oscillator. As frequency increases, the propagation delay of the op-amp can begin to introduce a phase shift, which causes the circuit to stop oscillating. Propagation delay is the time required for the signal to pass through a component (in this case the op-amp). Most Wien-bridge oscillators are limited to frequencies below 1 MHz. Refer to Figure 18.9 of the text for a summary of Wien-bridge oscillator characteristics.
The Colpitts Oscillator
The Colpitts oscillator is a discrete LC oscillator that uses a pair of tapped capacitors and an inductor to produce regenerative feedback. A Colpitts oscillator is shown in Figure 18-5. The operating frequency is determined by the tank circuit. By formula:
FIGURE 18-5 Colpitts oscillator.
The key to understanding this circuit is knowing how the feedback circuit produces its 180° phase shift (the other 180° is from the inverting action of the CE amplifier). The feedback circuit produces a 180° voltage phase shift as follows:
The first two points are fairly easy to see. is between the collector and ground. This is where the output is measured. is between the transistor base and ground, or in other words, where the input is measured. Point three is explained using the circuit in Figure 18-6.
Figure 18-6 is the equivalent representation of the tank circuit in the Colpitts oscillator. Lets assume that the inductor is the voltage source and it induces a current in the circuit. With the polarity shown across the inductor, the current causes potentials to be developed across the capacitors with the polarities shown in the figure. Note that the capacitor voltages are 180° out of phase with each other. When the polarity of the inductor voltage reverses, the current reverses, as does the resulting polarity of the voltage across each capacitor (keeping the capacitor voltages 180° out of phase).
The value of the feedback voltage is determined (in part) by theof the circuit. For the Colpitts oscillator,is defined by the ratio of . By formula:
The validity of these equations is demonstrated in Example 18.1 of the text.
As with any oscillator, the product of must be slightly greater than 1. As mentioned earlier and . Therefore:
As with any tank circuit, this one will be affected by a load. To avoid loading effects (the circuit loses some efficiency), the output from a Colpitts oscillator is usually transformer-coupled to the load, as shown in Figure 18.14 of the text. Capacitive coupling is also acceptable so long as:
where is the total capacitance in the feedback network
Other LC Oscillators
Three other oscillators are mentioned briefly in this chapter: the Hartley oscillator, the Clapp oscillator, and the Armstrong oscillator.
The Hartley oscillator is similar to the Colpitts except that it uses a pair of tapped coils instead of two tapped capacitors. For the circuit in Figure 18-7, the output voltage is developed across and the feedback voltage is developed across . The attenuation caused by the feedback network () is found as:
The tank circuit, just like in the Colpitts, determines the operating frequency of the Hartley oscillator. As the tapped inductors are in series, the sum of must be used when calculating the value of.
FIGURE 18-7 Hartley oscillator.
The Clapp oscillator is simply a Colpitts oscillator with an extra capacitor in series with the coil. It is labeled as in Figure 18-8. The function of is to reduce the effects of junction capacitance on operating frequency. If you refer to Figure 18.17 of the text, you can see that:
is always much lower in value than either or , so it becomes the dominant capacitor in any frequency calculation. The reason we still need and is to provide the phase shift needed for regenerative feedback. has not replaced and . It is simply there to determine the operating frequency. Since are eliminated from the frequency calculation, junction capacitance has little or no effect on operating frequency.
FIGURE 18-8 Clapp oscillator.
The Armstrong oscillator uses a transformer to achieve the 180° phase shift required for oscillation, as shown in Figure 18-9. As you can see from the figure, the output from the transistor is applied to the primary of the transformer and the feedback is taken from the secondary. Note from the polarity dots on the transformer that the secondary is inverted relative to the primary. This is how the 180° phase shift is accomplished. The capacitor, , and the primary of the transformer determine the circuits operating frequency.
FIGURE 18-9 Armstrong oscillator.
Note: Any of the LC oscillators in this section can be constructed using FETs or op-amps. There are also several two-stage oscillator circuits. Many of these circuits can be constructed in common-base or common-gate configuration. To identify any LC oscillator, look for the circuit recognition features. These recognition features are listed in Table 18-1.
In applications where extremely stable operating frequencies are required, the oscillators that we have studied so far come up short. They can experience variations in both frequency and amplitude for several reasons:
In any system where stability is paramount, crystal-controlled oscillators are used. Crystal-controlled oscillators use a quartz crystal to control the operating frequency.
The key to the operation of a crystal-controlled oscillator is the piezoelectric effect, which means that the crystal vibrates at a constant rate when it is exposed to an electric field. The physical dimensions of the crystal determine the frequency of vibration. Thus, by cutting the crystal to specific dimensions, we can produce crystals that have very exact frequency ratings. There are three commonly used crystals that exhibit piezoelectric properties. They are Rochelle salt, quartz, and tourmaline. Rochelle salt has the best piezoelectric properties but is very fragile. Tourmaline is very tough, but its vibration rate is not as stable. Quartz crystals fall between the two extremes and are the most commonly used.
Quartz crystals are made from silicon dioxide (). They develop as six-sided crystals as shown in Figure 18.20 of the text. When used in electronic components, a thin slice of crystal is placed between two conductive plates, like those of a capacitor. Remember that its physical dimensions determine the frequency at which the crystal vibrates.
FIGURE 18-10 Crystal symbol, equivalent circuit, and frequency response.
The electrical operation of the crystal is a function of its physical properties, but it can still be represented by an equivalent circuit. The equivalent circuit in Figure 18-10 represents specific crystal characteristics:
= the capacitance of the crystal itself
= the mounting capacitance, or the capacitance between the crystal and the two conducting plates
L = the inductance of the crystal
R = the resistance of the crystal
The response curve in Figure 18-10 is explained in detail in Section 18.6 of the text. The primary points are as follows:
This means that a crystal can be used to replace either a series or a parallel resonant LC circuit. It should also be noted that there is very little difference between and . The spacing between these frequencies in the response curve (Figure 18-10) is exaggerated for illustrative purposes only.
A crystal can produce outputs at its resonant frequency and at harmonics of that resonant frequency. This concept was introduced when we looked at tuned class C amplifiers. The resonant frequency is often referred to as the fundamental frequency, and the harmonic frequencies as overtones. Crystals are limited by their physical dimensions to frequencies of 10 MHz or below. If the circuit is tuned to one of the harmonic frequencies of the crystal (overtones), then we can produce stable outputs much higher than the 10 MHz limit of the crystal itself. This type of circuit is said to be operating in overtone mode.
A Colpitts oscillator can be modified into a crystal-controlled oscillator (CCO) as shown in Figure 18-11. Note that the crystal is in series with the feedback path and is operating in series-resonant mode (). At the impedance of the crystal is almost zero and allows the feedback signal to pass unhindered. As the crystal has an extremely high Q, the circuit will only oscillate over a very narrow range of frequency. By placing a crystal in the same relative position, Hartley and Clapp oscillators can be converted into CCOs.
FIGURE 18-11 Crystal-controlled Colpitts oscillator.
Oscillators can be very challenging to troubleshoot. With the exception of the biasing resistors, every component is directly involved in producing an output signal. If any of these components fails, then there will be no output at all. As with any circuit, you start troubleshooting an oscillator by eliminating the obviouscheck the power supply. If the oscillator is faulty, then you should keep in mind the following:
In many cases it is simpler and less time consuming to simply replace the reactive components. If you decide to pursue this route, replace one component at a time and retest the circuits operation. When it starts to operate properly, you know you have found the faulty component.