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by Ian Sinclair
Oscillators are probably the most used and least understood of all circuit building blocks, get to know and love them in this the fifth part of Into Electronics.
POSITIVE FEEDBACK is the process of taking some of the signal at the output of an amplifier and connecting it back, in phase, to the input. How much effect this has depends on how much of the signal is fed back. Small amounts of positive feedback (as we call this) can increase the gain of an amplifier and also increase the input impedance. A simple example of this use of positive feedback is the circuit of Fig. 5.1. This is an emitter follower (see earlier parts) with a capacitor feeding signals back from the emitter to the base. Because the voltage gain of an emitter-follower is always lees than unity this has no effect on the gain of the whole circuit, but it does make the input impedance for signals very much higher than that of the unaltered emitter follower This use of positive feedback is called bootstrapping.
The name comes from the ( US) inventor of the circuit who remarked that "it looks a bit like pulling yourself up with your own bootstraps.--A two-stage bootstrap circuit with a very high input resistance is shown in Fig. 5.2. The bootstrap circuit is stable because there is unity (or slightly less than unity) gain in the amplifier that is bootstrapped. If we attempt to use positive feedback in an amplifier which has voltage gain, then we run into difficulties because the amount of feedback has to be very carefully controlled. Any change in the gain of the amplifier or in component values may be enough to make the circuit unstable so that the amplifier oscillates.
For this reason, positive feedback, other than boot strapping, is seldom used in amplifier circuits.
The main use of positive feedback, then, is to make amplifier circuits into oscillators. There are two kinds of oscillators, the sine-wave type, in which the amount of positive feedback is controlled so as to give a sinewave with a good wave-shape; the other sort is the aperiodic type in which the positive feedback is allowed to run wild. This second type of oscillator uses so much positive feedback that it spends most of its working life with the transistors either bottomed or cut-off. Because it's simpler, we'll look at this type first.
THE WILD ONES
Take a look at the circuit in Fig. 5.3. It's a simple two-transistor amplifier, and the output signal will be in phase with the input signal but greatly amplified. Now make the dotted connection and there is a positive feedback loop. This is 100% positive feedback; all the signal at the output is connected back to the input and it converts a simple two stage amplifier into an oscillator of a type called the astable multivibrator. The word astable means 'not stable', and that's a good description. The positive feedback is so effective that the circuit cannot exist for more than a few nanoseconds with both transistors conducting. It's an important circuit, so let's go over the action carefully.
When the circuit is switched on, the voltages at the collectors and also at the bases of the two transistors will start to rise. Because of the inevitable slight differences between transistors, one will conduct before the other, so that its collector voltage will start to fall again. Let's say that it's 01 that is conducting--then the voltage at the collector of Q1 is falling and the capacitor coupling through C1 will cause the voltage at the base of Q2 to drop as well. A drop of voltage at the base of Q2 will cause the collector voltage of Q2 to rise and this rise of voltage is coupled by C2 to the base of 01 to rise and this rise of voltage is coupled by C2 to the base of Q1, completing the positive feedback loop and making the voltages change very, very quickly. The whole process is over in a matter of nanoseconds, and it ends with Q1 conducting fully, its collector voltage bottomed at about 0.2 V. and Q2 cut off with its base voltage at about -5.3 V. Why -5.3 V, you ask, very reasonably? Well, it's like this: suppose that the base of 02 was about to conduct, at around 0.5 V when all this happened. The collector voltage of Q1 changes from 6 V (not conducting) down to about 0.2 V (bottomed). That's a drop of 5.8 V. Now a capacitor will couple a voltage change like this, so that the voltage at the base of 02 also drops by 5.8 V, from 0.5 V to -5.3 V, making pretty sure that 02 is shut off. Meantime, the connection of R2 to the + 6 V line makes equally sure that Q1 stays fully conducting.
Once it gets into this connection, there's no more positive feedback, because there's no more amplification when one transistor is bottomed and the other cut-off. It would stick like this for good if it were not for one important point: the base of Q2 is connected to the +6 V line through R2.
Since there's a voltage difference across R2 (+ 6V at one end, and -5.3 Vat the other), current flows. Where? Into the capacitor C1, that's where, so that C1 charges up. The voltage of one plate of this capacitor is held at about 0.2 V by the collector voltage of Q1; the voltage of the other plate now rises in the shape of an exponential curve (Fig. 5.4C) from -5.3 V. Left alone, it would eventually get to + 6 V in the usual time of about four time constants (4 x R2 x C1). It's not left alone, though. When the voltage at the base of Q2 reaches about 0.5 V, Q2 starts to conduct and one again the positive feedback loop takes control.
Once the positive feedback loop takes control, the circuit goes wild again. Q2 is forced into full conduction, Q1 is shut off within a few nanoseconds. The same performance as before now happens as C2 charges, allowing the voltage at the base of Q1 to rise from about -5.3 V until Q1 can start to conduct again. . and there we go again. Fig. 5.4 shows the waveforms, comparing the graphs so that you can see what is happening at each electrode at the same time. Notice, by the way, that when one base is being driven negative, the other is being driven positive. The base voltage cannot, how ever, greatly exceed around 0.6 V because of the current that can flow between the base and the emitter of the transistor. The base-emitter junction effectively acts as a short circuit, preventing the base voltage from rising above about 0.6 V. In a circuit of this type, the positive feedback is just a way of ensuring that the circuit flips over from one stage to the other very quickly. The real control is exercised by the time constants R2.C1 and R3 C2. If these are identical, both parts of the wave take equal times. The total wave-time for a complete cycle is given by 0.7 (R2 C1 + R3.C2). If the two time constants are not equal, then the wave is not symmetrical, but there's a limit to the mark-space ratio (on/off ratio) that we can get by altering the time constants.
Problems? Well, the simple circuit can suffer from sticking if the bias resistors R2, R3 are either too low (around 1 k) or too high (220 k or more). Sticking means that both transistors are bottomed or cut-off together, so that oscillation will not start. The remedy is to keep to sensible values of bias resistors. Next problem--a poor wave-shape at the collector of each transistor. The cause is the time needed to charge the coupling capacitor.
Looking at the collector of Q2: when Q2 cuts off, C2 has to charge from about 0.2 V up to + 6 V through R4. One plate of C2 is held at about 0.5 V by the base of Q1, the other has to reach + 6 V, and current must flow through R4, which takes time (a time constant of C2.R4). This makes the rising part of the wave at the collector of Q2 rather slow. The remedy is to add a resistor and a diode as shown in Fig. 5.5 at the collector of Q2. Now when Q2 cuts off, the voltage can rise quickly at the collector by R5, and can take its time. When the collector voltage of 02 drops, of course, the action is quite normal because the diode now conducts.
Last problem--in the simple circuit, the frequency varies rather a lot when we change the voltage, and the theory says it shouldn't. When theory and practice disagree like this, there's usually something wrong with the practice! In this case it's the base-emitter junction of the transistors breaking down so that the base voltage cannot go as negative as the signal (through the capacitor) is trying to force it. The remedy is simple--a silicon diode connected into each base lead, using a type which can stand the reverse voltage rather better than the base-emitter junction of the transistor.
THE SERIAL ASTABLE
Got your breath back? Fig. 5.7 shows quite a different type of astable, a serial type. This circuit also uses two transistors, but the type of action is quite different.
Instead of switching so that the transistors conduct alternately, this circuit works so that we have either both transistors conducting together or both cut off. The output is a series of short negative pulses, and there is only one time constant. One transistor is a PNP type, the other an NPN. It all works like this: When the circuit is switched on, C1 is uncharged and will take some time to charge through R1. As a result, the emitter voltage of Q1 is still low by the time its base voltage has reached the level set by R3 and R4 (a voltage equal to half of supply voltage when R3 = R4). Now this ensures that Q1 is not conducting, because a PNP transistor conducts only when its emitter voltage is more positive than its base voltage (or its base voltage more negative than its emitter voltage, if you like it that way round). No current flows through Q1, then, and there's no base current flowing into Q2 either to switch that one on.
As C1 charges up, though, the voltage at the emitter of Q1 will become higher than the voltage at the base of Q1. When this happens, Q1 conducts, current flows into the base of Q2, so that Q2 conducts and is collector voltage drops right down to about 0.2 V. The base of Q1 is connected to the collector of Q2 to complete the positive feedback loop, though, so that Q1 is now well and truly conducting, with C1 now discharging like mad through R2 and the base-emitter junction of 01 will drop until it's too low to keep current flowing through Q1. When that happens, there's no current flowing into the base of Q2, so that it shuts off. The collector voltage of Q2 then rises, bringing the base voltage of Q1 with it, up to the value set by R3 and R4.
Q1 now has its base at the voltage set by R3 and R4, and the emitter of Q1 is at a low voltage, so that Q1 is cut off.
C1 now starts to charge again through R1, and the whole cycle repeats.
The waveforms at various parts of the circuit are shown in Fig. 5.8. The output at point A consists of short-duration negative-going pulses, and of near sawtooth waves at B. The circuit is economical in components and takes very little current from the supply because when both transistors do conduct most of the current is supplied by the charged capacitor C1.
THE HALF-TIME TYPE
The kind of Multivibrator which we've just de scribed is the astable, which cannot stay in any stable state but has to oscillate continuously. There's a related circuit, the monostable, which has one stable state. Fig. 5.9 shows one type of monostable. R3 keeps the base of Q2 conducting, at a voltage of around 0.5 V to 0.6 V. With the base passing current, the collector voltage of Q2 is low because of the current through R4, and so the base of Q1, which is connected to the collector of Q2 through resistor R5 is also at a low voltage. When a collector voltage bottoms, it can go to a voltage of about 0.2 V, less than the 0.5 V, or so that is needed to make a base conduct, so that Q1 is quite definitely not conducting. There's nothing in the circuit itself, no charging capacitors, to change this so that the circuit can remain in this state (Q1 off, Q2 on) until the cows come home.
The cows come home when a short positive pulse is fed through C1 and D1 to the base of Q1. Only a small change of voltage is needed to make Q1 start to conduct, then the old positive feedback loop takes over, ending up with Q2 off (base negative) and Q1 held on with current flowing through R5. The diode D1 isolates the base of Q1 from any negative pulse which would otherwise turn off Q1 before the end of the timing period. What timing? Oh yes, there's a timing action as C2 charges up because of the current flowing through R3 During this time the collector voltage of Q2 is high, and the collector voltage of Q1 is low. When the base voltage of Q2 reaches a level of about 0.5 V (in a time of about 0.7-C3. R3, Q2 conducts and the positive feedback ensures a quick snap back to the original conditions. There it remains, waiting again for the next trigger pulse.
The monostable is ideal for generating short pulses at long intervals, the job which cannot be done by using very unequal time constants in an astable multivibrator.
The trigger pulses can be obtained from the square wave of the astable by using a differentiating circuit, as shown in Fig. 5.11.
The diode at the input of the monostable circuit selects only the positive pulses to trigger the monostable. The time of the monostable pulse (its pulse-width) is decided by the values of C2, R3 in Fig. 5.9.
SYNCHRONIZE YOUR PULSES
One of the many useful points about an astable is that it's rather unstable. Now for many purposes that's about as useful as a lead life-jacket, because so many oscillators have to be very stable. Stable in this respect means that the frequency can be set and will not thereafter change when temperature changes or as components slowly change value. The oscillator that sets the frequency of a radio or TV transmitter must, for example, be particularly stable so that the transmitter is always at its correct frequency. The oscillator of an electronic watch has to be stable so that the time can be held accurate to within a few seconds a month. We wouldn't use a plain astable for either of these jobs, but the instability of the astable is useful to us nevertheless.
Take a problem--how do you generate a square wave with exactly the mains frequency, but which will keep going when the mains supply stops? You can generate a 50 Hz wave using an astable but the frequency will change--unless it's synchronized. Synchronization means forcing an oscillator to run at the frequency of a wave that is fed into it. If we feed a wave, say a 3 V. 50 HZ sine wave from a transformer into the base of one transistor of an astable running at some frequency between 40 Hz and 60 Hz then the astable will be forced to run at 50 Hz. There s not much choice about it. If the frequency of the astable is higher or lower than the synchronizing frequency, then at some time or other there will be a 50 Hz positive peak of the synchronizing signal at the base of the transistor when that transistor is just about to switch on (Fig. 5.12). The synchronizing signal ensures that the transistor switches at that moment, and the next positive peak of the synchronizing signal will ensure that the same happens again, and so on. The astable is synchronized, it runs at the same, frequency as the synchronizing signal.
A monostable will do even better, because it gives one output pulse for each synchronizing pulse, no more, no less--this is called triggered operation. The difference between the two is that the monostable does not run unless it is triggered, the astable keeps running, though its speed may not be correct when the synchronizing pulses are missing.
The square wave from an astable can be used to generate another important waveform, the timebase or linear sweep. As the name "timebase" suggests, this is a waveform which is used for timing operations, particularly in oscilloscopes and in digital voltmeters. A simple timebase makes use of the charging and discharging of a capacitor through a resistor. If we put in a square wave at the input of the R-C circuit shown in Fig. 5.1 3 (an Integrator), then the voltage signal across the capacitor is a sloping waveform; it's the exponential charge and discharge curve. Now if we could make the resistor a large value for the upward slope and a small value for the downward slope we would get the type of sweep waveform we need, with a slow steady rise and a rapid-fall of voltage. Say no more, we have the circuit in Fig. 5.14.
When the transistor is cut off by the negative part of the input wave, C charges through R, giving the slow rising part of the sweep wave. The positive part of the input wave then makes the transistor conduct, the collector-emitter part of the transistor has a low resistance that discharges C rapidly and the result is a sweep waveform. It's not perfect, but it's a start, and various improvements aimed at keeping the charging current through the resistance constant during the time of the sweep result in the good linear sweeps that we use for oscilloscope time-bases. Take a look at the circuit of Fig. 5.15 for example, which uses a PNP transistor to control the current into C1. If you have time, construct this circuit and have a look at the waveform.
SINES OF THE TIMES
We've spent a lot of time on square-wave generators like astables, but what about sine-waves ? Nowadays, the types of circuit that we use have less need of sinewaves, but we still need to generate waves of perfect sine shape for a lot of uses, not least the carrier waves of radio transmitters. A sinewave oscillator, like any other oscillator, uses an amplifying circuit along with positive feedback, but it needs two other important features.
One is some sort of automatic limiting action, so that the feedback does not simply whack the amplifier between the cut-off and bottomed states as happens in the astable circuits. The other requirement is a circuit that will control the frequency and shape of the sine wave.
That excellent circuit, the tuned circuit, does a lot of what we want. A tuned circuit, such as the parallel connection of an inductor and a capacitor, responds only to frequencies very near to its resonant frequency of about 1 / N/LC. The type of response, as far as a parallel circuit is concerned, is its resistance to signals, which is maximum at the frequency of resonance and very small for signals at other frequencies. If we use a parallel tuned circuit as the load of an amplifier which has a little bit of positive feedback, then there will be enough amplifier gain for oscillation to start only at the frequency to which the parallel tuned circuit is tuned. The transistor itself will prevent the oscillation amplitude from becoming too great if we can arrange it so that the transistor runs out of gain when the amplitude of the oscillation becomes too large. This happens when the collector voltage is low, or if the bias is reduced. Both of these methods of control ling the amplitude would cause a distorted signal but for two things. One is that the amount of positive feedback is kept small, so that a reduction of gain stops or reduces the amplitude of oscillation rather than allowing a large and distorted signal to be generated. The other point is that the tuned circuit itself will sort out a distorted wave, and extract a well-shaped sine-wave from it.
A sinewave oscillator circuit is shown in Fig. 5.16.
This is a type called a Colpitts oscillator, and its trade mark is the signal potential divider using two capacitors. These two capacitors are connected across the inductor L, and arranged so that a fraction of the output signal is fed back to the emitter of the transistor.
This is positive feedback, because if the base voltage is held steady, then a rise in the emitter voltage causes less bias voltage between base and emitter, so less base current, therefore less collector current, and so causes a rise of collector voltage. To make sure that the base voltage remains steady, a capacitor C3 must be connected as shown. Without this capacitor, the base voltage can follow the emitter voltage at high frequencies so that oscillation does not occur. The tuned circuit for this oscillator consists of L, with the capacitors C1 and C2 in series with each other (but connected in parallel with L). Oscillators that use inductors and capacitors are useful for generating radio frequency waves, particularly if we need to alter the frequency. Using a variable capacitor as part of the tuned circuit lets us do just that, making the oscillator a VFO, (variable frequency oscillator).
The Colpitts oscillator is not ideal from this point of view because both plates of the variable capacitor would have a signal voltage on them. This makes adjustment rather difficult, because a variable capacitor is constructed with one set of plates connected to the central shaft. If this set of plates is connected to a signal voltage, then touching the control (tuning) knob will change the frequency of the oscillator even before the control is adjusted, because the capacitance between your hand and the capacitor plates is now part of the tuned circuit.
When variable tuning is needed, other circuits which allow the moving plates of the tuning capacitor to be earthed are more suitable. The Hartley oscillator circuit is of this type, and is shown in Fig. 5.17.
THE CRYSTAL OSCILLATOR
Sinewave oscillators which use LC tuned circuits ,are useful, but their frequency can be altered by small changes of supply voltage and by changes of tempera ture. For generating sinewaves of very precise frequency, something better than the LC circuit is needed, and that something is the quartz crystal, Quartz crystals are just what the name says they are--crystals of Quartz (silicon oxide). The quartz is carefully cut to shape, and opposite faces are coated with silver so that wire contacts can be soldered in place. With this done, the crystal will now behave like a tuned circuit. At one particular frequency, depending on the size and shape of the crystal, the crystal can resonate to a frequency applied to its connections, vibrating mechanically at that frequency. At this resonant frequency, the crystal behaves like an LC circuit, but one with values of Land C that we could not possibly obtain when we use ordinary components. The usefulness of a tuned circuit for generating a good shape of sinewave is measured by a figure called the Q factor. A conventional LC tuned circuit might have a Q factor of 150 with luck, but a quartz crystal can notch up a Q figure of 30 000. This makes crystal oscillators the natural choice when a very precise value of frequency has to be generated and when the oscillator frequency must be unaffected by charges in other components. Quartz crystals are there fore used in digital watches, radio transmitters, frequency meters and in any other application which needs a fixed frequency.
A typical crystal oscillator is shown in Fig. 5.18. The oscillator is of the Colpitts variety, but the frequency is controlled almost entirely by the crystal, so that the output frequency is much more stable than that of any LC Colpitts circuit.
HOW LOW CAN YOU GET?
We have a pretty satisfactory set of circuits for generating sinewaves at radio frequencies, but we run into problems if we try to use the same circuits to generate lower frequencies, audio frequencies, for example with a range of 20 Hz to 20 kHz. LC oscillators are of very little use because a very large value of inductance will be needed for the low frequencies, and the values of capacitance will also have to be large, ruling out the use of the usual 500 pF variable capacitor as a method of tuning.
There are two ways around this problem. One is the use of the beat-frequency oscillator (BFO). This type of circuit uses two oscillators, both working at radio frequencies of several hundred kHz. The output signals at frequencies f1 and f2 are fed into a mixer stage which produces (surprise, surprise) a mixture of signal frequencies including the difference frequency f 1--f2 and the sum f1 + f2. Now if the frequencies f1 and f2 are close, such as 320 kHz and 325 kHz, then the difference frequency is low, 5 kHz in this example, and can easily be separated from all the other signal frequencies. The BFO is a simple way of generating low frequency sinewaves, but if its performance is to be good then both of its oscillators must be very stable. A frequency change of 10 Hz, may be noticeable in a 320 kHz oscillator, but it does make rather a lot of difference when the difference frequency is only 20 Hz. The BFO circuit is still used, in metal detectors for example, but not so much now as a generator of low frequency sine waves.
The modern method of generating low frequency signals is the RC oscillator, so let's have a look at these. Like any other oscillator, the RC type consists of an amplifier, a positive feedback connection, a frequency selective circuit (tuned circuit) and a method of stabilizing the amplitude. The trouble with frequency selective circuit which use resistors and capacitors only is that they are not nearly so selective as the LC circuits. The Q factor which measures how good they are at selecting a frequency is only around 2 to-6 (compare LC at about 50 to 150, crystals 5000 upwards). Because of this, we can't rely on the RC circuits to keep a sinewave looking like a sinewave, and every RC oscillator needs some other method of adjusting the feedback so that the oscillator is just oscillating with an amplitude that stops well short of bottoming or cutting off the transistor.
Figure 5.20 shows a phase-shift RC oscillator--probably the simplest type. It's possible to make this type of oscillator using only one transistor, but the results are rather unpredictable, and as often as not the circuit totally refuses to oscillate. The circuit shown in Fig. 5.21 is a bit more reliable. Q2 is an emitter follower (with unity gain) and Q1 is a common-emitter amplifier, load R4 which provides voltage gain. The phase-shift network is R1, C1, R2, C2, R3, C3 three lots of RC time constants. Each of these RC time constants has two effects on a sine wave--it reduces the amplitude and it phase shifts the current wave relative to the voltage wave. If the total phase shift in the three sections is 180', then the sinewave of current into the base of Q1 is 180° out of phase with the voltage wave at the collector of Q2. For a sinewave, a 180° phase shift has the same effect as inverting the wave, so that the feedback through this network is positive. The circuit will oscillate if the gain of Q2 is just slightly more than the loves through the RC network (not forgetting RV1) and Q1.
We have to adjust the gain in this simple circuit by setting RV1, which provides a bit of negative feedback. If RV1 is set so that the circuit is only just oscillating, the shape of the sinewave that is produce can be quite good.
The phase-shift circuit isn't used much, however, because it is rather difficult to provide variation of the frequency (too many quantities to change) and also because there are other networks which are more selective. Really well-shaped sinewaves are produced only if the amplifier has its gain automatically controlled.
A BRIDGE TOO FAR?
Figure 5.22 shows the circuit of a Wein-bridge oscillator. This circuit calls for an amplifier with two inputs so that both negative- and positive-feedback loops can be connected. This, of course, can be as simple as using a transistor base as one input and the emitter of the same transistor as the other, but to avoid cluttering up the diagram, the amplifier is shown as a triangle with negative feedback going to the input marked--and positive feedback to the input market +. The Wein bridge is actually the network consisting of C1, R1, C2, R2, connected as shown. The action of this circuit is that it has zero phase shift at one frequency, when f = 1/2 pi CR with C = C1 = C2 and R = R1 = R2), ,where f is the frequency of oscillation.) With the Wein bridge circuit connected into the positive feedback loop, there is positive feedback only when the phase shift of the network is zero, which is at the frequency f o. As usual, the sinewave shape is good only if the amplifier gain can be controlled so that it just compensates for the loses in the network; this requires a gain of about 3 times. The easiest way of providing the gain and regulating it is to make the amplifier a high-gain type and arrange R3 and R4 so that the negative feedback adjusts and controls the gain. One commonly used method is to use a thermistor for R4 and a resistor with twice the thermistor resistance for R3. Twice what resistance?. Well, we use a thermistor which will run at a temperature which is a bit above room temperature when signals current passes through it, and we pick the value of resistance it will have at this temperature. When the circuit is switched on at first, the oscillations quickly build up to full amplitude, but the current through the thermistor heats up the tiny element until the resistance drops, adjusting the gain of the amplifier, and reducing the amplitude of oscillation. Too small an amplitude, of course, will allow the thermistor to cool, raising its resistance, decreasing the negative feedback and in creasing the gain so that the amplitude can build up.
This negative feedback loop then controls the gain of the amplifier to ensure that the waveshape remains good and the amplitude constant.
Another method that is used to control the gain of the amplifier is to rectify the signal output and use the rectified signal to provide bias for a FET, using .the source-drain connections of the FET as the resistor R4.
This method is not affected by the temperature of the air surrounding a thermistor, so that it is a better method of stabilization.
Well that wasn't too bad was it, next month we take our first cautious steps into the wonderful world of Digits.
(adapted from: Hobby Electronics magazine, Mar. 1979)
Also see: Interfering Waves
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