A transistor oscillator is an amplifier whose output is fed back to its own input through a frequency-selective network. It produces a steady tone at the one frequency where the round trip has a loop gain of at least one and no phase shift left over, and it starts itself from circuit noise.
Intuition
An amplifier listening to itself
Hold a microphone in front of the loudspeaker it is feeding and you get a howl. The room, the microphone and the amplifier form a loop; some frequency travels round that loop and comes back larger than it left, so it goes round again, and again, until something runs out of room. That is feedback that has stopped being useful, and it is also, exactly, an oscillator.
The only difference between the howl and a useful oscillator is that one of them chooses its frequency and the other does not. Put something frequency-selective in the loop — a tuned circuit, a crystal, a chain of RC sections — and the loop can only satisfy its conditions at one frequency, so that is the frequency you get.
There are two conditions, and both have to hold at the same frequency.
The signal has to come back at least as large as it left. A loop gain below one means every trip round is smaller than the last, and whatever started dies away.
And it has to come back in step. A signal that returns half a cycle late fights the thing that produced it. That is negative feedback, which is what makes amplifiers well behaved, and it is the opposite of what is wanted here.
Get both at one frequency and the circuit produces a tone with nothing at its input but the noise it started from. Get the second one wrong and you have built a rather good amplifier by accident.
Practitioner
The circuit, and the loop inside it
The feedback comes from between the two capacitors, not from either end.
This is a Colpitts oscillator, named after the arrangement that picks the frequency: a coil in parallel with two capacitors in series, with the feedback taken from the junction between them.
Three things on the schematic decide whether it works.
The base is held at signal ground by a bypass capacitor. That makes the stage common-base for the signal — in at the emitter, out at the collector — and a common-base stage does not invert. This matters enormously and is easy to miss.
The feedback comes from the tap between the two capacitors. Taken from either end of the pair instead, it would be either the full output or nothing, and the circuit would not oscillate.
The tank sits at the collector, fed through a choke that passes the bias current and blocks the signal. The coil reaches ground through a blocking capacitor, so it cannot short that bias current to ground.
Worked example — The frequency, and the gain around the loop
The two capacitors are in series as far as the coil is concerned: 180 pF with 10 nF gives 177 pF. With 10 µH that resonates at 3.78 MHz. The larger capacitor is more than fifty times the smaller, so it is the small one that sets the frequency.
At that frequency the coil's reactance is 237.8 Ω, and a coil of 60 presents a parallel resistance of 14.3 kΩ at resonance.
The bias comes from 47 kΩ over 10 kΩ across the 12 V supply, which puts 2.11 V on the base. The emitter sits a 0.65 V drop below that, at 1.46 V, and 3.3 kΩ turns it into 0.44 mA. At a thermal voltage of 25.9 mV the transconductance is 17.1 mS.
The coil is not the only thing across the tank. The emitter is a low resistance, one over the transconductance, which is 58.6 Ω, and the capacitive divider steps it up. The collector swings 56.6 times as far as the tap, so a resistance at the tap looks that ratio squared times larger from the collector: 188 kΩ. The transistor's own output resistance, its Early voltage of 74 V over the bias current, adds 168 kΩ. All three in parallel come to 12.3 kΩ, and that is the load the transistor really drives.
So the stage gain is 210, the divider sends back 0.0177 of it, and the loop gain is 3.7.
Counting the coil alone would have given 4.3. The loads are why the larger capacitor is so large. Shrink it, and the step-up ratio falls with it; the emitter's few tens of ohms then land almost directly across the tank and drag the loop gain under one. A margin of a few times is all an oscillator needs.
Engineer
The two conditions, and where they meet
Enough gain, and no phase left over — only one frequency satisfies both.
The conditions have a name, the Barkhausen criterion, and the figure is the whole of it: a magnitude that must reach one, and a phase that must reach zero, at the same place.
Following the phase around this loop, one stage at a time:
- The emitter rises. The base is held still by its bypass capacitor, so the base-emitter voltage falls, the collector current falls, and the collector voltage rises. In phase — a common-base stage does not invert.
- At resonance the tank is purely resistive, so the collector voltage stays in phase with the current making it. Still in phase.
- The capacitive divider is a plain attenuator with nothing reactive left over at resonance, so the tap follows the collector. Still in phase.
Round trip: nothing. The disturbance reinforces itself, and it does so at exactly one frequency, because that third step is only true where the tank is resistive.
Away from resonance the tank becomes reactive and the phase walks off — inductive below, capacitive above — so the loop condition fails on both sides. That is the selectivity a tuned circuit buys. Its sharpness is the tank's Q: the coil's 60, pulled down to 52 by the loads across it.
It starts from noise, and it does not take long.
Worked example — Where the signal comes from, and how fast it arrives
Nothing drives this circuit. It starts from whatever is already there — thermal noise in the resistors, shot noise in the junction, the step when the supply comes up. Call it 10 µV.
Every trip round the loop multiplies what is present, so the amplitude grows exponentially. The growth rate follows from the excess loop gain and the tank's stored energy: 623 k per second here.
Starting from 10 µV, that reaches its working amplitude of 11.6 V in 22.4 µs, which is about 85 cycles at 3.78 MHz.
And then it stops growing, and not because it has hit the rail. As the swing grows, the transistor spends most of each cycle switched off and passes its current in a short pulse near each peak. The emitter resistor holds the average of those pulses at the bias current, 0.44 mA, and a short pulse carries a component at the oscillation frequency of nearly twice its average. While the transistor is off, the emitter no longer loads the divider, so the tank sees only the coil and the transistor's output: 13.2 kΩ. Twice 0.44 mA into 13.2 kΩ is 11.6 V, and at that amplitude the gain round the loop, averaged over a cycle, is exactly one.
Those pulses are rich in harmonics, and only the tank's selectivity keeps them out of the voltage. Designs that care about waveform purity add an explicit limiting mechanism — a thermistor, a diode clamp, or automatic gain control — so that the loop gain is brought down smoothly.
Professional
What the frequency actually depends on
The components pick the frequency, and they are not fussy.
Worked example — What a five per cent capacitor does
The small capacitor sets the frequency, so it is the one to watch. The nominal 180 pF gives 3.78 MHz; a part at the top of a 5.0 % tolerance gives 3.70 MHz instead.
That is -89.6 kHz — -23669 parts per million — before anything has warmed up, moved, or aged.
Temperature adds its own. At 100 parts per million per degree, a 30 °C rise moves the frequency by -1470 ppm.
Note which is larger. The tolerance dominates, and it is a one-time error you can trim out. The temperature drift is smaller and you cannot, which is why an LC oscillator that has been set on frequency still wanders.
An LC oscillator knows roughly what frequency it is; a crystal knows exactly.
A crystal holds to 20 parts per million — 1183 times better than the component tolerance above — and it does so for the same reason the LC tank works at all, only more so. A quartz plate is a mechanical resonator with a Q in the tens of thousands, so the phase around the loop swings through zero far more steeply, and the loop has correspondingly less freedom about where to sit.
The circuit around it barely changes. A crystal oscillator is the same amplifier with the same two conditions; only the selective element is different.
Four things that follow
The oscillator's frequency is set by the loop, not by the tank alone. The transistor's own capacitances sit in parallel with the tank capacitors and shift the frequency slightly, and they change with bias and temperature. It is why oscillators are trimmed after assembly rather than calculated exactly.
A tank's Q is the whole of its selectivity. A 60 of sixty gives a phase slope steep enough to hold the frequency to a fraction of a per cent. Loading the tank — with the next stage, or with the transistor's own input resistance — lowers that Q and widens the frequency's freedom, which is why oscillators are buffered rather than connected directly to whatever they drive.
Hartley, Clapp and Armstrong are the same circuit with a different tap. A Hartley taps a coil instead of a capacitor divider; a Clapp puts a third capacitor in series with the coil so the transistor's capacitance matters less; an Armstrong uses a separate winding. All of them are ways of getting a defined fraction of the output back, in phase, at one frequency.
Not every oscillator needs a resonator. A ring of inverting stages, or a chain of RC sections that adds up to half a cycle of phase shift, oscillates by the same criterion with far worse stability — and that is often exactly what is wanted for a clock that does not need to be accurate.
Three more you can build
Every part on these three is a stock value, and each circuit has been run in a simulator with the manufacturers' transistor models to check that it oscillates where the arithmetic says it will.
The tap has moved to the coil, and it goes to ground.
Worked example — A Hartley at just under a megahertz
As far as the capacitor is concerned the two coils are in series: 47 µH and 10 µH make 57 µH, and with 470 pF across them the tank resonates at 972 kHz.
This stage is common-emitter, so it inverts. The tank puts that right. Its middle is held at ground, so its two ends swing in opposite directions, and with the collector on one end and the base on the other the tank adds back the half cycle the transistor took away.
The smaller coil sets how much comes back: the base end swings about 0.21 as far as the collector end. The 100 Ω left unbypassed in the emitter raises the input resistance at the base, so the low end of the tank is only lightly loaded.
No coil and no crystal: three RC sections find the half cycle between them.
Worked example — Half a cycle from three RC sections
One RC section can shift the phase by up to a quarter of a cycle, and it only gets close to that where it passes almost nothing. Three of them reach half a cycle while still passing something usable, and the frequency where they do is the oscillator's.
Each section here is 10 kΩ and 10 nF, and the first is fed from the 22 kΩ collector resistor, 2.2 times R. For this ladder the half cycle falls at 1 / (2πRC√(6 + 4k)), which is 414 Hz.
The third section has no resistor of its own. The base is the resistor: the two bias resistors in parallel with the transistor's input come to about the same as R.
The ladder loses a lot on the way round, and the transistor has to make it up. It needs a current gain of at least 45, well inside what a BC547B gives. With no resonator to hold it, a real one lands within a few per cent of that frequency rather than on it.
The small capacitor in series with the coil does most of the tuning.
Worked example — A Clapp, and what the third capacitor buys
Round the coil, all three capacitors are in series: 1.0 nF, 1.0 nF and 100 pF come to 83.3 pF, and with 10 µH that gives 5.51 MHz.
The small one dominates. With the coil on its own it would give 5.03 MHz, and the two large capacitors only nudge that. They are also the ones the transistor's own capacitances sit across, so whatever the transistor does to them moves the frequency far less than it would in a plain Colpitts.
This stage is an emitter follower, with a gain just under one and no inversion. The gain the loop needs comes from the tank: with two equal capacitors, the base swings about twice as far as the emitter.
Common mistakes
- Taking the feedback from the wrong point — from either end of the capacitor pair rather than between them. One wire's difference, and the circuit becomes a tuned amplifier that never starts.
- Forgetting that the base bypass capacitor sets the configuration — without it the stage is common-emitter and inverts, so the loop phase is 180° and nothing oscillates.
- Making the larger capacitor too small — the emitter's input resistance, multiplied by the divider's step-up squared, sits across the tank. Let that ratio fall and a few tens of ohms at the emitter swamp the coil, and the loop gain collapses.
- Designing for a loop gain of exactly one — component tolerance and temperature would then stop it starting. Excess gain is deliberate: 3.7 here, enough to start whatever the parts do.
- Expecting a clean sine from the transistor's current — it flows in short pulses near each peak, which is what holds the amplitude at 11.6 V, and pulses are rich in harmonics. The tank filters them; purity needs a gentler limiter.
- Trusting the calculated frequency — a 5 % capacitor alone moves it 23669 ppm, and the transistor's own capacitances move it further.
- Loading the tank directly with the next stage — that lowers the Q, which widens the phase slope and lets the frequency wander.
Parts used in this topic
Frequently asked questions
What are the two conditions an oscillator must satisfy?
A loop gain of at least one, and a loop phase of zero — both at the same frequency. This circuit has a loop gain of 3.7 at 3.78 MHz and a phase that passes through zero only there, because only at resonance is the tank purely resistive.
Where does the signal come from when it starts?
From noise. Thermal noise in the resistors, shot noise in the junction, and the step as the supply comes up all contain a component at the loop's frequency. Starting from about 10 µV, the loop grows it to 11.6 V in 22.4 µs — about 85 cycles.
What stops the amplitude growing?
The transistor's own current. As the swing grows it conducts only in short pulses near each peak, and the 3.3 kΩ emitter resistor holds their average at 0.44 mA. A short pulse carries a component at the oscillation frequency of nearly twice its average, and twice 0.44 mA into the tank's 13.2 kΩ is 11.6 V. There the gain round the loop, averaged over a cycle, is exactly one. The pulses are rich in harmonics, which is why oscillators that need a clean sine add a deliberate limiter.
Why is the feedback taken from between the two capacitors?
Because that tap gives a defined fraction of the output — 0.0177 here — with no phase shift. Taken from the top of the pair the feedback would be the whole output; taken from the bottom it would be nothing. The tap is what turns a stage gain of 210 into a loop gain of 3.7.
Why is the loop gain so much smaller than the stage gain suggests?
Because the divider returns only a small fraction of the collector swing, and because the tank is loaded by more than its coil: the emitter's input resistance, stepped up through the divider, and the transistor's own output resistance sit across it too. Counting the coil alone gives 4.3; with all three loads it is 3.7, which is what a simulation of the circuit gives.
Why is a crystal so much better than an LC tank?
Because its Q is thousands of times higher, so the loop phase crosses zero far more steeply and the circuit has correspondingly less freedom about where to settle. A crystal holds 20 ppm where a 5 % capacitor alone puts this LC oscillator 23669 ppm off — 1183 times worse.
Knowledge check
What frequency does this tank pick, and why that one? (Show answer)
Work out the loop gain. (Show answer)
How does the oscillation start, and what stops it growing? (Show answer)
Follow the phase around the loop. (Show answer)
How far does the frequency move, and against what? (Show answer)
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