Oscillators and Frequency Stability

Every signal you will ever transmit begins in an oscillator. It is the one stage that decides what frequency you are on — and therefore the one stage that decides whether you are inside your authorised band or outside it. The examiner tests this chapter in two ways: identify the circuit from its tank, and state the condition for oscillation. Both are easy marks once you can see what the circuit is doing, and both are routinely got wrong by people who have learnt the names without the mechanism.

What an oscillator actually does

An oscillator converts DC from the power supply into AC at a wanted frequency, with no input signal applied to it. That last clause is the whole point. An amplifier needs something to amplify; an oscillator supplies its own input, by returning a portion of its output to its own input. Switch on the supply and a signal appears. Nothing goes in but direct current.

Two consequences follow, and both are examined. First, an oscillator is not a rectifier — a rectifier converts AC into DC, which is the opposite conversion. Second, not every oscillator produces a sine wave. A multivibrator, a relaxation oscillator and the clock in a digital rig all produce square or sawtooth waveforms and are perfectly good oscillators. The statement “all oscillators generate sine waves” is false.

The feedback loop

An oscillator is an amplifier with a path from its output back to its input. The feedback must be positive — also called regenerative or in-phase — so that what comes back reinforces what is already there. Negative feedback, which the amplifier lesson shows reduces gain and improves linearity, does exactly the wrong thing here.

Going once round the loop, the signal passes through the amplifier, whose voltage gain is written A, and then through the feedback network, which returns a fraction of the output written β. The product A × β is the loop gain.

The Barkhausen criterion — both conditions, not one

For oscillation to start and be sustained, two things must be true at the same time, at the frequency of oscillation:

Take them one at a time.

• The gain condition. The signal must return to the input at least as large as it left. If the loop gain is less than one the oscillation dies away within a few cycles. If it is exactly one the amplitude is held steady, which is the ideal steady state. In practice a real oscillator is designed with a loop gain comfortably greater than one so that it starts reliably, and then the amplifier is allowed to run into mild limiting, which pulls the effective loop gain down to unity on its own.
• The phase condition. The signal must return in phase. Total phase shift round the loop must be zero degrees — which is the same thing as 360 degrees, since a full turn brings you back where you started. A common-emitter stage already inverts by 180°, so in a common-emitter oscillator the feedback network is required to supply the other 180°. In a Hartley or Colpitts that inversion comes free from the way the tank is tapped.

How it starts from nothing

If an oscillator supplies its own input, where does the very first cycle come from? From noise. Switching on the supply produces a step, and every resistor and junction in the circuit generates a small amount of random noise containing energy at every frequency. The tuned circuit picks out the one frequency it is resonant at and rejects the rest. That tiny seed goes round the loop, comes back larger, goes round again, and builds up within milliseconds until the amplifier can grow it no further. Nothing has to be injected; the circuit starts itself.

LC oscillators — the tank decides the frequency

An LC oscillator uses a parallel tuned circuit — the tank — as its frequency-determining network, for the reason the resonance lesson gives: at resonance the tank presents its highest impedance and the current inside it is a clean sine wave. The frequency is the resonant frequency:

What separates one LC oscillator from another is where the feedback is tapped off the tank. That is the whole of the identification question.

The Clapp deserves its own sentence because the exam asks what it adds. Put a small capacitor in series with the tank inductor and, because capacitors in series are dominated by the smallest, that one capacitor now sets the frequency almost by itself. The transistor's own junction capacitances — which shift with temperature and with supply voltage, and which in a plain Colpitts sit directly across C1 and C2 — are swamped. A Clapp is therefore noticeably more stable than a Colpitts built from the same parts.

The tuned-collector oscillator is the transistor descendant of the valve circuit known as tuned-plate tuned-grid. Its tank sits in the collector and feedback is taken through a coupled winding — the same idea as an Armstrong, which uses an explicit tickler coil.

Worked example — a Colpitts for 80 metres

A Colpitts tank uses L = 10 µH, C1 = 400 pF and C2 = 400 pF. What frequency does it run on?

Capacitors in series combine like resistors in parallel, so two equal capacitors give half:

Cs = (C1 × C2) ÷ (C1 + C2) = (400 × 400) ÷ 800 = 200 pF

LC = 10 × 10⁻⁶ × 200 × 10⁻¹² = 2 × 10⁻¹⁵

√(LC) = 4.47 × 10⁻⁸, so f = 1 ÷ (2π × 4.47 × 10⁻⁸) = 3.56 × 10⁶ Hz

That is 3560 kHz — inside the Indian 80 m allocation of 3500–3700 kHz. Notice that the feedback ratio is set by C1 against C2, and the frequency by the two of them in series, so in a Colpitts you cannot change one without thinking about the other.

RC oscillators — no coil at all

At audio frequencies an LC tank would need an impractically large and lossy coil, so the frequency-determining network is made from resistors and capacitors instead.

The phase-shift oscillator uses three cascaded RC sections in the feedback path of an inverting amplifier. Each section contributes roughly 60° of phase shift, giving 180°, which added to the amplifier's own 180° makes the 360° Barkhausen demands. The Wien bridge uses a series RC and a parallel RC arm which together give zero phase shift at one frequency only, so it is used with a non-inverting amplifier. The Wien bridge is the standard audio signal generator circuit and gives the cleanest sine wave of any of these.

Where you meet them in a rig: sidetone generators, audio test oscillators, the tone source in a two-tone test set, and the AFSK tones for digital modes.

The crystal oscillator

Quartz is piezoelectric: squeeze a slice of it and a voltage appears across its faces; apply a voltage across its faces and it physically deforms. Drive it with alternating voltage and it vibrates mechanically, and like any mechanical resonator — a tuning fork, a bell — it has one frequency it strongly prefers, fixed by how the slice was cut and ground. It is not adjustable by any component you can turn.

Electrically, the crystal behaves as a series L, C and R (the mechanical resonance) with the capacitance of the holder and its electrodes in parallel. That gives it two resonances a few kilohertz apart: a series resonance, where its impedance falls to a low value, and a parallel resonance a little higher, where its impedance rises to a very high value. Which one a circuit uses depends on how the crystal is connected. The Pierce oscillator — the one inside almost every piece of digital equipment you own — puts the crystal in the feedback path between collector and base, working it near parallel resonance; it is essentially a Colpitts with the crystal replacing the coil.

The reason to use one is Q. A good LC tank might reach a Q of 200. A quartz crystal reaches tens of thousands, sometimes over 100 000. Q measures how sharply the resonator rejects any frequency but its own, so a crystal holds the oscillator to its frequency far more firmly than any coil and capacitor can. Add that quartz has a very small temperature coefficient and does not care about the transistor's junction capacitances, and you have an oscillator that drifts by parts per million where an LC oscillator drifts by parts per thousand.

Worked example — what stability is worth

You are working a station on 14.200 MHz.

A crystal good to 1 part per million drifts by 14 200 000 × 0.000001 = 14.2 Hz — inaudible on SSB.

A plain LC VFO good to 100 parts per million drifts by 14 200 000 × 0.0001 = 1420 Hz — nearly one and a half kilohertz, which on SSB turns a voice into a growl and on CW is a different signal altogether.

VFO, VXO and synthesiser

A VFO — variable frequency oscillator — is an LC oscillator with a variable capacitor, and it will tune continuously across a whole amateur band; that freedom is bought with the drift just calculated. A VXO — variable crystal oscillator — is a crystal oscillator with a small series inductor or a trimmer added so the crystal can be pulled a few kilohertz either side of its marked frequency: nearly crystal stability, but only a narrow tuning range, and pull it too far and it stops oscillating or jumps to another mode. A frequency synthesiser gives you both. One crystal reference is divided down and a phase-locked loop forces a voltage-controlled oscillator to a programmed multiple of it, so every frequency in the band inherits the crystal's stability and is selected by a digital control. Every commercial transceiver you will buy in India today is synthesised, which is why the frequency on the display is the frequency on the air.

Frequency stability and what spoils it

The last row is the one that matters most in practice, and it is why the transmitter chain puts a buffer immediately after the master oscillator. The buffer has a high input impedance so it barely loads the oscillator, a gain of about one, and good isolation in the reverse direction. Without it, every keydown pulls the oscillator and the signal chirps; every touch of the antenna tuner moves your frequency. Note the corollary that the exam likes: something several stages downstream, such as the length of the coaxial feeder, cannot cause oscillator drift in a properly buffered transmitter.