Chapter 19: The Oscillator

A circuit that turns DC power into an AC signal

An oscillator turns the DC from its supply into an AC signal of its own. It contains an amplifier, but one fed from its own output; a plain amplifier only enlarges a signal fed to it.

Generating the RF signal that ends up at the antenna

In a transmitter the oscillator generates the radio-frequency signal that, after later stages, is applied to the antenna. Keying is normally done in those later stages, so that the oscillator’s frequency is not disturbed.

Low-frequency AC, such as the 50 Hz mains

Machines such as alternators suit low frequencies like the 50 Hz mains. At radio frequencies, electronic circuits (oscillators) are by far the most practical way to generate signals.

A mixer

Working with a mixer, a receiver’s oscillator moves the incoming signal to a new frequency; mixers come in a later chapter. An RF amplifier only strengthens a signal, leaving its frequency unchanged.

Oscillator circuits that differ in how their tuned circuit is arranged

Colpitts, Hartley and Clapp are oscillator circuits told apart by the layout of the tuned (tank) circuit: a split capacitor in the Colpitts, a tapped coil in the Hartley. Each can work on any band.

Clapp

The Clapp, a series-tuned Colpitts, is an oscillator, like the Colpitts, Hartley and crystal oscillators. Butterworth is a type of filter, Yagi an antenna and Zener a diode.

It draws each stage, such as an amplifier, as one symbol

A block diagram draws each functional stage, such as an amplifier or a filter, as one symbol, giving an overview of how a system works. A circuit diagram shows every component and its wiring.

An amplifier

A triangle always stands for an amplifier, so it needs no label: the signal enters at the flat side and leaves at the point. Other blocks, such as filters, are drawn as labelled boxes.

The path a signal takes, on one wire or on two

A line shows a signal passing from one block to the next; the signal may travel on one wire against earth or on a pair of wires. In a circuit diagram, by contrast, each line is one wire.

The direction in which the signal flows

Arrowheads show which way the signal passes from block to block. That is not the direction of the current: most signals are AC, so the current flows both ways in turn.

A separate tuned circuit at both the input and the output

An oscillator needs amplification and feedback from output to input, arriving in phase so that it reinforces the input. One frequency-selective network in the loop is enough; tuned circuits at both ends are not required.

Thermal noise in the circuit

At switch-on there is no input signal, only the thermal noise that every conductor produces; the loop builds up the frequency at which the fed-back noise is in phase. Hum is mains pickup, not this starting signal.

It has components spread across all frequencies

Broadband noise has components spread across all frequencies, so whatever frequency an oscillator’s loop favours, some noise is there to start it. It is not concentrated at any tuned frequency.

The audio-frequency part of thermal noise

The hiss is thermal noise, the part of it that falls in the audio range. A hum would be different: that is mains pickup, at the mains frequency and its harmonics, not thermal noise.

The random motion of electrons caused by heat

Heat keeps the electrons in every conductor moving at random, and that motion is thermal noise; it is present even with no current flowing. Heat flowing away into the air makes no electrical noise.

Only there does the fed-back signal arrive exactly in phase

The network passes nearby frequencies too, but their fed-back signal is out of phase and partly cancels what caused it, so they die out. At one frequency it returns exactly in phase and grows on every trip.

Makes it lead or lag by an amount set by its frequency

The network’s output leads or lags its input, and by how much depends on the exact frequency. That is why the fed-back signal is in phase at one frequency only; a fixed shift at every frequency would favour none.

The supply voltage of its amplifier

As the signal grows, the amplifier’s gain falls, for example because its output cannot swing beyond its supply voltage, until the loop just sustains the signal. The tuning capacitor sets the frequency, not the amplitude.

Positive feedback

Feedback that adds to, and so reinforces, the input is positive feedback, and it is what makes an oscillator oscillate. Negative feedback opposes the input and steadies an amplifier instead.

Positive feedback round the loop

The loudspeakers’ sound reaches the microphone, is amplified again and builds up into a howl: positive feedback, the effect that makes an oscillator work. Negative feedback would weaken the sound instead.

The total gain a signal gets on one trip round the loop

Loop gain is the overall gain from any point, once round the loop and back: the amplifier’s gain less every loss, such as the output take-off and the phase-shift network. The amplifier alone is only part of it.

2 dB

In decibels the gains and losses simply add: 13 − 2 − 9 = 2 dB. Leaving out the 2 dB taken by the output gives 4 dB; adding every figure as a gain gives 24 dB.

16 dB

Loop gain = amplifier gain − losses, so the losses are 20 − 4 = 16 dB. Adding the 4 dB to the 20 dB gives 24 dB, which would make the loop gain −4 dB, not +4 dB.

0,8

As ratios, the gains round the loop multiply: 20 × 1/25 = 0,8. Dividing the other way, 25 ÷ 20 = 1,25, inverts it; at 0,8, below 1, the oscillation would die away.

To make up for the losses around the loop

The output take-off and the network both lose signal, so the amplifier’s gain must make up those losses. Its phase shift does not cancel the network’s; the two add, and together must total 0° or a multiple of 360°.

Exactly 1 (0 dB)

For a steady amplitude each trip round the loop must return the signal exactly as strong as it left: a gain of 1, which is 0 dB. A loop gain of 0 would pass nothing back at all.

More than 1

To grow, each trip round the loop must return the signal stronger than it left, so the loop gain must start above 1. As the amplitude rises the amplifier’s gain falls until the loop gain settles at exactly 1.

4 times

Each 3 dB doubles the power, so 6 dB is 2 × 2 = 4 times: above 1, so the signal would keep growing. A ratio of 2 is what 6 dB means for voltage, not power.

It dies away, getting steadily weaker

With a loop gain below 1, each trip returns only 0,9 of the signal, so the amplitude shrinks until the oscillation stops. A steady amplitude needs a loop gain of exactly 1.

0° or a whole multiple of 360°

Only a total of 0°, 360°, 720° and so on brings the signal back in step with itself, so that it reinforces rather than cancels. A total of 180° would oppose the input: negative feedback.

180°

The total must be a whole multiple of 360°: 180° + 180° = 360°. Adding 360° would give 540°, which is not a multiple of 360°, and adding 0° would leave 180°, negative feedback.

They add phase shift around the loop

At high frequencies a wire is a noticeable part of a wavelength, so it delays the signal and adds phase shift, about 1,2° per centimetre at 100 MHz. Its tiny resistance is not the problem.

6°

λ = 300 ÷ 50 = 6 m, so 10 cm is 0,1 ÷ 6 of a wavelength: 360° × 0,1 ÷ 6 = 6°. Using the manual’s 1,2° per cm, which is for 100 MHz, gives 12°.

1,7°

λ = 300 ÷ 144 = 2,083 m, so 1 cm adds 360° × 0,01 ÷ 2,083 = 1,73°, nearest 1,7°. The manual’s 1,2° is for 100 MHz; a shorter wavelength means more phase per centimetre.

Parasitic oscillations

Unwanted oscillations, which arise wherever the loop also meets both criteria at another frequency, are parasitic oscillations. Harmonics are multiples of a signal produced by distortion, not separate oscillations.

It is made frequency selective, like a bandpass filter

Made into a bandpass filter, the network passes frequencies near the wanted one but attenuates others, so even where their phase is right their loop gain stays below 1 and they cannot oscillate.

It gives a phase shift and bandpass filtering at the same time

Near resonance its reactance swings from inductive to capacitive, giving a phase shift that changes quickly with frequency, and as the amplifier’s load it builds up a large voltage only near resonance. So it does both jobs.

Highly inductive

Below resonance the coil’s reactance is the smaller, so it takes most of the current and the pair looks highly inductive; just above resonance it turns highly capacitive. Zero reactance belongs to a series circuit at resonance.

The voltage leads the current

In an inductive reactance the voltage leads the current; in a capacitive one the current leads the voltage. That change of phase relationship around resonance is where a tuned circuit’s phase shift comes from.

The Barkhausen criteria

The Barkhausen criteria are a loop gain of exactly 1 and a total loop phase shift of 0° or a whole multiple of 360°. Kirchhoff’s laws deal with the currents and voltages in a circuit.

At or very close to 7,1 MHz

An oscillator whose phase-shift network is a tuned circuit runs at, or very near, that circuit’s resonant frequency, where its phase and selectivity favour the signal. The amplifier’s gain peak does not set the frequency.

The resonant frequency of its tuned circuit

The tuned circuit is the phase-shift network, and the phase criterion is met at, or very near, its resonant frequency, f = 1 ÷ (2π√LC). The amplifier’s gain peak does not set it.

The tuning capacitance is split into two capacitors

In a Colpitts the tuning capacitance is split in two: the amplifier’s output is fed across one capacitor and its input comes from across the other. A tapped coil instead marks the Hartley oscillator.

A Colpitts oscillator

Splitting the tuning capacitance in two, with output and input taken across different halves, defines the Colpitts. The Hartley does the same job with a tap on the coil instead of two capacitors.

Its parallel tuned circuit

The tank circuit is the oscillator’s parallel tuned circuit, the coil and capacitors that store energy and set the frequency. A reservoir capacitor belongs to a power supply’s smoothing, not to an oscillator.

As a common-emitter amplifier

With R1, R2, R3 and L1, Q1 forms a common-emitter amplifier: the signal goes in at the base and comes out at the collector, which feeds the tuned circuit. The manual’s Hartley, VCO and crystal circuits use emitter followers instead.

From Q1’s collector, through a coupling capacitor

The output comes from Q1’s collector through C4, which passes the RF but blocks the collector’s DC. The manual’s Hartley, VCO and crystal circuits take theirs from an emitter instead.

194 pF

In series, 1/CTotal = 1/C1 + 1/C2, so CTotal = (330 × 470) ÷ (330 + 470) = 194 pF, less than either. Adding them, 800 pF, is the rule for capacitors in parallel.

5,72 MHz

Two equal capacitors in series give half of one, 235 pF, so f = 1 ÷ (2π√(3,3 × 10⁻⁶ × 235 × 10⁻¹²)) = 5,72 MHz. Adding them as if in parallel, 940 pF, gives 2,86 MHz.

9 MHz

In series they give (220 × 680) ÷ 900 = 166 pF, so f = 1 ÷ (2π√(1,8 × 10⁻⁶ × 166 × 10⁻¹²)) = 9,2 MHz, nearest 9 MHz. Taking 900 pF, as if in parallel, gives 3,95 MHz.

A shift of frequency as the key is pressed and released

Chirp is the frequency shifting as the transmitter is keyed, because keying changes how much signal the following stages draw from the oscillator. Key clicks are a different fault, caused by switching the carrier too sharply.

A buffer stage between the oscillator and the amplifier

A buffer between them gives the oscillator a steady load however the amplifier is loaded, so the frequency holds. A regulated supply cures shifts caused by supply changes, but here the trouble is the load.

To isolate the oscillator from changes in its load

Changes in the load on an oscillator can shift its frequency, so the buffer keeps the load the oscillator sees constant. Building the signal up to full power is the job of later amplifier stages, not the buffer.

Its input impedance is high and its output impedance low

A high, steady input impedance barely loads the stage before it, while a low output impedance can supply the current the next stages need. Low input and high output impedance describe a common-base stage instead.

Common collector (emitter follower)

The buffer is often a common-collector stage, an emitter follower: it presents a steady, high impedance to the oscillator and a low output impedance to the stages after it. Its voltage gain is only about 1.

The Hartley oscillator

The Hartley feeds its tuned circuit through a tap on the coil, which the manual draws as a centre tap. The Colpitts uses a split pair of capacitors instead, and a crystal oscillator has no tapped coil.

A tapped coil in its tuned circuit carries the feedback

A Hartley feeds the amplifier’s output into its tuned circuit through a tap on the coil; a split pair of capacitors marks the Colpitts. The manual draws a centre tap; real designs often tap nearer the earthy end.

As an emitter follower (common collector)

Q1 is an emitter follower, biased by R1, R2 and R3: its output, at the emitter, feeds the tap on the coil through C3. The common-emitter stage is the one in the manual’s Colpitts circuit.

The coil steps the voltage up, like a transformer

Driven at the tap, the coil works as an autotransformer: its hot end swings further, so the base gets back more voltage than the emitter gave. Current gain alone cannot lift the loop’s voltage gain to 1.

An autotransformer

A tapped coil works as a transformer with a single winding, an autotransformer: a voltage between the tap and the earthy end appears larger across the whole coil. An isolating transformer needs two separate windings.

Common emitter, common collector or common base

The manual’s Colpitts uses a common-emitter stage and its Hartley, VCO and crystal circuits emitter followers; a common-base stage works too, as in many VHF oscillators. What matters is enough loop gain at the right phase.

To block DC, so the coil cannot short the bias to earth

C2 passes RF from the tuned circuit to the base but blocks DC; without it, L1 would join the base to earth and kill the bias from R1 and R2. A capacitor passes RF and blocks DC, never the reverse.

C1 is a variable capacitor, used to tune the frequency

An arrow through a capacitor marks it as variable, while an electrolytic shows a + sign; C1 and L1 form the tuned circuit, so C1 tunes the VFO. The manual’s text once says L1 and C2, a slip.

An oscillator whose frequency can be varied, usually with a knob

A variable frequency oscillator is one whose frequency can be changed, typically by turning a knob on a variable capacitor, as with C1 in the manual’s Hartley. V and F stand for variable frequency, not voltage-fed.

So that a DC control voltage can vary the frequency

A varicap’s capacitance changes with the reverse bias on it, so as part of the tuning capacitance it lets a control voltage set the frequency: a voltage-controlled oscillator. It tunes the oscillator; it does not set the output level.

An oscillator tuned by a DC control voltage

A voltage-controlled oscillator has a varicap as part of its tuning capacitance, so changing the DC control voltage on it changes the frequency. It is the frequency, not the output voltage, that the voltage controls.

Its capacitance falls, so the frequency rises

More reverse bias widens the depletion layer, like moving a capacitor’s plates apart, so the capacitance falls; with less C, f = 1 ÷ (2π√LC) rises. Capacitance rising with reverse bias is the classic wrong way round.

10 MHz

f varies as 1 ÷ √C, so a quarter of the capacitance doubles it: 5 × √(60 ÷ 15) = 5 × 2 = 10 MHz. Leaving out the square root gives 20 MHz.

11 MHz

f varies as 1 ÷ √C: 8 × √(50 ÷ 28) = 8 × 1,336 = 10,7 MHz, nearest 11 MHz. Forgetting the square root gives 8 × 50 ÷ 28 = 14,3 MHz.

To add to the varicap’s rather small capacitance

A varicap’s capacitance is typically low, so C1 in parallel adds to it; capacitances in parallel simply add. Keeping the control voltage away from Q1’s base bias is the job of C2, not C1.

From Q1’s emitter, through a coupling capacitor

Q1 is an emitter follower, so the output comes from its emitter, through the DC blocking capacitor C5; its collector goes straight to the supply. The manual’s Colpitts is the one that takes its output from a collector.

The series-tuned Colpitts

In the Clapp the tuning capacitance sits in series with the coil, so the manual calls it a series-tuned Colpitts; its VCO and crystal circuits both use it. The ordinary Colpitts has a parallel tuned circuit.

The piezoelectric effect

Quartz is piezoelectric: a voltage across it bends it slightly, and as it springs back it produces a voltage, so it behaves like a tuned circuit. The photoelectric effect concerns light, not mechanical movement.

A voltage bends the crystal slightly, and its return makes a voltage

A voltage across the crystal distorts it a little, and as it springs back to shape it generates a voltage across itself; this vibration makes it act like a series tuned circuit. Heat plays no part.

A series tuned circuit

The manual likens a crystal to a series tuned circuit, which lets it set an oscillator’s frequency. Real crystals also show a parallel resonance just above, caused by their holder’s capacitance, but the basic model is series.

Very good frequency stability

A crystal-controlled oscillator holds its frequency very steadily, with little drift, which LC oscillators struggle to match. A wide tuning range is exactly what it lacks: it can be pulled only slightly.

It can be tuned over only a very small range

A crystal oscillator is essentially a fixed-frequency oscillator: a variable capacitor can pull it only slightly. Drift is the weakness of ordinary LC oscillators; crystals are prized for avoiding it.

A slow, gradual change in its frequency

Drift is the frequency creeping away over time, for example as parts warm up; it troubles LC oscillators far more than crystal ones. A falling output level is a change of amplitude, not drift.

Pulling the crystal

Changing the capacitance in series with a crystal pulls its frequency, though only a little. Pushing is a different term, for a shift caused by changes in the supply voltage.

A crystal oscillator with an adjustable frequency

VXO stands for variable crystal oscillator: a crystal oscillator whose frequency can be pulled, over a small range, by a variable capacitor. The V stands for variable, not for very high frequency.