Oscillators Questions and Answers

Q: What distinguishes an Armstrong oscillator?

The Armstrong, or tickler, uses a separate winding coupled to the tank, so the transformer's turns ratio and winding sense set the fraction and the phase. The capacitive divider is the Colpitts and the tapped inductor the Hartley. Its advantage is that the phase can be reversed simply by reversing the winding, and its drawback is that a transformer is a less convenient component than a pair of capacitors - which is why it has largely fallen out of use.

Q: Why does an LC oscillator's frequency drift with temperature?

Both reactive components have temperature coefficients, and since the frequency depends on the square root of their product, the drift is half the sum of their fractional changes. Gain and feedback fraction affect amplitude rather than frequency, and the supply is regulated. That the drift is halved by the square root, and that components with opposite coefficients can be chosen to cancel, are the two facts a stable LC design rests on.

Q: How can an LC oscillator's temperature drift be reduced?

Choosing a capacitor whose capacitance rises with temperature to work with an inductor whose inductance falls lets the two drifts cancel in the product, and capacitors are made in a range of specified coefficients for exactly this purpose. A high quality factor improves stability against phase disturbances rather than against component drift, and gain and current affect amplitude. Cancelling two drifts against each other is cheaper than making either component stable, which is why the technique is standard.

Q: What physical effect makes a quartz crystal behave as a resonator?

Quartz is piezoelectric: mechanical strain produces a voltage across it and an applied voltage strains it, so an electrical circuit can excite and sense a mechanical resonance. The Hall effect is a transverse voltage in a magnetic field, the photoelectric effect concerns light and electrons, and the Seebeck effect produces a voltage from a temperature difference. It is the mechanical resonance, far sharper than any electrical one, that gives the crystal its extraordinary quality factor.

Q: How does a crystal's equivalent circuit represent it?

The mechanical resonance appears as a series inductance, capacitance and resistance, with the electrodes' own capacitance in parallel across the whole thing. That structure gives the crystal its two resonances: a series one where the branch is purely resistive, and a parallel one slightly above it where the branch's net inductance resonates with the holder capacitance. The two-resonance behaviour follows entirely from the equivalent circuit, which is why the circuit is worth knowing rather than merely the frequencies.

Q: What is the relation between a crystal's two resonant frequencies?

The parallel resonance sits just above the series one, typically by a few tenths of a per cent, and between them the crystal is inductive - which is exactly the region a Pierce oscillator uses. A crystal specified for series operation and one for parallel operation at the same nominal frequency are physically different parts. Knowing which resonance a circuit uses is essential when ordering a crystal, since the wrong one lands the frequency off by that few tenths of a per cent.

Q: In which region does a crystal appear inductive?

Between the two resonances the series branch is net inductive and has not yet been cancelled by the holder capacitance, so the crystal presents an inductive reactance - and a very rapidly varying one, which is what makes it so effective as the inductor in a Colpitts-like arrangement. Below the series resonance and above the parallel one it is capacitive. The narrow inductive window is where nearly every crystal oscillator operates, and it is only a few kilohertz wide at ten megahertz.

Q: What is a Pierce oscillator?

The Pierce is a Colpitts in which the crystal, operating in its inductive region, replaces the tank inductor - which is why it is the standard arrangement in almost every microprocessor clock. The two load capacitors form the divider exactly as in a Colpitts. Recognising a crystal oscillator as a familiar LC topology with one element substituted makes its operation immediately readable rather than a separate thing to learn.

31.

What distinguishes an Armstrong oscillator?

A.An RC network provides the phase shift
B.A transformer provides the feedback
C.A capacitive divider provides the feedback
D.A tapped inductor provides the feedback

Answer: B

The Armstrong, or tickler, uses a separate winding coupled to the tank, so the transformer's turns ratio and winding sense set the fraction and the phase. The capacitive divider is the Colpitts and the tapped inductor the Hartley. Its advantage is that the phase can be reversed simply by reversing the winding, and its drawback is that a transformer is a less convenient component than a pair of capacitors - which is why it has largely fallen out of use.

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32.

Why does an LC oscillator's frequency drift with temperature?

A.The feedback fraction rises with temperature
B.The supply voltage falls as the equipment heats
C.The inductance and capacitance both change with it
D.The amplifier's gain falls as the components warm

Answer: C

Both reactive components have temperature coefficients, and since the frequency depends on the square root of their product, the drift is half the sum of their fractional changes. Gain and feedback fraction affect amplitude rather than frequency, and the supply is regulated. That the drift is halved by the square root, and that components with opposite coefficients can be chosen to cancel, are the two facts a stable LC design rests on.

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33.

How can an LC oscillator's temperature drift be reduced?

A.Increase the tank's quality factor as far as possible
B.Reduce the amplifier's gain to the minimum needed
C.Operate the device at a much lower current
D.Pair components with opposite temperature coefficients

Answer: D

Choosing a capacitor whose capacitance rises with temperature to work with an inductor whose inductance falls lets the two drifts cancel in the product, and capacitors are made in a range of specified coefficients for exactly this purpose. A high quality factor improves stability against phase disturbances rather than against component drift, and gain and current affect amplitude. Cancelling two drifts against each other is cheaper than making either component stable, which is why the technique is standard.

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34.

What physical effect makes a quartz crystal behave as a resonator?

A.The piezoelectric effect
B.The Hall effect
C.The photoelectric effect
D.The Seebeck effect

Answer: A

Quartz is piezoelectric: mechanical strain produces a voltage across it and an applied voltage strains it, so an electrical circuit can excite and sense a mechanical resonance. The Hall effect is a transverse voltage in a magnetic field, the photoelectric effect concerns light and electrons, and the Seebeck effect produces a voltage from a temperature difference. It is the mechanical resonance, far sharper than any electrical one, that gives the crystal its extraordinary quality factor.

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35.

How does a crystal's equivalent circuit represent it?

A.Two capacitors in series with a small inductance
B.A series RLC branch in parallel with a holder capacitance
C.A parallel RLC circuit in series with a resistance
D.A single inductance with a very high quality factor

Answer: B

The mechanical resonance appears as a series inductance, capacitance and resistance, with the electrodes' own capacitance in parallel across the whole thing. That structure gives the crystal its two resonances: a series one where the branch is purely resistive, and a parallel one slightly above it where the branch's net inductance resonates with the holder capacitance. The two-resonance behaviour follows entirely from the equivalent circuit, which is why the circuit is worth knowing rather than merely the frequencies.

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36.

What is the relation between a crystal's two resonant frequencies?

A.They coincide unless the crystal is loaded
B.They differ by a factor of two
C.The parallel resonance lies slightly above the series one
D.The parallel resonance lies slightly below the series one

Answer: C

The parallel resonance sits just above the series one, typically by a few tenths of a per cent, and between them the crystal is inductive - which is exactly the region a Pierce oscillator uses. A crystal specified for series operation and one for parallel operation at the same nominal frequency are physically different parts. Knowing which resonance a circuit uses is essential when ordering a crystal, since the wrong one lands the frequency off by that few tenths of a per cent.

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37.

In which region does a crystal appear inductive?

A.Below its series resonance
B.Above its parallel resonance
C.At every frequency, by construction
D.Between its series and parallel resonances

Answer: D

Between the two resonances the series branch is net inductive and has not yet been cancelled by the holder capacitance, so the crystal presents an inductive reactance - and a very rapidly varying one, which is what makes it so effective as the inductor in a Colpitts-like arrangement. Below the series resonance and above the parallel one it is capacitive. The narrow inductive window is where nearly every crystal oscillator operates, and it is only a few kilohertz wide at ten megahertz.

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38.

What is a Pierce oscillator?

A.A Colpitts arrangement with the crystal as the inductor
B.A Hartley arrangement with the crystal tapped
C.An RC phase shift oscillator with a crystal filter
D.A relaxation oscillator gated by a crystal

Answer: A

The Pierce is a Colpitts in which the crystal, operating in its inductive region, replaces the tank inductor - which is why it is the standard arrangement in almost every microprocessor clock. The two load capacitors form the divider exactly as in a Colpitts. Recognising a crystal oscillator as a familiar LC topology with one element substituted makes its operation immediately readable rather than a separate thing to learn.

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39.

Why does a crystal oscillator hold its frequency so much better than an LC type?

A.Its feedback fraction is closer to unity
B.Its quality factor is orders of magnitude higher
C.Its amplitude is more tightly controlled
D.Its amplifier operates at a lower gain

Answer: B

A crystal's quality factor runs from tens of thousands to over a million, against a few hundred for a good LC tank, so the phase characteristic is enormously steeper and any phase disturbance in the loop moves the frequency by a correspondingly tiny amount. Amplitude control, gain and feedback fraction affect the output rather than the frequency. Every question about frequency stability comes back to the steepness of the phase characteristic, and quartz provides the steepest available at reasonable cost.

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40.

A crystal has \( Q = 20000 \) at \( 10 \ \mathrm{MHz} \). Its bandwidth is about

A.50 Hz
B.200 Hz
C.500 Hz
D.5 kHz

Answer: C

Bandwidth is the resonant frequency divided by the quality factor:

\[ B = \frac{10 \times 10^{6}}{20000} = 500 \ \mathrm{Hz} \]

giving 500 Hz, or fifty parts per million of the centre frequency. That such a narrow window exists at all is what makes the crystal a frequency standard, and it explains why the oscillator's frequency cannot be pulled far even deliberately.

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