Oscillators Questions and Answers

Q: A Wien bridge uses \( R = 10 \ \mathrm{k\Omega} \) and \( C = 10 \ \mathrm{nF} \). Its frequency is about

The centre frequency is where the two arms' phases cancel:\[ f = \frac{1}{2\pi R C} \approx 1592 \ \mathrm{Hz} \]giving about 1592 Hz. The value 650 Hz would follow from the phase shift oscillator's formula with its root six. That the same components give quite different frequencies in the two topologies is worth noticing, and it is entirely due to the different phase conditions being solved.

Q: What does a twin-T network provide in an oscillator?

The twin-T is a notch filter, and its very rapid phase change through the null gives an unusually sharp frequency selection when placed in a negative feedback path. The circuit oscillates at the notch, where the negative feedback disappears. It provides attenuation rather than gain, has one null rather than two frequencies, and its phase varies with frequency rather than being fixed. Using a null rather than a peak to select a frequency is an inversion worth understanding, since the same idea appears in notch-based measurement circuits.

Q: Why are RC oscillators preferred to LC types at audio frequencies?

At a few hundred hertz an LC tank would need an inductance of henries with a capacitance of microfarads, physically large, expensive and lossy, while resistors and capacitors of the required values are trivial. The quality factor of an RC network is actually poor, stabilisation is needed either way, and LC oscillators work at low frequencies in principle. What is practical to manufacture at a given frequency decides the topology far more often than any theoretical consideration.

Q: What distinguishes a Hartley oscillator?

A Hartley takes its feedback from a tap on the inductor, so the two inductive sections form the divider that sets the feedback fraction. The capacitive divider is the Colpitts, a crystal is a different family, and RC sections belong to the audio topologies. The whole distinction between Hartley and Colpitts is which reactive element is tapped, and once that is fixed everything else about the two circuits is the same.

Q: What distinguishes a Colpitts oscillator?

A Colpitts uses two capacitors in series across the inductor, with the feedback taken from their junction, so their ratio sets the feedback fraction. The tapped inductor is the Hartley. It is easier to make two good capacitors than one accurately tapped inductor, which is why the Colpitts is by far the more common of the two in modern equipment and why it adapts so readily to integrated form.

Q: A Colpitts uses \( L = 100 \ \mathrm{\mu H} \) with \( C_{1} = C_{2} = 1 \ \mathrm{nF} \). Its frequency is about

The two capacitors appear in series across the inductor:\[ \begin{aligned} C_{s} &= \tfrac{C_{1}C_{2}}{C_{1}+C_{2}} = 0.5 \ \mathrm{nF} \\ f &= \tfrac{1}{2\pi\sqrt{LC_{s}}} \approx 712 \ \mathrm{kHz} \end{aligned} \]giving about 712 kHz. Using one nanofarad rather than the series combination gives 503 kHz, which is the commonest error. The series rule for capacitors is what makes the Colpitts calculation differ from the Hartley's.

Q: A Hartley has a total tank inductance of \( 50 \ \mathrm{\mu H} \) and \( C = 200 \ \mathrm{pF} \). Its frequency is about

The two inductive sections add, since they are in series:\[ f = \frac{1}{2\pi\sqrt{LC}} \approx 1.59 \ \mathrm{MHz} \]giving about 1.59 MHz. Inductances in series add while capacitances in series combine reciprocally, which is exactly why the Hartley uses the total inductance and the Colpitts the series capacitance. Getting that pair of rules the right way round is most of distinguishing the two calculations.

Q: What sets the feedback fraction in a Colpitts oscillator?

The two capacitors form a divider, so the fraction returned is set by their ratio - a small capacitor across the input and a large one to earth gives a small fraction. The inductance sets the frequency with them, the quality factor governs stability, and the transconductance supplies the gain that must overcome the fraction. Separating which component sets the frequency from which sets the feedback is what makes an oscillator designable rather than merely recognisable.

41.

What gain must a Wien bridge oscillator's amplifier provide?

A.Ten
B.Three
C.Twenty-nine
D.One

Answer: B

The Wien network attenuates by a factor of three at its centre frequency, so the amplifier must supply a gain of exactly three for the loop gain to be one. That is easily arranged with a two-to-one resistor ratio in a non-inverting stage, which is one reason the topology is so popular. Twenty-nine is the phase shift oscillator's requirement. A modest and easily set gain requirement is a practical advantage, since the amplitude control then has only a small range to work over.

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42.

A Wien bridge uses \( R = 10 \ \mathrm{k\Omega} \) and \( C = 10 \ \mathrm{nF} \). Its frequency is about

A.159 Hz
B.3184 Hz
C.1592 Hz
D.650 Hz

Answer: C

The centre frequency is where the two arms' phases cancel:

\[ f = \frac{1}{2\pi R C} \approx 1592 \ \mathrm{Hz} \]

giving about 1592 Hz. The value 650 Hz would follow from the phase shift oscillator's formula with its root six. That the same components give quite different frequencies in the two topologies is worth noticing, and it is entirely due to the different phase conditions being solved.

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43.

Why is the Wien bridge preferred for a laboratory sine wave generator?

A.Its output amplitude is larger than other topologies give
B.It needs no amplitude stabilisation of any kind
C.Its frequency is independent of the resistor values
D.Its frequency is easily varied with a ganged potentiometer

Answer: D

Both resistors can be varied together with a two-gang control, giving a continuously tunable frequency over a decade with a range switch changing the capacitors - exactly what a bench generator needs. Amplitude is a matter of design, stabilisation is essential rather than dispensable, and the frequency depends on the resistors directly. A topology whose frequency-setting elements can both be adjusted by one mechanical control is far more convenient than one requiring three, which is why the three-section phase shift oscillator is rarely made tunable.

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44.

What does a twin-T network provide in an oscillator?

A.A notch that gives a sharp phase transition
B.A gain of twenty-nine at its centre frequency
C.Two independent frequencies of oscillation
D.A ninety degree shift at every frequency

Answer: A

The twin-T is a notch filter, and its very rapid phase change through the null gives an unusually sharp frequency selection when placed in a negative feedback path. The circuit oscillates at the notch, where the negative feedback disappears. It provides attenuation rather than gain, has one null rather than two frequencies, and its phase varies with frequency rather than being fixed. Using a null rather than a peak to select a frequency is an inversion worth understanding, since the same idea appears in notch-based measurement circuits.

Discuss in Forum

45.

Why are RC oscillators preferred to LC types at audio frequencies?

A.LC oscillators cannot be made to oscillate below a megahertz
B.The inductors required would be impractically large
C.RC networks have a higher quality factor at low frequencies
D.RC oscillators need no amplitude stabilisation

Answer: B

At a few hundred hertz an LC tank would need an inductance of henries with a capacitance of microfarads, physically large, expensive and lossy, while resistors and capacitors of the required values are trivial. The quality factor of an RC network is actually poor, stabilisation is needed either way, and LC oscillators work at low frequencies in principle. What is practical to manufacture at a given frequency decides the topology far more often than any theoretical consideration.

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46.

What distinguishes a Hartley oscillator?

A.A crystal replaces the tank circuit entirely
B.Three RC sections provide the phase shift
C.A tapped inductor supplies the feedback
D.A tapped capacitor divider supplies the feedback

Answer: C

A Hartley takes its feedback from a tap on the inductor, so the two inductive sections form the divider that sets the feedback fraction. The capacitive divider is the Colpitts, a crystal is a different family, and RC sections belong to the audio topologies. The whole distinction between Hartley and Colpitts is which reactive element is tapped, and once that is fixed everything else about the two circuits is the same.

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47.

What distinguishes a Colpitts oscillator?

A.A tapped inductor supplies the feedback
B.The tank is formed from two inductors in series
C.The amplifier must be non-inverting
D.A capacitive divider supplies the feedback

Answer: D

A Colpitts uses two capacitors in series across the inductor, with the feedback taken from their junction, so their ratio sets the feedback fraction. The tapped inductor is the Hartley. It is easier to make two good capacitors than one accurately tapped inductor, which is why the Colpitts is by far the more common of the two in modern equipment and why it adapts so readily to integrated form.

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48.

A Colpitts uses \( L = 100 \ \mathrm{\mu H} \) with \( C_{1} = C_{2} = 1 \ \mathrm{nF} \). Its frequency is about

A.712 kHz
B.503 kHz
C.1.42 MHz
D.356 kHz

Answer: A

The two capacitors appear in series across the inductor:

\[ \begin{aligned} C_{s} &= \tfrac{C_{1}C_{2}}{C_{1}+C_{2}} = 0.5 \ \mathrm{nF} \\ f &= \tfrac{1}{2\pi\sqrt{LC_{s}}} \approx 712 \ \mathrm{kHz} \end{aligned} \]

giving about 712 kHz. Using one nanofarad rather than the series combination gives 503 kHz, which is the commonest error. The series rule for capacitors is what makes the Colpitts calculation differ from the Hartley's.

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49.

A Hartley has a total tank inductance of \( 50 \ \mathrm{\mu H} \) and \( C = 200 \ \mathrm{pF} \). Its frequency is about

A.500 kHz
B.1.59 MHz
C.3.18 MHz
D.796 kHz

Answer: B

The two inductive sections add, since they are in series:

\[ f = \frac{1}{2\pi\sqrt{LC}} \approx 1.59 \ \mathrm{MHz} \]

giving about 1.59 MHz. Inductances in series add while capacitances in series combine reciprocally, which is exactly why the Hartley uses the total inductance and the Colpitts the series capacitance. Getting that pair of rules the right way round is most of distinguishing the two calculations.

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50.

What sets the feedback fraction in a Colpitts oscillator?

A.The quality factor of the tank circuit
B.The transconductance of the amplifying device
C.The ratio of the two capacitances
D.The ratio of the inductance to the capacitance

Answer: C

The two capacitors form a divider, so the fraction returned is set by their ratio - a small capacitor across the input and a large one to earth gives a small fraction. The inductance sets the frequency with them, the quality factor governs stability, and the transconductance supplies the gain that must overcome the fraction. Separating which component sets the frequency from which sets the feedback is what makes an oscillator designable rather than merely recognisable.

Discuss in Forum

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