Oscillators Questions and Answers

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.

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.

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.

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.

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.

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.

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.

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.

Answer: D

The Clapp inserts a small capacitor in series with the inductor, and since it is much smaller than the other two it dominates the resonant frequency - which makes the frequency far less sensitive to the transistor's own capacitances. The other options describe different circuits. Arranging for a stable component to dominate a frequency, so that unstable ones matter little, is a general technique and this is its classic application.

Answer: A

The transistor's junction capacitances appear in parallel with the two divider capacitors and drift with temperature and bias, but the small series capacitor dominates the frequency, so those drifts are swamped. The quality factor and the gain requirement are not what changes. Making a frequency depend on the most stable component available, rather than on the sum of several unstable ones, is what the extra capacitor buys.