Oscillators Questions and Answers

Answer: C

The three RC sections attenuate by a factor of twenty-nine at the frequency where they give a hundred and eighty degrees, so the amplifier must supply at least that much gain for the loop gain to reach unity. Three is the Wien bridge's requirement, where the network attenuates by only three. The attenuation and the gain requirement are two statements of one fact, and computing the network's loss at its phase-shift frequency is what gives the number.

Answer: D

The three-section network oscillates where its phase reaches one hundred and eighty degrees:

\[ f = \frac{1}{2\pi R C \sqrt{6}} \approx 650 \ \mathrm{Hz} \]

giving about 650 Hz. The value 1592 Hz omits the root six and is the Wien bridge's frequency for the same components. The root six is what distinguishes the two topologies numerically, and it comes directly from solving the three-section network's phase condition.

Answer: A

The series and parallel RC arms cancel each other's phase at one frequency, so the network passes the signal with zero shift and a non-inverting amplifier completes the loop. That is why a Wien bridge uses a non-inverting configuration while a phase shift oscillator uses an inverting one. Whether a network shifts by zero or by a hundred and eighty degrees decides which kind of amplifier it must be paired with, and that pairing is the first thing to establish about any oscillator.

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.

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.

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.