Oscillators Questions and Answers

Answer: A

The Barkhausen criterion demands a loop gain of one in magnitude and a total phase shift around the loop of zero, or equivalently a whole number of full turns. Both must hold at the same frequency, and it is that coincidence which picks out the frequency of oscillation. Positive feedback and a resonant element are how the conditions are usually met rather than the conditions themselves, and bandwidth is a property of the amplifier. Two conditions at one frequency is the whole of oscillator theory, and every topology in this subject is an arrangement for satisfying them.

Answer: B

A loop gain of exactly one would sustain whatever amplitude already existed but could never build one, so a practical oscillator is designed with a loop gain somewhat above one and grows from circuit noise until something limits it. The amplifier's gain is constant until the amplitude limiting acts, the phase condition is amplitude-independent, and the supply's rise is incidental. Designing a loop to be marginally unstable, and then arranging what stops it growing, is the practical reading of the criterion.

Answer: C

Every circuit contains thermal and shot noise across a wide band, and the supply's own step excites the resonant circuit as well - the loop selects whatever component lies at its frequency and amplifies it repeatedly until limiting sets in. No injected pulse is needed, nothing is stored between runs, and offset is a direct quantity rather than a signal. That an oscillator needs no starting signal, only the absence of anything preventing growth, is what makes an unwanted oscillation so hard to suppress once a loop meets the conditions.

Answer: D

Growth continues until a non-linearity - clipping at the supply rails, a lamp's rising resistance, a diode network, or an automatic gain control loop - pulls the average loop gain back to exactly one. The phase condition is unaffected by amplitude, and neither supply current nor tank losses provide the regulation. Which non-linearity is used decides how clean the output is: hard clipping gives a distorted waveform, while a gentle amplitude control preserves the sine.

Answer: A

A small filament lamp heats as the amplitude grows, its resistance rises, and the negative feedback increases until the loop gain settles at exactly one - a gentle amplitude control that limits without ever clipping, so the output stays a clean sine. Its thermal inertia is what makes the control slow enough not to distort the waveform, though that is a consequence rather than the mechanism. Harmonics are what the arrangement avoids, and the frequency is set by the RC network. Regulating amplitude smoothly rather than clipping it is the difference between a laboratory oscillator and a squarewave generator.

Answer: B

Clipping holds the amplitude by flattening the waveform's peaks, so the output is no longer a sine and carries strong odd harmonics. It is perfectly acceptable where a squarewave or a clock is wanted and unacceptable in a signal generator. Frequency does shift a little with supply, but that is a separate mechanism. The choice of limiting mechanism is the choice of output purity, and it is decided by what the oscillator is for rather than by any theoretical consideration.

Answer: C

The frequency-determining network gives the right phase shift at exactly one frequency, and the gain condition is arranged to be satisfied there, so only that component of the noise grows. The amplifier's bandwidth is far wider, the transient is broadband, and the non-linearity acts on amplitude rather than selecting frequency. It is the coincidence of the two conditions that does the selecting, which is why the sharpness of the phase characteristic decides how precisely the frequency is defined.

Answer: D

A sharp resonance means a small change in frequency produces a large change in phase, so any phase disturbance elsewhere in the loop is corrected by only a tiny shift in frequency. That is why a crystal, with a quality factor in the tens of thousands, holds a frequency so much better than an LC tank at a few hundred. Stored energy and low losses are what produce the high quality factor rather than the mechanism of stability. Frequency stability is always a question of how steep the phase characteristic is at the operating point.

Answer: A

The common-emitter amplifier already inverts, contributing one hundred and eighty degrees, so the network must supply the other hundred and eighty to bring the total round to zero or a full turn. Ninety degrees would leave the loop short, and three hundred and sixty from the network alone would need the amplifier to be non-inverting. Working out what the amplifier already contributes, and requiring the network to make up the difference, is how every oscillator topology is read.

Answer: B

Each RC section approaches but never reaches ninety degrees, so two can never total the hundred and eighty required and at least three are needed, each contributing sixty at the oscillation frequency. Selectivity improves as a side effect, and the gain requirement actually rises with more sections rather than falling. A limit that is approached asymptotically but never attained is what forces the third section, and recognising that saves attempting the two-section version.