Oscillators Questions and Answers

Answer: C

The number of harmonics is 0.

A tuned (LC) oscillator uses a resonant tank circuit as its frequency-selective network. The tank presents high impedance and supports oscillation only at its resonant frequency, so the ideal output is a pure sinusoid at that single frequency, with no harmonics added to the fundamental.

Practical oscillators show some harmonic distortion from the non-linearity of the active device, but the high-Q tank suppresses it, which is why the textbook answer is that no harmonics accompany the base frequency. Options giving 1, 2 or 5 harmonics describe non-sinusoidal, relaxation-type outputs.

Answer: D

The answer is (A) is false and (R) is true.

A sinusoidal oscillator is basically an amplifier with positive feedback, satisfying the Barkhausen criterion: loop gain of at least one and total phase shift of 0° or 360° at the oscillation frequency. A multivibrator is itself a relaxation oscillator that produces square waves; an oscillator is not a multivibrator with feedback added, so the Assertion is false.

The Reason is true: a series R with a shunt C forms a low-pass filter, and a series C with a shunt R a high-pass filter. Such R-C sections are used in RC phase-shift and Wien bridge oscillators, but that fact does not rescue the Assertion.

Answer: B

The frequency is nearly 5 kHz.

For the three-section RC phase shift oscillator, using the standard formula:

\[ f = \frac{1}{2\pi RC\sqrt{6}} \]

\[ \begin{aligned} 2\pi RC\sqrt{6} &= 2\pi(10^{3})(13 \times 10^{-9})(2.449) \\ &\approx 2.0 \times 10^{-4}\ \text{s} \end{aligned} \]

so \(f \approx 5000\) Hz. The \(\sqrt{6}\) arises because the three RC sections must together give 180° of phase shift. Leaving it out gives about 12 kHz, and none of the other options follows from these values.

Answer: B

The oscillator that uses no feedback is the UJT relaxation oscillator.

A UJT relaxation oscillator works by charging a capacitor through a resistor until the voltage reaches the UJT's peak point; the UJT then switches on, discharges the capacitor and switches off, and the cycle repeats. Oscillation comes from the negative-resistance region of the UJT, not from feeding part of the output back to the input.

The phase shift, Wien bridge and Colpitts oscillators are feedback oscillators: an amplifier with a frequency-selective feedback network (an RC ladder, a Wien network, or an LC tank) that satisfies the Barkhausen criterion at one frequency.

Answer: B

The frequency is nearly 159 kHz.

In a Hartley oscillator the tank circuit is a capacitor across two inductors in series, so (neglecting mutual inductance) \(L = L_{1} + L_{2}\):

\[ \begin{aligned} L &= 12 + 8 = 20\ \mu\text{H} \\ LC &= 20 \times 10^{-6} \times 0.05 \times 10^{-6} = 10^{-12} \\ f &= \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi \times 10^{-6}} \\ &\approx 159\ \text{kHz} \end{aligned} \]

Using only the 12 \(\mu\)H coil gives about 205 kHz, and only the 8 \(\mu\)H coil about 252 kHz; neither is an option. 139, 179 and 279 kHz do not follow from these component values.

Answer: D

The Wien bridge oscillator is not an LC tuned oscillator.

The Wien bridge oscillator sets its frequency with a resistor-capacitor network, \(f = 1/2\pi RC\), which makes it an RC oscillator, used mainly in the audio range.

The other three are LC oscillators whose frequency is set by a tank circuit. The Colpitts oscillator uses a tapped capacitance (two capacitors) with one inductor, the Hartley a tapped inductance (two inductors) with one capacitor, and the Clapp oscillator is a Colpitts with an extra capacitor in series with the inductor for better frequency stability.

Answer: B

The correct code is (a)-(ii), (b)-(iii), (c)-(i), (d)-(v).

A Wien bridge oscillator is an RC oscillator used in the audio frequency range (ii). Voltage shunt feedback samples the output voltage, which lowers the output impedance (iii). A crystal oscillator gives very stable frequencies in the radio frequency range (i). Current shunt feedback mixes the feedback in shunt at the input, which lowers the input impedance (v).

The other codes swap these: a Wien bridge is not an RF circuit, and a crystal oscillator is not an AF circuit, so any code pairing them that way is wrong.

Answer: C

The key is Non-linearity, and texts give more than one reason for the margin.

An oscillator needs a loop gain \(A\beta = 1\) in steady state (the Barkhausen condition). In practice the loop gain is set a little above 1 so that oscillations start from noise and grow. As the amplitude rises, the non-linearity of the amplifier, for example saturation, lowers the average gain until it settles at 1. The key reads the question this way, with the margin taken up by the non-linearity.

Other books say the margin makes up for component ageing or losses. Noise is what starts the oscillation, not what the margin compensates, and a phase shift is removed by tuning the circuit to the frequency at which the loop phase is zero. Change in feedback voltage is not a standard answer. The choice follows the key.

Answer: B

Oscillators operate on the principle of positive feedback.

An oscillator is an amplifier whose output is fed back to its input in phase. By the Barkhausen criterion, sustained oscillation needs a loop gain of magnitude one and a total phase shift of 0° or 360° around the loop. Noise at the frequency that meets this condition is reinforced on every pass until the amplitude is limited by the circuit's nonlinearity.

Negative feedback opposes the input and stabilises an amplifier, so it suppresses oscillation. High gain alone is not enough without the right phase, and 'signal feedthrough' is an unwanted coupling, not an operating principle.

Answer: B

A crystal oscillator is used where high frequency stability is required.

A quartz crystal acts as a resonant circuit with an extremely high Q, often 10,000 to over 100,000, and its resonant frequency depends on its cut and dimensions, changing very little with temperature or supply voltage. Crystal oscillators therefore hold their frequency to a few parts per million, which is why they time clocks, microprocessors and radio transmitters.

Wien bridge (RC), Hartley and Colpitts (LC) oscillators use ordinary components whose values drift with temperature and ageing, and their much lower Q gives poorer frequency stability.