Consider the following statements regarding an RC phase shift oscillator : i. amplifier gain is positive. Which is correct ?
ii. amplifier gain is negative.
iii. phase shift introduced by the feedback network is 180°.
iv. phase shift introduced by the feedback network is 360°.
ii, iii
The Barkhausen condition requires the total phase shift around the loop to be 360°, and the RC oscillator splits that shift equally between amplifier and network : 180° each. So the amplifier is inverting — negative gain — and the network supplies 180°. Statements ii and iii, option 2.
\(A\beta=1,\qquad \angle A\beta=0^{\circ}\ \text{or}\ 360^{\circ}\)
| Element | Phase shift |
|---|---|
| Amplifier (inverting) | 180° |
| RC feedback network | 180° |
| Loop total | 360° |
Why three RC sections are needed. A single RC section can approach 90° of phase shift but never reach it, since
\(\phi=\tan^{-1}\dfrac{1}{\omega RC}\)
tends to 90° only as \(\omega\to0\), where the output vanishes. Two sections could in principle give 180° but only at zero output. Three sections each contributing about 60° give the required 180° at a finite frequency with usable amplitude — hence the three-section ladder that defines the circuit.
The design consequences follow at once. For identical sections the oscillation frequency is
\(f=\dfrac{1}{2\pi RC\sqrt{6}}\)
and at that frequency the ladder attenuates by a factor of 29, so the amplifier must supply
\(|A|\ge29\)
to satisfy \(|A\beta|=1\). Both numbers — the \(\sqrt{6}\) and the 29 — come from the same ladder analysis.
Why options 1 and 4 fail. A positive amplifier gain would mean a non-inverting amplifier contributing 0°, in which case the network would have to supply the whole 360° — which the three-section RC ladder cannot do. And a network supplying 360° by itself is not what this circuit does; a passive RC ladder of three sections tops out below 270°.
The contrast worth remembering is the Wien-bridge oscillator, which takes the opposite route: its network gives zero phase shift at the oscillation frequency, so its amplifier must be non-inverting, with a gain of exactly 3. Both satisfy Barkhausen; they simply divide the 360° differently.
Hence, statements ii and iii are correct.
Similar Questions
The phase locked loop (PLL) is one of the interesting applications of the lock-in amplifier. Apart from FM stereo decoders, tracking filters, motor speed control, FM demodulators, etc. it has found wide applications in generation of local oscillator frequencies in house-hold TV and FM tuners as automatic frequency control (AFC). Indeed, PLL has emerged as one of the fundamental building blocks in electronics and it is commercially available as a single package. Basically, a PLL is a lock-in amplifier in which the reference signal is provided by its own output, converted to frequency by a voltage controlled oscillator (VCO). When locked to the input frequency the dc output is small but sufficient to drive the VCO to produce a frequency which is equal to that of the signal. In this tracking situation, the input signal and the VCO output are almost in phase quadrature and the lock-in amplifier produces a small dc voltage which is often referred to as error voltage. The moment input signal is fed, the VCO frequency starts changing and the PLL is said to be in the capture mode. The VCO continues to change its frequency until it equals that of the input and stays there ; the PLL is then in the phase-locked state. In this state, if there is any change in the input frequency, the loop automatically tracks it through its repetitive action.
Assertion (A) : In applications such as FM and FSK, VCO plays an important role.
Reason (R) : The frequency control is easily possible by varying d.c. voltage.
Which of the following oscillations makes use of both positive and negative feedback ?
For a FET based phase shift oscillator, what should be the value of capacitor (C) for oscillator operation at 1 kHz. The resistor (R) in the feedback network is 20 kΩ.
The current amplification factor in radian square of Colpitts oscillator is :
The voltage controlled oscillator is used for :
The PLL is in the free-running state when :
Assertion (A) : A monostable multivibrator can be used to alter the pulse width of a repetitive pulse train.
Reason (R) : Monostable multivibrator has a single stable state.
Select your answer using the codes given below :
In an RC phase shift oscillator the frequency of oscillation is given by
Important Questions from Types of Oscillators
Electronic ohmmeter uses OP-AMP as a/an:
Which of the following statements about the Wien Bridge Oscillator is CORRECT?
Hartley Oscillator is a:
Which of the following is the fixed frequency oscillator?
If R = 51 kΩ and C = 0.001 μF, the resonant frequency of a Wien Bridge oscillator is:
