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.
3.25 × 10–9 F
An RC phase-shift oscillator with three equal sections oscillates at
\(f=\dfrac{1}{2\pi RC\sqrt{6}}\)
so rearranging for C,
\(C=\dfrac{1}{2\pi Rf\sqrt{6}}\)
Substituting the given values, \(R=20\ \text{k}\Omega\) and \(f=1\ \text{kHz}\):
\(2\pi Rf=2\pi\times20\times10^{3}\times10^{3}=1.2566\times10^{8}\)
\(C=\dfrac{1}{1.2566\times10^{8}\times2.449}=\dfrac{1}{3.078\times10^{8}}=3.25\times10^{-9}\ \text{F}\)
— option 4, that is 3.25 nF.
Option 3 is the trap, and it is worth naming. It carries the right mantissa with an exponent of −3 instead of −9 — 3.25 millifarads rather than 3.25 nanofarads, a factor of a million. A moment's judgement rules it out: a millifarad is an electrolytic capacitor the size of a thumb, and no audio-frequency oscillator uses one in a phase-shift network, where the capacitor must be small and non-polarised.
Where the \(\sqrt{6}\) comes from. Three identical RC sections must together supply 180° of phase shift, since the FET amplifier is inverting and provides the other 180° that the Barkhausen condition requires. Analysing the ladder gives
\(\beta=\dfrac{1}{1-5\alpha^{2}-j\left(6\alpha-\alpha^{3}\right)},\qquad \alpha=\dfrac{1}{\omega RC}\)
The phase is 180° when the imaginary part vanishes, which needs \(\alpha^{2}=6\) — hence the \(\sqrt{6}\) in the frequency. Substituting back gives an attenuation of exactly \(1/29\), so the amplifier must supply a gain of at least 29 for oscillation to start.
Why three sections and not two. A single RC section approaches but never reaches 90°, so two can never deliver 180° at any finite frequency. Three sections each contributing about 60° reach it comfortably while the output is still usable.
A caution on the formula. The version above assumes the FET's input impedance is high enough not to load the last section, which is exactly why a FET is specified. A BJT version loads the network and uses a modified expression involving the collector resistance.
Hence, C = 3.25 × 10−9 F.
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.
Consider the following statements regarding an RC phase shift oscillator :
i. amplifier gain is positive.
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°.Which is correct ?
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 ?
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:
