The current amplification factor in radian square of Colpitts oscillator is :
\(\frac{C_1}{C_2}\)
The question in focus is about the current amplification factor of a Colpitts oscillator given in terms of capacitance elements. The Colpitts oscillator is a type of LC oscillator where the tank circuit comprises two capacitors \( C_1 \) and \( C_2 \) and an inductor \( L \). The amplification factor often refers to the gain factor required for sustained oscillations.
The critical concept here is the feedback ratio determined by the arrangement of the capacitors in the tank circuit:
A Colpitts oscillator uses capacitative feedback where the feedback fraction \( \beta \) is given by:
\(\beta = \frac{C_2}{C_1 + C_2}\)
For oscillation to occur, the loop gain \( A \beta \) must be equal to 1. Assuming that \( A \) represents the gain of the amplifier, the condition \( A \beta = 1 \) leads to:
\(A = \frac{C_1 + C_2}{C_2}\)
Since the correct answer is expressed as a ratio \( \frac{C_1}{C_2} \), this term plays a significant part in factors involving the stabilization of oscillation and is related to gain control in practical circuits.
Conclusion: The correct formulation of the gain or current amplification factor in a Colpitts oscillator is presented as the ratio of the capacitor \( C_1 \) to \( C_2 \), making the correct option:
\(\frac{C_1}{C_2}\)
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 ?
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 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:
