Wien Bridge Oscillator and Its Derivation - Advantages

Summary

The Weinbridge oscillator is an RC oscillator that utilizes a two-stage amplifier and a feedback network to generate stable oscillations. Its primary advantage lies in the ability to vary the frequency by adjusting capacitor values. The oscillator's design features a balanced Weinbridge circuit with series and parallel arms, providing excellent frequency stability and low distortion. The formula for oscillation frequency is derived based on component values, with the gain requirement for sustained oscillation set at a minimum of 3. Despite its advantages, the oscillator depends on discrete components for frequency adjustments, which may limit flexibility.

Takeaways

• 😀 The Weinbridge oscillator is an RC oscillator with a two-stage amplifier and a feedback network.
• 😀 It offers frequency variation by adjusting the capacitors in the feedback network, providing good frequency stability.
• 😀 The feedback network is a balanced Weinbridge circuit, consisting of a series arm (R1, C1) and a parallel arm (R2, C2).
• 😀 The oscillator operates over a frequency range of 10 Hz to 100 kHz, making it versatile for different applications.
• 😀 The Weinbridge oscillator behaves as a lead network at low frequencies and as a lag network at high frequencies.
• 😀 The two-stage common-emitter amplifier or op-amp is used to generate the necessary 360-degree phase shift for sustained oscillations.
• 😀 The frequency of oscillation is derived by calculating the impedances of the feedback network and applying the condition for sustained oscillations.
• 😀 The formula for the frequency of oscillation is f = 1 / (2π √(R1 R2 C1 C2)), and under balanced conditions, it simplifies to f = 1 / (2π RC).
• 😀 The feedback factor (β) for the Weinbridge oscillator is 1/3, which is derived from the impedance calculations.
• 😀 To maintain sustained oscillations, the amplifier gain must be at least 3, as per the Barkhausen criterion.

Q & A

What is a Weinbridge oscillator?

A Weinbridge oscillator is an RC oscillator that consists of a two-stage amplifier circuit and a feedback network. The feedback network uses a balanced Weinbridge circuit, which does not produce any phase shift, making it different from other types of oscillators.

What is the major advantage of the Weinbridge oscillator over the RC phase shift oscillator?

The major advantage of the Weinbridge oscillator is that its frequency can be varied by adjusting the values of capacitance in the feedback network, providing better frequency stability and flexibility.

What is the role of the two-stage amplifier in a Weinbridge oscillator?

The two-stage amplifier in a Weinbridge oscillator produces a 360-degree phase shift, which is essential for sustaining oscillations. This phase shift, combined with the feedback network, ensures the proper conditions for continuous oscillations.

What components make up the feedback network in a Weinbridge oscillator?

The feedback network in a Weinbridge oscillator consists of two arms: a series arm with a resistor and capacitor (R1, C1) in series, and a parallel arm with a resistor and capacitor (R2, C2) in parallel. These components help determine the frequency of oscillation.

What is the frequency-sensitive role of the series and parallel arms in the Weinbridge oscillator?

The series and parallel arms of the Weinbridge feedback network are frequency-sensitive because varying the capacitances (C1 and C2) in these arms allows control over the frequency range of the oscillator.

What does it mean that the Weinbridge circuit is known as a lead-lag network?

The Weinbridge circuit is referred to as a lead-lag network because at low frequencies, it acts as a lead network (the phase leads), and at high frequencies, it acts as a lag network (the phase lags). This refers to the phase shift behavior of the circuit.

How is the frequency of oscillation derived for a Weinbridge oscillator?

The frequency of oscillation for a Weinbridge oscillator is derived by equating the imaginary part of the feedback gain to zero under resonant conditions, leading to the formula: f = 1 / (2π√(R1 R2 C1 C2)), where R1 = R2 and C1 = C2 in the balanced case.

What is the formula for the frequency of oscillation in a balanced Weinbridge oscillator?

In the balanced Weinbridge oscillator, where R1 = R2 and C1 = C2, the frequency of oscillation is given by: f = 1 / (2π RC), where R is the resistance and C is the capacitance in the feedback network.

What is the feedback factor (β) in a Weinbridge oscillator and how is it calculated?

The feedback factor (β) in a Weinbridge oscillator is the ratio of the output voltage to the input voltage. It is calculated by substituting the values of the series and parallel impedances in the feedback network and simplifying the expression, ultimately yielding a value of 1/3 for the balanced circuit.

What is the minimum amplifier gain required for sustained oscillations in a Weinbridge oscillator?

For sustained oscillations in a Weinbridge oscillator, the amplifier gain must be greater than or equal to 3. This gain ensures that the system meets the Barkhausen criterion for continuous oscillations, where the feedback gain must be 1.