Wein Bridge Oscillator MCQ Quiz - Objective Question with Answer for Wein Bridge Oscillator - Download Free PDF

At frequency of oscillation the feedback factor is

\(\beta = \frac{R_2 C_1}{(R_1 C_1 + R_2 C_2 + R_2 C_1)}\)

\(\beta = \frac{100 \times 10^3 \times 0.5 \times 10^{-6}}{\left[ (2 \times 10^3 \times 0.5 \times 10^{-6} ) + (100 \times 10^3 \times 2 \times 10^{-9} + (100 \times 10^3 \times 0.5 \times 10^6)\right)]} \)

\(\beta = \frac{50}{1 + 0.2 + 50} = \frac{50}{51.2} = 0.976\)

Explanation:

Wein bridge oscillator is the commonly used circuit for generating a sinusoidal waveform of the required frequency.

Wein bridge oscillator:

The circuit diagram of the Wein bridge oscillator is shown below:

• The Wein bridge oscillator uses two RC networks connected together to produce a sinusoidal oscillator.
• The Wein bridge oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance depending upon the circuit frequency
• At the resonant frequency, the phase shift is 00.

The feedback network consists of series and parallel connections of two RC networks that act as a lead-lag network in feedback.

Here Z_p and Z_s form a voltage divider and voltage across Zp will act as feedback voltage.

\(V_f=\frac{V_oZ_p}{Z_p+Z_s}\)

\(β=\frac{V_f}{V_o}=\frac{Z_p}{Z_p+Z_s}\)

On putting values of Z_p & Z_s, we will get the value of β as:

\(\beta=\frac{1}{3 \ + \ j(ω RC-\frac{1}{ω RC})}\)

Open-loop gain of the above circuit is:

\(A=1 \ + \ \frac{R_2}{R_1}\)

So loop gain will be:

\(Loop \ Gain=\frac{A}{3 \ + \ j(ω RC-\frac{1}{ω RC}) }\)

At ω = ω₀, the phase of loop gain must become zero and hence imaginary part should be zero.

\(\omega _o-\frac{1}{\omega_oRC}=0\)

\(\omega _0=\frac{1}{RC}\)

\(f _0=\frac{1}{2\pi RC}\)

Here f₀ is the frequency of oscillation.

Since in the circuit Positive feedback is present  and feedback element are series RC + Parallel RC so it is Wein Bridge Oscillator.

(a) Wein Bridge oscillator:

It is an audio frequency oscillator.

Its frequency of oscillation:

\({f_0} = \frac{1}{{2\pi }}\sqrt {RC} \)

→ for sustained oscillation R₂ ≥ 2 R₁        {A ≥ 3}

NOTE:

If non identical RC element are present in the feedback:

Then \({f_0} = \frac{1}{{2\pi \sqrt {{R_s}{R_p}{C_s}{C_p}} }}\;\)

For sustained oscillation

\(A \ge 1 + \frac{{{R_s}}}{{{R_p}}} + \frac{{{C_p}}}{{{C_s}}}\)

Wien bridge oscillator:

A Wien bridge oscillator is an RC coupling amplifier that has good stability at resonant frequency f_o.

In this oscillator, Op-Amp acts as a Non-inverting amplifier which provides a zero phase shift.

Hence, the RC feedback network should also produce a zero phase shift at resonant frequency f_o.

So, the circuit behaves as an oscillator at f_o.

Feedbacks used in Wien bridge oscillator:

The Wien bridge oscillator uses both positive and negative feedbacks with one path each.

The path for positive feedback is through the Lag-lead circuit.

The path for negative feedback is used for voltage division. 

Explanation:

Wein bridge oscillator is the commonly used circuit for generating a sinusoidal waveform of the required frequency.

Wein bridge oscillator:

The circuit diagram of the Wein bridge oscillator is shown below:

• The Wein bridge oscillator uses two RC networks connected together to produce a sinusoidal oscillator.
• The Wein bridge oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance depending upon the circuit frequency
• At the resonant frequency, the phase shift is 00.

The feedback network consists of series and parallel connections of two RC networks that act as a lead-lag network in feedback.

Here Z_p and Z_s form a voltage divider and voltage across Zp will act as feedback voltage.

\(V_f=\frac{V_oZ_p}{Z_p+Z_s}\)

\(β=\frac{V_f}{V_o}=\frac{Z_p}{Z_p+Z_s}\)

On putting values of Z_p & Z_s, we will get the value of β as:

\(\beta=\frac{1}{3 \ + \ j(ω RC-\frac{1}{ω RC})}\)

Open-loop gain of the above circuit is:

\(A=1 \ + \ \frac{R_2}{R_1}\)

So loop gain will be:

\(Loop \ Gain=\frac{A}{3 \ + \ j(ω RC-\frac{1}{ω RC}) }\)

At ω = ω₀, the phase of loop gain must become zero and hence imaginary part should be zero.

\(\omega _o-\frac{1}{\omega_oRC}=0\)

\(\omega _0=\frac{1}{RC}\)

\(f _0=\frac{1}{2\pi RC}\)

Here f₀ is the frequency of oscillation.

Concept:

For sinusoidal oscillations to begin, the voltage gain of the Wien Bridge circuit must be equal to or greater than 3, i.e.

A_v ≥ 3.

For a non-inverting op-amp configuration, this value is set by the feedback resistor network and is given as:

\(\frac{V_{out}}{V_{in}}=1+\frac{R_2}{R_1}\) = 3 or more

Analysis:

For the given circuit, the voltage gain (non-inverting) will be:

\(\frac{V_{out}}{V_{in}}=1+\frac{R_2}{R_1}=1+\frac{1.9k}{1k}\)

\(\frac{V_{out}}{V_{in}}=2.9\)

Since the voltage gain is less than 3, sinusoidal oscillation cannot start.

Since in the circuit Positive feedback is present  and feedback element are series RC + Parallel RC so it is Wein Bridge Oscillator.

(a) Wein Bridge oscillator:

It is an audio frequency oscillator.

Its frequency of oscillation:

\({f_0} = \frac{1}{{2\pi }}\sqrt {RC} \)

→ for sustained oscillation R₂ ≥ 2 R₁        {A ≥ 3}

NOTE:

If non identical RC element are present in the feedback:

Then \({f_0} = \frac{1}{{2\pi \sqrt {{R_s}{R_p}{C_s}{C_p}} }}\;\)

For sustained oscillation

\(A \ge 1 + \frac{{{R_s}}}{{{R_p}}} + \frac{{{C_p}}}{{{C_s}}}\)

Explanation:

Wein bridge oscillator is the commonly used circuit for generating a sinusoidal waveform of the required frequency.

Wein bridge oscillator:

The circuit diagram of the Wein bridge oscillator is shown below:

• The Wein bridge oscillator uses two RC networks connected together to produce a sinusoidal oscillator.
• The Wein bridge oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance depending upon the circuit frequency
• At the resonant frequency, the phase shift is 00.

The feedback network consists of series and parallel connections of two RC networks that act as a lead-lag network in feedback.

Here Z_p and Z_s form a voltage divider and voltage across Zp will act as feedback voltage.

\(V_f=\frac{V_oZ_p}{Z_p+Z_s}\)

\(β=\frac{V_f}{V_o}=\frac{Z_p}{Z_p+Z_s}\)

On putting values of Z_p & Z_s, we will get the value of β as:

\(\beta=\frac{1}{3 \ + \ j(ω RC-\frac{1}{ω RC})}\)

Open-loop gain of the above circuit is:

\(A=1 \ + \ \frac{R_2}{R_1}\)

So loop gain will be:

\(Loop \ Gain=\frac{A}{3 \ + \ j(ω RC-\frac{1}{ω RC}) }\)

At ω = ω₀, the phase of loop gain must become zero and hence imaginary part should be zero.

\(\omega _o-\frac{1}{\omega_oRC}=0\)

\(\omega _0=\frac{1}{RC}\)

\(f _0=\frac{1}{2\pi RC}\)

Here f₀ is the frequency of oscillation.

Concept:

For sinusoidal oscillations to begin, the voltage gain of the Wien Bridge circuit must be equal to or greater than 3, i.e.

A_v ≥ 3.

For a non-inverting op-amp configuration, this value is set by the feedback resistor network and is given as:

\(\frac{V_{out}}{V_{in}}=1+\frac{R_2}{R_1}\) = 3 or more

Analysis:

For the given circuit, the voltage gain (non-inverting) will be:

\(\frac{V_{out}}{V_{in}}=1+\frac{R_2}{R_1}=1+\frac{1.9k}{1k}\)

\(\frac{V_{out}}{V_{in}}=2.9\)

Since the voltage gain is less than 3, sinusoidal oscillation cannot start.

Wien bridge oscillator:

A Wien bridge oscillator is an RC coupling amplifier that has good stability at resonant frequency f_o.

In this oscillator, Op-Amp acts as a Non-inverting amplifier which provides a zero phase shift.

Hence, the RC feedback network should also produce a zero phase shift at resonant frequency f_o.

So, the circuit behaves as an oscillator at f_o.

Feedbacks used in Wien bridge oscillator:

The Wien bridge oscillator uses both positive and negative feedbacks with one path each.

The path for positive feedback is through the Lag-lead circuit.

The path for negative feedback is used for voltage division. 

At frequency of oscillation the feedback factor is

\(\beta = \frac{R_2 C_1}{(R_1 C_1 + R_2 C_2 + R_2 C_1)}\)

\(\beta = \frac{100 \times 10^3 \times 0.5 \times 10^{-6}}{\left[ (2 \times 10^3 \times 0.5 \times 10^{-6} ) + (100 \times 10^3 \times 2 \times 10^{-9} + (100 \times 10^3 \times 0.5 \times 10^6)\right)]} \)

\(\beta = \frac{50}{1 + 0.2 + 50} = \frac{50}{51.2} = 0.976\)

Since in the circuit Positive feedback is present  and feedback element are series RC + Parallel RC so it is Wein Bridge Oscillator.

(a) Wein Bridge oscillator:

It is an audio frequency oscillator.

Its frequency of oscillation:

\({f_0} = \frac{1}{{2\pi }}\sqrt {RC} \)

→ for sustained oscillation R₂ ≥ 2 R₁        {A ≥ 3}

NOTE:

If non identical RC element are present in the feedback:

Then \({f_0} = \frac{1}{{2\pi \sqrt {{R_s}{R_p}{C_s}{C_p}} }}\;\)

For sustained oscillation

\(A \ge 1 + \frac{{{R_s}}}{{{R_p}}} + \frac{{{C_p}}}{{{C_s}}}\)