If the Wein Bridge Oscillator based on op-amp is tuned at 1KHz, what is the op-amp gain?

1. Break Down the Problem

To determine the op-amp gain for a Wien Bridge Oscillator set to 1 kHz, we need to analyze the oscillator's circuit and its frequency equation.

2. Relevant Concepts

The frequency of a Wien Bridge Oscillator is given by the formula:

$f = \frac{1}{2\pi R \sqrt{C_1 C_2}}$

Where:

• $f$ is the frequency (1 kHz),
• $R$ is the resistance in the circuit,
• $C_1$ and $C_2$ are the capacitors used.

Additionally, for oscillation to occur, the condition for gain $(A)$ in a Wien Bridge Oscillator is:

$A = 3$

3. Analysis and Detail

1. Assign the frequency $f = 1\, \text{kHz} = 1000\, \text{Hz}$.
2. Rearrange the frequency equation to find R, assuming $C_1$ and $C_2$ are equal (let's assume $C_1 = C_2 = C$): $1000 = \frac{1}{2\pi R \sqrt{C^2}} \Rightarrow R = \frac{1}{2\pi \times 1000 \times C}$
3. Knowing that the gain required for a Wien Bridge Oscillator is $A = 3$, this indicates the configuration's necessary gain condition.

4. Verify and Summarize

For the Wien Bridge Oscillator to function at the desired frequency of 1 kHz, the op-amp gain must be set to 3. The choice of resistances and capacitances must be adjusted accordingly to maintain this frequency and gain relationship.

Final Answer

The op-amp gain for the Wien Bridge Oscillator tuned at 1 kHz is $A = 3$.