In the RC Phase shift oscillator using op-amp, what is the value of the op-amp feedback resistance (Rf), if R1 = 1K Ohm?

1. Break Down the Problem

To find the value of the op-amp feedback resistance ($R_f$) in an RC phase shift oscillator, we need to understand how the oscillator works and the relationships between its components.

2. Relevant Concepts

In a typical RC phase shift oscillator using an op-amp, the feedback resistance is directly related to the input resistor ($R_1$). The relationship can be expressed with the formula that typically applies to the oscillator's gain and feedback resistor configuration. The gain of the amplifier at the oscillation condition must equal 1.

3. Analysis and Detail

For a phase shift oscillator, the formula for the gain ($A$) at the frequency of oscillation is given by:

$A = \frac{R_f}{R_1} + 1$

Where:

• $A$ is the gain,
• $R_f$ is the feedback resistance,
• $R_1$ is the input resistor.

For an oscillator, we need $A = 3$ to overcome the losses in the RC network. Therefore:

$3 = \frac{R_f}{R_1} + 1$

Subtracting 1 from both sides gives:

$2 = \frac{R_f}{R_1}$

Multiplying both sides by $R_1$:

$R_f = 2 \cdot R_1$

Given that $R_1 = 1K \, \Omega$:

$R_f = 2 \cdot 1K \, \Omega$

Calculating gives:

$R_f = 2K \, \Omega$

4. Verify and Summarize

The calculations affirm that with $R_1 = 1K \, \Omega$, the feedback resistance $R_f$ required for the RC phase shift oscillator is $2K \, \Omega$.

Final Answer

The value of the op-amp feedback resistance ($R_f$) is $2K \, \Omega$.