The circuit in Fig: How would you attenuate the passband gain by 6 decibels without adding another RC op-amp stage?

To attenuate the passband gain by 6 decibels in a circuit without adding another RC op-amp stage, you can follow these steps:

1. Break Down the Problem

   • Understand that a reduction of gain by 6 decibels corresponds to a linear gain factor.
   • The formula to convert decibels to a linear scale is given by: $\text{Gain} = 10^{\frac{\text{dB}}{20}}$
   • Therefore, to achieve a gain reduction of 6 dB, we need to calculate the linear gain factor.

2. Relevant Concepts

   • Calculate the linear gain for a target of -6 dB: $\text{Gain}_{\text{target}} = 10^{\frac{-6}{20}} = 10^{-0.3} \approx 0.5$

3. Analysis and Detail

   • To achieve a passband gain of approximately 0.5, you can use feedback or adjust the resistor values in the existing op-amp configuration. For instance:
     • Use a voltage divider at the input or feedback path.
     • Adjust the feedback resistor (R_f) or input resistor (R_in) such that the gain equation for an inverting or non-inverting op-amp configuration reflects the desired reduction.

4. Verify and Summarize

   • After modifying the resistor values to achieve the desired gain, verify that the total gain is indeed reduced to 0.5 by recalculating the circuit's gain based on the new resistor values.
   • Ensure the modifications maintain stability and functionality of the circuit.

Final Answer

To attenuate the passband gain by 6 dB without adding another RC op-amp stage, adjust the feedback or input resistor values in your circuit to achieve a gain of approximately 0.5.