Dimension an active 4th order bandpass filter with complex poles f1=4 kHz and f2=6 kHz with Q1=1 and Q2=1.7. How would you adjust the passband gain?

Designing a 4th order bandpass filter with complex poles involves several steps. Here's a step-by-step guide:

1. Identify the filter type: The filter is a 4th order bandpass filter. This means it will have two stages, each stage contributing a 2nd order response.

2. Identify the pole frequencies: The pole frequencies are given as f1=4 kHz and f2=6 kHz. These are the -3dB cut-off frequencies of the filter.

3. Identify the Quality factors: The quality factors are given as Q1=1 and Q2=1.7. These values determine the sharpness of the resonance at the pole frequencies.

4. Calculate the component values: The component values for the filter can be calculated using the pole frequencies and quality factors. The standard formulas for a 2nd order active bandpass filter can be used. These formulas involve the resistances and capacitances of the filter circuit, and they depend on the chosen filter topology (Sallen-Key, Multiple Feedback, etc.).

5. Adjust the passband gain: The passband gain of the filter can be adjusted by changing the feedback resistance in the filter circuit. The gain in dB can be calculated as 20*log10(Rf/R1), where Rf is the feedback resistance and R1 is the resistance in the input path. To increase the gain, Rf can be increased or R1 can be decreased. To decrease the gain, Rf can be decreased or R1 can be increased.

Please note that this is a general guide and the actual design process may vary depending on the specific filter topology and component values.