I've thought about designing an active first-order bandpass filter with variable center frequency and fixed bandwidth, using OpAmps, as a project for an Applied Electronics class. My first try was to use the following topology, fixing the capacitor values and changing the frequencies by varying the resistances. But to do this without changes in the bandwidth, the bandwidth's derivative in respect to R should be 0. It happens that the only solution to this equation is to have equal capacitances, what would lead to equal frequencies to both low and high-pass filters. Given this mathematical no-go, please give me some advice on how to proceed about this project idea.

Thank you.

EDIT: Thanks to the commenters, I've realised a fixed bandwidth wasn't really necessary for me, and using the State Variable Filter topology solved my problem.

I've thought about designing an active first-order bandpass filter with variable center frequency and fixed bandwidth, using OpAmps, as a project for an Applied Electronics class. My first try was to use the following topology, fixing the capacitor values and changing the frequencies by varying the resistances. But to do this without changes in the bandwidth, the bandwidth's derivative in respect to R should be 0. It happens that the only solution to this equation is to have equal capacitances, what would lead to equal frequencies to both low and high-pass filters. Given this mathematical no-go, please give me some advice on how to proceed about this project idea.

Thank you.

EDIT: Thanks to the commenters, I've realised a fixed bandwidth wasn't really necessary for me, and using the State Variable Filter topology solved my problem.

I've thought about designing an active first-order bandpass filter with variable center frequency and fixed bandwidth, using OpAmps, as a project for an Applied Electronics class. My first try was to use the following topology, fixing the capacitor values and changing the frequencies by varying the resistances. But to do this without changes in the bandwidth, the bandwidth's derivative in respect to R should be 0. It happens that the only solution to this equation is to have equal capacitances, what would lead to equal frequencies to both low and high-pass filters. Given this mathematical no-go, please give me some advice on how to proceed about this project idea.

Thank you.

I've thought about designing an active first-order bandpass filter with variable center frequency and fixed bandwidth, using OpAmps, as a project for an Applied Electronics class. My first try was to use the following topology, fixing the capacitor values and changing the frequencies by varying the resistances. But to do this without changes in the bandwidth, the bandwidth's derivative in respect to R should be 0. It happens that the only solution to this equation is to have equal capacitances, what would lead to equal frequencies to both low and high-pass filters. Given this mathematical no-go, please give me some advice on how to proceed about this project idea.

Thank you.

EDIT: Thanks to the commenters, I've realised a fixed bandwidth wasn't really necessary for me, and using the State Variable Filter topology solved my problem.