Electrical – First-order analog active bandpass filter with variable center frequency

band passfrequencyoperational-amplifier

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.

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.

simulate this circuit – Schematic created using CircuitLab

The shown bandpass circuit (GIC bandpass) uses an active simulated inductor. The corresponding equations are:

R1=R, R5=R6, k2=R2/R1, k4=R4/R1, Co=C3=C

Midband gain: Ao=2

Midband frequency: wo=1/[RC*SQRT(k2k4)]

Quality factor: Q=1/[SQRT(k2k4)]=woRC

Because bandwidt BW=wo/Q=1/RC we can tune the frequency with k2 or k4 (single-element tuning) without changing the bandwidth BW.

As an alternative, we can tune the midfrequency wo by varying R1=R without touching the quality factor Q.