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I have set Tow-Thomas filter to get bandpass output. I want center frequency to be precise as much as possible. If there occurse center frequency shift in the lab, what are possible way to compensate this shift?

Tow Thomas Filter

If we take R2=R3=R=R4 and C1=C2=C,

Q = R1 / R , ω0 = 1/(RC) , H = -R1/R

where Q is quality factor, w0 is center angular frequency and H is center frequency gain.

I thought one possible compensation, to target a higher/lower frequency to get desired center frequency. But this is very cumbersome, since it requires to change at least 3 resistors.

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    \$\begingroup\$ First identify the cause of the frequency shift. Is it dependent on supply voltage, or temperature of some of the components? \$\endgroup\$ May 20, 2017 at 10:54
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    \$\begingroup\$ Temp and supply will affect GBW which in turn affects f as well as C. Use plastic or NPO caps only unless PTC Ceramic are needed \$\endgroup\$ Mar 12, 2018 at 13:55

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Your assumptions provide the answer.

If we take R2=R3=R=R4

But, of course, there is no need to do that. Specifically, you can make small changes to R2 to vary the center frequency without making appreciable changes to other characteristics. So, for instance, you might replace R2 with two resistors in series: a fixed R2a and a variable R2b. Setting R2a to 90% of R2, and r2b to 20% of R2 will allow an adjustment range of about +/- 5% around the nominal.

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For my opinion, there are two options:

(1) When the unwanted frequency shift is caused by (unavoidable) tolerances of the various PASSIVE parts, follow the recommendatins as mentioned by the experienced member WhatRoughBeast.

(2) When the error in the mid frequency is due to the finite GBW of the ACTVE blocks (because the desired center frequency is pretty high), you can (a) use other opamps (with higher GBW) or (b) compound opamp blocks (with active phase compensation) or (c) apply a specific tuning procedure (literature available) with the help of Spice-based simulation packages on the basis of good and detailed opamp models.

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Say if you want +-5% and say if R is 100K then you can switch between 95K and 105K .This will give you your extremes .I used alalog 4066 Cmos switch .Then I generated a PWM of about 50KHz with a simple LM393.Now my filter job was for power harmonic stuff so the bandpass center frequency was very low compared to the PWM clock frequency.My lashup filter could be tuned by my DC control volts that determined PWM duty cycle .Sure you could use a micro to make the required PWM nowdays.I measured the phase angle to tune up the filter at the center frequency by constructing a relatively orthodox analog Pll .This worked on a Biquad BPF meaning that you could do analog and not have to worry too much about componant tolerances while wanting good Q .

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