# Bandpass filter design (with op amps) capable of having different center frequencies

Discussion in 'Homework Help' started by Melawrghk, Sep 30, 2012.

1. ### Melawrghk Thread Starter New Member

Sep 9, 2010
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Hi all,

I need to design a bandpass filter using a Tow-Thomas biquad. The filter must work with center frequency at 1000Hz, and bandwidth of 100Hz.
Using a resistor and a switch, I must be able to shift the center frequency over to 1300Hz, but keep the bandwidth the same.

I can design them separately, but I can't seem to be able to find a resistor position that will allow for switch from one to the other.

This is the circuit: http://en.wikipedia.org/wiki/File:BiquadFilter1.PNG
I tried putting parallel resistors across R1, R3, R4. I also tried changing gain of the inverter at the end. I could try doing a feedforward variation, but that will give me a 2nd order transfer function in the numerator, which I don't need anyway (so I don't think it will work).

Any hints will be appreciated!

Apr 26, 2005
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3. ### Melawrghk Thread Starter New Member

Sep 9, 2010
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I don't see how that is helpful. Most of the links are already purple, because I have looked through it before posting here. I understand how to make a filter centered at one frequency using the biquad.

I need to make two center frequencies realizable with one circuit, an extra resistor and a switch.

4. ### JoeJester AAC Fanatic!

Apr 26, 2005
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Did they mention the two frequencies you need for center?

5. ### Melawrghk Thread Starter New Member

Sep 9, 2010
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Yes, this is mentioned in my original post. Nevertheless, I will reiterate:

Center frequencies: 1000Hz and 1300Hz. Bandwidth must stay the same at 100Hz.

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
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How tight a spec is there on any bandwidth changes - ±1% .... ±0.5% ...??

7. ### bountyhunter Well-Known Member

Sep 7, 2009
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In one of the references listed by Joe, it gives the frequency as a function of the resistors. You can "vary" one of the resistors just by connecting a second resistor around it and switching it into parallel. That should vary the center frequency. See below:

http://en.wikipedia.org/wiki/Electronic_filter_topology

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8. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Problem is that [as the link also indicates] the Q and hence bandwidth also change as either R2 or R4 are changed to vary the center frequency. The OP's question states that the bandwidth must remain the same at 100Hz. That's why I asked whether there was some "slack" on this requirement.

9. ### The Electrician AAC Fanatic!

Oct 9, 2007
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If we use the approximation for bandwidth, B = ωo/Q mentioned in the Wikipedia article, the bandwidth is given by B = 1/(R3*C1). Hence, changing R2 or R4 will change ωo, but if we don't change R3 or C1 the bandwidth won't change.

10. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Good point Electrician,

I thought I'd checked the ratio ω0/Q but messed up the math.

I did a simulation based on an ideal op amps. It works fine for changing only R2 say. The difference in B is very small within the limitation of picking the -3dB point on an output graph.

This should re-assure the OP it does work.

11. ### JoeJester AAC Fanatic!

Apr 26, 2005
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I did a simulation with E24 capacitors and E96 resistors and using OPA627E opamps. It indeed does work

Below is the graph ...

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