# Interpolating data of a bandpass filter with Q=10.4

1. Apr 28, 2017

### Gianmarco

Hello everyone.
I'm trying to interpolate the data taken (frequency in Hz vs A in dB) from a bandpass filter with Q = 10.4.
The problem is that I'm not entirely sure about the transfer function that I should use to interpolate it. I'm trying to extrapolate the peak frequency, Q factor and amplification A at the peak. I've attached the data (the first column has frequencies and the 3rd has Vo/Vi in dB, the remaining columns are errors) and a plot of it. If anyone has any idea, I'd be very grateful cause I've been up all night trying all sorts of transfer functions but none seems to get even close. Thanks in advance

#### Attached Files:

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• ###### BP10.txt
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2. Apr 28, 2017

### tech99

Looks like a simple LC resonant circuit. So, if it is a parallel LC circuit connected across the line, at frequencies well away from resonance the response will fall at 6dB per octave, as it looks like a single L or C.

3. Apr 28, 2017

### Gianmarco

Hey tech, thank you for answering :) I was in a hurry so I didn't have time to post the circuit, I'll attach a picture of it. It's a universal second order filter, and I'm taking the output at the BP exit. I'm looking for an analytical expression of the band pass filter so that I can extrapolate the peak frequency f0 and the Q factor. My book says it should be $$T(s)=\frac{a_1s}{s^2 + \frac{f_0}{Q}s + f_0^2}$$ but I'm not sure about what this a1 term is or even if I should set s=f/f0 or just s=f when I fit the data.

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