Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm currently busy with a 'small' project of translating an analog device (synthesizer, based on schematics) into a digital counterpart.

What I do is basically simulate the device using a SPICE model. Then I look at the outputs, and see if can fit some equation on it.

Based on the mathematical approximation of the circuit's behaviour, I implement an algorithm/DSP that shows the same behaviour as the analog version.

Now I've come to a small problem.

The circuit shows something that is a 2nd order active high pass filter. In my SPICE model, I did an AC simulation to get the frequency response of this filter (gain), and the phase response.

The next step was to find the transfer function for the filter. Well, that step already takes a week, so that's why this forum is my last resort, where I would like to show the problem. And hopefully someone has an answer.

Okay, the problem is as follows:

I use a standard transfer function for a 2nd order high pass filter:

[tex]H(s) = \frac{s^2}{s^2 + \omega_0/Q s + \omega_0^2}[/tex]

The following values give a perfect fit for the frequency response (ie gain, [tex]|H(s)|[/tex])

[tex]\omega_0 = 228.711[/tex]

[tex]Q = 1.58195[/tex]

look!

(freq_gain.png)

But when you look at the phase response, there is no fit at all:

(freq_phase.png)

(the phase jumps 360 degrees at 51.5 Hz)

So apparently, the transfer function is wrong or incomplete. Now my question is: how should the transfer function look like, to make sure both the measured frequency response and the measured phase response are perfectly captured in the equation?

For your reference, here is the schematic that was simulated:

(hpf.png)

Thank you in advance for your help!

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# Incomplete transfer function for phase response

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