# Designing an RLC circuit from a given transfer function.

1. Oct 12, 2009

### MonsterAar

Designing a circuit from a given transfer function.

I hope you don't mind that I haven't used the default format. It doesn't lend itself well to my problem.

The original problem is as follows:
We were given a 'black box' that contained a passive circuit and we experimentally determined a transfer function for the circuit by passing through various frequencies and recording the magnitude and phase of the outputs.

This was then used to create a bode plot. This bode plot showed a pole at approximately 56Hz and a zero at approximately 1660Hz. The DC gain of the circuit is 0.064.

From this information I deduced the transfer function of the circuit to be:
$$H(\omega)=0.064\frac{1+j\frac{\omega}{1660}}{1+j\frac{\omega}{56}}$$

The task now asks for us to design a circuit to cancel out the effects of the black box on the input signal. Basically we have to design a circuit so that when we have input-blackbox-our circuit-output, the input=output. So, I need to design a circuit with the inverse of the above transfer function.

IE. I need to design a circuit with the following transfer function:
$$H(\omega)=15.625\frac{1+j\frac{\omega}{56}}{1+j\frac{\omega}{1660}}$$

This is where I get stuck. How do I go about designing a circuit with a DC gain of 15.625, a pole at 1660Hz and a zero at 56Hz?
I understand I'll have to use an op-amp to get the DC gain greater than 1. Other than this I'm stuck.

Thanks,
Luke

Last edited: Oct 12, 2009
2. Oct 14, 2009

### CEL

Consider a voltage divider composed of two resistors and a capacitor in series. The input voltage acts on all three components and the output voltage is taken on the series of the capacitor and one of the resistors.
What is the transfer function of this circuit?