Wien network analysis

by Cor van Rij

The Wien network is a highly useful network that can be used in many places in the analogue electronics. It is used to create selective bandpass filters and selective notch filters. But probably the most well known application is the use of this network in the so-called Wien sinus oscillator.

In the network on the left, the well-known Wien network is shown. The impedance of the resistor is and of the condenser is and where .

This circuit can be simplified to the circuit on the right. In this network Z1 is the sum of R and Zc


And where impedance of Z2 equals to the parallel resistance of R and Zc.

This can be simplified to:


The output voltage of this circuit is equal to:


If we now fill in the values for Z1 and Z2 as found in (1) and (2) and we simplify the formula:

And finally we get the well known formula for the transfer function of the Wien network:


Now, if we assume that: we get:

Thus at we see that the attenuation of the Wien network is 1/3 and there is no phase-shift at all. So, we can conclude that the center frequency of the Wien Network is equal to:
which is the well-known formula for the Wien network.