ECE 100
Lab 5
Design of an Oscillator
Winter 2011
We have given a good deal of thought to preventing circuits from oscillating, but, of course, there are times when
you want the circuit to oscillate. Such a circuit is the “WienBridge Oscillator”. It has been a popular oscillator in
the audio frequency range and is of historical interest because it was the first product developed and sold by the
HewlettPackard company.
The basic oscillator is sketched to the right. It is based on an amplifier with a
voltage gain K = 3, here shown implemented as a follower with gain. The
feedback is through the RC network shown where the two R’s and the two C’s
are the same.
1. System Level Design:
Show that the feedback factor B(s) = sRC/(1 + 3sRC + (sRC)
2
). The loop gain will be T(s) = K B(s) because the
feedback is to the positive input terminal. For this circuit the Nyquist plot is quite useful. You can do it with
Matlab as follows:
>> s=tf('s');
>> tau = 1e4;
>> t = 3*s*tau/(1+3*s*tau+(s*tau)^2);
>> nyquist(t)
You will see a beautiful circular trace that goes right through the –1 point twice, meaning there are two poles on
the
ω
axis. If K > 3 the poles are in the RHP and if K < 3 they are in the LHP. The resonant frequency is
ω
0
=
1/RC. To make a real oscillator we need K a bit greater than 3 so the oscillator will start up, but when it reaches
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 Spring '09
 Resonator, transient setup menu

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