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ass5_f2011 - ECE 100 Lab 5 Design of an Oscillator Winter...

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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 “Wien-Bridge 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 Hewlett-Packard 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 = 1e-4; >> 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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ass5_f2011 - ECE 100 Lab 5 Design of an Oscillator Winter...

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