# wienbr - c Copyright 2009. W. Marshall Leach, Jr.,...

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c ° Copyright 2009. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. Oscillators Conditions for Oscillations Figure 1 shows the block diagram of an ampli f er A ( s ) with a feedback network b ( s ) that can be connected from its output to its input by F ipping the switch from position A to position B. In position A, the switch connects the feedback network to a test signal source V t . The transfer function from V t to V o is V o V t = b ( s ) A ( s ) Let s = . Suppose there is some frequency at which V o /V t =1 6 0 . If the test signal source puts out a sine wave at this frequency, the ampli f er output will be a sine wave of the same amplitude and phase. If the switch is changed to position B, the signal input to the feedback network will not change. In this case the output signal from the ampli f er drives its input and the circuit is a stable oscillator. Figure 1: Block diagram of an oscillator. If | V o /V t | > 1 at the frequency for which 6 V o /V i =0 , the circuit will oscillate when the switch is closed and the amplitude of the output voltage will increase with time until the ampli f er overloads or clips. If | V o /V t | < 1 at the frequency for which 6 V o /V i =0 , the amplitude of the output voltage will decrease or damp out with time until the output becomes zero. Thus the condition for a stable output sine wave is the loop gain | V o /V t | must be unity at the frequency for which its phase is

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## wienbr - c Copyright 2009. W. Marshall Leach, Jr.,...

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