# Analysis of a Digitally Controlled Wien Bridge Oscillator

Posted on Feb 6, 2014

It uses standard components, gives a good sine wave and is fairly immune to the type of op ampit is designed around. It can, however, be misunderstood, and over simplifications as to its operation can leave the designer thinking that it is not as well trained as originally thought. In pursuit of gaining an understanding of our trusty friend, it is wise to go back to basics.

The circuit of a standard Wien Bridge oscillator is shown in Figure 1. A circuit will oscillate if, at a given frequency, it has greater than unity gain and zero phase shift from input, through the device, through the feedback network and back to the input. Looking at the circuit in Figure 1, R1 and C1 produce a positive phase shifted current with respect to the output voltage. When this current meets R2 and C2, these components produce a voltage that is phase shifted in a negative direction. At one frequency the phase shift caused by R1 and C1 will be offset by an equal and opposite phase shift caused by R2 and C2 and the net phase shift will be zero. The circuit is now in danger of oscillating. For the mathematically inclined, the transfer function of the network made up by R1, C1, R2, C2 can be considered. Since the output impedance of the op amp will be low and the input impedance of the inputs very high, it is relatively straightforward to derive the transfer function of the Wien Network (the resistive divider made up of R1 and C1 on the top and R2 and C2 on the bottom). One strong cup of coffee and a rainy Sunday afternoon yields the transfer function as: Put simply (if this is possible) the imaginary `j` terms represent a 90 ° phase shift in the transfer function (either positive or negative). The real, non `j` terms represent zero phase shift in the transfer function. As the magnitude-of the real and imaginary...

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