State Variable Oscillator

The major functional blocks necessary to design a general purpose audio oscillator, and give all the details of my current prototype. Implementation is in the mode of an analog computer, since the desired outputs are sine and cosine values as a function of time. The following snapshot shows my prototype connected to an X-Y oscilloscope, to display a Lissajous pattern.
State Variable Oscillator - schematic

The circle shown on the scope indicates a nearly perfect 90 degree phase shift between sine and cosine outputs. This quadrature relationship is maintained across the frequency range of the oscillator. I`ve always been fascinated by oscillators, because so many of my past breadboards oscillated but shouldn`t have. And even when I want a circuit to oscillate, it often seems to be out of control. I have found that a number of authors, including Bob Metzler 1 and Don Lancaster 2, identify the state variable oscillator as the circuit of choice for generating low distortion sine waves for audio use. These authors don`t show the details of how to implement such a circuit, but luckily one day while surfing the web I came across a reference to the article "Design for a Low-Distortion, Fast-Settling Source" in the August 1980 issue of the Hewlett-Packard Journal 3. That article describes the internal workings of the HP8903A Audio Measurement System, including sketch schematics. Based on this information, I have been able to develop the following analysis. The electronic circuit needed to satisfy this equation is a simple analog computer having two integrators and a summer, as shown in this simulation diagram. The integrator outputs are identified by the state variables x1 and x2. This circuit is paraphrased from an excellent application note 4 for the Burr-Brown UAF42 state variable filter. Pin numbers shown are for the UAF42, which...

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