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A Sine Wave Generator

One type of signal that is in frequent demand is the sine wave. Of course, we could use an op amp in place of a transistor as the gain element in a Wien Bridge oscillator or a Twin-T oscillator, but they have a problem with requiring multiple capacitors and resistors in some odd configurations for setting the frequency of oscillation. Can we do something with analog integrators and inverters to obtain the same result?

The circuit to the right implements the mathematical relationship between the sine and cosine trigonometric functions. Mathematically, if you integrate a sine wave, you get an inverted cosine wave. Basically, it's the same waveform but shifted 90° in phase. Then, if you integrate that cosine wave, you get another 90° phase shift, producing a negative sine wave. Of course, each op amp integrator introduces an inversion as well, so the output of the first integrator is actually a non-inverted cosine wave. This is reversed again by the second integrator, so its output is still a negative sine wave. All we have to do is invert that negative sine wave to get our original sine wave back again. The circuit to the right accomplishes this.

In this circuit, R1 is adjusted to ensure that oscillations start and to help set the output amplitude. The Zener diodes serve to limit the output signal amplitude by limiting the gain of the cosine amplifier beyond the desired level. This prevents the circuit from amplifying the signal beyond its ±10 volt limits.

The clipping effect caused by the Zener diodes does introduce some distortion, but with a reasonable setting of R1 this effect is very slight, and the distortion it causes will be significantly reduced by the second integrator.

The oscillator circuit above is a classic, but does have its problems. Op amp offsets must be precisely balanced or they will accumulate on the two integrators and gradually damp out the oscillations. A better way is to redesign the circuit so that it will tend to balance its own offsets. Such a circuit is shown to the right.

This circuit lends itself nicely to a dual op amp such as the 1458. All three capacitors are the same, and R1 is made very slightly less than R to ensure that oscillations will start when power is applied. Under these conditions, the frequency of oscillation is f = 1/2πRC. The maximum frequency of this type is determined by the frequency response of the op amps you use. Loop gain will decrease as frequency increases, and oscillations cannot be sustained if the loop gain is less than 1.

Because the loop gain of this circuit must be greater than 1 to maintain oscillations, this circuit will also tend to clip the output waveforms. However, the same double-Zener clipping circuit can be applied to the cosine integrator, to limit the signal amplitude and prevent either op amp from saturating.

With both sine and cosine waves available, this circuit is sometimes known as a quadrature oscillator.

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