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Sine-Cosine Waveform Generator Circuit

Last Updated on July 21, 2020 by Swagatam 2 Comments

The circuit discussed below is designed to generate precision sine and cosine waveforms, which are perfectly identical with their dimensions, but are 90° out of phase.

Table of Contents
  • How the Circuit Works

There are a variety of applications which often demand a couple of sinewave frequencies which are of the identical frequency, but 90° out of phase.

Simply put, a sine signal and a cosine signal together from a single package.

This kind of signals are widely-used in SSB and quadrature modulation, electronic systems of circles and ellipses and conversions involving rectilinear and polar coordinates.

Sine and cosine signals could be acquired from a quadrature oscillator that includes a couple of integrators configured as demonstrated in the diagram.

In the shown diagram, A1 is wired like a non-inverting integrator, while A2 is rigged in the form of an inverting integrator.

How the Circuit Works

The reason why this circuit would generate a sine and cosine signal might not be quickly evident, nevertheless can be easily described.

At output B shows up a signal that is a function of time, f(t). Since this is, minus the integral of the signal at A, it is very clear that the signal at A is, minus the differential of the signal at B, that is - df / dt.

In the same manner, the input signal at the integrator A, that is - d2 f / dt2

However, we also find that the signal at the input of A1 is also the output signal of A2.

Therefore, - d2 f / dt2 = f(t)

These conditions are fulfilled through the sine-cosine signals, because if

f(t) = sin ω t (output B)

d(sin ω t) /dt = cos ω t (output A)

d(cos ω t) /dt = d2(sin ω t) / dt2 = -sin ω t = -f(t)

Output A as a result generates a cosine signal and output B a sine signal. P1 can be used to alter the loop gain of the circuit to ensure that it oscillates without any issues or errors.

In case, may be on account of part tolerances, the circuit fails to oscillate at a set adjustment of P1, you may need to to increase its value to 10 k.

D1, D2 and R4 to R7 are used to stabilize the amplitude of the signal. The sine-cosine frequency rate could be modified by replacing other desired values of capacitor for C1 to C3, by evaluating them through the explained formulas.

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Filed Under: Oscillator Circuits Tagged With: Cosine, Generator, Sine, Waveform

About Swagatam

I am an electronics engineer and doing practical hands-on work from more than 15 years now. Building real circuits, testing them and also making PCB layouts by myself. I really love doing all these things like inventing something new, designing electronics and also helping other people like hobby guys who want to make their own cool circuits at home.

And that is the main reason why I started this website homemade-circuits.com, to share different types of circuit ideas..

If you are having any kind of doubt or question related to circuits then just write down your question in the comment box below, I am like always checking, so I guarantee I will reply you for sure!

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Reader Interactions

Comments

  1. Jesse Lu says

    November 7, 2024 at 11:00 pm

    Hi, I try to use this circuit for emulating the sin-cosine encoder signal output. But I need both +SINE, -SINE, +COSINE, and Negative COSINE. What is the easiest way to generate the -SINE, and – COSINE signal from this SINE/COSINE generator?
    Thanks

    Reply
    • Swagatam says

      November 8, 2024 at 8:58 am

      Hey, I think you can try measuring the signal across the Sine/Cosine outputs and the (+) supply and the (-) supply separately, to get the required +/- results.

      Reply

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