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# Best Fit Synchronizing

IP.com Disclosure Number: IPCOM000083002D
Original Publication Date: 1975-Mar-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 44K

IBM

Grant, P: AUTHOR

## Abstract

This method is directed to achieving a best fit between a sine wave and another periodic wave, by finding the fundamental of the second wave by a waveform subtraction operation. The approach used is that best fit can be described as equating the error (difference) between wave shapes in the first quadrant to the error in the second quadrant, or, for faster and more accurate results, equating the first and third quadrant errors to the second and fourth. The illustrated circuit employs the full four-quadrant version of the method.

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Best Fit Synchronizing

This method is directed to achieving a best fit between a sine wave and another periodic wave, by finding the fundamental of the second wave by a waveform subtraction operation. The approach used is that best fit can be described as equating the error (difference) between wave shapes in the first quadrant to the error in the second quadrant, or, for faster and more accurate results, equating the first and third quadrant errors to the second and fourth. The illustrated circuit employs the full four-quadrant version of the method.

Assume that the distorted waveform input 6 (theta) is a sawtooth (Fig. 1) and f (theta) is a sine wave. In this example, the zero crossings of g (theta) are the same as fundamental g' (theta). If f (theta) = g' (theta) and is subtracted from g (theta) as illustrated in Fig. 2a, the error signal g (theta) - g (theta) is as illustrated in Fig. 2b.

Utilizing the circuit of Fig. 3, this subtraction operation is carried out by A1. The first and third quadrants of the resultant error signal are passed by gate S1 and then are added in an integrator I1. Similarly, the second and fourth quadrants are passed by S2 and added in the other integrator I2. S1 and S2 are analog switches (FET's) biased by the logic quadrant signals out of the voltage- controlled oscillator (VCO). When f (theta) is in phase with g' (theta), I1 = - I2 so that the output of A2 is zero.

Ideally, the oscillator control voltage between A2 and the VCO shou...