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# High Speed Digital Phase Detector

IP.com Disclosure Number: IPCOM000085045D
Original Publication Date: 1976-Feb-01
Included in the Prior Art Database: 2005-Mar-02
Document File: 3 page(s) / 41K

IBM

## Related People

Beraud, JP: AUTHOR

## Abstract

This circuit determines the phase of a sinusoidal signal at any instant of the cycle, by comparing the instantaneous values of the signal and its Hilbert transform.

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High Speed Digital Phase Detector

This circuit determines the phase of a sinusoidal signal at any instant of the cycle, by comparing the instantaneous values of the signal and its Hilbert transform.

The values of the signal X = A cos Omega t and its Hilbert transform X = A cos(Omega t - Pi/2) are sampled and digitized at the same time by not shown devices. The two digitized signals are fed to a logical device which detects and combines the signs of the two digital numbers, in a known manner, to determine the quadrant and supply two output binary signals Pi and Pi/2 defining the number of this quadrant.

In parallel with this operation, another logical device determines the absolute values of X and X and a comparator compares these absolute values. The result of this comparison is combined with the signal Pi/2 to determine the number of the half-quadrant in the quadrant. This number is represented by the output binary signal Pi/4.

Besides, absolute values 3X3 and 3X3 are fed to a multiplier-comparator through delay units (for example, shift registers). The purpose of the multiplier- comparator is to determine the value Alpha of the fractional half-quadrant part of the phase. It operates according to the following principles:

If K is the number of the half-quadrant defined by output signals Pi, Pi/2 and Pi/4, one may write: X = A cos Omega t = A cos(K Pi/4 + Alpha) = A cosx and X = A cos(Omega t - Pi/2) = A sin Omega t = A sinx with x = K Pi/4+ or Alpha = x - K Pi/4.

According to the value of K, either Alpha or Beta = Pi/4-Alpha = (K + 1)Pi/4-x is measured, by multiplying 3X3 or 3X3 by given values and comparing the products with 3X3 or 3X3. The choice between Alpha and Beta and their relations with 3X3 or 3X3 are given by the following rules.

1 Degree ) if K is even, Alpha is measured from A cos Alpha and A sin Alpha which are defined by the equations: cos Alpha = cosx cosK /4 + sinx sinK /4 from which A cos Alpha = X cosK Pi/4 + X sinK Pi/4 and sin Pi = sinx cosK Pi/4 - cosx sinK Pi/4 from which A sin Alpha = X cosK pi/4 - X sinK Pi/4 Consequently: - if K = 0 or 4, A cos Alpha = 3X3 and A sin

Alpha = 3X3 - if K ; 2 or 6, A cos Alpha = 3X3 and A sin Alpha = 3X3.

2 degrees) if K is odd, Beta is measured from A cos Beta and A sing which are defined by the equations: cos Beta = cos(K + 1) Pi/4 cosx + sin(K + 1)Pi/4 sinx from which A cos Beta = X cos(K + 1)Pi/4 + X sin(K + 1)Pi/4 and sin alpha = sin(K + 1)Pi/4 cosx - cos(K + 1)Pi/4 sinx from which A sin Beta = X sin(K + 1)Pi/4 - X cos(K + 1)Pi/4.

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