# High Speed Digital Phase Detector

Original Publication Date: 1976-Feb-01

Included in the Prior Art Database: 2005-Mar-02

## Publishing Venue

IBM

## Related People

## 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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__Page 1 of 3__**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 ^{3}X^{3} and ^{3}X^{3} 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 ^{3}X^{3} or ^{3}X^{3} by given values and comparing the
products with ^{3}X^{3} or ^{3}X^{3}. The choice between Alpha and Beta and their relations
with ^{3}X^{3} or ^{3}X^{3} 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 = ^{3}X^{3} and A sin

Alpha = ^{3}X^{3} - if K ; 2 or 6, A cos Alpha = ^{3}X^{3}
and A sin Alpha = ^{3}X^{3}.

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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