Quick and Easy 90 Degrees Phase Shifter

by DSPStore Staff

A number of signal processing applications require the use of quadrature processing techniques, that is, where quadrature waveforms (those which differ by a constant 90° phase shift) are required. A wideband 90° phase shift with constant gain is very difficult to realize in any technology. Usually there has to be a compromise between phase accuracy and gain accuracy, with some techniques providing perfect phase quadrature but poor amplitude matching, and others giving accurate gain but imperfect phase. The method presented here uses the Hilbert transform which, when applied to a band- limited signal, generates the exact quadrature of the waveform (i.e. all components are phase shifted by 90°).

In any practical implementation of the transform, the lower the frequency content of the waveform, the greater the difficulty in realizing an accurate quadrature replica.

Digital implementation of the Hilbert transform is achieved most readily using finite impulse response (FIR) filtering techniques. A simple MATLAB routine is given below which will generate a Hilbert FIR filter (ht).

These filters have the characteristic of providing an exact 90° phase shift over the entire filter bandwidth, but with a non-constant gain characteristic, the gain accuracy (usually specified as a passband ripple in dB) being determined by the number of stages (taps) used to implement the filter.

The filter output is in quadrature with the delayed input signal, the required delay corresponding to the filter delay given by the formula:

DELAY = (N - 1)/2 samples

The delayed input signal is easily obtained by selecting the appropriate delayed filter input sample. As the filter is linear phase, the delay across the band is constant, see the phase plots shown in figure 1. for the Hilbert filter output and the Delay output.