Group Delay Principles

For many networks, the amount of insertion phase is not as important as the linearity of the phase shift over a range of frequencies The analyzer can measure this linearity and express it in two different ways: directly, as deviation from linear phase, or as group delay, a derived value.

Group delay is the measurement of signal transmission time through a test device. It is dehned as the derivative of the phase characteristic with respect to frequency. Since the derivative is basically the instantaneous slope (or rate of change of phase with respect to frequency), a perfectly linear phase shift results in a constant slope, and therefore a constant group delay (see Figure 6-19).

pg6182_C

Figure 6-19. Constant Group Delay

Note, however, that the phase characteristic typically consists of both linear and higher order (deviations from linear) components The linear component can be attributed to the electrical length of the test device, and represents the average signal transit time. The higher order components are interpreted as variations in transit time for different frequencies, and represent a source of signal distortion (see Figure 6-20).

4Frequency

Group Delay = T g= 2

$ in Radians

w in Radians/Set

-1 d@ $ in Degrees = -.-

360” d f f inHz(w=2rcf)

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Figure 6-20. Higher Order Phase Shift

The analyzer computes group delay from the phase slope. Phase data is used to find the phase change, AC& over a specified frequency aperture, Af, to obtain an approximation for the rate of change of phase with frequency (see Figure 6-21). This value, ~z, represents the group delay in seconds ass- linear phase change over Af. It is important that A+ be 5 180”, or errors will

6-38 Application and Operation Concepts