# Group Delay

Group delay is a measure of phase distortion. Group delay is the actual transit time of a signal through a device under test as a function of frequency. When specifying group delay, it is important to specify the aperture used for the measurement.

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What Is Group Delay?

Group delay is:

• A measure of device phase distortion.
• The transit time of a signal through a device, versus frequency.

• The derivative of the device's phase characteristic with respect to frequency.

Refer to the graphic below for the following discussion: The phase characteristic of a device typically consists of both linear and higher order (deviations from linear) phase-shift components.

 Linear phase-shift component: Higher-order phase-shift component: Represents average signal transit time. Represents variations in transit time for different frequencies. Attributed to electrical length of test device. Source of signal distortion.

Refer to the graphic below for the following discussion: In a group delay measurement:

• The linear phase shift component is converted to a constant value (representing the average delay).

• The higher order phase shift component is transformed into deviations from constant group delay (or group delay ripple).

• The deviations in group delay cause signal distortion, just as deviations from linear phase cause distortion.

• The measurement trace depicts the amount of time it takes for each frequency to travel through the device under test.

Refer to the following equation for this discussion on how the analyzer computes group delay: • Phase data is used to find the phase change (-df).

• A specified frequency aperture is used to find the frequency change  (dw).

• Using the two values above, an approximation is calculated for the rate of change of phase with frequency.

• This  approximation represents group delay in seconds (assuming linear phase change over the specified frequency aperture).

Group Delay versus Deviation from Linear Phase

Group delay is often a more accurate indication of phase distortion than Deviation from Linear Phase.

Deviation from linear phase results are shown in the upper region of the following graphic: Device 1 and device 2 have same value, despite different appearances. Group Delay results are shown in the lower region:
Device 1 and device 2 have different values of group delay. This is because in determining group delay, the analyzer calculates slope of phase ripple, which is dependent on number of ripples which occur per unit of frequency.

What Is Aperture?

During a group delay measurement, the analyzer measures the phase at two closely spaced frequencies and then computes the phase slope. The frequency interval (frequency delta) between the two phase measurement points is called the aperture. Changing the aperture can result in different values of group delay. The computed slope (delta phase) varies as the aperture is increased. This is why when you are comparing group delay data, you must know the aperture that was used to make the measurements.

Refer to the graphic below for the following discussion: Narrow aperture: Wide aperture: Provides more fine detail in phase linearity. Provides less fine detail in phase linearity because some phase response averaged-out or not measured. Makes measurement susceptible to noise (smaller signal-to-noise ratio) and analyzer phase detector resolution. Makes measurement less susceptible to noise (larger signal-to-noise ratio).

The analyzer's default setting for group delay aperture is the frequency span divided by the number of points across the display. There are two ways to set the aperture to a different value.

1. Adjust the number of measurement points or the frequency span.

• Increasing the number of points or reducing the frequency span narrows the aperture.

• Decreasing the number of points and/or increasing the frequency span widens the aperture.

Note: if the aperture is too wide (more than 180° of phase shift between adjacent frequency points), errors in group delay data will occur.

1. Use the analyzer's smoothing function.

• Performs a single-sweep, moving average of adjacent data-points over a specified percentage of the frequency span.

• Results in an action similar to changing the frequency interval between points.

• Allows a wider aperture because greater than 180º of phase shift can occur over the smoothing aperture.

Group delay measurements can be made on the following sweep types:

• Linear frequency

• List frequency sweep segment

The group delay aperture varies depending on the frequency spacing and point density, therefore the aperture is not constant in segment sweep. In segment sweep, extra frequency points can be defined to ensure the desired aperture.

Accuracy Considerations

It is important to keep the phase difference between two adjacent measurement points less than 180° (see the following graphic). Otherwise, incorrect phase and delay information may result. Undersampling may occur when measuring devices with long electrical length. You can verify that the phase difference measured between two adjacent points is less than 180° by adjusting the following settings until the measurement trace no longer changes:

Electrical delay may also be used to compensate for this effect. The frequency response is the dominant error in a group delay test setup. Performing a thru-response measurement calibration significantly reduces this error. For greater accuracy, perform a 2-port measurement calibration.

Particularly for an amplifier, the response may vary differently at various temperatures. The tests should be done when the amplifier is at the desired operating temperature.

How to Measure Group Delay

1. Preset the analyzer.

2. If your device under test is an amplifier, it may be necessary to adjust the analyzer's source power:

• Set the analyzer's source power to be in the linear region of the amplifier's output response (typically 10-dB below the 1-dB compression point).

• Select an external attenuator (if needed) so the amplifier's output power will be sufficiently attenuated to avoid causing receiver compression or damage to the analyzer's port 2.

3. Connect the device under test as shown in the following graphic. 1. Select an S21 measurement.

2. Select the settings for your device under test, including the following:

• number of measurement points: maximum

• format: delay

• scale: autoscale

3. Remove the device under test and perform a measurement calibration.

4. Reconnect the device under test.

5. Scale the displayed measurement for optimum viewing.

6. Use the analyzer's smoothing feature to increase the aperture, reducing noise on the trace while maintaining meaningful detail. To increase the aperture:

• Switch on the analyzer's smoothing feature.

• Vary the smoothing aperture (up to 25% of the span swept).

7. Use the markers to measure group delay (expressed in seconds) at a particular frequency of interest.

8. Print the data or save it to a disk. 