Thus for a 2hz signal, the time delay experienced is 0. Now the output lags the input signal by 0. What this says is that constant phase delay does not equal constant time delay! Deriving the time delay from phase delay is dependent on the frequency itself. The only way for all frequencies to get delayed by the same time delay is if the phase response is linear. When the phase response is linear, we know all the frequencies get time delayed by the same amount.
Thus if all frequencies are delayed the same amount, we have this notion of a "group" delay. Group refers to all frequencies.
If we feed an input signal into a filter with a constant group delay, all frequencies will be time delayed the same amount. Referring to the picture below, the outputted signal matches the input signal except it is slightly delayed. If instead we fed that input signal into a filter with a non-constant group delay. The frequencies will time delay different amounts resulting in an output signal that looks nothing like the inputted signal.
So even though each filter is low-pass, one filter distorts the signal such that it doesn't resemble the inputted signal. This is why linear-phase constant group delay filters are desirable in some applications. Group delay is a useful measure of time distortion, and is calculated by differentiating, with respect to frequency, the phase response of the device under test DUT : the group delay is a measure of the slope of the phase response at any given frequency.
Variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. Mathematically, this means that the quasi-sinusoidal driving signal has the form.
This can be checked intuitively by looking at the transform pair of a delayed impulse, compare the time domain delay to the frequency domain phase. Sign up to join this community.
The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What is meant by "Group delay"? Ask Question. Asked 1 year, 7 months ago. Active 5 months ago. Viewed times. Using front-panel hardkey [softkey] buttons. Press Avg. Group Delay Aperture dialog box help. Although the Group Delay Aperture is defined as the difference in frequency between two data points see What Is Aperture?
The number of adjacent data points can be set using any of the following methods:. Learn how. Points Number of adjacent data points to average. Default setting is 11 points. Choose a value between 2 and the current number of points in the channel. Percent of Span The data points within this percentage of the current frequency span are averaged. The span must contain at least two data points. Frequency The data points within this frequency range are averaged.
The frequency range must contain at least two data points. When the frequency span or number of points is reduced so that the current Group Delay Aperture is NOT attainable, the Aperture is adjusted to the new frequency span or number of points.
OK Applies setting changes and closes the dialog box. Cancel Closes the dialog. Setting changes are NOT applied. Otherwise, incorrect phase and delay information may result. Undersampling may occur when measuring devices with long electrical length.
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. Set the source power to be in the linear region of the amplifier's output response, typically 10 dB below the 1 dB compression point.
Unfortunately, there is no free beer in electronics. A Bessel filter has a maximally flat group delay, but has a very smooth transfer curve. Its frequency cut-off region is not as steep as a Chebyshev filter or even a Butterworth filter. All that said, using the online rf-tools. Compare Figure 6 with Figure 3 and you will clearly see the difference. However, there is—as expected—substantial improvement in the group delay Figure 7. In the full passband of the filter, this group delay stays between 0.
Do you want to see the behavior of such a Bessel filter in the time domain? I ran the same Spice simulation again, but this time using the LC values of the Bessel filter. The result is shown in Figure 8. Compare the input signals in green and output signals in red at kHz and kHz, respectively. If you look closely, you will see that the delays on the signal envelopes are similar. This is clearly visible on the right of the two plots.
And if you examine what happens when the sum of these two bursts passes through such a filter Figure 8, right plots , you will see that the waveforms are nearly not distorted. The shape of the signal is unchanged. Now comes the fun part. Rather, it is a measure of the time delay between the input and output signal envelopes. In fact, a group delay can be negative!
I told you that the group delay is positive when the slope of the phase is negative, meaning the phase shift is decreasing when the frequency is increasing. Could this group delay be negative if the phase slope were the other way around?
Moreover, could this actually happen with real circuits? The answer to both questions is affirmative. I found a good and simple example on the Applied Radio Labs website [2], and reproduced it using my Proteus circuit simulator.
Once again, you can use the free LTspice instead if you prefer. As shown in Figure 9 , the circuit is simply three components in parallel: L, C and R—connected between the signal and the ground. This configuration makes a notch filter also called a rejection filter. As shown on the left plot in Figure 9, it attenuates any signal around MHz. Now look at the phase response in red. It is decreasing before and after the rejection region, but is increasing close to MHz.
Therefore, the slope of the phase shift is positive for such a frequency, and the group delay must be negative. Of course, I ran a time-domain simulation for you, with a MHz bursted sine applied on the input. The result is shown on the right plot of Figure 9. Look at the input green and output red curves. The maximum amplitude of the output is actually before the maximum amplitude of the input!
This is just an illusion of a time advance. The illusion would disappear if the signal were not a burst of sine and contained an unpredictable event.
Such an event would appear on the output after its application to the input. So why does such a circuit seem to predict the future? In fact, because the circuit is a notch filter, it resonates at MHz and strongly attenuates a MHz signal. However, this attenuation takes some time to occur because the L and C must be energized.
In any case, the measured group delay is indeed negative! WRAPPING UP Group delay may not be the easiest concept to understand, but for many system designs, creating a filter without taking into account its phase behavior may not be a good idea.
I hope you grasped the concept. Launch LTspice and reproduce my examples. Then modify the circuit and check the phase and group delay behavior. After that, try switching on your soldering iron and reproduce the same thing using actual circuits.
You will learn a lot, and you will likely have lot of fun! Or, maybe you would like to give me some feedback. For example, did you prefer my articles on wireless, on strange behavior of passive circuits, on signal processing or on EMC? Email me at rlacoste alciom. References: [1] www.
Group delay, by Christopher J. Analog Devices www. Written by Robert Lacoste.
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