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# Group delay

Updated July 6, 2011

Here's the index to our ever-expanding content on group delay:

Group delay - what is it?

Group delay rule of thumb

Group delay flatness and consistency

Group delay data smoothing (separate page)

Dispersion (separate page)

Group delay in waveguide structures (separate page)

Group delay in filters (separate page)

Measuring group delay (separate page)

Simulating group delay using Agilent's ADS (separate page)

Extracting dielectric properties from group delay (new for August 2010!)

Time delay units (TDUs) (new for January 2011!)

Want a spreadsheet for calculating group delay from S-parameters? Go to our download area, and get our S-Parameter Utilities spreadsheet! It even smooths noisy phase data!

### Group delay - what is it?

Group delay is defined as the rate of change of transmission phase angle with respect to frequency. The units work out to time when the angle is in radians and frequency is in radians/time (seconds, nanosecond, picosecond or whatever is convenient, depending on the length of the path). When group delay is extracted from S-parameters, unless the network is a perfect measurement of a perfect transmission line, there will be variations over frequency. But within a small amount of bandwidth, group delay is usually nearly constant. Thanks to Martin, for keeping us on out toes!

Martin further wishes to point out that group delay can actually can be negative (in some rare occasions).

Group delay can be construed as a measurement of how long it takes a signal to traverse a network, or its transit time. It is a proportional to the length of the network, and usually a weak function of frequency. In this sense, we at Microwaves101 show you how top use group delay to extract dielectric material properties.

In considering group delay, remember that in free space all electromagnetic signals travel at the speed of light, "c", which is approximately 3x108 meters per second.

A very good rule of thumb that you should tattoo on your arm if you can't remember it is that E-M radiation travels one foot in one nanosecond, unless there is something to slow it down (a dielectric). A more exact value is 0.983571 feet per nanosecond in free space.

You should know that the speed of light is exactly equal to 1/()^0.5, where is the permittivity of the medium, and is its permeability. While the one-nanosecond-per-foot rule works for free space , what about coax cables? The group velocity is reduced in coax by 1/sqrt(R). Most coax cables use 100% PTFE filling, which has a dielectric constant of about 2.2 This works out to a group delay of 1.45 nanoseconds for one foot of solid PTFE coax. Keep in mind that some flexible cables use PTFE that is partially filled with air; these cables provide group delay on the order of 1.3 to 1.4 nanoseconds per foot.

See our separate page on group delay in waveguide structures.

Group delay in microwave filters is another great topic, you can find more info here (thanks, Cheryl!) Filters end up contributing a lot of delay to microwave circuits, even though they are often physically very compact. Remember that the higher the filter order and the tighter the bandwidth requirements, the more group delay a filter introduces.

### Group delay flatness and consistency

Flat and consistent group delay (versus frequency) is important in radar systems. With radar we are trying to measure distances accurately using electromagnetic energy. The frequency content of a radar pulse is complex and can span one GHz of bandwidth or more. When we process the pulse, we'd like to know that it's spectrum will be treated the same over the intended bandwidth of frequencies, otherwise distortion will render radar range measurements inaccurate. Inductors, capacitors, transistors, amplifiers, transformers, etc. can all contribute to eroding the group delay flatness of a network.

Group delay consistency (unit-to-unit, over temperature, over frequency, over attenuation state) is extremely important in receivers such as monopulse, where amplitude and phase tracking is required to achieve good null depths. OK, we haven't dealt with the topic of monopulse systems, be patient and we'll get to that later!

The group delay of TEM transmission lines is very well behaved, and flat with frequency. Group delay flatness can be an issue in waveguide, especially near the lower cutoff frequency. The group delay of microwave filters is another story altogether. The group delay in a tiny edge-coupled filter can be the longest delay in a microwave receiver. It often produces the most variation in group delay from unit-to-unit, and across frequency.

Group delay flatness is one of many microwave concepts that has an audio analogy. If the time delay of audio frequencies varies within a sound system, your music listening experience would be seriously compromised.

Time delay units are networks that provide switchable delays to microwave signals.

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