Updated July 6,
here to go to our discussion of group velocity
Here's the index to our ever-expanding
content on group delay:
- what is it?
rule of thumb
flatness and consistency
delay data smoothing (separate page)
delay in waveguide structures (separate page)
delay in filters (separate page)
group delay (separate page)
group delay using Agilent's ADS (separate page)
dielectric properties from group delay (new for August
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!
- 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
Martin further wishes to point
out that group delay can actually can be negative (in some rare
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,
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.
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.
delay units are networks that provide switchable delays to microwave