Electronics > Beginners

Difference between phase response and group delay

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IconicPCB:
since spped of light varies with refractive index, it is not unreasonable to expect a wave front become retarded ( delayed as it travels through a medium.) IF the refractive index is wavelength sensitive , you would see different coloured content of an image separate into various colour groupings as it traveled through such a medium. This colour separation would result in a smeared image over time.

So it is with electronic medium where a group delay inequality exists across the frequency band of interest. The signal enter such a medium and then as it traverses the medium ( circuit ) it separates various frequency components according to group delay characteristics of the medium and deliveres them so separated to the output of the circuit. The delay imparted various frequency components will result in a skewing and smearing of the electronic signal.

delay is not phase shift in this instance as it applies to components of a signal ( THINK OF FOURIER TRANSFORM OF A COMPLEX SIGNAL SHAPE)

mriver:
Sorry for bumping this old thread, but I couldn't help after reading this awesome explanation @Orolo. Can you please also comment on the difference between phase delay (\$ \tau_p \$) and group delay (\$ \tau_g \$) defined as

\$ \tau_p = - \frac{\phi}{\omega} \$

\$ \tau_g = - \frac{d \phi}{d \omega} \$

where \$ \phi \$ is the phase?

What I meant, If I know \$ \tau_p \$ as a function of \$ \omega \$, is there any additional use of \$ \tau_g \$?

bson:

--- Quote from: orolo on October 13, 2017, 08:06:11 am ---It's \$\LaTeX\$! I can't thank enough the guys who developed the LaTeX add-on for blogs and forums, it's easy to use and a game changer. But I understand that abusing it can come off as pedantic or annoy people who don't like math that much.

--- End quote ---
Yup, it's LaTeX, but other formats are supported as well.  http://mathjax.org

One problem is while it's easy to add custom JS to forums, blogging software, etc, in the case of this forum software this isn't honored for previews and so mathjax markup can't be previewed.  But there's a live demo at https://www.mathjax.org/#demo which makes it easy to edit a non-trivial expression and then copy it into a post here... I don't trust my off-the-cuff LaTeX skills and tend to have to go through a whole bunch of edits otherwise until I get it right.  |O

bson:

--- Quote from: mriver on August 10, 2018, 06:05:52 am ---Sorry for bumping this old thread, but I couldn't help after reading this awesome explanation @Orolo. Can you please also comment on the difference between phase delay (\$ \tau_p \$) and group delay (\$ \tau_g \$) defined as

\$ \tau_p = - \frac{\phi}{\omega} \$

\$ \tau_g = - \frac{d \phi}{d \omega} \$

where \$ \phi \$ is the phase?

What I meant, If I know \$ \tau_p \$ as a function of \$ \omega \$, is there any additional use of \$ \tau_g \$?

--- End quote ---
Phase delay is an absolute measurement; group delay is the curve slope.  It just so happens that the latter resolves to a unit of second (angle/frequency, where freq=angle/s), but don't let this deceive you; they measure two different things.

G0HZU:
A simple way to understand group delay is to think of it as the rate of change of phase with respect to frequency.

If designing an oscillator it is often a design aim to go for highest loaded Q in the resonator (at zero degrees around the loop). This should give low phase noise and good stability. Another way to describe the same aim is to go for the highest 'group delay' in the resonator (at zero degrees around the loop). This might sound crazy at first, but if you think of group delay as 'rate of change of phase wrt frequency' then it makes total sense that you want to design for a steep phase slope (so you get good stability and low phase noise) and a steep phase response wrt frequency is the same as asking for high group delay.

Some VNAs have a DELAY function and this is usually just calculating (and displaying) group delay based on the phase vs frequency response.

So if you were looking at the open loop bode plot (gain and phase) of an oscillator on a VNA, it is much easier to also look at group delay to see where the slope of the phase is at its greatest. This is also where you want the zero phase point to be and you also want greater than unity gain around the loop to ensure oscillation will take place when the loop is closed after the open loop test. The alternative is to try and look at the phase response and see where it is steepest but this is very hard to do! It's like trying to find the very steepest part of the slope in a Z character that has some subtle wobbles in the slope shape. This can be hard to do quickly by eye but the group delay function in the VNA does it for you!

Note that if you measure group delay with a VNA and look through a classic parallel LC trap circuit you will see negative group delay in (nano)seconds. This obviously doesn't mean the signal arrives at port 2 before it leaves port 1 on the VNA. It just means that the phase vs frequency slope is flipped near the notch frequency. So you get a negative slope and so you see negative group delay on the VNA.

See the plot below for the open loop response of an oscillator. It shows the gain and phase and group delay plot. It also show loaded Q. The green trace is 'group delay' and you can see how much easier it is to see where the steepest part of the blue phase response is. It is at the peak of the green group delay plot.

See also the phase noise response of this oscillator after it was built and tested. Because the loaded Q is high (or in other words, the group delay is high) at the zero phase point in the loop the phase noise should be low and the plot proves this.

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