phase margin for unity-gain amplifier - Page 1
Forum section: electronics / beginners

author: exe
author_rank: Unknown
timestamp: March 13, 2020, 08:00:36 pm
content: My friends,I have a question I cannot answer myself: how to find a phase margin in case of unity gain?My best guess is: there is no such thing, unless there is a sort of peaking. In order to work stable, peaking (=amplification above unity gain) should only occur where phase margin > 0.Is that correct?

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 14, 2020, 02:44:12 pm
content: Quote from: exe on March 13, 2020, 08:00:36 pmIf you assume a second-order system, you can calculate the phase margin given the overshoot.Here are two figures that should help.The first shows how overshoot is defined.The second is a nomograph.

author: exe
author_rank: Unknown
timestamp: March 14, 2020, 02:55:24 pm
content: thank you very much, that is very helpful as doesn't require breaking the loop.

author: rstofer
author_rank: Super Contributor
timestamp: March 15, 2020, 03:41:45 pm
content: Here is MathWorks' explanation.https://www.mathworks.com/help/control/ref/margin.htmlGain margin is shows as 6.0 dB when the phase goes to -180 degPhase margin is shown as 21.4 degrees when the gain goes to 1Bottom line: When the gain is >= 1, the phase is more positive than -180 degrees and the system won't oscillate.If anybody wants to run the example on Octave (free), you need to load the control package at the command prompt in Octave. You MAY need to install it as well, details on Google.Code:pkg load controlsys = tf(1,[1 2 1 0]margin(sys)Attached is the plot showing both phase and gain margin. Interesting stuff!

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 15, 2020, 06:35:04 pm
content: If you want to look only in the frequency domain and don't want the hassle of looking at phase and magnitude, you can calculate zeta from the peaking of a unity-gain frequency response. Then use zeta to calculate phase margin (formula on the nomograph)

author: f5r5e5d
author_rank: Frequent Contributor
timestamp: March 15, 2020, 07:14:47 pm
content: a delay can be placed inside the feedback loop in sim, stepping the delay time can emulate added phase shift

author: exe
author_rank: Unknown
timestamp: March 15, 2020, 10:17:31 pm
content: Is it possible to create a unity-gain buffer without peaking?

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 16, 2020, 03:22:30 am
content: Quote from: exe on March 15, 2020, 10:17:31 pmYes, look at my previous post. It must be compensated enough to give adequate phase margin. Only opamps you design yourself, or opamps that offer external compensation under your control will allow you to achieve that, however.Compensating for lower phase margin gives a faster response but with possible overshoot. It is a tradeoff.

author: exe
author_rank: Unknown
timestamp: March 16, 2020, 12:22:13 pm
content: Quote from: Wimberleytech on March 16, 2020, 03:22:30 amIf there is no overshot, how can I calculate the phase margin? From the time it takes output to reach the steady level?

author: Wimberleytech
author_rank: Super Contributor
timestamp: March 16, 2020, 03:49:06 pm
content: Quote from: exe on March 16, 2020, 12:22:13 pmNo, what you are capturing with that measurement is bandwidth (and perhaps slew-rate, which is a large-signal effect).