# What is the gain margin of the system, when the phase crossover frequency does not exist?

I have a simple questions

I have a system in which the system will never reach -180 degrees for any frequency.

Does that make the gain margin infinite ? If yes, does that mean that the system will always be stable for any gain ?

Thanks • Can it reach +180 degrees? You do realize that what you are describing doesn't exist? – Andy aka May 17 '20 at 10:57
• The point is that as frequency rises into the MHz and GHz range, there is a natural delay incurred that grows with frequency and this delay is equivalent to a phase shift and YOU WILL always get 180 degrees at some point in the spectrum because the speed of light is finite. – Andy aka May 17 '20 at 11:13
• In addition to andy's comment, your circuit has a phase margin of roughly 60 degrees, it is measured when the gain falls below 0db – Reroute May 17 '20 at 11:16
• No, because the gain will normally have fallen below unity hence, it can't become unstable. – Andy aka May 17 '20 at 11:22
• Adding a system or circuit diagram may help but from the plot you have all we can say is it is more than 70dB. No real circuit matches the model as there are parasitic values. – Warren Hill May 17 '20 at 12:42

What is the gain margin of the system, when the phase crossover frequency does not exist?

You use the word "exist" and in any circuit that "exists", due to the speed of light being finite, there will always be a frequency where there is an inversion of signal aka 180 degrees phase shift.

I have a system in which the system will never reach -180 degrees for any frequency.

No you don't - not in this universe.

• A signal with a frequency of 300 MHz has a 1 metre wavelength (or less) hence: -
• A 50 mm long wire at 3 GHz produces an end-to-end phase shift of 180 degrees.
• At 30 GHz, 180 degrees phase shift is obtained with a 5 mm long wire.
• Ok, but from the range of frequency that I have, I cannot determine the gain margin ? Maybe I am not understanding something but, I have a second order system. This means that the -180degrees will be reached at infinite frequency right ? – Samwel Portelli May 17 '20 at 11:33
• Not in a system that "exists" - a theoretical system yes, but a physical system, no. I've given you a system example (a piece of wire) that produces a phase shift of 180 degrees between input and output once the frequency has risen high enough. The gain will be a tad under 1 and hence it's gain margin will be small but, it won't produce oscillations if used with feedback. – Andy aka May 17 '20 at 11:40