# what is the correct gain/phase margin and bandwidth

I am interested in finding the gain margin, phase margin and bandwidth of a system via the bode frequency response.

I do know how to find each. For each one of them, first you have to find a certain frequency based on where the bode plot passes through a value. Specifically:

• Gain margin: that frequency is the one at which the phase of the open loop system is at -180 degrees

• Phase margin: that frequency is the one at which the gain of the open loop system is at 0 db

• Bandwidth: the frequency is the one from which the gain of the closed loop system passes through -3db

My question:

In all the above cases, if the bode passes multiple times through a specific db/degree, which do we choose?

For example, in the case of the bandwidth. At the bode plot of the closed loop system, in the gain plot, if the system passes through the -3db at ω=10, 50 and 105 rad/second (so it goes up and down a few times) which frequency do we chose as the bandwidth? (and this question extended to the gain and phase margin as well.)

Kind regards,