reading the frequency and the magnitued from a GH bode plot

Question

Lets say i have a GH(jw) bode plot, And i have an input signal of sin(wt) to the system. Is the GH(jw) bode plot actually can tell me the magnitued and the phase for each frequency i give in the input of the system, Or is it only tells me about the stability of the system? Is it allowed to take the phase and magnitued out of the GH(jw) bode diagram and calculate the output signal? Or should i use the trasfer function of the closed loop T(jw) and place my frequency in it and find the magnitued and the phase?

Answer 1

If it's a unity feedback system (\$\small H=1\$), express \$\small GH\$ as a complex number at the frequency of interest: \$\small GH=x+jy\$, then the closed loop response at that frequency is \$\small T(j\omega) =\large \frac{x+jy}{(1+x)+jy}\$. Then determine magnitude and phase angle in the usual way.

If it's not unity feedback, you need to know \$\small G(j\omega)\$ or \$\small H(j\omega)\$ to work out the system frequency response.

Answer 2

I suppose you speak about a system with feedback: An active block with the gain G(jw) and a feedback block H(jw) which also may be frequency-dependent (but it can also be a simple voltage divider). In this case, the gain of the whole feedback loop (called "loop gain") is

T(jw)=G(jw)H(jw)=GH.

If the feedback loop is closed (negative feedback), we have a closed-loop function

H(jw)=G/(1+GH)

Of course, you can measure the frequency response of both configurations after applying a suitable sinusoidal signal at the input. The frequency must be tuned over the desired range. Then, you can determine the magnitude and phase shift at the output if compared with the input signal. This gives you the frequency response of both functions. And you can construct the corresponding BODE diagrams for both functions.

However, as you have assumed, the BODE diagram for the open-loop response T(jw) normally is used in most cases for finding the stability margins. More than that, it allows to decide which measures are to be taken in case the stability is not as desired.

The BODE plot for the closed-loop response H(jw) primarily is used for determining the overall gain and the bandwidth of the whole system.