# reading the frequency and the magnitued from a GH bode plot

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?

• What is your goal? Of course, you can measure open loop or closed loop. Results are, of course, different - but what do you want?
– LvW
Jun 14, 2016 at 7:39
• My goal is to know if can use the diagram to calculate the output of a sinwt input? Or is the diagram builted to tell me about the stability of the system only. Jun 14, 2016 at 8:07

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.

• In fact, what your saying, is that i cant take from the diagram the data of magnitued and phase, and i must use the T(jw) to know the phase and the magnitued to calculate the response? Jun 14, 2016 at 8:00
• Unless the system is unity feedback, yes.
– Chu
Jun 14, 2016 at 13:22

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.

• So if the diagram is a GH of unity feedback system, and i am been asked to measure the frquency response of a sinwt, can i take the data directly from the diagram, or first i need to calculate T(jw)=G/(1+G×1) and then place the frequency in the T(jw) function and find the magnitued and the phase? Because it doesnt give me the same result like the data in the diagram. Maybe the diagram tells me about the stability only. Jun 14, 2016 at 9:05
• If you are asked to measure the frequency response (of course, for a sinus input - not necessary to mention it) you must know for which configuration! Open loop or closed loop? Both can be measured (and/or simulated resp. calculated). I still do not know what your need is!
– LvW
Jun 14, 2016 at 9:47