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I'm looking at the following circuit and I don't know how to find the gain of the constant gain block. The only information I'm given are the Bode plots (magnitude and phase) of the two transfer function blocks. I'm also given the phase margin of the closed loop system (which is 60 degrees).

enter image description here

Edit: The circuit actually looks like this. The problem is asking to find K1 since it is equal to Vi/Vt. To give more information, the system is for a DC-DC converter and I'm not given any information about Vi or Vt. I've thought about this for a while now - there's no way to find Vi or Vt right? If the only information I am given is the phase margin and the Bode plots of G1 and G2. enter image description here

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  • \$\begingroup\$ You may be able to do it using the phase margin, right? Using the bode plots, and phase margin, you actually know the gain at one point. You can use that to solve for K. I think. Been a while since I studied this in school, and I have not had to use this much in my career. \$\endgroup\$
    – mkeith
    Oct 18 '20 at 22:52
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The procedure is quite simple.

When you have the BODE plot for the LOOP GAIN (open-loop transfer function) you only must shift the magnitude plot up or down until the desired phase margin is met. This shifting will not influence the phase plot. As a result of this shifting the frequency where the magnitude crosses the horizontal axis (0 dB) will be shifted as well.

Of course, the amount of shifting gives you the required constant gain (in dB).

Remember that the loop gain is nothing else than the product of the remaining blocks (better; the corresponding transfer function). In the BODE plot, both functions are to be added, of course (due to the log display).

Are you familiar with the definition of the phase margin? It is defined NOT for the closed-loop but for the loop gain!

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  • \$\begingroup\$ Thanks for your comment. I'm still confused about how I can get the gain of K1 since the gain of K2 is unknown. The only information I'm given about K2 is that the gain is equal to Vi/ Vt which is basically the output voltage from K1 divided by the input voltage to K1. \$\endgroup\$
    – syz
    Oct 19 '20 at 14:16
  • \$\begingroup\$ The above described method gives you only an information about the product K1*K2. Both play the same role within the circuit. If you need K1, you must have some additional information about K2 (or make a suitable guess). \$\endgroup\$
    – LvW
    Oct 19 '20 at 15:01
  • \$\begingroup\$ Makes sense thank you! \$\endgroup\$
    – syz
    Oct 19 '20 at 16:17

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