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I am trying to get the small signal transfer function for a circuit that looks like this: It is an inverting amplifier connected to an output and a capacitor in series with an inductor

It is an inverting amplifier connected to an output branch and a branch with a capacitor in series with an inductor. I have not been able to figure out how the small signal transfer function would look for something like this so any help would be greatly appreciated.

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    \$\begingroup\$ What is the TF of the inverting amplifier? \$\endgroup\$
    – Andy aka
    May 2 '19 at 15:23
  • \$\begingroup\$ There was no TF given \$\endgroup\$
    – SJGVols
    May 2 '19 at 15:25
  • \$\begingroup\$ If it's an ideal amplifier, then the load on the output is immaterial. If you're seeing this on a homework problem you need to know the transfer function and output impedance of the amplifier. If you're seeing it on a schematic you need the part number, and then you'll need to figure out the TF and output impedance. \$\endgroup\$
    – TimWescott
    May 2 '19 at 15:25
  • \$\begingroup\$ I see what you are getting at. This was given to me by my professor as a bonus question on our last lab and I was never able to answer it so I was curious about it. This was the only diagram he gave with just the instruction of finding the small signal transfer function. \$\endgroup\$
    – SJGVols
    May 2 '19 at 15:28
  • \$\begingroup\$ He also asked how the circuit would change if Tr << Tres, Tr = Tres, and Tr >> Tres but I did not understand that at all so I figured I would try and figure out the transfer function first. Tr being rise time and Tres being associated with the resonance frequency of the LC network. \$\endgroup\$
    – SJGVols
    May 2 '19 at 15:31
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One way to get a reasonably interesting, but not impossible to calculate, answer is to assume the amplifier has a one-pole frequency response, and an arbitrary real output impedance.

Keeping the output impedance \$R_A\$ as a free parameter, you should be able to qualitatively predict the overall behavior with the given load, and also say something about how the step response would depend on the amplifier's output rise-time and the resonant frequency of the LC load.

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