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Help in deriving Zin small-signal expression

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The Electrician:
promach, you have asked about intuitive understanding.  Have a look at the Wikipedia page on the gyrator: https://en.wikipedia.org/wiki/Gyrator

Go down the page to the part titled: Application: a simulated inductor

The circuit shown only uses a single opamp, and it's not a true gyrator, but read the explanation; you might find this circuit easier to intuitively understand.

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Also, when you say "I am planning to derive the Rout2 algebra as well as measure the output impedance in simulation.", just what is it that you do to "derive the Rout2 algebra"?  danmc may know what you mean, but I don't.

promach:
I am trying to determine suitable mosfet sizing for the following transconductance circuit block.

It seems to me that I need to minimize 1/(Gm1Gm2Rout1)  as well as maximize Rout2 ?

This is the small signal model I have drawn up to derive the Rout2 algebra. I need some help in formulating the small-signal mesh/nodal equations to obtain Rout2

       

promach:
Why is   sC/(Gm1Gm2) placed in series with 1/(Gm1Gm2Rout1) ?

The Electrician:

--- Quote from: promach on May 15, 2018, 01:52:40 pm ---Why is   sC/(Gm1Gm2) placed in series with 1/(Gm1Gm2Rout1) ?

--- End quote ---

Read this: https://en.wikipedia.org/wiki/Equivalent_series_resistance

Real inductors and capacitors are not loss free.  When a voltage or current is applied to them there are parasitic loss mechanisms that cause a loss of energy.  Those losses can be modeled as resistors in series, or in parallel, or both sometimes.

The Electrician:

--- Quote from: promach on May 15, 2018, 01:09:22 pm ---I am trying to determine suitable mosfet sizing for the following transconductance circuit block.

It seems to me that I need to minimize 1/(Gm1Gm2Rout1)  as well as maximize Rout2 ?

This is the small signal model I have drawn up to derive the Rout2 algebra. I need some help in formulating the small-signal mesh/nodal equations to obtain Rout2

--- End quote ---

Just above the fourth image down in your thread at the Designer's Guide forum I see nodal equations and a solution for gm obtained using Maxima.  To obtain Rout2 inject 1 amp into the node where you want to get Rout2 and solve for the voltage Vout there.  Then Rout2 will be Vout/1 amp; the expression obtained for Vout will also be the expression for Rout2.

You can expect that expressions you derive for various voltages, currents, and impedances will be huge, nearly intractable expressions just like the one you already obtained for gm.

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