Intuitive way of Finding Equivalent Impedance

We have already started our little discussion on the Intrinsic Gain Method in the last two blogs.

Here we will find the equivalent impedance of any MOSFET circuit in a very structured way. This post is very important to kickstart our main discussion of finding the gain of any MOSFET circuit. 

For the time being, let me frame a question for you. >

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Q) Find Req for the bellow (left) circuit.

Solution (right):

 $R_{eq}= V/I$

$I=V_{X}/R$

Using KVL, $V=I \times R_{out} + A \times V_{X}$

=> $V=I \times R_{out} + A \times I \times R$

=> $V/I = A \times R + R_{out}$ >

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Without going into details, let's find out the intrinsic gain and output impedance of common gate NMOSFET.

We have already found the gain of common gate in POST 2.$Gain=M= (1+ g_{m}r_{o})$. For output impendence you need to short the input (Vgs=0, gm current source eliminated) and apply a voltage source, $Rout=r_{o}$. >

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With this knowledge, let me frame two general questions. These are the backbone of finding the impedance of any circuit.

with the help of the above two results, we can immediately find out the result of the first one and it is $R_{eq}= r_{o} +MR$. >

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Let's just find it out for Q2.

The equivalent circuit to find out the $R_{eq}$ is given below.

Solution(Q2):

$R_{eq}=V/I$

But, $I=\frac {M \times V}{r_{o}+R} $

Now, $V/I=R_{eq}= \frac {r_{o}+R}{M}$

With the help above standard result we can find impedance of any circuit. >

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But to use this above results more efficiently, let's try a some intuitive approach. 

Intuition:

Rule: 

1) Draw a mirror line on the source of MOSFET (N or P)

2) 

i) All the resistors connected between mirror to ground will be multiplied by M if you see it from the drain.

ii) All the resistors connected between mirror to ground will be divided by M if you see it from source.

Let's just apply these rules on circuits we have discussed so far.

The above diagrams is self explanatory of the fact of using mirror concept. This can be applied to P-MOS also, as in terms of incremental model of P and N are identical.             

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Post 2                                                                                           Post 4

                                                 Post3