# I WANT TO GET A DEEP UNDERSTANDING OF Miller's theorem

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#### ZengLei

##### Full Member level 1
MY Question is:
1.In what conditions we must take the Miller's theorem into consideration??
2.In what conditions the Miller's theorem will work???In a passive or in a active circuit??

I think Miller's theorem will work only in a invert ciruit,Am'i right?

Hi
Good luck

### ZengLei

Points: 2
miller effect is taken into consideration when the differential of output by input or input by output of the system is high,.....
miller effect can be taken into consideration both in active and passive circuits... in active circuits if gain is high and in passive circuits if attenuation is high,,,,

it is not valid in invert circuits alone.,,,

### ZengLei

Points: 2
And I think the system must be linear so we could use it...

V
Points: 2
linearity is not a compulsion... the only requirement is a capacitor between input and output and some amount of change between input and output....

Miller states that the capacitance doubles if the direction of charge changes!

and this is the major issue these days in high speed IC;s

pl look into sedra smith book for some problems.. doing them will enhance ur understanding!!!

### ZengLei

Points: 2
ZengLei,
This quote from Wikipedia provides a conscies definition of Miller's theorem.
.
"Miller's theorem states that, if the gain ratio of two nodes is 1:K, then an impedance of Z connecting the two nodes can be replaced with a Z/(1-k) impedance between the first node and ground and a KZ/(K-1) impedance between the second node and ground. (Since impedance varies inversely with capacitance, the internode capacitance, C, will be seen to have been replaced by a capacitance of KC from input to ground and a capacitance of (K-1)C/K from output to ground.) When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance."
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For more detailed analysis, see the following:
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A.B. Macnee "On the presentation of Miller's Theorem"
.
Luis Moura "Error Analysis in Miller's Theorem"

Points: 2