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Problem 2—What is Miller's theorem in circuit theory?

Answer:

Miller's theorem is a very important theorem often used to simplify circuits for analysis. In order to explain Miller's theorem, consider the circuit in Fig 1 below. According to Miller's theorem, the impedance element Z in Fig 1 can be replaced by two impedances Z' and Z" as shown in Fig 2.

Z' = Z
1 – k and Z" = Z × k
k – 1 ,

where k = V2
V1 , the ratio of voltages at the two nodes 1 and 2.

There is a dual for the above circuit in terms of current as shown below. The circuit in Fig. 4 is equivalent to that in Fig. 3 where Z is replaced by Z' and Z".

Again,

Z' = Z × 1
1 – A and Z" = Z × A – 1
A ,

where A = – I2
I1 (notice the – sign)

Miller's theorem is often used to simplify FET circuits; its dual is used in BJT circuits during analysis.

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