Miller's Theorem 1
MILLER'S THEOREM
• The introduction of an impedance that connects amplifier input and output ports adds a great
deal of complexity in the analysis process. One technique that often helps reduce the
complexity in some circuits is the use of Miller's theorem.
• Miller's theorem applies to the process of creating equivalent circuits. This general circuit
theorem is particularly useful in the high-frequency analysis of certain transistor amplifiers at
high frequencies.
Miller's Theorem generally states:
Given any general linear network having a common terminal and two terminals
whose voltage ratio, with respect to the common terminal, is given by:
V2 = A V1 . (10.5-1)
If the two terminals of the network are then interconnected by an impedance, Z,
an equivalent circuit can be formed. This equivalent circuit consists of the same
general linear network and two impedances; each of which shunt a network
terminal to common terminal. These two impedances have value (Figure 10.5-1):
ZZ
AZA Z
A
12
11
=−=− (10.5-2)
General Linear
Network
V = A V
2 1 21
VV
Z
++
−−
Ι
Ι
Ι
Ι
1i 2i
in out
General Linear
Network
V = A V
2 1 21
VV
+
−
+
−
ZZ
12
ΙΙ ΙΙ
1s 2sin out
with with
(a) (b)
Figure 10.5-1 Miller Equivalent Circuits
a) Interconnecting Impedance
b) Port-Shunting Impedances
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