Answer 3

THE MAGAZINE FOR COMPUTER APPLICATIONS
Circuit Cellar Online offers articles illustrating creative solutions
and unique applications through complete projects, practical
tutorials, and useful design techniques.

WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 3—Prove Miller's theorem.

Answer:

Referring to figures 1 and 2 above, we need to prove that

Z' = Z
1 – k and Z" = Z × k
k – 1 , where k = V2
V1

The current through Z in Fig. 1 is

I = V1 – V2
Z

For Fig. 2 to be equivalent of Fig. 1, the same current I must flow through Z' and Z". The direction of I is same as in Fig. 1 through Z' and opposite through Z".

In case of Z', set the current through it equal to that in Fig 1:

V1
Z' = V1 - V2
Z

Then, solve for Z' and divide top and bottom by V1:

Z' = Z × V1
V1 – V2 = Z × 1
1 – V2/V1

In the case of Z", I flows in opposite direction, so V2/Z" = -I = -(V1-V2) /

V2
Z" = –I = V2 - V1
Z

Again, solve for Z" and divide top and bottom by V1:

Z" = Z × V2
V2 – V1 = Z × V2/V1
V2/V1 – 1

Contributor: Naveen P N

4-01 — NEXT Q&A

For questions or comments about
Test Your EQ, e-mail eq@circuitcellar.com.