# Substitution theorem

#### Solardon

Joined Oct 5, 2006
5
I am still in the DC part of electronics study. Anyway, I am in network analysis.

There are two theorems that I do not see covered in textbooks. The reciprocity theorem and the substitution theorem. I found the reciprocity theorem in an older textbook. Mention was made as to the substitution theorem - that it was rarely used. In DC circuit analysis, what is the substitution theorem?

#### Papabravo

Joined Feb 24, 2006
18,401
I agree that it is rarely used. It tells you that if you know the voltage between two nodes and the current through that branch then you can substitute an arbitrary network as long as the voltage and current remain unchanged.

#### Dave

Joined Nov 17, 2003
6,969
I agree that it is rarely used. It tells you that if you know the voltage between two nodes and the current through that branch then you can substitute an arbitrary network as long as the voltage and current remain unchanged.
I have never come across the "substitution theorum" in circuit analysis, and it doesn't appear in modern texts on the subject. From your description Papabravo, I take it that its not used much these days because it has little practical relevance to circuit analysis?

I will also move this to the General Electronics Chat forum where it is better suited.

Dave

#### Solardon

Joined Oct 5, 2006
5
Sorry for posting in the math section. I was thinking that this theorem would be like the Millman's theorem and explainable in equation form. I have figured out the substitution theorem now and will be doing experiments with it at my test bench. Seems like a pretty interesting theorem to me. Since I am self teaching myself electronics, I have the liberty to study electronics the way I like - including the lesser known stuff. Network analysis is a fascinating subject for me. Anyway, thank you, Don.

#### Dave

Joined Nov 17, 2003
6,969
Sorry for posting in the math section. I was thinking that this theorem would be like the Millman's theorem and explainable in equation form. I have figured out the substitution theorem now and will be doing experiments with it at my test bench. Seems like a pretty interesting theorem to me. Since I am self teaching myself electronics, I have the liberty to study electronics the way I like - including the lesser known stuff. Network analysis is a fascinating subject for me. Anyway, thank you, Don.
Did you find any detailed information on "substituition theorum" (i.e. websites, books)? If so, which ones.

I'm just interested in looking at the finer details since I haven't come across this term before.

Dave

#### milee

Joined Sep 20, 2007
15
well i read "substitution theorem " along with the Kirchhoff's voltage and current law...so i think it would be helpful if we go through this terms first....

#### chesart1

Joined Jan 23, 2006
269
Substitution Theorem: If a voltage across or current through any bilateral branch of a circuit are known,this branch can be replaced by any combination of elements that will maintain the same voltage across and current through the chosen branch.

Another words, for branch equivalence, the terminal voltage and current must be the same.

This theorem cannot be used to solve networks with two or more sources that are not in series or parallel.

From Introductory Circuit Analysis Written by Robert L Boylestad.
Amazon.com: Introductory Circuit Analysis (10th Edition): Books: Robert L. Boylestad