# Insertion Loss of a T-Network

## Homework Statement

Calculate the insertion loss of the T-network given the values:
Rs = 75Ω
Rl = 100Ω
Ra = 13Ω
Rb = 13Ω
Rc = 213Ω
The transmission matrix and Network are below:

2. Homework Equations

## The Attempt at a Solution

Constructing the matrix:
A = 1+Ra/Rc = 1+13/213 = 1.061
B = Ra+Rb+(Ra*Rb)/Rc = 13+13+(13*13)/213 = 26.7934
C = 1/Rc = 1/213 = 0.004694
D = 1+Rb/Rc = 1+13/213 = 1.061

[ A B ] = [ 1.061 26.7934 ]
[ C D ] = [ 0.004694 1.061 ]

Insertion Loss Ail = 20log [ (ARl+B+(C*Rl+D)*Rs) / ( Rs + Rl ) ]
= 20log [ (1.061*100+26.7934+(0.00469*100+1.061)*75) / (75+100) ]
=20log [ 247.6434 / 175 ]
=20log [ 1.415 ]
=3.015 db

Would someone be able to advise if this is correct, seems far too simple to be correct. Any help is appreciated and thanks in advance.

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berkeman
Mentor
You can check your answer by writing the KCL equations and solving them. Do you get the same insertion loss using that method? Can you show that work?

You can check your answer by writing the KCL equations and solving them. Do you get the same insertion loss using that method? Can you show that work?
Hi Berkeman, I'm trying to do the KCL using loop analysis to check but as I don't have values for voltage or current I can't seem to be able to work it out? It's the value of V I am struggling to cancel out.

berkeman
Mentor
KCL analysis uses node equations, not loops. Just label arbitrary voltages at each node, and calculate Vo/Vi...

KCL analysis uses node equations, not loops. Just label arbitrary voltages at each node, and calculate Vo/Vi...
I'm trying to do this but can't seem to work it without a value for the voltage source.

So i made the three nodes at the top V1, V2 & V3 and made the following equations

V2/13 - V3/13 - V3/100 = 0
V2/13 - V1/13 - V1/75 = 0
V1/13 + V3/13 - V2/213 - 2*V2/13 = 0

Struggling to move on from here without at least one of the V Values. Even if I do V3 / V1 so that
( V2/13 - V3/13 - V3/100 ) / ( V2/13 - V1/13 - V1/75 ) = 0
Which I got to V3 = (100*V2) / 113

The Electrician
Gold Member
Let the circle just below be a voltage source of Vs. Calculate the power delivered to the load without Ra, Rb and Rc in place; with just a direct connection from the output of Rs to RL. Then calculate the power delivered to RL WITH Ra, Rb and Rc in place. The ratio of the two powers will give the insertion loss.