Insertion Loss of a T-Network

In summary, according to the homework statement, the insertion loss for a T-network with the given values is 3.015 db.
  • #1
Jason-Li
119
14

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:

Q.png


2. Homework Equations

q1.png


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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  • #2
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? :smile:
 
  • #3
berkeman said:
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? :smile:

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.
 
  • #4
KCL analysis uses node equations, not loops. Just label arbitrary voltages at each node, and calculate Vo/Vi...
 
  • #5
berkeman said:
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
 
  • #6
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.
 

1. What is the definition of insertion loss in a T-network?

Insertion loss in a T-network refers to the amount of signal power that is lost when a device is inserted into a transmission line. It is typically measured in decibels (dB) and is a measure of the attenuation or reduction in signal strength.

2. How is insertion loss calculated in a T-network?

Insertion loss in a T-network can be calculated by comparing the power of the signal at the input of the network to the power at the output. This can be done using a power meter or by measuring the voltage or current at each end of the network.

3. What factors can affect the insertion loss of a T-network?

The insertion loss of a T-network can be affected by various factors such as the quality of the components used, the length and type of transmission line, and the frequency of the signal being transmitted. Environmental factors such as temperature and humidity can also have an impact on insertion loss.

4. How can insertion loss be minimized in a T-network?

There are several ways to minimize insertion loss in a T-network. One way is to use high-quality components with low loss. Additionally, using shorter transmission lines and using components with a higher power handling capacity can also help reduce insertion loss. Proper shielding and grounding can also help minimize any external interference that may contribute to insertion loss.

5. Why is insertion loss an important factor to consider in a T-network?

Insertion loss is an important factor to consider in a T-network because it directly affects the performance and efficiency of the network. High insertion loss can result in a weaker signal and may lead to errors or disruptions in the transmission. It is also important to monitor insertion loss over time to ensure the network is functioning properly and to identify any potential issues that may arise.

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