# Matching without losses with a network

Discussion in 'Homework Help' started by Guitarras, Nov 24, 2013.

1. ### Guitarras Thread Starter New Member

Dec 10, 2010
14
0
Hello,

Question:

I need to mark the area of all values for a load in a Smith Chart that can be matched without losses to $50 ohm$ with the following circuit.

(the plane of the load is in the output)

Approach:
(a) Before this question it was asked to find all values for a load in the Smith Chart that can be matched to $50 ohm$ with the same circuit.
In order to do this I noticed that the parallel R makes the impedance moving to the left along a line of constant susceptance. In order to match takes place this line needs to intersect the circle with constant resistance $r = 1$ that after, the series capacitor can "remove" the imaginary part (since it makes the impedance moving CCW along a circle of constant resistance) until we reach the center of the Smith Chart (perfect match). For this point I found an area limited by the following conditions:
- $r >= 1$ and $r < inf$ (right part of the real axis)
- interior of the circle $r = 1$
- below the susceptance line of $b = -0.5$ (in normalized impedance intercepts both points (1,1) and (0,2))
- above the line $x = 0$ (only capacitive loads in the area given above)

(b) Now, returning back to my question, my problem is doing the same but without losses.
First I thought it could be only the line of pure reactances (where $r = 0$) from the area found in (a), this means: $2 < x < inf$. Since pure reactances don't have losses.
But then I was wondering if the question about without losses would be not in respect to the load but to the matching network. Well, with the resistor R we will always have losses with this network unless the resistor would be, ideally, infinite (open circuit then). This means that the answer would be all the loads along the circunference $r = 1$ could be matched with that series capacitor.

Can somebody discuss this with me to see if I'm thinking well here or even if I can reach the correct answer?

Best regards.

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
I agree. The only possible lossless match case would require the load impedance real value component to be 50 ohms and the imaginary part to be non zero positive. R1 would be infinite.

Guitarras likes this.