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AAiT ECE Department ECEG6312 Assignment2

By Shimelis Adugna [GSE/1109/03] Page 1

ASSIGNMENT-2: Due date: 08-Jun-13

By: Shimelis Adugna (GSE/1109/03) Instructor: Dr. Ing. Mohammed Abdo

1. Given the circuit shown, determine the input impedance. Use .

Solution:

1st

change all TL length to wavelength scale:

. .,

. .

2nd

Normalize . . and locate it on the Smith chart and read value on the wavelengthscale .and add .toward the generator to obtain .on the wavelength scale.

Draw a radial line b/n center of the chart and ...point and read ..at theintersection point of the line and ||constant circle.

3rd

Change .. to admittance of . . by rotating 180o. De-normalize ..

.. now normalize back with to obtain .. .. 4th Calculate admittance for stub .starting from admittance short circuit point towards the generato(0.1050.25. or .) and obtain . ... Locate on the smith chart.

5th

change to .. by rotating by 180o on constant|| circle. De-normalize with and normalize back with . This becomes ..

...

6th

Locate on the smith chart & read.on the wavelength scale for & move .length corresponding totowards the generator on constant ||circle to obtain...and read . . athe intersection point of radial line from wavelength scale and ||constant circle.

The input impedance . .

7/27/2019 Zz ASG_2 Microwave

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AAiT ECE Department ECEG6312 Assignment2

By Shimelis Adugna [GSE/1109/03]

7/27/2019 Zz ASG_2 Microwave

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AAiT ECE Department ECEG6312 Assignment2

By Shimelis Adugna [GSE/1109/03] Page 3

2. Given . Design matching network such that impedance seenat the input is

Solution: the MN will be realized using a piece of lossless TL and Stub both having same as shown above. Since the stub isconnected in parallel, it is convenient to work with admittances. Accordingly

.. ..Obtained by rotating

by 180

o

. . Obtained by rotating by 180o

1st

Locate these admittances on smith chart. We want to match to i.e. we want to pass from admittance of (having . ) to an admittance of (having . ).

This can be done by using a piece of TL of length LTL. Hence, we move on a constant circle|| from . until we come tothe . circle. At this point (point B) we read the corresponding admittance . . .

To determine the length of the TL that can take us from

to

, we move on the wavelength scale (clockwise direction) from

(where .) to (where

.) w/c gives net length of.. .. . . . . Now to arrive at .. from .. we need a susceptance of.... Locate this susceptance value on the exterior of the smith chart. It corresponds .on the wavelength scale. But since

we are using a short circuit stub, .of this length is contributed by the SC itself. Hence, we need only or net lengthof.. .

. . . .