EE223 Microwave Circuits Fall2014 Lecture3

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EE223 Microwave Circuits (Fall 2014) Lecture 3
Dr. Atif Shamim EE Program King Abdullah University of Science and Technology (KAUST) 1

Terminated Lines

LOAD REFLECTION COEFFICIENT L:
Terminated Lines

Reflection Coefficient at Some Location z
VOLTAGE STANDING WAVE RATIO: (also known as SWR)

Problem
Problem: A 50 line is teminated in a 150 load. Find (a) L (b) VSWR.
Answer: , 3
When the load is mismatched, not all of the available power from the generator is delivered to the load. This loss is called Return Loss, and is defined in dBs as
RL= 20 log  dB

Input Impedance Zin
INPUT IMPEDANCE Zin
Applying wave equations (6.21) and (6.23), we now look into the line at z = l to obtain:

Input Impedance Zin
Figure 68 (p. 277) The terminated Tline can be replaced by an equivalent lumpedelement input impedance.
Use of (6.56) Replace: Tline plus load ZL by: Zin
Note: The input impedance, Zin , refers to the ratio of the total voltages and currents, while the characteristic impedance, Zo , refers to the ratio of the voltage to the current for only one of the waves, the incident one or the reflected one

Special Cases of Lossless Terminated Lines
Line terminated in a short circuit (ZL =0) For this case =1, and Zin = j Zo tan l Line terminated in an open circuit (ZL =) For this case =1, and Zin = j Zo cot l Terminated Tline with length l=/2 Zin = ZL (meaning that /2 does not alter impedance) Terminated Tline with length l=/4 Zin = Z02 /ZL (quarter wave transformer)

Problems
1) Find the input impedance of a lossless 50 T line terminated into a 150 load for lengths
(a) /8 (b) /4 Answer: (a) 30 j40 , (b) 16.7
2) Find the input impedance for a 0.6 m long T line
of characteristic impedance 75 + j 25 , having a propagation constant of 0.01 +j 0.1 m1 and terminated into a load 25 j40 .
Answer: 23 j34

Complex Loads
In general, use sdomain impedance values of R, L, C to model complex loads
= 32nH

Problem
A /6 line with Zo =50 is terminated in a 25 resistance. Find the input impedance along with its equivalent lumpedelement circuit at 1.0 GHz.
Answer: Zin= 57+ j 37 ; this resembles a 57 resistor in series with a 5.9 nH inductor.

Purely Reactive Load
PURELY REACTIVE LOAD ZL = jX

The Complete Circuit

The Complete Circuit
Figure 610 (p. 279) The circuit after adding a source, and the equivalent circuit.

Example 6.3

Example 6.3

Figure 611 (p. 21) Circuit for Example 6.3.

The Smith Chart
Figure 612 (p. 281) The Transmission Line Calculator, commonly referred to as the Smitha Chart.
Most commonly used graphical tool Polar plot of the voltage reflection coefficient (=  ej)  is plotted as radius from the center of the chart ( 1) angle is measured from the right hand side of the horizontal diameter (180o 180o) Real utility in its ability to transform from reflection coefficients to normalized impedances/admittances and vice versa

Constant Resistance and Reactance Circles
EE223 Microwave Circuits(Fall 2014)Lecture 3Terminated LinesTerminated Lines Reflection Coefficient at Some Location zProblemInput Impedance ZinInput Impedance Zin Special Cases of Lossless Terminated LinesProblemsComplex LoadsProblemPurely Reactive LoadThe Complete Circuit The Complete Circuit Example 6.3Example 6.3Figure 611 (p. 21)Circuit for Example 6.3.The Smith ChartConstant Resistance and Reactance Circles