EE-223 Microwave Circuits (Fall 2014) Lecture 4

Dr. Atif Shamim EE Program King Abdullah University of Science and Technology (KAUST) 1

The Smith Chart

Figure 6-12 (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

Using the Smith Chart

Using The Smith Chart

Figure 6-16 (p. 288) A T-line terminated in a load (a) shown with values normalized to Z0 in (b). (c) The location of the normalized load impedance is found on the Smith Chart.

(c)

Reflection Coefficient on Smith Chart

Figure 6-16d (p. 289) (d) Reflection coefficient and angle.

Movement along a T-Line

Figure 6-17 (p. 290) Movement along a T-line corresponds to movement along a constant- [L] circle on the Smith Chart.

Problems

1. Locate the following load impedances terminating a 50 T-Line: (a) ZL=0 (a short circuit), (b) ZL= (an open circuit), (c) ZL = 100 +j 100 (d) ZL= 100 - j 100 (e) ZL= 50 .

2. A 0.334 long Zo = 50 T-Line is terminated in a load ZL= 100 j 100 . Use the Smith Chart to find (a) L, (b) VSWR, (c) Zin, and (d) the distance from the load to the first voltage minimum. Answers: (a) 0.61e-j30o, (b) 4.3, (c) Zin= 22.5 + j 45 , and (d) 0.208

Solution (Problem 1)

Solution (Problem 2 and 4)

Problem

3. A load impedance of 40 +j 70 terminates a 100 transmission line that is 0.3 long. Find the reflection coefficient at the load, the reflection coefficient at the input to the line, the input impedance, the SWR on the line, and the return loss.

Answers: |L|=0.59, = 104o, SWR= 3.87, Return Loss= 4.6 dB, Zin= 36.5 j 61.1, |in|=0.59, = 248o

Impedance to Admittance

The Smith chart can be used for normalized admittance in the same way that is used for normalized impedances, and it can be used to convert between impedance and admittance.

A /4 transformation is equivalent to rotating the chart by 180o. This is also equivalent to imaging a given impedance (or admittance) point across the center of the chart to obtain the corresponding admittance (or impedance point.

The same Smith chart can be used for for both impedance and admittance calculations during the solution of a given problem.

Problem

4. A load of ZL = 100 + j 50 terminates a 50 line. What are the load admittance and the input admittance if the line is 0.15 long?

See Solution on the Smith Chart of Problem 2 in a previous slide

EE-223 Microwave Circuits(Fall 2014)Lecture 4The Smith ChartConstant Resistance and Reactance CirclesUsing the Smith Chart Using The Smith Chart Reflection Coefficient on Smith Chart Slide Number 7Movement along a T-LineSlide Number 9Slide Number 10ProblemsSolution (Problem 1)Solution (Problem 2 and 4)ProblemImpedance to AdmittanceProblem