ELEC 401 MICROWAVE ELECTRONICS Lecture on Smith Chart Instructor: M. İrşadi Aksun Acknowledgements: Some Smith Chart figures were taken from the textbook “Fundamentals of Applied Electromagnetics” by F. T. Ulaby.

Outline Chapter 1: Motivation & Introduction Chapter 2: Review of EM Wave Theory Chapter 3: Plane Electromagnetic Waves Chapter 4: Transmission Lines (TL) Chapter 5: Smith Chart & Impedance Matching Chapter 6: Microwave Network Characterization Chapter 7: Passive Microwave Components

Smith Chart - Introduction Smith chart is a graphical tool that represents a mapping between impedance and reflection coefficient; It was introduced by Phil Smith of RCA in 1936; It is nothing but the polar plot of reflection coefficient with the corresponding impedances written on it; It is a very convenient tool for presentation purpose.

Smith Chart - Introduction Polar plot of Point A: Point B:

Smith Chart - Introduction To show how the chart is constructed, we first write the relationship between input impedance and the reflection coefficient: By equating the real and imaginary parts Reactance circles Resistance circles

Smith Chart - Introduction Resistance circles Equation of a circle with radius R located at (x0,y0) Reactance circles

Smith Chart - Introduction Unit circle Point P represents a normalized impedance Z=2-j1. The reflection coefficient has a magnitude OP/OR, and an angle -26.6 degrees. R O -26.60 P Point R is an arbitrary point on the R=0 circle, which is also |G|=1.0 circle.

Smith Chart - Application Show the locations of the following impedances: Show the locations of the following admittance:

Smith Chart - Applications Find the admittance from a given impedance, or vice versa: Constant |G| circle

Smith Chart - Applications Constant |G| circle Find the input impedance of a TL terminated in a load impedance ZL. Length l in terms of l z=0 z=-l

Smith Chart - Applications Constant |G| circle Length in terms of l Find the SWR, voltage maxima and minima. z=0 z=-l Voltage Max. Current Min. Voltage Min. Current Max. Voltage Max. Current Min.

Smith Chart - Applications Example: A 5.2 cm long, lossless 100 W line is terminated in a load impedance ZL=30+j50 W. a) Calculate |GL|, fL, and VSWR: VSWR=4.2 b) Determine the impedance at the input for the frequency of 750 MHz and l=l0: Constant |G| circle

Smith Chart - Applications Example: A 50W coaxial cable, filled with a dielectric material of er=2.25, is connected to a generator with 50W internal impedance and 200 MHz signal frequency. The TL is terminated in an unknown impedance at a distance of 10 cm from the generator. a) Knowing that the input impedance at the source terminal was measured and noted as 25+j5 W, what is the load impedance? b) Find the VSWR; c) What should the length of the line be in order to have a real input impedance at the source terminal? z=0 z= -10cm

Smith Chart - Applications 1. Locate Zin on the S.C.; 2. Draw the constant |G| circle; 3. Starting from Zin move toward load by 0.1l on constant |G| circle; Constant |G| circle 0.48l (0.48+0.1)l z= -0.1l z=0

Smith Chart - Applications Example: A length of TL with 50W characteristic impedance is connected to a generator with 50W internal impedance and to an unknown load impedance ZL. The VSWR and the locations of the maximum and minimum of standing wave are measured and the following information is obtained: i) First voltage minimum occurs at a distance of l/5 from the load terminals; ii) VSWR=Vmax/Vmin = 2.0 Find the load impedance by using the above information. Standing wave Vmax Vmin z=0 z= -l

Draw the SWR=2.0 circle SWR=2 circle Find the s=2.0 point on the Smith Chart. Draw a circle that is centered at s=1.0 and passes through s=2.0 point s=2.0

On the SWR=2.0 circle, start from Vmin point and go 0.2λ toward load. Normalized load impedance is: 1.55 - j0.65 Load impedance is: 77.5 – j32.5 Vmax , Imin Vmin , Imax 0.2λ