Numerical 2 Shunt Stub (Z L=60+j80Ω and Z0 =100ΩΩ)

Smith Chart Shunt Stub Matching Numerical

Given

\[
Z_L = 60 + j80 \ \Omega
\]

\[
Z_0 = 100 \ \Omega
\]

Step1: Normalize the load by dividing it by the characteristic’s impedance by the line

                \[
Z_{in}=\frac{Z_L}{Z_0}=\frac{60+j80}{100}=0.6+j0.8
\]

Step 2: Plot Zn in the smith Chart

Step3: Draw the SWR Circle using prime center as the pivot point and Zn as a point of circumference of circle

                SWR = 4:1

Step3: Draw a line from the normalized load impedance through the prime center of the chart out to the wavelength scale towards generator scale

WTGb = 0.436 λ

Furthermore, Note where this line crosses the swr circle opposite from the normalized load. This is normalized admittance Yn labelled as Point B on the Chart

                Yn = 0.3 – j0.4

Step 5: From the normalized admittance point B. move clockwise around the SWR circle until it crosses the R=1 circle for the first time. The is point C on the Chart and is denoted as normalized Susceptance (Bn)

Yc = 1 + j 1.5

Step 6: Draw a line from the perimeter center of chart through the susceptance point C to the wave length scale. Note the reading on wavelength towards generator scale.

WTGc = 0.176 λ

Step 7: The difference in wavelength between the reading of step 4 WTGb and the recorded in Step 6 WTGC moving clockwise distance from the load terminals to point where the matching sub will be connected.

\[
D_s=(0.176-0.436)\lambda+0.5\lambda
\]

\[
D_s=-0.26\lambda+0.5\lambda
\]

\[
D_s=0.240\lambda
\]

Alternatively,

\[
D_s=(0.5-0.436)\lambda+0.176\lambda
\]

\[
D_s=0.064\lambda+0.176\lambda
\]

\[
D_s=0.240\lambda
\]

Step 8: The reactive portion recorded in step 5 normailized susceptance of (j1.5) must be cancelled. Find the opoosite value (-j1.5) on the R- Circle on the chart noted as point D. Record the wavelength towards the generator reading at point D

                WTGd = 0.344 λ

Step 9: For shorted stub (admittance case), the length of the shorted stub is measured from the point of infinity () to point D

\[
L_s=(0.344-0.25)\lambda
\]

\[
L_s=0.094\lambda
\]

 

For open shunt stub the length of stub is measured from the point of 0 wavelength to point D in clockwise directions

\[
L_o=0.344\lambda
\]