Single Stub Matching - Maple Help

Single Stub Matching of a Transmission Line

Introduction

A single short circuited transmission line is a distance d from the load and of length d.

Given a characteristic impedance of Z0 and a load with complex impedance ZL, this application will calculate the values of d and l.

 • The real part of the impedance at the stub location must match the transmission line characteristic impedance
 • The imaginary part of the impedance at the stub location must equal 0

Reference:

Iskander, Magdi F., Electromagnetic Fields and Waves, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1992.

 > $\mathrm{restart}:\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{assume}\left(\mathrm{d},\mathrm{real},\mathrm{l},\mathrm{real}\right)\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$

Parameters

Resistances

 >
 >

Equations

Wavelength and propagation constant

 > $\mathrm{λ}≔1⟦\mathrm{m}⟧:$
 > $\mathrm{β}≔2\cdot \mathrm{π}/\mathrm{λ}:$
 > $\mathrm{circuit}≔\frac{\mathrm{Z__0}\cdot \mathrm{cos}\left(\mathrm{β}\cdot \mathrm{d}\right)+\mathrm{I}\cdot \mathrm{Z__L}\cdot \mathrm{sin}\left(\mathrm{β}\cdot \mathrm{d}\right)}{\mathrm{Z__L}\cdot \mathrm{cos}\left(\mathrm{β}\cdot \mathrm{d}\right)+\mathrm{I}\cdot \mathrm{Z__0}\cdot \mathrm{sin}\left(\mathrm{β}\cdot \mathrm{d}\right)}-\mathrm{I}\cdot \mathrm{cot}\left(\mathrm{β}\cdot \mathrm{l}\right):$

Stub Location

The location and length of the stub are

 >
 $\left\{{\mathrm{d~}}{=}{0.05894468942}{}⟦{m}⟧{,}{\mathrm{l~}}{=}{0.1111779245}{}⟦{m}⟧\right\}$ (4.1)