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Single Stub Matching of a Transmission Line

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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.

 

> 

restart; assume(d, real, l, real)

Parameters
 

Resistances

> 

Z__0 := 50*Unit('ohms')
> 

Z__L := (35-47.5*I)*Unit('ohms')

Equations
 

Wavelength and propagation constant

> 

lambda := Unit('m')
> 

beta := 2*Pi/lambda
> 

circuit := (Z__0*cos(beta*d)+I*Z__L*sin(beta*d))/(Z__L*cos(beta*d)+I*Z__0*sin(beta*d))-I*cot(beta*l)

Stub Location
 

The location and length of the stub are

> 

fsolve({Im(circuit) = 0, Re(circuit) = 1}, {d = .1*Unit('m'), l = .1*Unit('m')})

{d = 0.5894468942e-1*Units:-Unit(m), l = .1111779245*Units:-Unit(m)}

 (4.1)