Description
In this laboratory, we will develop several simple functions relating the load impedance ZL, reflection coefficient
-
and input impedance Zin for a lossless transmission line with characteristic impedance Z0, phase constant β and length l.
1. Reflection coefficient and input impedance
Write a function that calculates the reflection coefficient Γ from the normalized load impedance zL = ZL / Z0,
[ Gamma ]= refcoeff(zL)
a function that calculates a rotated (phase shifted) reflection coefficient Γ’ from the reflection coefficient Γ and round-trip phase = 2βl,
-
Gammarot ]= rotrefcoeff(Gamma,theta)
and a function that calculates the normalized input impedance zin = Zin / Z0 from the reflection coefficient Γ and round-trip phase = 2βl,
[ zin ]= inputZ(Gamma,theta)
|
as defined by the following equations, |
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Γ = |
− 1 |
Γ’ = Γexp(− ) |
= |
1 |
+ Γ’ |
= |
1 + Γexp(− ) |
= 2 |
|
|
+ 1 |
1 |
− Γ’ |
1 − Γexp(− ) |
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Alternatively, you might wish to calculate input impedance zin directly from the rotated coefficient Γ’. In the following, you may find it useful to recall,
2
=
For all of the calculations that follow, consider the case of a lossless transmission line with a characteristic impedance Z0 = 75 Ω, phase velocity vp = 2 x 108 m/s, and length l = 0.25 m.
at high F, its inductive
Take a frequency range f = 1atMHzlowF,itstocapacitive300MHz in steps of Δf = 1 MHz.
ECSE 354 – Electromagnetic Waves
ECSE 354 – Electromagnetic Waves
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