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Standing wave pattern plot, Study notes of Physics Fundamentals

standing wave in electronics domain

Typology: Study notes

2015/2016

Uploaded on 07/15/2016

SABIR_UL.Alam
SABIR_UL.Alam 🇮🇳

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OBJECTIVE:
Plot the standing wave pattern, V(z) Vs length of the line using
MATLAB for given data Z0 =50 , ZL=0, 25, 50, 75, 100 and attenuation
constant α=0, 0.001, 0.002, 0.003,0.004, 0.005, 0.1 .The incident wave amplitude
=1 V and operating frequency f=10 GHz also length of the line=2λ.
THEORY:
Transmission line is a medium through which the EM wave travelling
from source to load, so to know the behavior of the EM travelling wave inside the
transmission line we have to analysis it but it is very difficult to analysis of an
infinitely long transmission line because the parameters are distributed through line
so we consider a small section Z from an infinitely long transmission line in
figure given below
Now the solution of the travelling wave consist two parts one is forward and
reflected shown in the figure Pin is the incident power in the load and Pref is the
reflected power from the load. The travelling voltage and current wave can be
written as
V= V+*exp(-γZ) + V-*exp(γZ)
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OBJECTIVE:

Plot the standing wave pattern, V(z) Vs length of the line using MATLAB for given data Z 0 =50 Ω, Z (^) L=0, 25, 50, 75, 100 Ω and attenuation constant α=0, 0.001, 0.002, 0.003,0.004, 0.005, 0.1 .The incident wave amplitude =1 V and operating frequency f=10 GHz also length of the line=2λ. THEORY: Transmission line is a medium through which the EM wave travelling from source to load, so to know the behavior of the EM travelling wave inside the transmission line we have to analysis it but it is very difficult to analysis of an infinitely long transmission line because the parameters are distributed through line so we consider a small section ∆Z from an infinitely long transmission line in figure given below

Now the solution of the travelling wave consist two parts one is forward and reflected shown in the figure Pin is the incident power in the load and P (^) ref is the reflected power from the load. The travelling voltage and current wave can be written as V= V+*exp(-γZ) + V-^ *exp(γZ)

I= I+exp(-γZ) + I -^ exp(γZ) Where V+=Incident voltage wave amplitude V-^ =Reflected voltage wave amplitude I+=Incident current wave amplitude I-^ =Reflected current wave amplitude γ=Propagation constant=α+jβ Now putting the above value- V= V+exp(-(α+jβ)Z) + V-^ exp((α+jβ)Z) V= V+exp(-αZ) exp(-jβZ)+ V^ -^ * exp(αZ)* exp(jβZ) = V+exp(-αZ)[ exp(-jβZ)+ (V-^ / V+)* exp(2αZ)* exp(jβZ)] = V+exp(-αZ)[{cos(βZ)-jsin(βZ)}+Γ{cos(βZ)+jsin(βZ)}] = V+exp(-αZ)[(1+^ Γ)cos(βZ) - j( 1-^ Γ)sin(βZ)] = V+exp(-αZ)(1+ Γ) cos(βZ) [1 – jStan(βZ)] Where Γ= (V-^ / V+) =Reflection coefficient S=(1+ Γ)/(1- Γ)=Standing wave ratio

CALCULATION:

From the MATLAB simulation we observed the sinusoidal standing wave for different value of load impedance and attenuation constant. If we increase the attenuation constant value by keeping load impedance value constant, than the amplitude of the standing wave decrease simultaneously.