Answer:
Reflection Coefficient = ![0.57e^{-i79.8}](https://tex.z-dn.net/?f=0.57e%5E%7B-i79.8%7D)
SWR=3.65
Position of ![V_{max} =3.11cm](https://tex.z-dn.net/?f=V_%7Bmax%7D%20%3D3.11cm)
position of ![i_{max} =1.11cm](https://tex.z-dn.net/?f=i_%7Bmax%7D%20%3D1.11cm)
Explanation:
To determine the above answers, let outline the useful formulas
refection coefficient
.
where terminal impednce = (30-i50)Ω
characteristics impedance= 50Ω
Secondly, the Standing Wave Ratio,![SWR=\frac{1+/p/}{1-/p/}](https://tex.z-dn.net/?f=SWR%3D%5Cfrac%7B1%2B%2Fp%2F%7D%7B1-%2Fp%2F%7D)
Now let us substitute values and solve,
a. ![p=\frac{terminalimpednce -characteristics impedance }{terminalimpednce +characteristics impedance } \\](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Bterminalimpednce%20-characteristics%20impedance%20%7D%7Bterminalimpednce%20%2Bcharacteristics%20impedance%20%7D%20%5C%5C)
![p=\frac{(30-i50)-50}{(30-i50)-50} \\](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B%2830-i50%29-50%7D%7B%2830-i50%29-50%7D%20%5C%5C)
![p=\frac{-20-i50}{80-i50} \\](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B-20-i50%7D%7B80-i50%7D%20%5C%5C)
multiplying the numerator and denominator by the conjugate of the denominator. we have
![p=\frac{-20-i50}{80-i50}*\frac{80+i50}{80+i50}\\](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B-20-i50%7D%7B80-i50%7D%2A%5Cfrac%7B80%2Bi50%7D%7B80%2Bi50%7D%5C%5C)
by carrying out careful operation, we arrived at
![p=\frac{900-i5000}{8900} \\p=0.1011-i0.56179\\](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B900-i5000%7D%7B8900%7D%20%5C%5Cp%3D0.1011-i0.56179%5C%5C)
To express in polar form i.e ![re^{i alpha}](https://tex.z-dn.net/?f=re%5E%7Bi%20alpha%7D)
![r=\sqrt{0.1011^{2}+0.56179^{2}} \\r=0.57\\](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B0.1011%5E%7B2%7D%2B0.56179%5E%7B2%7D%7D%20%5C%5Cr%3D0.57%5C%5C)
to get the angle
alpha=![tan^{-1} \frac{0.56179}{0.1011} \\alpha=-79.8\\](https://tex.z-dn.net/?f=tan%5E%7B-1%7D%20%5Cfrac%7B0.56179%7D%7B0.1011%7D%20%5C%5Calpha%3D-79.8%5C%5C)
hence the Reflection Coefficient,<em>p</em> = ![0.57e^{-i79.8}](https://tex.z-dn.net/?f=0.57e%5E%7B-i79.8%7D)
b. we now determine the Standing Wave Ratio,![SWR=\frac{1+/p/}{1-/p/}](https://tex.z-dn.net/?f=SWR%3D%5Cfrac%7B1%2B%2Fp%2F%7D%7B1-%2Fp%2F%7D)
![swr=\frac{1+0.57}{1-0.57} =3.65\\](https://tex.z-dn.net/?f=swr%3D%5Cfrac%7B1%2B0.57%7D%7B1-0.57%7D%20%3D3.65%5C%5C)
c. to determine the position of the maximum voltage nearest to the load,
we use the equation
![Position of V_{max}=\frac{\alpha λ}{4\pi}+\frac{λ}{2}\\](https://tex.z-dn.net/?f=Position%20of%20V_%7Bmax%7D%3D%5Cfrac%7B%5Calpha%20%CE%BB%7D%7B4%5Cpi%7D%2B%5Cfrac%7B%CE%BB%7D%7B2%7D%5C%5C)
were
is the wavelength of 8cm
lets convert α to rad by multiplying by π/180
![Position of V_{max}=\frac{-79.8 *8cm*\pi}{4\pi*180 } +\frac{8cm}{2} \\](https://tex.z-dn.net/?f=Position%20of%20V_%7Bmax%7D%3D%5Cfrac%7B-79.8%20%2A8cm%2A%5Cpi%7D%7B4%5Cpi%2A180%20%7D%20%2B%5Cfrac%7B8cm%7D%7B2%7D%20%5C%5C)
.
d. also were we have minimum voltage,there the maximum current will exist, to find this position nearest to the load
.
since the voltage minimum occure at 1.11cm. we can conclude that the current maximum also occur at this point i.e 1.11cm