A50 (ohm) lossless transmission line is terminated in a load with impedance z= (30-j50) ohm. the wavelength is 8cm. determine:

(a) reflection coefficient (solved: 0.1 - j0.56 or 0.56 angle -79.9)
(b) standing wave ratio (solved: 3.64)
(c) position of voltage max. nearest the load
(d) position of current max. nearest the load

Reflection Coefficient =

SWR=3.65

Position of

position of  

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,

Now let us substitute values and solve,

a.  

multiplying the numerator and denominator by the conjugate of the denominator. we have

by carrying out careful operation, we arrived at

To express in polar form i.e

to get the angle

alpha=

hence the Reflection Coefficient,p =

b. we now determine the Standing Wave Ratio,

c. to determine the position of the maximum voltage nearest to the load,

we use the equation

were is the wavelength of 8cm

lets convert α to rad by multiplying by π/180

.

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

this is true

explanation:

i looked it up