Question

Using a slotted line, the following results were obtained:
a) distance of first minimum from the load = 4 cm;
b) distance of second minimum from the load = 14 cm;
c) voltage standingwave ratio = 1.5.
If the line is lossless and Z0 = 50 , find the load impedance.

Answer 1

Answer:

$Z_L=67 - j16.4$Ω

Explanation:

Given that

d(min,0)= 4 cm

d(min,1)= 14 cm

Voltage standingwave ratio = 1.5

Zo = 50 Ω

We know that

d(min,1) - d(min,0) = λ/2

Now by putting the values

14 - 4 = λ/2

λ = 20 cm

We also know that

β=2π/λ

β=2π/0.2 = 10π rad/m

So we can say that

θr= 2β d(min,n) - (2 n + 1)π rad

θr=2×10π ×0.04 −π = -0.2 π rad

We know that

π rad = 180 °

θr= = -0.2 π rad= -36 °

We know that

$\Gamma =\dfrac{S-1}{S+1}$

Here S= 1.5

$\Gamma =\dfrac{S-1}{S+1}$

$\Gamma =\dfrac{1.5-1}{1.5+1}$

$\Gamma =0.2$

$Z_L=Z_o\dfrac{1+\Gamma }{1-\Gamma }$

by putting the values

$Z_L=50\times \dfrac{1+0.2e^{-j36^{\circ}} }{1-0.2e^{-j36^{\circ}} }$

$Z_L=67 - j16.4$Ω