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

`Z_L=67 - j16.4`Ω

Step-by-step 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 =(S-1)/(S+1)`

Here S= 1.5

`\Gamma =(S-1)/(S+1)`

`\Gamma =(1.5-1)/(1.5+1)`

`\Gamma =0.2`

`Z_L=Z_o(1+\Gamma )/(1-\Gamma )`

by putting the values

`Z_L=50* \frac{1+0.2e^{-j36^(\circ)} }{1-0.2e^{-j36^(\circ)} }`

`Z_L=67 - j16.4`Ω