An infinitely long lossy transmission line with characteristic impedance Z01 = 200Ω is feeded by a λ/2 section of 100Ω lossless transmission line as shown in figure. If a voltage generator Vsg = 4 V with an internal resistance Vg = 100Ω is applied to the whole configuration, then the average power (in mWatt) transmitted to the infinite transmission line will be ______. (Answer up to one decimal place)Correct answer is '17.8'. Can you explain this answer?

Question

An infinitely long lossy transmission line with characteristic impedance Z01 = 200Ω  is feeded by a λ/2 section of 100Ω  lossless transmission line as shown in figure. If a voltage generator Vsg = 4 V with an internal resistance Vg = 100Ω  is applied to the whole configuration, then the average power (in mWatt) transmitted to the infinite transmission line will be ______. (Answer up to one decimal place)Correct answer is '17.8'. Can you explain this answer?

Answer

As we know, the input impedance of infinitely long lossy transmission line is equal to its characteristic impedance. So, the input impedance to line 1 will be

Z_in1 = Z₀₁ = 200 Ω

From the shown arrangement of the transmission line, it is clear that the effective load impedance for line 2 will be equal to the input impedance of line 1.

i.e. Z_L2 = Z_in1 = 200 Ω

Since the length of the line 2 is λ/2, so the input impedance of line 2 will be equal to its load.

i.e. Z_in2 = Z_L2 = 200 Ω

(l = λ/2)

Therefore, the reflection coefficient at the load terminal of line 2 is given as

Now, the input voltage of line 2 is determined by using voltage division rule as

Again, the voltage at any point on line 2 is given as

whereV₀⁺ is voltage of incident wave β is phase constant of the voltage wave and z is distance from load. So, for z = −λ/2

= – 2 volt

Therefore, the incident average power to the line 2 is given as

So, the reflected average power at the input terminal of line 1 (load terminal of line 2) is

Thus, we get the transmitted power to the line 1 as

P_av^t = P_avⁱ - P_av^r = 20 - 2.2 = 17.8 m Watt

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