You are given a “black box” with two terminals. You play around with the box for

ID: 1924683 • Letter: Y

Question

You are given a “black box” with two terminals. You play around with the box for awhileand make the following observations:

(i) The output voltage from the box is sinusoidal.

(ii) The peak magnitude of the open-circuit voltage at the terminals is 5 V.

(iii) When you connect a 50 resistor across the terminals, the peak magnitude of thevoltage across the resistor is 2.795 V.

(iv) If you short the terminals, the peak magnitude of the current through the short circuitis 100 mA.

Find the power available from the “black box.” Express your answer in dBm.

Please ask if you have any doubt.I will help you.

From (i) we can learn that there is a sinusoidal voltage source and from (ii) its amplitude is 5V.

Let the black box contains impedance of Z = R + jX .

Now ,from (iv) we see that the current when shortcircuited is 100mA = 0.1A ,which tells that magnitude of impedance is

5/0.1 = 50 i.e R2 + X2 = 2500.

From (iii) ,we have that voltage across the resistor 50 is 2.795V .This gives current is 2.795/50 = 0.0559A

I = 5/Z ,where Z2 = (R + 50)2 + X2.Gives Z = 5/0.0559 = 89.45 .

From the two equations , (R + 50)2 - R2 = (89.45)2 - 2500 = 5501.3 gives 100R + 2500 = 5501.3 implies

R = 30 (approximately).This value when substitute this value in the above equation gives X = 40.

therefore the Z = 30 + j40 .

I am not sure of what is meant by power available.But it can be maximum if external resistance matches Z

and the power = V2/2R = 0.078W and the dBm conversion depends on the unit of reference.

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