Question 17.2: A 5-V voltage source is connected at port 1 in Figure 17–2 a......
A 5-V voltage source is connected at port 1 in Figure 17–2 and a 50-Ω resistor is connected at port 2. Find the port currents I_{1} and I_{2}.
Using the impedance parameters found in Example 17–1, the i-ν relationships of the two-port network in Figure 17–2 are
V_{1} = 40I_{1} + 15I_{2}
V_{2} = 15I_{1} + 52.5I_{2}
The external connections at the input and output port mean that V_{1} = 5 and V_{2} = –50I_{2}. Substituting these constraints into the two-port i-ν relationships yields
5 = 40I_{1} + 15I_{2}
-50I_{2} = 15I_{1} + 52.5I_{2}
The result is two linear equations in the two unknown port currents. Solving these equations simultaneously yields I_{1} = 132 mA and I_{2} = –19.4 mA. The minus sign here means that the output current I_{2} actually flows out of port 2 as you would expect.