Find the z-parameters of the two-port network and setermine

Question

1. Find the z-parameters of the two-port network given in FIGURE 1.

2. (a) A transmission line has a length, l, of 0.4λ. Determine the phase change, βl, that occurs down the line.

(b) A 50 ? lossless transmission line of length 0.4λ is terminated in a load of (40 + j30) ?. Determine, using the equation given below, the input impedance to the line.

Z_in = Z_o (Z_L cosβl + jZ₀ sinβl/Z_o cosβl + jZ_L sinβl)

3. (a) State what is meant by a ‘distortionless' and a ‘lossless' transmission line.

(b) A transmission line has the primary coefficients as given in TABLE A. Determine the line's secondary coefficients Zo, α and β at a frequency of 1 GHz.

4. Calculate the insertion loss of the T-network of FIGURE 2, given the values in the table. (Use equation (6) of Lesson 3.) The transmission matrix for the T- network is:

5. FIGURE 5(a) represents a 50 Hz, high-voltage, transmission line. The relationships between the sending and receiving end voltages and currents are given by the complex ABCD equations:

V_s = V_R(A₁+ jA₂) + IR(B₁+ jB₂)

Is = V_R(C₁+ jC₂) + IR(D₁+ jD₂)

where the subscripts ‘S' and ‘R' are for the sending-end and receiving- end respectively.

(a) Given the parameter values in TABLE C and an open-circuit received voltage measured as 88.9 kV, calculate the values of VS and IS and hence the power (P_SO) absorbed from the supply by the transmission line on open circuit.

(b) If the line is modelled by the T-circuit of FIGURE 3(b), see if you can estimate the primary line coefficients R, L, G and C. The line is 50 km long.