Find the z-parameters of the two-port network - calculate

Question

Question: 1

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

Fig. 1

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

Z_in = Z₀ (Z_Lcosβl + jZ_O sin βl)/(Z_Ocosβl + jZ_L sin βl)

Question 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 Z_o, α and β at a frequency of 1 GHz.

R	2 Ω/m
L	8 nH/m
G	0.5 mS/m
C	0.23 pF/m

TABLE A

Question 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:

Question 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) + I_R(B₁ + jB₂)

I_s = V_R(C₁ + jC₂) + I_R(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 V_s and I_s 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.

A1	0.8698
A2	0.03542
B1	47.94 Ω
B2	180.8 Ω
C1	0 S
C2	0.001349 S
D1	0.8698
D2	0.03542

Table C