Question

A two-port network is driven at both ports such that the port voltages and currents nave me following values:

V1=10∠0,
V2=12∠90ᵒ,
I1=0.1∠30ᵒ,
I2=0.15∠120ᵒ.

Determine the incident and reflected voltages at both ports, if the characteristic impedance is 50Ω.

Answer 1

To determine the incident and reflected voltages at both ports of a two-port network with given port voltages and currents, one calculates the voltage reflection coefficient and incident voltage, and from these, determines the reflected voltages using the characteristic impedance.

Step-by-step explanation:

The question involves determining the incident and reflected voltages at both ports of a two-port network with a given characteristic impedance of 50Ω. Incident and reflected voltages are calculated using the formulas for voltage reflection coefficient (Γ) and incident voltage (V+), given by:

• Γ = (V - Z0 I) / (V + Z0 I)
• V+ = ½ (V + Z0 I)

For port 1 (V1 = 10∠0°, I1 = 0.1∠30°),

• Γ₁ = (10∠0° - 50Ω × 0.1∠30°) / (10∠0° + 50Ω × 0.1∠30°)
• V+1 = ½ (10∠0° + 50Ω × 0.1∠30°)

For port 2 (V2 = 12∠90°, I2 = 0.15∠120°),

• Γ₂ = (12∠90° - 50Ω × 0.15∠120°) / (12∠90° + 50Ω × 0.15∠120°)
• V+2 = ½ (12∠90° + 50Ω × 0.15∠120°)

After calculating Γ₁, Γ₂, V+1, and V+2 using the given characteristics of the two-port network and the phasor form of the voltages and currents, you would then be able to find the reflected voltage (V-) using the following:
V- = Γ V+.