SWR can be computed from the reflection coefficient magnitude |Γ| using which formula?

SWR can be computed from the reflection coefficient magnitude |Γ| using which formula?

• A. SWR = (1+|Γ|)/(1−|Γ|).
• B. SWR = (1−|Γ|)/(1+|Γ|).
• C. SWR is equal to RL.
• D. SWR cannot be calculated from Γ.

Answer: (C)

The key idea is how the reflected wave affects the standing-wave pattern on the line. The reflection coefficient magnitude |Γ| tells you how strong the reflected wave is relative to the forward wave. The standing-wave ratio measures how much the voltage (or current) varies along the line, from its minimum to its maximum. If you have a forward wave of amplitude V+ and a reflected wave of amplitude ΓV+, the total voltage reaches a maximum when the two waves add in phase and a minimum when they subtract. This gives V_max = V+(1 + |Γ|) and V_min = V+(1 − |Γ|). The ratio of these extremes defines SWR: SWR = (1 + |Γ|) / (1 − |Γ|). If you know the load resistance RL and the line impedance Z0, you can relate |Γ| to them with |Γ| = |RL − Z0| / (RL + Z0), and then plug that into the SWR formula. Remember, SWR is a dimensionless ratio, so it isn’t equal to RL (which is a resistance in ohms).

The key idea is how the reflected wave affects the standing-wave pattern on the line. The reflection coefficient magnitude |Γ| tells you how strong the reflected wave is relative to the forward wave. The standing-wave ratio measures how much the voltage (or current) varies along the line, from its minimum to its maximum.

If you have a forward wave of amplitude V+ and a reflected wave of amplitude ΓV+, the total voltage reaches a maximum when the two waves add in phase and a minimum when they subtract. This gives V_max = V+(1 + |Γ|) and V_min = V+(1 − |Γ|). The ratio of these extremes defines SWR: SWR = (1 + |Γ|) / (1 − |Γ|).

If you know the load resistance RL and the line impedance Z0, you can relate |Γ| to them with |Γ| = |RL − Z0| / (RL + Z0), and then plug that into the SWR formula. Remember, SWR is a dimensionless ratio, so it isn’t equal to RL (which is a resistance in ohms).