A transmission line has a characteristic impedance of 50 ohm and is connected to a load of 100 ohm. The VSWR is _________.
2
When a transmission line is terminated in a load that does not equal its characteristic impedance, part of the incident wave is reflected back toward the source. The forward and reflected waves add along the line to form a standing wave, and the ratio of the maximum voltage to the minimum voltage of this pattern is the Voltage Standing Wave Ratio (VSWR). VSWR is a measure of how well the load is matched: a value of 1 means a perfect match with no reflection, while larger values indicate worse matching.
Given: Z0 = 50 Ω, ZL = 100 Ω.
Step 1 — Reflection coefficient (Γ): Γ = (ZL − Z0) / (ZL + Z0) = (100 − 50) / (100 + 50) = 50/150 = 1/3.
Step 2 — VSWR: VSWR = (1 + |Γ|) / (1 − |Γ|) = (1 + 1/3) / (1 − 1/3) = (4/3) / (2/3) = 2.
A quick sanity check: for a purely resistive mismatch, VSWR equals the ratio of the larger resistance to the smaller one, i.e. 100/50 = 2, which confirms the result.
- The value 1 would only occur for a matched load (ZL = Z0), which is not the case here.
- The value 4 corresponds to the square of the impedance ratio, an error made if the ratio is mishandled; VSWR is never below 1, and 0.5 is impossible since VSWR by definition is always ≥ 1.
Hence the correct VSWR is 2.
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