Microwave measurements – Using SWR to determine impedance Assertion (A): At microwave frequencies, the load impedance is commonly determined by measuring the standing wave ratio (SWR). Reason (R): Both SWR and the reflection coefficient depend on the characteristic impedance and the load impedance.

Introduction:
Direct impedance bridges become impractical at microwave frequencies because distributed effects dominate and lumped standards are difficult to realize. Instead, engineers use standing-wave measurements (SWR, minima positions) on a slotted line or a network analyzer to infer the complex reflection coefficient and thus the load impedance.

Given Data / Assumptions:

• Lossless/low-loss transmission line segment with known characteristic impedance Z0.
• Measurable SWR and position of minima or phase via detector/probe or VNA.
• Linear, time-invariant system and steady-state single-tone excitation.

Concept / Approach:

SWR is related to the magnitude of the reflection coefficient Γ by SWR = (1 + |Γ|) / (1 − |Γ|). The reflection coefficient depends on ZL and Z0 via Γ = (ZL − Z0) / (ZL + Z0). Knowing |Γ| (and often its phase from minima location) allows recovery of ZL using Smith Chart or analytic inversion. Hence R explains A: because SWR and Γ depend on ZL and Z0, measuring SWR lets us determine ZL.

Step-by-Step Solution:

Verification / Alternative check:

Network analyzer readings of S11 magnitude/phase directly yield Γ; Smith Chart transformation confirms the same ZL derived from SWR/minima measurements.

Why Other Options Are Wrong:

Options B–E deny the causal link: since Γ (and thus SWR) explicitly depends on ZL and Z0, R clearly explains A.

Common Pitfalls:

Using SWR alone (without phase) gives two possible impedances mirrored across the resistance axis; phase or minima position resolves ambiguity.

Final Answer:

Both A and R are correct and R is the correct explanation of A.