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.
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ABoth A and R are correct and R is the correct explanation of A
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BBoth A and R are correct but R is not the correct explanation of A
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CA is correct but R is wrong
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DA is wrong but R is correct
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EBoth A and R are wrong
Answer
Correct Answer: Both A and R are correct and R is the correct explanation of A
Explanation
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:
1) Measure SWR and, if needed, the distance to the first minimum from a reference.2) Compute |Γ| from SWR.3) Determine the angle of Γ from minima position or VNA phase.4) Convert Γ to ZL using ZL = Z0 * (1 + Γ) / (1 − Γ).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.