A resistive microwave load with impedance ZL = 150 Ω is connected to a 50 Ω coaxial line. What will be the standing wave ratio (SWR) on the line?
Electronics and Communication Engineering
Microwave Communication
Difficulty: Medium
Choose an option
-
AMore than 3
-
BLess than 3
-
CEqual to 3
-
DEither more than 3 or equal to 3 depending on frequency
-
EExactly 2
Answer
Correct Answer: Equal to 3
Explanation
Introduction / Context:Standing wave ratio (SWR) is a measure of impedance mismatch between a transmission line and its load. It indicates how much of the incident signal is reflected due to mismatch.
Given Data / Assumptions:
- Line impedance Z0 = 50 Ω.
- Load impedance ZL = 150 Ω (purely resistive).
- Formula: SWR = (1 + |Γ|) / (1 − |Γ|).
- Reflection coefficient Γ = (ZL − Z0) / (ZL + Z0).
Concept / Approach:
SWR is always ≥ 1. If ZL = Z0, SWR = 1 (perfect match). If ZL differs from Z0, reflections occur, raising SWR.
Step-by-Step Solution:
Γ = (150 − 50) / (150 + 50) = 100 / 200 = 0.5.SWR = (1 + 0.5) / (1 − 0.5) = 1.5 / 0.5 = 3.Thus, the SWR = 3 (exactly).Verification / Alternative check:
Measured VSWR in microwave labs for this ratio confirms the theoretical result of 3.
Why Other Options Are Wrong:
- More than 3: incorrect, exact value is 3.
- Less than 3: mismatch is significant, not smaller.
- Either more than 3 or equal: introduces ambiguity not present in calculation.
- Exactly 2: would occur if ZL = 100 Ω, not 150 Ω.
Common Pitfalls:
Forgetting to take absolute value of Γ; misapplying formula.
Final Answer:
Equal to 3