Standing Wave
Understanding Standing Waves
Standing waves are the physical manifestation of impedance mismatch on a transmission line. Every time energy reflects from a mismatch, the interference between forward and reverse waves creates a stationary pattern of voltage highs and lows. The severity of this pattern, measured as VSWR, determines how much power is wasted, how much stress components experience, and how much the impedance varies along the line.
Standing Wave Parameters
V(z) = V+(1+Γe−j2βz)
Maxima/minima spacing:
Δz = λ/2 between adjacent maxima
Δz = λ/4 between max and min
VSWR from standing wave:
VSWR = Vmax/Vmin
Standing Wave Effects by VSWR
| VSWR | |Γ| | Power Reflected | Vpeak (100W) | Impact |
|---|---|---|---|---|
| 1.0:1 | 0.000 | 0% | 141V | No standing wave |
| 1.5:1 | 0.200 | 4% | 170V | Acceptable |
| 2.0:1 | 0.333 | 11% | 189V | Antenna BW limit |
| 3.0:1 | 0.500 | 25% | 200V | PA protection |
| ∞:1 | 1.000 | 100% | 283V | Open/short, damage |
Key Equations
Power: dB = 10log(P2/P1)
Voltage: dB = 20log(V2/V1)
dBm to watts:
P(W) = 10(dBm−30)/10
0 dBm = 1 mW, +30 dBm = 1 W
Wavelength:
λ = c/f = 300/f(MHz) meters
Comparison
| VSWR | Vmax/Vmin | % Reflected | Mismatch loss | Condition |
|---|---|---|---|---|
| 1.0 | 1.0 | 0% | 0 dB | Traveling wave |
| 1.5 | 1.5 | 4% | 0.18 dB | Good match |
| 2.0 | 2.0 | 11% | 0.51 dB | Marginal |
| 5.0 | 5.0 | 44% | 2.55 dB | Poor |
| ∞ | ∞ | 100% | ∞ dB | Pure standing |
Frequently Asked Questions
How formed?
Mismatch reflects wave. Incident+reflected interfere: constructive = V_max, destructive = V_min. Spaced lambda/2. Pattern is stationary. No standing wave when matched (|Γ|=0). Full standing wave when open/short (|Γ|=1).
Dangerous?
V_max can exceed connector ratings (arcing). 100W, VSWR 3:1: 200V peak. Reflected power damages PAs. Standing waves increase I^2*R loss. Modern PAs have VSWR protection to fold back power when reflection detected.
Slotted line?
Historical measurement: probe slides along slotted TL, samples voltage. Measures VSWR directly. Position of minimum gives Gamma phase. Replaced by VNA for all practical measurements. Now used for education.