When does a wire become a transmission line?

A wire behaves as a simple conductor when its physical length is much shorter than the wavelength of the signal it carries. The rule of thumb is that transmission line effects become significant when the wire length exceeds about one-tenth of the wavelength. At 100 MHz (lambda = 3 meters), any connection longer than 30 cm must be treated as a transmission line. At 10 GHz (lambda = 3 cm), even a 3 mm bond wire is electrically significant. At DC or low audio frequencies, a 1-meter cable is just a wire. At 5 GHz WiFi, that same cable is 17 wavelengths long and every impedance discontinuity creates reflections, standing waves, and signal degradation. This frequency-dependent transition from wire to transmission line is why RF PCB layout rules differ fundamentally from digital PCB rules.

Why is 50 ohms the standard impedance?

The choice of 50 ohms is a compromise between two optima for air-dielectric coaxial cable. Minimum attenuation occurs at 77 ohms (the ratio of outer to inner conductor diameter that minimizes conductor losses). Maximum power handling occurs at 30 ohms (the ratio that maximizes the voltage times current product before breakdown). The geometric mean of 77 and 30 is approximately 48 ohms, rounded to 50 for convenience. European broadcast systems chose 75 ohms (closer to minimum attenuation, since power handling was not critical for receive-only cables), which is why TV and video cables are 75 ohms. Military and instrumentation systems chose 50 ohms as the best overall compromise, and it became the worldwide standard for RF test equipment and transmitter systems.

What happens when a transmission line is not terminated in its characteristic impedance?

When the load impedance differs from Z0, a portion of the incident wave reflects back toward the source. The reflection coefficient is Gamma = (ZL minus Z0) / (ZL plus Z0). An open circuit (ZL = infinity) reflects 100 percent of the power with zero phase shift. A short circuit (ZL = 0) reflects 100 percent with 180 degrees phase shift. A 75-ohm load on a 50-ohm line reflects 20 percent of the power (Gamma = 0.2, return loss = 14 dB). The incident and reflected waves combine to form a standing wave pattern along the line, with voltage maxima and minima that repeat every half wavelength. The VSWR is (1 plus magnitude of Gamma) / (1 minus magnitude of Gamma). At 50 ohm with 75 ohm load: VSWR = 1.5:1.

Fundamentals

Transmission Line

At DC, a wire is a wire. At 5 GHz, a 10 cm PCB trace is not a wire; it is a 1.7 wavelength transmission line where every bend, via, and connector creates reflections that ripple through the frequency response. The critical concept is that when a signal's wavelength becomes comparable to the physical length of the conductor, the voltage and current are not uniform along the wire. They propagate as waves, with a characteristic impedance Z₀ set by the distributed inductance and capacitance of the structure. Any point where Z₀ changes reflects part of the wave back toward the source. Matching the load to Z₀ eliminates reflections and delivers maximum power. This is the foundation of all RF interconnection.

Category: Fundamentals

Standard: 50 Ω (RF), 75 Ω (video)

Effects Begin: Length > λ/10

Transmission Line Types

Type	Z₀ Range	Loss	Shielding	Freq. Range	Use Case
Coaxial (flexible)	50 or 75 Ω	Moderate	Excellent	DC to 18 GHz	Cables, interconnects
Coaxial (semi-rigid)	50 Ω	Low	Excellent	DC to 65 GHz	Lab, phase-stable
Microstrip	20 to 120 Ω	Moderate	Partial	DC to 30 GHz	PCB traces
Stripline	30 to 120 Ω	Moderate	Full	DC to 60 GHz	PCB inner layers
Rectangular waveguide	Variable	Very low	Full	Cutoff to 2× cutoff	High-power radar, sat
CPW	30 to 100 Ω	Low to moderate	Good	DC to 110 GHz	MMIC, mmWave

Characteristic impedance (lossless):
Z₀ = √(L/C) where L, C are per unit length

Reflection coefficient:
Γ = (Z_L − Z₀) / (Z_L + Z₀)
75 Ω load, 50 Ω line: Γ = 0.2, RL = 14 dB, VSWR = 1.5

Propagation velocity:
v = c / √ε_r
Solid PTFE coax (ε_r = 2.1): v = 0.69c = 207 mm/ns. A 10 ns pulse occupies 2.07 meters of cable. Foam-dielectric coax (ε_r = 1.5): v = 0.82c = 245 mm/ns, lower loss but larger diameter.

Common Questions

Frequently Asked Questions

When is a wire a transmission line?

When length > λ/10. At 100 MHz (λ = 3 m): connections >30 cm. At 10 GHz (λ = 3 cm): even 3 mm bond wires matter. At 5 GHz WiFi, a 10 cm trace is 1.7 wavelengths with standing waves at every discontinuity.

Why 50 Ω?

Minimum coax attenuation at 77 Ω. Maximum power handling at 30 Ω. Geometric mean: ~48 Ω, rounded to 50. TV uses 75 Ω (receive only, favoring low loss). Military/instruments use 50 Ω as the compromise standard.

What if not matched?

Γ = (Z_L − Z₀)/(Z_L + Z₀). Open: Γ = 1 (100% reflected). Short: Γ = −1. 75 on 50: Γ = 0.2, VSWR = 1.5. Incident and reflected waves form standing wave pattern repeating every λ/2.

Related Terms

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RF Fundamentals

Transmission Line Calculator

Select line type (coax, microstrip, stripline, CPW). Enter dimensions and dielectric. Compute Z₀, velocity factor, wavelength, and loss per meter at any frequency.

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