Transmission Line
Understanding Transmission Lines
At frequencies where the physical length of a conductor is a significant fraction of a wavelength, the conductor becomes a transmission line and must be analyzed using electromagnetic wave theory rather than simple circuit theory. The boundary is roughly when the line length exceeds lambda/10.
Types of Transmission Lines
- Coaxial cable: A center conductor surrounded by dielectric and an outer shield. Supports TEM mode from DC to its cutoff frequency. Standard impedances: 50 and 75 ohms.
- Rectangular waveguide: A hollow metallic tube. No center conductor. Lowest loss at microwave/mmWave. Supports TE and TM modes above cutoff frequency.
- Microstrip: A conductor strip on a dielectric substrate with ground plane below. Used in PCBs and MMICs. Quasi-TEM mode.
- Stripline: A conductor strip between two ground planes. True TEM mode. Better shielding than microstrip but harder to fabricate.
- Coplanar waveguide (CPW): A center strip with ground planes on either side, all on the same surface. Popular in MMICs.
Transmission Line Effects
- Reflections: Impedance discontinuities cause reflections (standing waves).
- Dispersion: Phase velocity varies with frequency, distorting wideband signals.
- Loss: Conductor and dielectric losses attenuate the signal exponentially with length.
- Delay: Signals travel at a fraction of the speed of light, determined by the dielectric constant.
Z0 = (138/√εr) × log10(D/d)
Characteristic impedance (microstrip, approx):
Z0 = (87/√(εr+1.41)) × ln(5.98h/(0.8w+t))
Propagation velocity:
v = c / √εeff
Electrical length:
θ = (360 × f × L) / v (degrees)
A quarter-wave line: θ = 90°, L = λ/4
Transmission Line Comparison
| Type | Mode | Z0 Range | Loss | Frequency |
|---|---|---|---|---|
| Coaxial cable | TEM | 50, 75 Ω | Moderate | DC - 65 GHz |
| Rectangular waveguide | TE/TM | N/A (wave Z) | Lowest | 1 - 300+ GHz |
| Microstrip | Quasi-TEM | 20 - 120 Ω | Moderate-High | DC - 100 GHz |
| Stripline | TEM | 20 - 120 Ω | Moderate | DC - 60 GHz |
| CPW | Quasi-TEM | 30 - 100 Ω | Moderate | DC - 300 GHz |
Frequently Asked Questions
What is a transmission line in RF?
A transmission line is a structure that guides electromagnetic energy between two points. At RF frequencies, ordinary wires radiate and lose energy. Transmission lines (coax, waveguide, microstrip) confine the electromagnetic field and deliver power efficiently with controlled impedance.
When does a wire become a transmission line?
When its physical length exceeds roughly one-tenth of a wavelength (lambda/10). At 1 GHz (lambda = 30 cm), any conductor longer than 3 cm must be treated as a transmission line. At 10 GHz, the threshold drops to 3 mm.
What is characteristic impedance?
Characteristic impedance (Z0) is the ratio of voltage to current in a traveling wave on the line. It is determined by the geometry and dielectric material, not by the line length. When the load impedance equals Z0, no reflections occur and maximum power is transferred.