Transmission Line (electrical)
An electrical transmission line is a distributed-parameter structure—such as a coaxial cable, twisted pair, or microstrip—designed to guide electromagnetic energy from a source to a load with minimal radiation and reflection losses. At high frequencies, the physical length of the line becomes comparable to the signal wavelength, making lumped-circuit analysis invalid; instead, the line is modelled using the telegrapher's equations that treat resistance, inductance, capacitance, and conductance as distributed per-unit-length quantities. Impedance matching between the line and its terminations is critical to prevent standing waves and power loss.
Key Formula
Z0 = sqrt((R + j*omega*L) / (G + j*omega*C))
LaTeX: Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}}
| Symbol | Meaning | Unit |
|---|---|---|
| Z_0 | Characteristic impedance | Ω |
| R | Series resistance per unit length | Ω/m |
| L | Series inductance per unit length | H/m |
| G | Shunt conductance per unit length | S/m |
| C | Shunt capacitance per unit length | F/m |
| ω | Angular frequency | rad/s |
Worked Example
Problem
A lossless coaxial cable has L = 250 nH/m and C = 100 pF/m. Calculate its characteristic impedance Z₀ and the velocity of propagation v_p.
Solution
Step 1: For a lossless line, R = 0 and G = 0, so Z₀ = sqrt(L/C). Z₀ = sqrt(250×10⁻⁹ / 100×10⁻¹²) Z₀ = sqrt(2500) = 50 Ω Step 2: Phase velocity v_p = 1 / sqrt(L × C) v_p = 1 / sqrt(250×10⁻⁹ × 100×10⁻¹²) v_p = 1 / sqrt(25×10⁻¹⁸) v_p = 1 / (5×10⁻⁹) = 2×10⁸ m/s
Answer
Z₀ = 50 Ω; v_p = 2×10⁸ m/s (≈ 0.67c)
Common Transmission Line Types and Typical Parameters
| Line Type | Z₀ (Ω) | Freq Range | Loss | Application |
|---|---|---|---|---|
| Coaxial (RG-58) | 50 | DC–3 GHz | Low | RF lab, instrumentation |
| Coaxial (RG-6) | 75 | DC–3 GHz | Low | Cable TV, antenna feed |
| Twisted Pair (Cat 6) | 100 | DC–500 MHz | Moderate | Ethernet LAN |
| Microstrip (PCB) | 50–100 | DC–40 GHz | Moderate | RF/microwave circuits |
| Waveguide (WR-90) | N/A | 8.2–12.4 GHz | Very Low | Radar, satellite |
Interactive Tools
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Related Terms
Antenna (electrical)
An antenna is a transducer that converts between guided electromagnetic waves in a transmission line and freely propagating electromagnetic waves in space, enabling wireless transmission and reception of signals. Key performance parameters include gain, radiation pattern, bandwidth, polarisation, and impedance; these are governed by the antenna's geometry, size relative to the operating wavelength, and surrounding environment. Antennas are central to radio broadcasting, mobile communications, radar, satellite links, and wireless sensor networks.
Electrical Modulation
Electrical modulation is the process of varying one or more properties of a high-frequency carrier signal—such as amplitude, frequency, or phase—in proportion to a lower-frequency information signal. It is fundamental to all modern communication systems because modulated carriers can travel long distances with minimal energy loss and can be multiplexed to share a single channel. Applications include AM/FM radio, cellular networks, Wi-Fi, and satellite communications.
Digital Signal Processing
Digital Signal Processing (DSP) is the mathematical manipulation of discrete-time, discrete-amplitude representations of signals—obtained by sampling and quantising an analogue source—to extract information, filter noise, compress data, or transform the signal into a desired form. Core operations include convolution, Fourier analysis via the FFT, FIR/IIR filtering, and modulation; these are implemented in real time on dedicated DSP chips or general-purpose microprocessors. DSP underpins audio processing, medical imaging, telecommunications, radar, sonar, and machine learning inference at the edge.
From Latin "transmittere" (to send across) and "linea" (line, thread). The mathematical treatment of distributed lines originated with Oliver Heaviside and Lord Kelvin in the 1880s during the development of the transatlantic telegraph cable.