What Is a Transmission Line
When you connect a signal generator to an oscilloscope with a BNC cable, run a clock signal across a circuit board, or plug in a USB or HDMI lead, you are not just running a wire from one place to another. Once the signal is fast enough, you are using a transmission line — a structure that guides electrical energy as an electromagnetic wave between two conductors. Understanding what that means, and why it matters, is the foundation of everything else in this module.
In a coaxial cable, the signal energy travels as a transverse electromagnetic (TEM) wave in the dielectric space between the inner conductor and the outer shield — not through the metal itself.
View LargerWhy Fast Signals Are Different from DC
Connect a 12-volt battery to a light bulb with 10 meters of wire and current flows immediately. The wire simply provides a low-resistance path, and as long as the voltage is high enough and the resistance is low enough, the circuit works. The length of the wire is almost irrelevant — you could use 1 meter or 100 meters and the bulb would glow the same.
Now replace that 12-volt DC source with a 14 MHz clock signal and send it down the same 10 meters of wire to another circuit board. Suddenly the length matters enormously. The behavior of that wire at 14 MHz is completely different from its behavior at DC or at 60 Hz. Here is why.
At DC, the only electrical property of a wire that matters is its resistance. At audio frequencies a small amount of inductance becomes noticeable but is still usually negligible. At higher frequencies — and for any signal with fast edges, whatever its repetition rate — two additional effects become critically important:
Inductance: Every conductor has inductance distributed along its length. At low frequencies this inductance has negligible reactance, but at 14 MHz the inductive reactance of even a short length of wire is significant. A 10-meter wire at 14 MHz has an inductive reactance of many ohms — enough to impede current flow and cause reflections.
Capacitance: Any two conductors separated by an insulator form a capacitor. In a two-conductor cable, the signal and return conductors are separated by air, foam, or solid insulation, and there is distributed capacitance between them along the entire length. At high frequencies this capacitance allows current to flow transversely between the conductors — current that would simply not flow at DC.
The combination of distributed series inductance and distributed shunt capacitance is the fundamental reason why a cable carrying a fast signal is not just a wire. Instead it behaves as a distributed circuit — an infinite number of tiny inductors in series and tiny capacitors in shunt, stretching along the entire length. The ratio of inductance to capacitance per unit length determines something called the characteristic impedance, which you will learn about in the next lesson.
There is also a more fundamental reason rooted in the speed of light. At 14 MHz, one complete cycle takes 1/14,000,000 of a second. In that time, an electromagnetic wave in free space travels about 21.4 meters — one full wavelength. A 10-meter wire is not a negligible fraction of that wavelength — it is almost half a wavelength long. At half a wavelength, the voltage and current at one end of the wire are not the same as at the other end. The phase of the wave changes continuously along the wire's length. This phase relationship is what creates reflections and standing waves, and what makes impedance transformation by line length possible.
The same thing happens with digital signals at much lower clock rates. What matters is not just the repetition rate but how fast each edge rises and falls. A 1 MHz signal with 2 ns edges contains significant energy at well over 100 MHz, and a connection only a few tens of centimeters long can be “long” for those edges.
The Two-Conductor Structure
A transmission line always consists of two conductors. This is not a coincidence — it is a fundamental requirement. A high-frequency signal can only travel as a wave along a structure that has both an electric field component (requiring two conductors at different potentials) and a magnetic field component (requiring current flowing in opposite directions in the two conductors). A single wire cannot support a complete electromagnetic wave by itself; it radiates energy into space instead of guiding it forward.
The two conductors can be arranged in several ways:
- Coaxial: An inner conductor surrounded by an outer cylindrical conductor (the shield), separated by a dielectric. The fields are completely contained inside the outer conductor, making coax a shielded, single-ended (unbalanced) line. BNC test leads and video cables are coaxial.
- Parallel pair: Two conductors side by side, separated by a fixed spacing. Twin-lead, a signal wire next to a ground wire in a ribbon cable, and the two wires of a twisted pair are all parallel lines. The fields extend outward between the conductors and are not shielded.
- Microstrip and stripline: A flat trace above a ground plane on a PCB (microstrip), or buried between two ground planes (stripline), separated by the board material. Every fast clock and data trace on a modern circuit board is one of these.
- Twisted pair: Two insulated wires twisted together. Twisting keeps the pair balanced and makes it reject interference, which is why Ethernet, USB, RS-485 and telephone wiring all use it.
In every case, current flows down one conductor and returns through the other. At any instant, current in the two conductors is equal in magnitude but opposite in direction. This opposing current flow is what creates the magnetic field that, combined with the electric field between the conductors, forms the complete electromagnetic wave that carries the signal along the line.
Energy Travels as a Wave, Not Through the Conductor
This is the single most important and most counterintuitive fact about transmission lines: the signal energy does not flow through the metal conductors. It flows in the space between them.
This seems wrong at first. After all, electrons do flow in the conductors — that is measurable. But electrons in a copper conductor move very slowly — on the order of a few millimeters per second. The signal energy itself travels at close to the speed of light. Clearly, the energy is not being carried by the electrons.
What actually carries the energy is the electromagnetic field: the electric field (E-field) pointing radially between the two conductors, and the magnetic field (H-field) circling around the conductors, perpendicular to the direction of travel. Together these form a transverse electromagnetic wave, or TEM wave. It is called transverse because both the electric and magnetic fields are perpendicular (transverse) to the direction of energy travel.
The conductors do two things: they provide the boundary conditions that confine and guide the fields, and they carry the surface currents that create and are driven by those fields. Without the metal conductors you could not have the fields in a confined, directed form — the energy would simply radiate outward. But the conductors themselves are the guide, not the carrier.
This has one important practical consequence: the dielectric material between the conductors affects how fast the wave travels and how much loss it causes. In a vacuum, the TEM wave travels at exactly the speed of light, 300,000,000 meters per second (3 × 10⁸ m/s). In a coaxial cable filled with solid polyethylene dielectric, the wave travels at about 66% of that speed, and on an FR-4 circuit board at roughly half. This is the velocity factor, which becomes important when you need to calculate signal delay or cut a cable to a specific electrical length.
The Distributed Circuit Model
To analyze transmission line behavior mathematically, engineers model the line as a series of infinitesimally small lumped circuit elements repeated along its entire length. For a lossless (ideal) transmission line, each tiny section of length Δx contains:
- L·Δx: A small series inductor representing the magnetic energy stored in the conductor current at that point (L is inductance per unit length, in henries per meter)
- C·Δx: A small shunt capacitor representing the electric energy stored in the field between the conductors (C is capacitance per unit length, in farads per meter)
As Δx approaches zero, this model becomes exact. The behavior of the line — characteristic impedance, wave speed, reflection behavior — all emerge from the ratio and product of L and C.
- Characteristic impedance Z0 = √(L/C) — determined by the geometry of the conductors and the dielectric
- Wave velocity v = 1/√(LC) — determines how fast the wave travels along the line
Both are properties of the line's construction, not its length or the frequency in use.
For a real (lossy) line, two additional elements are added: a series resistance R·Δx representing conductor loss (resistive losses in the metal), and a shunt conductance G·Δx representing dielectric loss (current leaking through the insulation). For most cables up to a few tens of megahertz, conductor loss dominates and dielectric loss is minor; on circuit boards at gigabit data rates, dielectric loss becomes just as important.
Understanding the distributed model explains why a transmission line of any length has the same characteristic impedance: Z₀ is determined by L and C per unit length, not by the total length. A 1-meter piece of RG-213 has 50-ohm characteristic impedance. So does a 100-meter piece. Characteristic impedance is a property of the cable's construction, not its length.
Types of Transmission Lines
You will meet several types of transmission line in everyday electronics, each with characteristics suited to different jobs.
| Type | Typical Z0 | Balanced? | Typical Loss | Common Uses |
|---|---|---|---|---|
| RG-58 / RG-316 coax | 50 Ω | No (single-ended) | Moderate | BNC test leads, signal generator and scope connections, internal RF wiring |
| RG-59 / RG-6 coax | 75 Ω | No (single-ended) | Low | Analog and SDI video, TV and satellite, S/PDIF coaxial audio |
| PCB microstrip / stripline | 50 Ω typical (set by geometry) | No, or differential pairs | Rises with frequency | Clock and data traces on circuit boards |
| USB differential pair | 90 Ω differential | Yes (differential) | Moderate | USB data inside the cable and on the board |
| Cat 5e / Cat 6 twisted pair | 100 Ω differential | Yes (differential) | Low | Ethernet, RS-485, long sensor and control runs |
| Ribbon cable (signal-ground-signal) | ~100–120 Ω | Depends on wiring | Moderate | Board-to-board buses, IDC headers |
| 300-Ω twin-lead | 300 Ω | Yes (balanced) | Moderate (wet) | Older TV and FM antenna connections |
Single-ended vs. differential is an important distinction. Coaxial cable and a PCB trace over a ground plane are single-ended (unbalanced) — one conductor (the shield or ground plane) is the reference, and the other carries the signal. Twisted pairs and differential trace pairs are balanced — the two conductors carry equal and opposite signals, and the receiver looks only at the difference between them. Interference that couples equally into both wires (common-mode noise) is cancelled at the receiver, which is why long or noisy runs such as Ethernet, USB and RS-485 use differential pairs. If a balanced pair is driven unequally, or a single-ended cable's shield carries current on its outside, the cable radiates and picks up interference; ferrite common-mode chokes, covered in the Interference and Noise module, address this.
Four common transmission lines: coaxial cable, twisted pair, ribbon cable and PCB microstrip. All work on the same principles.
View LargerWhy This Matters in Practice
Understanding that a fast connection is not just a wire — that it is a guided-wave structure with specific electrical properties — changes how you design boards, choose cables and read an oscilloscope. Several important practical consequences follow directly from the theory above.
Cable impedance must match the system impedance
Signal generators, oscilloscope 50 Ω inputs, spectrum analyzers and most RF test equipment are designed around 50 Ω; video equipment is designed around 75 Ω; USB around 90 Ω and Ethernet around 100 Ω differential. When the cable matches the equipment, the signal arrives cleanly. If you connect a 75 Ω video cable into a 50 Ω system, there is an impedance mismatch at every connection point, which causes reflections. For short cables and slow signals the effect is small; for long cables and fast edges it can be the difference between a clean signal and a corrupted one.
Unterminated lines ring
If a line is driven by a low-impedance source and ends in a high-impedance input — the normal situation for a logic output driving a logic input — each edge travels to the far end, reflects, travels back, reflects again, and so on. On the oscilloscope this appears as overshoot, undershoot and ringing on every edge. If the ringing crosses the logic threshold, the receiver sees extra edges: a clock input may count twice, or a data line may read the wrong bit. Correct termination, covered later in this module, stops the reflections.
Cable loss increases with frequency and length
Every cable loses some of the signal to heat, and the loss rises with frequency because of skin effect and dielectric loss. A cable that carries a 10 MHz signal almost perfectly may badly round off the edges of a 1 Gb/s data stream. This is why long HDMI and USB runs need active cables or repeaters, and why gigabit Ethernet has a 100-meter limit on Cat 5e.
Cables can radiate and pick up interference
When common-mode current flows on the outside of a cable's shield, or a twisted pair is driven unequally, the cable becomes an accidental aerial. It radiates the signal, causing interference to other equipment, and picks up noise from its surroundings. Good grounding of shields, differential signalling, and ferrite chokes on cables prevent this.
Even “slow” signals can need transmission-line thinking
A common rule of thumb is that a connection behaves as a transmission line when its one-way delay is more than about one-sixth of the signal's rise time. Modern logic families have rise times of 1–3 ns even when the clock is only a few megahertz, so a trace or cable only a few centimeters long can need care. Do not assume that because a signal's repetition rate is low you can treat the connection as a simple wire.
You are sending a 25 MHz SPI clock between two boards over a 30 cm ribbon cable. The microcontroller's output rise time is 2 ns. Signals travel along the ribbon cable at about 70% of the speed of light. Is transmission line theory relevant?
By the clock frequency alone: one wavelength at 25 MHz in free space = 300/25 = 12 meters; in the cable, 12 × 0.70 = 8.4 meters. The 0.3 m cable is only 1/28 of a wavelength, so it looks short.
By the edges: the cable's delay is 0.3 m / (0.70 × 3 × 10⁸ m/s) = 1.43 ns. One-sixth of the 2 ns rise time is 0.33 ns. The cable's delay is more than four times that limit, so the edges will see a transmission line. Without termination, expect overshoot and ringing on every clock edge — exactly the kind of fault that causes an SPI link to work on the bench and fail when the cable is lengthened.
Frequently Asked Questions
Does the signal current actually flow through the metal conductor, or not?
Both, in a sense. Electrons do move back and forth in the conductor surface at the signal frequency — this is a real current that can be measured. But these surface currents are the result of the electromagnetic wave in the space between the conductors, not the cause of it. The energy is stored and transported in the electromagnetic fields, not in the electron motion. If you could instantly replace the copper conductors with perfect conductors (zero resistance), the wave would travel exactly the same way and at the same speed — but no resistive heat would be generated. The practical implication is that conductor losses (skin effect, resistance) cause cable attenuation, and these losses occur in the thin surface layer of the conductor, not throughout its bulk.
Can I use any two-wire cable as a transmission line?
Technically yes, but the characteristic impedance and loss will be determined by the geometry and dielectric of whatever cable you use. Speaker wire, for example, has a characteristic impedance of around 100–150 ohms depending on conductor spacing and insulation material — not one of the standard values. It also has higher loss than proper coaxial cable or twisted pair. For short runs and slow signals, improvised cables can work. For any run where loss matters or where impedance matching is important, use purpose-designed transmission line with known, specified characteristics.
Why does my signal look different when I use a longer cable?
Because the cable is a transmission line, and the far end is probably not terminated in the cable's characteristic impedance. Each edge reflects from the mismatched end, and the reflection returns to the source after a delay set by the cable length. With a short cable the reflections arrive while the edge is still rising and blend into it; with a longer cable they arrive later and show up as separate steps, overshoot or ringing. Loss also rises with length, rounding off the edges. The fix is to terminate the line correctly — for example a 50 Ω feed-through terminator at the oscilloscope input when looking at a 50 Ω source — not to hunt for a “magic length” of cable.
My coax has a DC resistance of 3 ohms per 100 feet. Why is its impedance specified as 50 ohms?
The DC resistance and the characteristic impedance are completely different quantities. The DC resistance is the ohmic loss of the conductor itself, measured with a multimeter, and it increases with length. The characteristic impedance is a property of the cable's distributed inductance and capacitance, determined by the physical geometry (conductor diameter, spacing, and dielectric material). For fast signals, the characteristic impedance determines how the line handles traveling waves and does not change with length. A 1-meter piece and a 1000-meter piece of RG-213 both have a characteristic impedance of 50 ohms, but the longer piece has 1000 times the DC resistance and much more RF loss.
Does it matter which end of a cable connects to the source?
For a plain cable, no — coaxial cable and twisted pair are reciprocal, meaning they work identically in both directions. A travelling wave propagates just as well either way. What does matter is where the termination goes: a parallel termination belongs at the far (receiving) end, and a series termination belongs right at the driver. Some cables also have a built-in direction for practical reasons — a USB cable has different connectors at each end, and an active HDMI or USB cable has electronics at one end that only work in one direction.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.