Electronics Guide

Characteristic Impedance

The characteristic impedance of a transmission line, written Z₀, is the ratio of voltage to current for a wave traveling in one direction along the line. Where the series resistance is negligible against the inductive reactance, which on ordinary board and cable geometries holds well below a gigahertz, it depends only on the distributed inductance L and capacitance C per unit length:

Z₀ = √(L / C)

Unlike ordinary impedance, characteristic impedance is not a measure of opposition to current flow; it describes the relationship between the voltage and the current of a wave propagating along the line. It is fixed by the cross-sectional geometry and the surrounding dielectric, not by the length of the line, so a driver launching an edge into a long line sees that impedance for the whole flight time, whatever sits at the far end. Two useful corollaries follow from the same per-unit-length quantities: the characteristic impedance equals the one-way delay divided by the total capacitance of the line, and equally the total inductance divided by that delay. Any feature that adds capacitance without adding inductance, such as a via pad, a test point, or an unpopulated connector footprint, therefore pulls the local impedance down.

Geometry sets the value in every structure. A microstrip trace takes its impedance from trace width, substrate thickness, and the permittivity of the laminate; widening the trace or thinning the dielectric beneath it raises capacitance and lowers the impedance. A coaxial cable takes its impedance from the ratio of the outer to the inner conductor diameter and from the dielectric between them. Both relationships are developed with worked numbers in the sections on line types below.

A small set of impedance values has become conventional, and the reasons are geometric. For air-dielectric coaxial line, the diameter ratio that maximizes power handling corresponds to about 30 ohms, while the ratio that minimizes attenuation corresponds to about 77 ohms. Fifty ohms sits between the two, and that compromise is what radio-frequency systems and test equipment adopted almost universally. Video and cable-television distribution standardized on 75 ohms instead, nearer the low-attenuation end, because a receiving system cares about signal level rather than about transmitted power. Filling the line with a dielectric scales both optima down by the square root of the relative permittivity, so these figures describe air-spaced construction rather than a solid-dielectric cable.

Digital interfaces set their own targets, and those targets belong to the individual specification rather than to a single convention. Single-ended nets commonly run at 50 ohms, while differential targets fall across 85, 90, and 100 ohms depending on the standard and, in several cases, on its generation. Ethernet twisted pair and general-purpose LVDS use 100 ohms differential, and USB 2.0 high-speed calls for 90 ohms. Reading the target from the relevant specification, rather than assuming that every differential pair wants 100 ohms, avoids a systematic mismatch that no amount of careful routing will recover.

Propagation Velocity and Delay

Electromagnetic waves travel along transmission lines at a velocity set by the same per-unit-length inductance and capacitance that fix the impedance:

v = 1 / √(L C)

In a vacuum this velocity equals the speed of light, but the dielectric materials in practical lines slow it down. The velocity factor, which expresses the actual velocity as a fraction of the speed of light, equals 1 / √ε_r for a non-magnetic dielectric, where ε_r is the relative permittivity of the medium the field occupies. Solid polyethylene has a relative permittivity near 2.25, which gives a velocity factor of about 0.67, conventionally quoted as 0.66 on cable datasheets. Foamed dielectrics trap air in the insulation, lowering the effective permittivity and raising the velocity factor toward 0.8. Traces on FR-4 printed circuit boards see an effective permittivity between that of the laminate and the surrounding air, giving velocity factors of roughly 0.6 for surface microstrip and near 0.5 for buried stripline, the latter working out to about 15 centimeters per nanosecond.

Propagation delay, the time required for a signal to travel from one end of a transmission line to the other, directly affects system timing. In high-speed digital systems, propagation delays through traces and cables must be accounted for in timing analysis. Matched-length routing, where multiple signal paths are designed with equal electrical length, ensures simultaneous signal arrival despite different physical routes.

The wavelength of a signal on a transmission line depends on both frequency and propagation velocity. For a narrowband or periodic signal, conductor lengths approaching a significant fraction of a wavelength, conventionally one-tenth, call for transmission line treatment. At 1 gigahertz on an inner-layer PCB trace propagating at 15 centimeters per nanosecond, the wavelength is 15 centimeters, so traces as short as 1.5 centimeters already show transmission line behavior. Digital nets are judged by a different and usually stricter measure, set by the edge rate rather than by the clock frequency, which the section on critical length below develops.

Reflection and Matching

When a traveling wave encounters an impedance discontinuity, such as the end of a transmission line or a junction between lines of different impedance, part of the wave reflects back toward the source. The reflection coefficient gives the ratio of the reflected wave amplitude to the incident wave amplitude. For a line of characteristic impedance Z₀ terminated in a load impedance Z_L:

Γ = (Z_L − Z₀) / (Z_L + Z₀)

The same expression applies at any discontinuity, with Z_L read as the impedance the wave is entering and Z₀ as the impedance it is leaving. A mid-line junction between a 50-ohm cable and a 75-ohm cable therefore reflects exactly as a mismatched termination does, which is why connectors, adapters, and layer transitions all deserve the same scrutiny as the load itself.

A matched termination, where Z_L equals Z₀, makes the coefficient zero: nothing reflects, and the load absorbs all the incident energy. Open and short circuits are the extreme mismatches and reflect the whole wave, equal in magnitude but opposite in sign. An open end gives a coefficient of +1, so the reflected wave adds to the incident one and momentarily doubles the voltage there. A short gives a coefficient of −1, so the reflected wave inverts, cancels the voltage at the short, and doubles the current instead. Practical mismatches fall between these limits and produce partial reflections that degrade signal quality and create EMC problems.

Standing waves result from the superposition of the incident and reflected waves. The standing wave ratio (SWR) is the ratio of the maximum to the minimum voltage magnitude along the line, and it follows directly from the magnitude of the reflection coefficient:

SWR = (1 + |Γ|) / (1 − |Γ|)

A perfect match gives an SWR of 1, an open or a short gives an unbounded SWR, and practical mismatches fall between the two. The fraction of the incident power that the load accepts is 1 − |Γ|², so a reflection coefficient of 0.2, an SWR of 1.5, sends 4 percent of the incident power back toward the source. High SWR also produces voltage maxima along the line that stress insulation and connectors, and current maxima that raise conductor loss. In EMC terms, the standing wave pattern raises the peak field around the line and worsens coupling to neighboring circuits.

Loss Mechanisms

Practical transmission lines dissipate energy through several mechanisms. Conductor losses arise from the resistance of the conductors, which increases at high frequencies due to skin effect confining current to a thin layer at the conductor surface. Dielectric losses result from energy dissipation in the insulating material, characterized by the loss tangent of the dielectric. Radiation losses occur when the transmission line radiates electromagnetic energy into space, typically most significant when the line is poorly shielded or improperly configured.

The two dominant mechanisms scale differently with frequency, and the difference decides which one governs a given design. Skin depth falls as the inverse square root of frequency, reaching roughly 2 micrometers in copper at 1 gigahertz, so conductor attenuation rises approximately as the square root of frequency. Dielectric attenuation rises roughly in proportion to frequency and to the laminate's dissipation factor. Conductor loss therefore dominates at low frequencies and dielectric loss overtakes it higher up, which is why material selection rather than copper weight governs the budget on long, fast channels.

Loss is expressed in decibels per unit length and must be budgeted so that signal levels remain adequate at the receiving end. Because the mechanisms attenuate the high-frequency content of an edge more than its low-frequency content, a lossy channel does not merely shrink the signal; it slows the edges and spreads each bit into its neighbors. Excessive loss also converts electrical energy to heat, which matters in high-power radio-frequency feeds even where the signal level itself is comfortable.

Coaxial Cables

Coaxial cables consist of a center conductor surrounded by a dielectric, an outer conductor (shield), and typically a protective jacket. This concentric geometry confines electromagnetic fields to the region between the conductors, providing excellent shielding and minimal radiation. Coaxial cables are widely used for RF signal distribution, test equipment connections, and video signals where shielding effectiveness is important.

The characteristic impedance of coaxial cable depends only on the ratio of the conductor diameters and on the permittivity of the dielectric between them:

Z₀ = (138 / √ε_r) × log₁₀(D / d)

Here D is the inner diameter of the outer conductor and d is the outer diameter of the inner conductor. The logarithm is base ten, and the constant 138 belongs to that base; the same relation written with a natural logarithm carries a constant of 60 instead. The two constants differ by the natural logarithm of ten, so reading the base-ten form as a natural logarithm inflates the answer by a factor of about 2.3 and turns an ordinary cable into an impedance no coaxial cable has.

The arithmetic is worth working once. Solid polyethylene has a relative permittivity of about 2.25, so √ε_r is 1.5 and the leading term is 92 ohms. Reaching 50 ohms then requires log₁₀(D / d) = 0.543, a diameter ratio of about 3.5: a cable with a 3.5-millimeter dielectric needs a 1.0-millimeter center conductor. Reaching 75 ohms in the same dielectric requires a ratio of about 6.5, which is why 75-ohm cable of a given outside diameter carries a noticeably thinner and more fragile center conductor than its 50-ohm counterpart. Checking the same geometry against the natural-logarithm form gives (60 / 1.5) × ln(3.5) = 50.1 ohms, confirming that the two expressions agree.

Shield effectiveness varies with construction type. Solid outer conductors provide the best shielding but reduce flexibility. Braided shields offer flexibility with good but imperfect shielding. Foil shields supplement braiding for improved high-frequency performance.

Transfer impedance quantifies the coupling directly. It is the longitudinal voltage developed on the inner circuit per unit length of cable, divided by the current flowing on the outside of the shield, and it is usually quoted in milliohms per meter at a stated frequency, with lower values indicating a better shield. Its frequency behavior separates the constructions. A solid tubular shield starts at its direct-current resistance and then falls steeply as skin effect confines the disturbing current to the outer surface. A braided shield falls at first for the same reason, but magnetic flux leaking through the apertures of the weave adds an inductive term that grows with frequency, so its transfer impedance passes through a minimum and then rises again. That rise, rather than any shortfall in coverage at low frequencies, is what limits braided cable at high frequencies.

Microstrip and Stripline

Microstrip transmission lines consist of a trace on one side of a dielectric substrate with a ground plane on the opposite side. This structure is common on printed circuit boards because it places traces on the accessible outer layers. The characteristic impedance depends on trace width, substrate thickness, and dielectric constant. Microstrip lines are not fully enclosed, making them more susceptible to coupling and radiation than enclosed structures.

Stripline consists of a trace between two ground planes, fully enclosed within the dielectric. This structure provides better shielding than microstrip, reducing coupling to adjacent traces and external fields. Stripline is commonly used for inner-layer routing on multilayer PCBs where improved isolation is needed. The enclosed structure also provides more consistent impedance, less affected by nearby components or traces.

Controlled impedance PCB fabrication produces traces with specified characteristic impedances within tight tolerances. The PCB manufacturer adjusts trace widths and dielectric thicknesses to achieve the target impedance. Specifying impedance requirements in PCB fabrication documentation ensures that manufactured boards support the intended transmission line behavior.

Twisted Pair

Twisted pair transmission lines consist of two insulated conductors twisted together. The twisting reduces susceptibility to external magnetic fields by alternating the orientation of the conductors relative to the field. Twisted pair is widely used for balanced signals in networking, telephony, and instrumentation applications.

Unshielded twisted pair (UTP) relies entirely on the twisting and balanced drive/receive circuits for noise immunity. Shielded twisted pair (STP) adds an overall shield for improved performance in high-interference environments. The characteristic impedance of twisted pair depends on wire gauge, insulation thickness, and twist pitch, with 100 ohms being common for networking applications.

Differential signaling over twisted pair provides excellent common-mode rejection when properly implemented. Both conductors experience the same induced noise, which a differential receiver rejects. This noise rejection allows twisted pair to operate in environments that would overwhelm single-ended transmission.

Waveguides

Waveguides are hollow conductive structures that guide electromagnetic waves through their interior. Unlike the transmission lines discussed above, which support TEM (transverse electromagnetic) wave propagation, waveguides support TE (transverse electric) and TM (transverse magnetic) modes. Waveguides are used primarily at microwave and millimeter-wave frequencies where their low loss and high power handling outweigh their size and complexity disadvantages.

Rectangular waveguides are most common, with standardized dimensions for different frequency bands. The lowest frequency that can propagate (the cutoff frequency) depends on the waveguide dimensions, with larger waveguides supporting lower frequencies. Below cutoff, waves attenuate exponentially rather than propagating, a property exploited in waveguide-below-cutoff structures for EMC shielding ventilation panels.

Critical Length Determination

An interconnect becomes electrically significant when its one-way propagation delay stops being negligible against the signal's rise or fall time. The governing quantity is the edge rate, not the clock period: a net that toggles at a few megahertz while carrying a 200-picosecond edge still needs transmission line treatment, and a designer who classifies nets by clock frequency alone will miss it. The common screening rule flags a line once its length exceeds somewhere between one-tenth and one-sixth of the distance the signal travels during one rise time, with one-sixth the most frequently quoted threshold.

The numbers follow from the propagation velocity. For a 1-nanosecond edge on an inner-layer PCB trace, where signals travel roughly 15 centimeters per nanosecond, the edge occupies 15 centimeters of trace and the critical length falls between 1.5 and 2.5 centimeters. Sharpen the edge to 100 picoseconds and the same rule puts the threshold between 1.5 and 2.5 millimeters, shorter than many connector pins, package escapes, and via structures. The threshold is only a screening guideline; the value tightens as the tolerable impedance deviation and timing margin shrink, so demanding designs often warrant transmission line treatment below these lengths. What finally matters is whether the resulting reflections stay inside the receiver's noise budget.

When interconnects are shorter than the critical length, they can be treated as lumped capacitance with minimal transmission line effects. However, as clock frequencies increase and edge rates become faster, the critical length shrinks, making transmission line analysis necessary for progressively shorter traces. Modern high-speed interfaces with sub-nanosecond edges require transmission line treatment for traces only a few millimeters long.

Reflections and Signal Integrity

Impedance mismatches in digital signal paths cause reflections that appear as overshoot, undershoot, and ringing on the waveform. The mechanism repays careful tracing, because the overshoot a receiver sees is governed by the source impedance rather than by the far-end mismatch. A driver of output impedance Z_S launches onto the line only the fraction Z₀ / (Z_S + Z₀) of its full swing. An unterminated receiver reflects that wave with a coefficient of +1 and doubles it. Whether the doubled wave overshoots the settled level therefore depends entirely on how large the launched wave was.

The arithmetic makes the point. Driving a 50-ohm line with an open far end, an ideal zero-impedance source launches the full swing, the far end reaches twice it, and the overshoot is 100 percent. A 20-ohm source launches 50 / 70 of the swing, and the doubled wave overshoots by 42.9 percent. A 50-ohm source launches exactly half, the doubled wave lands on the settled level, and the overshoot is zero. The far-end mismatch is identical in all three cases, so it cannot be what sets the overshoot. This is why series termination at the driver is effective, and why an unterminated net driven by a strong, low-impedance buffer rings hardest.

Once the reflected wave returns to the source it re-reflects there unless the driver is matched, and the energy bounces back and forth, decaying on each round trip by the product of the two reflection coefficients. A source impedance below the line impedance gives a negative source coefficient, and that inversion is what turns the second round trip into undershoot and sustains the alternating ringing that follows.

Reflections degrade signal integrity by reducing noise margin and potentially causing false switching. The receiver sees the reflected signal superimposed on the transmitted signal, potentially interpreting noise as valid data transitions. In severe cases, reflections can cause ringing that crosses logic thresholds multiple times, triggering multiple switching events from a single intended transition.

From an EMC perspective, reflections increase common-mode currents on signal traces, enhancing radiation. The standing waves created by reflections concentrate energy at specific locations along the line, potentially creating hot spots that radiate more strongly. Proper termination eliminates reflections, improving both signal integrity and EMC performance.

Termination Strategies

Series termination places a resistor at the source end of the transmission line, matching the combined source impedance to the line characteristic impedance. When the driver output impedance and the series resistor together match Z₀, no reflection occurs at the source. The voltage launched on the line is half the supply voltage, but upon reaching the open-circuit load, reflection doubles it to the full level. This technique works well for point-to-point connections with one receiver.

Parallel termination places a resistor at the load end of the line, matching the load impedance to Z₀. This approach absorbs incident energy without reflection, maintaining signal amplitude from source to load. However, parallel termination requires continuous DC current through the termination resistor, increasing power consumption. Thevenin termination using two resistors to a split supply provides DC bias while maintaining AC termination.

AC termination uses a series RC network at the load, providing termination at signal frequencies while blocking DC current. This approach reduces power consumption compared to pure parallel termination but requires careful selection of component values to provide appropriate termination across the signal bandwidth.

Active termination uses voltage regulators or other active circuits to provide termination impedance with reduced power consumption. Some integrated circuits include on-die termination (ODT) that can be programmed to match various transmission line impedances. Active termination adds complexity but can significantly reduce power in systems with many terminated lines.

Return Path Considerations

Every transmission line requires a return path for current flow. In PCB designs, the ground plane typically provides this return path, with return current flowing directly beneath the signal trace to minimize the loop area. Interruptions in the return path, such as gaps in the ground plane, force return current to flow around the discontinuity, creating large current loops that radiate and couple to other circuits.

Reference plane changes, where a signal transitions from one ground plane to another through a via, create return path discontinuities. The return current must transition between planes, either through the via barrel capacitance or through explicit return path vias placed near the signal via. Failure to provide adequate return path continuity at layer transitions increases emissions and crosstalk.

Differential signaling provides its own return path through the paired conductors, reducing dependence on ground plane continuity. However, common-mode currents still require a return path to the ground plane. Differential pairs should maintain proximity to their reference plane, particularly in regions where common-mode rejection is important.

Coupling Mechanisms

Inductive coupling occurs when the magnetic field from current on one line links with an adjacent line, inducing voltage in the coupled line. The coupled voltage is proportional to the mutual inductance between lines and the rate of change of current. Fast edge rates increase inductive coupling by increasing di/dt.

Capacitive coupling occurs when the electric field from voltage on one line couples to an adjacent line through the mutual capacitance between them. The coupled current is proportional to the mutual capacitance and the rate of change of voltage. Like inductive coupling, capacitive coupling increases with faster edges.

In typical PCB geometries, both inductive and capacitive coupling occur simultaneously. Their relative magnitudes depend on the dielectric environment surrounding the conductors. In stripline, the homogeneous dielectric makes the inductive and capacitive coupling coefficients essentially equal, so their contributions cancel at the far end of the coupled line. In microstrip, the mixed environment of air above and substrate below leaves the coefficients unequal, so a net far-end coupling remains. Understanding this balance, or lack of it, helps predict crosstalk behavior and select appropriate mitigation strategies.

Near-End and Far-End Crosstalk

Near-end crosstalk (NEXT) appears at the end of the victim line closest to the signal source on the aggressor line. For typical PCB geometries, both capacitive and inductive coupling contribute to NEXT with the same polarity, causing the effects to add. NEXT increases with coupling length up to a saturation point determined by the signal rise time.

Far-end crosstalk (FEXT) appears at the end of the victim line opposite the signal source. In stripline, the capacitive and inductive contributions to FEXT tend to cancel, resulting in low far-end crosstalk. In microstrip, the cancellation is imperfect, and significant FEXT can occur. FEXT increases linearly with coupling length without saturation.

Crosstalk Reduction Techniques

Increasing separation between traces reduces coupling by decreasing mutual inductance and capacitance. The three-width (3W) rule, which calls for a center-to-center spacing of at least three trace widths (an edge-to-edge gap of two widths), provides a practical guideline for many applications. Greater spacing may be necessary for particularly sensitive signals or when routing over longer parallel distances.

Ground traces or guard traces between signal traces provide shielding and reduce direct coupling. For maximum effectiveness, guard traces should be frequently connected to the ground plane through vias. Without adequate grounding, guard traces can actually increase coupling by providing an additional coupling path.

Differential signaling reduces crosstalk susceptibility because coupled signals appear as common-mode interference rejected by the differential receiver. Proper differential routing maintains close coupling between the pair members so that coupled noise affects both conductors equally.

Layer assignment strategies route critical signals on inner layers (stripline) where coupling is lower. Orthogonal routing, where signals on adjacent layers run perpendicular to each other, minimizes the parallel coupling length. Careful floorplanning keeps aggressor and victim signals separated throughout their routes.

Radiation from Transmission Lines

Transmission lines radiate when the current in the signal conductor does not match the current in the return path, creating a net current that acts as an antenna. Common-mode current on cables, which represents the imbalance between signal and return currents, is the primary source of radiated emissions from many electronic products. Proper transmission line design minimizes this imbalance.

Return path discontinuities force return current to flow in larger loops, increasing the effective antenna area. Maintaining uninterrupted return paths and minimizing loop areas reduces radiation. Where discontinuities are unavoidable, filtering or shielding may be necessary to control the resulting emissions.

Unterminated or poorly terminated transmission lines exhibit standing waves that concentrate electromagnetic energy at specific locations. These concentrations can create radiation hot spots that dominate the emissions from a product. Proper termination eliminates standing waves and reduces peak field levels.

Susceptibility Considerations

Just as transmission lines can radiate, they can receive external electromagnetic energy. Long cables act as antennas, coupling RF energy into the circuits they connect. Shielded cables, properly terminated to the enclosure, prevent external fields from inducing currents on the internal conductors.

Common-mode rejection in balanced transmission lines provides inherent immunity to external fields. Differential receivers see coupled noise as a common-mode signal that they reject. Maintaining balance throughout the transmission path, from driver through line to receiver, maximizes this immunity.

Filtering at cable entry points removes RF energy that couples to cables before it can affect internal circuits. The filter design should address both differential-mode and common-mode energy, as coupled interference may appear in either mode depending on the cable geometry and field characteristics.

Cable Shielding and Grounding

Shielded cables reduce both emissions and susceptibility by confining electromagnetic fields. The shield effectiveness depends on material, coverage, and termination. Braided shields provide good flexibility and reasonable shielding, while solid shields offer superior performance at the cost of flexibility. Foil shields supplement braiding for improved high-frequency performance.

Shield grounding practices significantly affect shielding effectiveness. Shields should be bonded to the enclosure through 360-degree termination to connectors, maintaining shield integrity at the interface. Pigtail connections, where the shield is gathered into a wire for connection to ground, defeat shielding effectiveness at high frequencies by introducing inductance in the shield path.

For low-frequency magnetic field shielding, connecting the shield at one end only may be appropriate to prevent ground loop currents. However, this approach compromises high-frequency shielding where the shield must be connected at both ends to provide a low-impedance return path. Many applications benefit from hybrid approaches that provide single-point grounding at low frequencies and multi-point grounding at high frequencies.

Time Domain Reflectometry

Time domain reflectometry (TDR) characterizes transmission lines by analyzing reflections from a fast-edge stimulus. A TDR instrument sends a step waveform down the line and displays the reflected signal as a function of time, which corresponds to distance along the line. Changes in impedance appear as steps or transitions in the TDR display, allowing identification of impedance variations, discontinuities, and termination conditions.

Spatial resolution follows directly from the rise time of the reflected step. Because the step must travel out to a feature and back before the next feature is reached, two discontinuities separate cleanly only when the distance between them exceeds half the distance the edge covers in one rise time. On a board trace propagating at 15 centimeters per nanosecond, a 20-picosecond system rise time separates features about 1.5 millimeters apart, while a 200-picosecond rise time blurs anything closer than about 15 millimeters into one feature. The rise time that counts is the one arriving back at the sampler, degraded by the cables, probes, and line loss in between, so an instrument's published figure describes a best case that a real fixture rarely delivers.

Network Analysis

Vector network analyzers (VNAs) characterize transmission lines in the frequency domain, measuring parameters such as return loss (S₁₁) and insertion loss (S₂₁). These measurements reveal impedance matching, loss characteristics, and resonances across the frequency range of interest. VNA measurements complement TDR by providing detailed frequency-domain information.

De-embedding techniques remove the effects of test fixtures and connections, revealing the characteristics of the device under test alone. Accurate de-embedding is essential for characterizing small structures where fixture effects can dominate raw measurements.

Eye Diagram Analysis

Eye diagrams overlay multiple bit periods of a digital signal to reveal signal quality at the receiver. The resulting pattern resembles an eye, with the opening indicating the available margin for correct data detection. Transmission line effects including loss, reflections, and crosstalk close the eye, reducing margin and increasing error rates.

Eye diagram measurements on actual systems verify that the complete signal path, including transmission lines, provides adequate signal quality. Eye mask testing compares measured eye diagrams against defined masks that specify minimum opening requirements for compliant operation.