Electronics Guide

Characteristic Impedance

The characteristic impedance of a transmission line, typically denoted Z0, represents the ratio of voltage to current for a traveling wave on the line. This impedance depends on the line's distributed inductance (L) and capacitance (C) per unit length according to the relationship Z0 = sqrt(L/C). Unlike ordinary impedance, characteristic impedance is not a measure of opposition to current flow but rather describes the relationship between voltage and current in a wave propagating along the line.

For common transmission line geometries, characteristic impedance depends on the physical dimensions and the dielectric material between conductors. Microstrip traces on PCBs have characteristic impedances determined by trace width, substrate thickness, and dielectric constant. Coaxial cables derive their impedance from the ratio of outer to inner conductor diameters and the dielectric properties of the insulation. Understanding these relationships allows engineers to design transmission lines with specific impedances for their applications.

Common characteristic impedance values have become standard in electronic systems. Fifty ohms is nearly universal for RF systems and test equipment, providing a reasonable compromise between power handling and loss. Seventy-five ohms is common for video and cable television systems, optimizing for lower loss at the expense of some power handling capability. Digital systems often use various impedances, with 50 ohms common for single-ended signals and 100 ohms for differential pairs.

Propagation Velocity and Delay

Electromagnetic waves travel along transmission lines at a velocity determined by the distributed inductance and capacitance: v = 1/sqrt(LC). In a vacuum, this velocity equals the speed of light, but the presence of dielectric materials in practical transmission lines reduces the propagation velocity. The velocity factor, expressing the actual velocity as a fraction of the speed of light, typically ranges from about 0.5 for coaxial cables with solid dielectric to 0.66 for common PCB materials.

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. When conductor lengths approach a significant fraction of the wavelength, typically cited as one-tenth or more, transmission line effects become important. For a 1 GHz signal on a typical PCB, the wavelength is approximately 15 centimeters, meaning traces as short as 1.5 centimeters exhibit noticeable transmission line behavior.

Reflection and Matching

When a traveling wave encounters an impedance discontinuity, such as at the end of a transmission line or at a connection between lines of different impedances, part of the wave reflects back toward the source. The reflection coefficient describes the ratio of reflected to incident wave amplitude and depends on the impedances involved. For a transmission line of impedance Z0 terminated in load impedance ZL, the reflection coefficient is (ZL - Z0)/(ZL + Z0).

A perfectly matched termination, where ZL equals Z0, produces no reflection and absorbs all incident energy. Open circuits and short circuits represent the extreme mismatches, producing reflections of equal magnitude but opposite phase. Practical mismatches produce intermediate reflections that can degrade signal quality and create EMC problems.

Standing waves result from the superposition of incident and reflected waves. The standing wave ratio (SWR) quantifies the degree of mismatch, with SWR = 1 for a perfect match and increasing values indicating greater mismatch. High SWR causes variations in voltage and current along the line, concentrates RF energy at voltage maxima, and reduces power transfer efficiency. In EMC terms, high SWR can increase radiation from transmission lines and exacerbate coupling to other 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.

Loss increases with frequency, making it a critical consideration in high-frequency and high-speed systems. Longer transmission lines and higher-loss dielectric materials exacerbate the effect. Loss is typically expressed in decibels per unit length and must be budgeted in system designs to ensure adequate signal levels at the receiving end. Excessive loss not only degrades signals but also converts electrical energy to heat, potentially affecting system reliability.

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 on the ratio of outer to inner conductor diameters and the dielectric constant: Z0 = (138/sqrt(er)) * log(D/d), where D is the inner diameter of the outer conductor and d is the outer diameter of the inner conductor. Common values include 50 ohms for RF systems and 75 ohms for video applications.

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. The transfer impedance specification quantifies how effectively the shield prevents external fields from inducing signals on the inner conductor.

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

A transmission line becomes electrically significant when the propagation delay along the line becomes comparable to signal rise or fall times. The common rule of thumb considers transmission line effects important when the line length exceeds one-sixth to one-tenth of the distance a signal travels during its rise time. For a signal with 1 nanosecond rise time on a typical PCB, this critical length is approximately 1 to 1.5 centimeters.

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 signal waveforms. A signal transitioning from a driver into a higher-impedance trace experiences a positive reflection that adds to the signal, causing overshoot. A termination with impedance lower than the line causes negative reflection, appearing as undershoot. Multiple reflections between source and load create ringing that persists until the reflections attenuate.

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 and 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. The relative magnitudes of the two mechanisms depend on the line geometry, with microstrip tending toward capacitive dominance and stripline toward inductive dominance. Understanding the coupling mechanism 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 rule, specifying minimum spacing of three trace widths between traces, 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.

TDR resolution depends on the rise time of the stimulus, with faster edges enabling detection of smaller features. Modern TDR instruments with picosecond rise times can resolve features as small as a few millimeters. This capability supports detailed characterization of PCB traces, connectors, and other transmission line structures.

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.