EMC System Concepts

Introduction

Electromagnetic Compatibility (EMC) engineering at the system level requires a conceptual framework that enables engineers to analyze, predict, and solve interference problems across complex electronic systems. While component-level EMC knowledge addresses individual circuits, system-level EMC concepts provide the tools to understand how multiple subsystems interact electromagnetically, how interference propagates through systems, and how architectural decisions affect overall electromagnetic performance.

System-level EMC thinking transforms what might otherwise seem like unpredictable interference problems into analyzable engineering challenges. By understanding the fundamental models and principles that govern electromagnetic behavior in systems, engineers can make informed design decisions that prevent problems rather than react to them. This systematic approach becomes essential as systems grow in complexity, integrating diverse technologies operating across wide frequency ranges within increasingly compact enclosures.

This article explores the key conceptual frameworks used in EMC system analysis, from the foundational source-path-receptor model to advanced topics like electromagnetic topology and transfer function analysis. These concepts provide the intellectual toolkit for tackling EMC challenges in modern electronic systems.

The Source-Path-Receptor Model

The source-path-receptor (SPR) model, sometimes called the source-path-victim model, is the most fundamental framework for analyzing EMC problems. Every electromagnetic interference situation can be decomposed into three essential elements, and effective EMC engineering involves addressing one or more of these elements.

The Source

The source is any element that generates electromagnetic energy that may potentially cause interference. Sources can be categorized by their nature:

Intentional Sources: Transmitters, oscillators, and signal generators designed to produce electromagnetic energy. While the energy is intentional, coupling to unintended receptors creates interference.
Unintentional Sources: Circuits and systems that generate electromagnetic energy as a byproduct of their primary function. Digital circuits with switching transitions, switch-mode power supplies, motors, and relay contacts are common examples.
Natural Sources: Lightning, electrostatic discharge (ESD), and cosmic radiation. While these cannot be controlled at the source, understanding their characteristics is essential for designing immune systems.

Source characterization involves understanding both the frequency content and the amplitude of emissions. Time-domain signals like switching waveforms must be analyzed in the frequency domain to understand their spectral content. A trapezoidal waveform, for example, has a spectrum that rolls off at 20 dB per decade above the first corner frequency (related to pulse width) and 40 dB per decade above the second corner frequency (related to rise time).

The Coupling Path

The coupling path is the medium through which electromagnetic energy travels from source to receptor. Understanding coupling paths is often the key to solving EMC problems, as these paths can be interrupted or attenuated more easily than modifying sources or receptors.

Coupling paths are categorized into four fundamental types:

Conductive Coupling: Direct electrical connection through shared conductors, typically power supply lines, ground connections, or signal cables. Common impedance in shared return paths is a frequent cause of conductive coupling.
Capacitive Coupling: Electric field coupling through parasitic capacitance between conductors. Particularly significant at high frequencies and small spacing, capacitive coupling increases with frequency and the mutual capacitance between conductors.
Inductive Coupling: Magnetic field coupling through mutual inductance between current loops. Current in one loop induces voltage in nearby loops, with coupling proportional to the loop areas, their orientation, and the rate of change of current.
Radiative Coupling: Electromagnetic wave propagation through space. Dominant at frequencies where conductor dimensions approach a quarter wavelength, radiative coupling involves true electromagnetic wave behavior with both electric and magnetic field components.

In practice, most coupling situations involve combinations of these mechanisms. At lower frequencies, conductive and inductive coupling typically dominate, while at higher frequencies, capacitive and radiative coupling become more significant.

The Receptor

The receptor (or victim) is any circuit or system that responds to the coupled electromagnetic energy in an undesirable way. Receptor susceptibility depends on:

Sensitivity: The minimum signal level the receptor can detect or respond to. Highly sensitive analog circuits are more susceptible than robust digital logic.
Bandwidth: The frequency range over which the receptor can respond. Wideband receivers are susceptible to interference across a broader spectrum.
Threshold Characteristics: Whether the receptor fails gracefully (degraded performance) or catastrophically (complete malfunction) when stressed.
Recovery Capability: Whether the receptor can automatically recover from interference or requires intervention.

Using the SPR Model

The SPR model provides a systematic framework for solving EMC problems by asking three questions:

Can the source be controlled? Reducing emissions through filtering, slowing edge rates, spreading spectrum, or shielding may eliminate the problem at its origin.
Can the path be interrupted? Adding filters, shields, physical separation, or proper grounding can break or attenuate the coupling path.
Can the receptor be hardened? Increasing noise margins, adding filtering, or improving shielding can make the receptor immune to the interference level.

Often, the most effective solution involves addressing multiple elements. The SPR model helps ensure that all options are considered and that the most cost-effective combination is selected.

Differential-Mode and Common-Mode Currents

Understanding the distinction between differential-mode (DM) and common-mode (CM) currents is essential for effective EMC analysis and design. These two current modes have fundamentally different characteristics and require different mitigation strategies.

Differential-Mode Current

Differential-mode current is the intended signal current that flows in a loop, traveling down one conductor and returning through another. In a two-wire system, DM currents are equal in magnitude but opposite in direction at any point along the transmission line.

Characteristics of differential-mode currents:

Desired Signal: DM current carries the intended information in the circuit and is what the circuit is designed to process.
Field Cancellation: Because the currents flow in opposite directions in close proximity, their magnetic fields tend to cancel, reducing far-field radiation.
Controlled Impedance: DM signals travel in transmission lines with well-defined characteristic impedance, enabling impedance matching.
Filtering: Differential-mode filters use series inductance and parallel capacitance across the line to attenuate unwanted DM signals.

Common-Mode Current

Common-mode current flows in the same direction on multiple conductors, returning through some unintended path such as a ground plane, chassis, or even parasitic capacitance to earth ground. CM currents are typically unintended and are often the dominant source of EMI problems.

Characteristics of common-mode currents:

Unintended Noise: CM currents are usually undesirable, representing noise or interference rather than signal.
Efficient Radiation: Because currents flow in the same direction, their fields add rather than cancel, making CM currents much more efficient radiators than DM currents of the same magnitude.
Undefined Return Path: The return path for CM current is often through parasitic elements, making the current path difficult to predict or control.
Cable Antenna Effect: Cables carrying CM current act as antennas, with the cable length determining resonant frequencies.

The 10X Rule of CM Radiation

A common rule of thumb in EMC engineering states that common-mode currents can produce the same level of radiation as differential-mode currents that are 10 to 100 times larger. This dramatic difference arises because:

DM current loops are typically small (centimeters), while CM current loops can be large (meters).
DM fields cancel; CM fields add.
Cables driven in common mode act as efficient antennas.

This means that even small CM currents (microamps or less) can cause significant EMI problems. A CM current of only 5 to 10 microamps on a 1-meter cable at 100 MHz can cause a product to fail FCC Class B emissions limits.

Mode Conversion

Mode conversion occurs when energy transfers between differential and common modes. This typically happens due to:

Asymmetry: Unequal impedances, unbalanced circuits, or asymmetric layout cause DM signals to partially convert to CM.
Ground Impedance: Non-zero impedance in the ground return path creates voltage drops that appear as CM signals.
Connector Imbalance: Connectors with different pin assignments or unequal conductor lengths can cause mode conversion.

Understanding mode conversion is crucial because even well-designed DM circuits can generate significant CM interference through inadvertent mode conversion.

Mitigation Strategies

Different strategies are required for DM and CM interference:

Differential-Mode Mitigation:

Series inductors and parallel capacitors (forming a pi or T filter configuration)
Proper impedance matching to prevent reflections
Shielded cables with shield connected at appropriate points

Common-Mode Mitigation:

Common-mode chokes (inductors wound such that DM flux cancels but CM flux adds)
Capacitors to ground from each conductor
Maintaining symmetry and balance in circuits and layout
Proper grounding to control CM return paths
Cable shielding with 360-degree termination to enclosure

Impedance Concepts in EMC

Impedance is a fundamental concept in EMC that extends far beyond simple resistance. Understanding both the impedance of EMC elements (filters, shields, grounds) and the impedance of the electromagnetic environment is crucial for effective EMC design.

Transfer Impedance

Transfer impedance characterizes how well a shielded cable or enclosure prevents external fields from inducing voltages on internal conductors (and vice versa). For a cable shield, transfer impedance is defined as the ratio of induced voltage per unit length to the current flowing on the outer surface of the shield:

Z_T = V_inner / (I_outer x L)

where V_inner is the voltage induced on the inner conductor, I_outer is the current on the shield exterior, and L is the cable length.

Key aspects of transfer impedance:

DC Resistance: At low frequencies, transfer impedance equals the DC resistance of the shield divided by its length.
Skin Effect: At higher frequencies, skin effect confines current to the shield surfaces, reducing Z_T because inner and outer surfaces become electromagnetically isolated.
Braid Penetration: In braided shields, magnetic field penetration through braid apertures causes Z_T to increase at high frequencies.
Solid vs. Braided: Solid shields have lower Z_T than braided shields at high frequencies due to absence of apertures.

Wave Impedance

Wave impedance characterizes the electromagnetic environment and varies with source characteristics, distance from the source, and frequency. It is defined as the ratio of electric to magnetic field magnitudes:

Z_w = E / H

In the far field (distance greater than wavelength / 2 pi), wave impedance equals the intrinsic impedance of free space: 377 ohms. In the near field, wave impedance depends on source type:

Electric (High-Impedance) Sources: Sources with high voltage and low current (like antennas with high input impedance) produce near fields with E/H greater than 377 ohms. Capacitive coupling dominates.
Magnetic (Low-Impedance) Sources: Sources with high current and low voltage (like current loops and transformers) produce near fields with E/H less than 377 ohms. Inductive coupling dominates.

This distinction is important for shielding because electric fields are more easily shielded than magnetic fields, and the effectiveness of different shield materials and thicknesses varies with wave impedance.

Impedance of Ground Systems

Ground systems have non-zero impedance that becomes significant at high frequencies. A "perfect" ground with zero impedance exists only at DC. At higher frequencies:

Inductance Dominates: Ground conductor inductance (approximately 1 nH per mm for wires and traces) creates impedance that increases with frequency.
Skin Effect: Current concentrates near conductor surfaces, increasing resistance.
Resonance: Ground planes and structures exhibit resonant behavior at frequencies where dimensions approach half wavelength.

A 10-cm ground wire has approximately 100 nH inductance, presenting 63 ohms impedance at 100 MHz. This impedance can cause significant ground bounce in digital systems and coupling in sensitive analog circuits.

Source and Load Impedance Matching

Impedance matching concepts from signal integrity directly apply to EMC:

Reflection Coefficient: Impedance mismatches cause reflections that can increase emissions and susceptibility at specific frequencies.
Filter Impedance Matching: EMI filters are designed for specific source and load impedances. Mismatched conditions can drastically reduce filter effectiveness.
Resonance Creation: Impedance mismatches combined with parasitic elements can create resonances that amplify interference at specific frequencies.

Resonance Effects in Systems

Resonance is one of the most important phenomena in EMC because it can dramatically amplify interference at specific frequencies. A structure resonating at an interference frequency can turn a minor emission or susceptibility problem into a major compliance failure.

Cable and Enclosure Resonances

Cables and enclosures resonate at frequencies where their dimensions are related to wavelength:

Quarter-Wave Resonance: A cable with one end open and one end grounded resonates when its length equals an odd multiple of quarter wavelength. For a 1-meter cable, the first resonance occurs near 75 MHz.
Half-Wave Resonance: A cable with both ends open or both ends grounded resonates when its length equals a multiple of half wavelength. For a 1-meter cable, the first resonance occurs near 150 MHz.
Cavity Resonance: Enclosures act as resonant cavities at frequencies where dimensions correspond to half wavelength. A 30-cm enclosure has cavity modes starting around 500 MHz.

PCB and Trace Resonances

Printed circuit board structures exhibit resonance effects:

Trace Resonance: Long traces, especially stubs, resonate at frequencies related to their electrical length.
Power-Ground Cavity: The space between power and ground planes forms a resonant cavity with modes determined by board dimensions.
Via Resonance: Via barrels have associated inductance and capacitance that create resonances at high frequencies.

Component Resonances

Real components have parasitic elements that create self-resonant frequencies (SRF):

Capacitor SRF: Package inductance and capacitance create a series resonance above which the capacitor becomes inductive.
Inductor SRF: Parasitic capacitance between windings creates a parallel resonance above which the inductor becomes capacitive.
Ferrite Bead Resonance: Ferrite beads exhibit complex impedance with resonant behavior affecting their EMC performance.

System-Level Resonance Analysis

At the system level, multiple resonances interact:

Mode Coupling: Resonant modes in different structures can couple, creating new resonances at frequencies not predicted by analyzing structures individually.
Filter Resonances: Improperly designed or installed EMI filters can resonate with source or load impedances, amplifying rather than attenuating interference.
Ground System Resonance: Complex ground systems with multiple paths can resonate, creating high-impedance ground at specific frequencies.

Resonance Mitigation

Several strategies address resonance problems:

Damping: Adding resistive elements to resonant structures reduces Q factor and peak amplitude.
Frequency Shifting: Modifying dimensions or adding reactive elements can move resonant frequencies away from problem frequencies.
Absorption: Using lossy materials (ferrites, absorbers) converts resonant energy to heat.
Bypassing: Multiple bypass capacitors with different SRFs extend effective bypass frequency range.

Reciprocity in EMC Analysis

The reciprocity theorem is a powerful principle in EMC that states: in a linear, bilateral medium, the ratio of a response to an excitation remains constant when the positions of excitation and measurement are interchanged. This seemingly abstract principle has profound practical implications for EMC testing and analysis.

The Reciprocity Principle

For antennas and electromagnetic coupling structures, reciprocity means that the pattern and efficiency of a structure are the same whether it is transmitting or receiving. A cable that is an efficient radiator at a particular frequency will also be an efficient receiver at that frequency.

Mathematically, for two ports in a reciprocal system:

Z₁₂ = Z₂₁

or equivalently for S-parameters:

S₁₂ = S₂₁

Practical Applications

Reciprocity simplifies many EMC analyses:

Emissions and Immunity Correlation: Understanding that structures efficient at radiating are also efficient at receiving helps predict susceptibility from emissions measurements.
Coupling Path Analysis: A coupling path can be analyzed in either direction with the same result, allowing engineers to choose the more convenient analysis direction.
Test Method Development: Some EMC tests exploit reciprocity by exciting the system at the receptor and measuring at the source location, which may be experimentally more convenient.
Shield Effectiveness: Shielding effectiveness is the same whether containing emissions or providing immunity, provided the measurement conditions are reciprocal.

Limitations of Reciprocity

Reciprocity holds only for linear, passive, bilateral systems:

Active Devices: Amplifiers, mixers, and other active components break reciprocity because gain is unilateral.
Nonlinear Effects: Rectification, intermodulation, and saturation effects in ferrites and other materials invalidate reciprocity.
Magnetic Bias: Ferrite materials under DC bias (as in isolators and circulators) exhibit non-reciprocal behavior.

Despite these limitations, reciprocity remains a valuable tool because the coupling paths and shielding structures of interest in EMC are typically passive and linear.

Superposition Principles

The superposition principle states that in a linear system, the response to multiple simultaneous excitations equals the sum of the responses to each excitation applied individually. This principle enables the decomposition of complex EMC problems into simpler, analyzable components.

Application to EMC Analysis

Superposition enables several EMC analysis techniques:

Multiple Source Analysis: When multiple interference sources are present, each can be analyzed separately and the results summed. This is particularly useful when sources operate at different frequencies.
Modal Decomposition: Differential and common-mode currents can be analyzed separately using superposition, with the total field being the sum of DM and CM contributions.
Frequency-Domain Analysis: Time-domain signals can be decomposed into frequency components (Fourier analysis), each analyzed separately, and results combined.
Near-Field and Far-Field Contributions: At intermediate distances, both near-field and far-field components may be significant and can be superposed.

Power Summation vs. Field Summation

An important consideration when applying superposition is whether to sum fields (voltages, currents) or powers:

Coherent Sources: When sources are correlated (phase-locked or from the same oscillator), fields add directly. This can result in constructive or destructive interference.
Incoherent Sources: When sources are uncorrelated (different oscillators, random noise), powers add. This is the root-sum-square (RSS) combination.

In EMC analysis, signals from the same clock source are coherent and should be summed as fields. Signals from different, unrelated sources are typically incoherent and should be combined as power.

Worst-Case Analysis

For compliance and margin analysis, worst-case assumptions are often used:

Coherent Maximum: All coherent contributions assumed to add in phase (worst-case constructive interference).
Incoherent Addition: For regulatory compliance, incoherent sources may be summed linearly (not RSS) as a conservative approach.

Electromagnetic Topology

Electromagnetic topology is a systematic approach to EMC analysis developed by Carl E. Baum and others that uses network theory concepts to describe electromagnetic coupling in complex systems. This framework provides a rigorous method for decomposing systems into hierarchical levels with well-defined interfaces.

Topological Decomposition

Electromagnetic topology represents systems as a hierarchy of nested volumes (topological levels) separated by surfaces:

Level 0: The external environment
Level 1: The first level of shielding (equipment enclosure)
Level 2: Second level of shielding (shielded subsystems)
Level N: Additional nested levels as needed

Each transition between levels is characterized by a transfer function that describes how electromagnetic energy couples through the boundary.

Topological Network Representation

The system is represented as a network where:

Volumes: Represented as nodes in the network
Surfaces: Represented as branches connecting nodes
Coupling Paths: Characterized by transfer functions (S-parameters, transfer impedance)
Sources and Sinks: Attached to appropriate nodes in the network

This representation allows system-level EMC analysis using standard network analysis techniques.

Penetration Points

In electromagnetic topology, penetration points are the locations where electromagnetic energy can cross topological boundaries:

Apertures: Holes, slots, and gaps in shields (intentional or parasitic)
Conductors: Cables, connectors, and traces that cross boundaries
Joints and Seams: Discontinuities in conductive surfaces

Each penetration point is characterized by its electromagnetic properties (shielding effectiveness, transfer impedance) across frequency.

Application to System Design

Electromagnetic topology guides EMC-conscious system architecture:

Zoning: Grouping circuits by EMC sensitivity and emission levels, with appropriate isolation between zones.
Interface Definition: Specifying EMC requirements at each topological boundary.
Hierarchical Protection: Implementing multiple levels of protection for sensitive circuits.
Cable Routing: Treating cables as topological elements that must be properly controlled.

Transfer Functions and Admittance

Transfer functions provide a mathematical description of how electromagnetic systems respond to excitation, characterizing the relationship between input and output quantities as a function of frequency. In EMC, transfer functions describe coupling paths, filter responses, and shield effectiveness.

Types of Transfer Functions in EMC

Several transfer function types are commonly used:

Voltage Transfer Function: H(f) = V_out(f) / V_in(f). Describes how voltage transforms through a network.
Current Transfer Function: G(f) = I_out(f) / I_in(f). Describes current transformation.
Transfer Impedance: Z_T(f) = V_out(f) / I_in(f). Used for shield and common-impedance coupling characterization.
Transfer Admittance: Y_T(f) = I_out(f) / V_in(f). Used for aperture coupling and capacitive transfer characterization.

Transfer Admittance for Apertures

Apertures in shielding enclosures couple electromagnetic energy through both electric and magnetic field mechanisms. The transfer admittance of an aperture characterizes its coupling properties:

For a small aperture in a thin shield:

Electric Polarizability: Relates to electric field coupling through the aperture. Depends on aperture shape and size.
Magnetic Polarizability: Relates to magnetic field coupling. Elongated apertures (slots) have higher magnetic polarizability.
Resonance: Apertures resonate when their dimensions approach half wavelength, greatly increasing coupling.

Using Transfer Functions for System Analysis

Transfer functions enable systematic EMC analysis:

Cascading: Transfer functions of series elements multiply (in the frequency domain), allowing complex paths to be analyzed step by step.
Frequency Response: Transfer functions reveal frequency-dependent behavior, including resonances and filter cutoffs.
Margin Calculation: Comparing source level, path transfer function, and receptor susceptibility yields interference margin.
Design Optimization: Transfer functions quantify the effect of design changes on EMC performance.

Measurement of Transfer Functions

EMC transfer functions are measured using network analysis techniques:

Vector Network Analyzers: Measure S-parameters of cables, filters, and structures from which transfer functions are derived.
Transfer Impedance Fixtures: Specialized fixtures for measuring cable shield transfer impedance.
Shielding Effectiveness Tests: Measure attenuation through shields to characterize their transfer function.

System Decomposition Methods

Complex electronic systems must be decomposed into manageable subsystems for effective EMC analysis. System decomposition provides a structured approach to understanding and solving EMC problems in systems too complex for holistic analysis.

Physical Decomposition

Physical decomposition divides systems based on hardware boundaries:

Equipment Level: Complete equipment units within a system (computers, power supplies, instruments).
Module Level: Functional modules within equipment (boards, cards, assemblies).
Component Level: Individual components and their immediate EMC environment.

Physical decomposition aligns with typical design and test responsibilities, making it natural for design teams organized around hardware units.

Functional Decomposition

Functional decomposition divides systems based on functional blocks:

Signal Domain: Analog, digital, RF, power, and control domains.
Frequency Range: Baseband, RF, microwave subsystems.
Sensitivity Level: High-sensitivity receivers, moderate-sensitivity circuits, robust power circuits.

Functional decomposition guides EMC zoning and segregation strategies.

Interface Analysis

After decomposition, interfaces between subsystems require careful attention:

Signal Interfaces: Signal type, level, bandwidth, and grounding requirements.
Power Interfaces: Voltage, current, ripple, and noise specifications.
EMC Interfaces: Emissions limits and immunity requirements at each interface.

Well-defined interfaces enable independent development and test of subsystems while ensuring system-level EMC compatibility.

Bottom-Up and Top-Down Analysis

Two complementary analysis approaches are used:

Bottom-Up Analysis:

Starts with component and circuit-level EMC characteristics
Builds up to module and equipment performance
Aggregates emissions and susceptibility to system level
Well-suited for detailed design phases

Top-Down Analysis:

Starts with system-level EMC requirements
Allocates requirements to subsystems and interfaces
Derives component-level specifications from system needs
Well-suited for early design phases and requirements definition

Integration and Verification

System decomposition must be validated through integration:

Staged Integration: Combining subsystems incrementally, testing EMC at each stage.
Interface Verification: Confirming that actual interface characteristics match design assumptions.
System-Level Testing: Final EMC verification of the complete integrated system.

Practical Application of System Concepts

Applying EMC system concepts requires integrating theoretical understanding with practical engineering judgment. This section discusses how these concepts come together in real-world EMC engineering.

Design Phase Application

During system design, EMC concepts guide fundamental decisions:

Architecture Definition: Electromagnetic topology principles inform zoning, partitioning, and interface definition.
Component Selection: Understanding impedance and resonance guides filter and suppression component selection.
Layout Strategy: Common-mode and differential-mode concepts influence routing and grounding approaches.
Cable Design: Transfer impedance specifications are derived from coupling path analysis.

Analysis and Prediction

System concepts enable EMC prediction:

Source Characterization: Identify and quantify all significant electromagnetic sources in the system.
Path Modeling: Develop transfer function models for each significant coupling path.
Receptor Analysis: Determine susceptibility thresholds and safety margins for all sensitive circuits.
Margin Calculation: Combine source, path, and receptor analysis to predict interference margins.

Troubleshooting with System Concepts

When EMC problems occur, system concepts guide diagnosis:

Apply SPR Model: Identify potential sources, coupling paths, and the affected receptor.
Mode Analysis: Determine whether the problem involves common-mode, differential-mode, or both.
Frequency Analysis: Identify resonances that might be amplifying interference.
Path Isolation: Use topological thinking to isolate and characterize the coupling path.
Solution Development: Apply appropriate mitigation to source, path, or receptor based on analysis.

Summary

EMC system concepts provide the intellectual framework for understanding and solving electromagnetic compatibility challenges in complex electronic systems. The source-path-receptor model offers a universal structure for analyzing interference problems, while understanding the distinction between differential-mode and common-mode currents is essential for both emissions control and immunity design.

Impedance concepts, including transfer impedance and wave impedance, quantify coupling mechanisms and guide shielding and filtering design. Resonance effects can dramatically amplify interference and must be identified and addressed through damping, frequency shifting, or absorption. The principles of reciprocity and superposition enable simplified analysis of complex scenarios.

Electromagnetic topology provides a rigorous framework for hierarchical system decomposition, treating shielded boundaries as network interfaces characterized by transfer functions. Transfer function and admittance analysis quantify coupling through all paths, enabling systematic margin calculations. System decomposition methods allow complex systems to be analyzed as manageable subsystems while maintaining awareness of interface requirements.

Together, these concepts form a comprehensive toolkit for EMC engineers. Mastery of these system-level principles, combined with detailed knowledge of electromagnetic phenomena and practical implementation techniques, enables engineers to design electromagnetically compatible systems and efficiently resolve interference problems when they occur.