Analog and Digital Electronics

Chapter 13
Electronic Design, PCB Implementation and EMC

Bachelor Program in Mechatronics Engineering
Analog and Digital Electronics   •   Bachelor

Electronic Design, PCB Implementation and EMC

Introduction and Context

Electronic design is the disciplined conversion of a functional requirement into a manufacturable, testable, safe, and compliant product. In mechatronics, this conversion connects sensors, actuators, embedded controllers, power converters, communication interfaces, and mechanical assemblies. A circuit that works on a laboratory breadboard may fail when placed on a printed circuit board (PCB) because parasitic inductance, capacitance, thermal constraints, electromagnetic interference (EMI), manufacturing tolerances, and regulatory requirements have not been considered.

A successful design therefore has several dimensions. It must perform its intended electrical function, remain stable over voltage and temperature ranges, tolerate realistic disturbances, dissipate heat safely, be manufacturable at acceptable cost, and satisfy applicable standards. These requirements are interdependent: a narrow trace may reduce cost but increase voltage drop and heating; a high-speed edge may improve timing but increase radiated emissions; a compact enclosure may improve portability but worsen thermal performance.

This chapter develops a practical design flow from requirements to schematic, component selection, PCB layout, verification, and electromagnetic compatibility (EMC) evaluation.

Learning Objectives

By the end of this chapter, a student should be able to:

  1. Translate system requirements into electrical specifications and design constraints.
  2. Develop schematics using sound partitioning, interfaces, and protection practices.
  3. Select components using electrical, thermal, reliability, availability, and regulatory criteria.
  4. Apply grounding, decoupling, signal-integrity, and power-integrity principles.
  5. Design PCB placement and routing strategies for mixed-signal and power circuits.
  6. Identify sources and coupling paths of electromagnetic interference.
  7. Estimate thermal behavior and perform first-order manufacturability checks.
  8. Plan verification, EMC pre-compliance testing, and design documentation.

1. From Requirements to a Design Architecture

Design begins with a requirements specification rather than with a preferred component. Requirements should be measurable and traceable. Typical categories include:

CategoryExample requirement
FunctionMeasure temperature from −20 °C to 80 °C
ElectricalOperate from 24 V DC ±10%
PerformanceAnalog accuracy better than ±0.5% of full scale
TimingGenerate a PWM output at 20 kHz
EnvironmentOperate at 0–50 °C and 10–90% relative humidity
SafetyLimit accessible current and provide reverse-polarity protection
EMCMeet applicable conducted and radiated-emission limits
ManufacturingUse standard components and a two-layer or four-layer PCB
ServiceProvide test points and field-replaceable connectors

A useful requirements process is:

  1. Identify inputs, outputs, operating conditions, and user interactions.
  2. Separate mandatory requirements from preferences.
  3. Convert qualitative statements into measurable limits.
  4. Allocate requirements to circuit blocks.
  5. Define verification methods: inspection, analysis, test, or demonstration.
  6. Record assumptions and unresolved risks.

A block diagram usually precedes the detailed schematic. A motor-control unit, for example, may contain input protection, an isolated or non-isolated power supply, a microcontroller, analog sensing, gate-drive circuitry, a power stage, communication interfaces, and mechanical connectors. Partitioning reduces complexity and makes noise paths visible.

Interfaces and Boundaries

Every boundary between blocks should be described by voltage range, current, impedance, bandwidth, connector type, and fault condition. For an analog sensor input, relevant specifications include common-mode range, source impedance, noise bandwidth, input protection, and required resolution. For a motor driver, relevant specifications include peak current, switching frequency, dead time, fault response, and heat removal.

A design margin prevents operation at the edge of a component rating. If a component is rated for 30 V and the worst-case circuit can experience 29 V including tolerance and transients, the apparent compliance may be inadequate. Ratings should be compared with worst-case—not nominal—conditions, including startup, shutdown, load dump, inductive switching, and fault states.

2. Schematic Development and Component Selection

A schematic is a functional and electrical model, not merely a drawing of physical connections. It should communicate signal direction, power domains, reference designators, component values, test points, connector pinouts, and safety boundaries.

Recommended Schematic Practices

  • Use named power rails and clearly identify analog, digital, and high-current returns.
  • Show protection components at external interfaces.
  • Place decoupling capacitors near the devices they serve in the schematic and annotate their intended location.
  • Identify no-connect pins explicitly.
  • Include pull-up, pull-down, bias, termination, and configuration components.
  • Use hierarchical sheets for complex systems.
  • Mark assembly options and design variants.
  • Provide design notes for critical tolerances and layout constraints.

A schematic review should check electrical rules, pin compatibility, polarity, voltage ratings, current ratings, connector orientation, unused pins, and failure modes. Simulation is valuable for filters, amplifiers, switching converters, and timing networks, but simulation models do not replace physical validation.

Component Selection

Component selection balances performance and lifecycle considerations. Important criteria include:

  • electrical ratings and derating;
  • tolerance, temperature coefficient, and aging;
  • package parasitics and thermal resistance;
  • availability, approved vendors, and obsolescence risk;
  • assembly process compatibility;
  • safety approvals and material restrictions;
  • cost at the expected production volume.

For a resistor carrying current I, its power dissipation is:

PR = I²R = V²/R

where R is resistance in ohms, V is voltage in volts, and PR is power in watts. The two forms apply to a resistive element under the usual DC or instantaneous resistive approximation. In practice, select a rating with appropriate derating and consider pulse duration and ambient temperature.

For a capacitor, stored energy is:

EC = ½CV²

where C is capacitance in farads and V is capacitor voltage. This is important in power-entry protection, discharge safety, and snubber design.

A tolerance stack-up should be considered when several component tolerances affect one result. For independent random variations, a root-sum-square estimate is often useful:

TRSS = √(T₁² + T₂² + ⋯ + Tn²)

This estimate assumes approximately independent, zero-mean variations. Worst-case addition is more conservative and is required when variations may be correlated or when a guaranteed limit is needed.

3. Grounding, Decoupling, and Return-Path Control

Current returns through a physical impedance, not through an abstract symbol. Even a ground plane has resistance and inductance. When changing current flows through that impedance, a voltage is produced. At higher frequencies, the inductive component often dominates:

VL = L(di/dt)

where L is inductance in henries and di/dt is the rate of current change in amperes per second. This relationship explains why a short, wide, continuous return path can be more effective than a long ground wire.

Grounding Strategies

A continuous ground plane usually provides a low-impedance return path and reduces loop area. Splitting a plane is not automatically beneficial; an incorrectly placed split can force high-frequency current around the split, increasing loop area and radiation. Partition noisy power switching regions from sensitive analog regions by placement and current-path control, while allowing high-frequency return currents to remain directly beneath their associated traces where possible.

Single-point grounding can be useful for low-frequency or high-current systems where separate returns prevent load currents from entering sensitive references. At high frequency, however, distributed plane behavior and controlled return paths are generally more important than a simplistic star-ground rule.

Decoupling

A decoupling network supplies transient current locally and reduces voltage disturbance on a power rail. A practical arrangement often includes:

  • a small ceramic capacitor close to each integrated circuit supply pin;
  • a larger local capacitor for lower-frequency load changes;
  • bulk capacitance near power-entry or converter regions;
  • appropriate voltage rating, bias derating, and DC-bias awareness for ceramic capacitors.

The approximate capacitive voltage change for a transient current is:

∆V = I∆t/C

where I is transient current, ∆t is the time for which the capacitor supplies it, and C is capacitance. This is a first-order estimate that neglects equivalent series resistance (ESR), equivalent series inductance (ESL), and regulator response. Including ESR gives an additional step approximately equal to I·ESR.

The capacitor impedance is frequency-dependent. Above its self-resonant frequency, ESL can dominate, so simply increasing capacitance does not guarantee better high-frequency performance. Placement, via inductance, and loop geometry are equally important.

4. Signal Integrity and Power Integrity

Signal integrity concerns whether a signal reaches its receiver with acceptable voltage, timing, noise, and waveform quality. A digital trace becomes a transmission line when its propagation delay is significant relative to the signal rise or fall time, even if the clock frequency appears modest. Reflections occur when the trace impedance and load impedance are mismatched.

The characteristic impedance of a trace depends on its geometry, dielectric material, distance to the reference plane, and conductor dimensions. Exact impedance requires a field solver or validated PCB calculator; it should not be inferred from trace width alone.

Common signal-integrity practices include:

  • route fast signals over a continuous reference plane;
  • avoid unnecessary layer changes and stubs;
  • control differential-pair spacing and length where required;
  • place termination near the source or receiver according to the interface topology;
  • separate high-current switching nodes from sensitive inputs;
  • slow edge rates when timing permits;
  • avoid routing clocks through noisy or externally accessible regions.

Power integrity concerns rail impedance, transient response, ripple, plane resonance, and current distribution. A switching converter layout should minimize the high-di/dt loop comprising the switching device, diode or synchronous switch, and input/output capacitors. The switching node should be compact because it has large voltage transitions and can capacitively couple to nearby conductors.

5. PCB Stack-Up, Placement, and Routing

The PCB stack-up determines mechanical strength, controlled impedance, plane availability, dielectric spacing, and manufacturability. A four-layer board commonly uses signal, ground, power, and signal layers, although many alternatives are possible. The selected stack-up should be agreed with the manufacturer before final routing.

Placement Sequence

  1. Place mechanical interfaces, connectors, mounting holes, displays, and heat-producing parts.
  2. Place power-entry protection and conversion circuitry near the power connector.
  3. Place processors and memory according to timing and reference-plane needs.
  4. Place analog front ends near their sensors and away from switching nodes.
  5. Place decoupling capacitors immediately adjacent to supply pins.
  6. Establish short, direct paths for high-current loops.
  7. Add test points and production-access features.

Routing should follow current flow and return-path logic. A trace crossing a plane split may have a large unintended return path. Vias introduce inductance and may create discontinuities in high-speed paths. Thermal reliefs, copper pours, and via arrays should be used deliberately rather than automatically.

Trace Heating and Voltage Drop

For a conductor with resistance R, the voltage drop is Vdrop = IR and power loss is P = I²R. Resistance may be estimated from:

R = ρℓ/A

where ρ is conductor resistivity in ohm-metres, ℓ is conductor length in metres, and A is cross-sectional area in square metres. PCB trace calculators additionally account for trace width, copper thickness, and temperature rise; their results are approximate and should be checked against manufacturer guidance and applicable standards.

Copper pours reduce resistance and spread heat, but narrow necks can become bottlenecks. High-current paths should be short, wide, and supported by multiple vias when changing layers.

6. Thermal Design

Electrical power becomes heat through conduction loss, switching loss, magnetic loss, and sometimes mechanical or environmental sources. A first-order junction-temperature estimate is:

TJ = TA + PDθJA

where TJ is junction temperature, TA is ambient temperature, PD is device power dissipation, and θJA is junction-to-ambient thermal resistance in °C/W. This equation assumes steady-state operation and a defined thermal environment. The value of θJA depends strongly on PCB copper area, airflow, board orientation, and enclosure construction.

A more detailed thermal path may be represented as:

TJ = TA + PD(θJC + θCS + θSA)

where θJC, θCS, and θSA are junction-to-case, case-to-sink, and sink-to-ambient thermal resistances. Interfaces, mounting pressure, insulation pads, and airflow affect these values.

Design for the worst credible combination of ambient temperature, input voltage, load, switching frequency, and blocked airflow. Thermal cycling also affects solder joints and component reliability, so acceptable steady-state temperature alone is not sufficient.

7. Electromagnetic Compatibility

EMC is the ability of equipment to function satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbance. It includes both emissions and immunity.

EMI coupling is commonly classified as:

  • Conducted coupling: disturbance travels through power or signal conductors.
  • Capacitive coupling: electric fields transfer energy between conductors.
  • Inductive coupling: changing magnetic fields induce voltage in loops.
  • Radiated coupling: energy propagates through space.

A practical EMC analysis identifies the source, coupling path, and victim. Sources include clock edges, switch-mode converters, motor commutation, relays, and ESD events. Victims include ADC inputs, reset lines, communication receivers, and safety-related control signals.

EMC Reduction Techniques

At the source, reduce voltage and current slew rates where performance allows, use snubbers or gate resistors, minimize switching loops, and select appropriate switching frequencies. Along the path, use filtering, shielding, controlled cable routing, common-mode chokes, feedthrough capacitors, and ferrites. At the victim, improve grounding, filtering, hysteresis, signal amplitude, software validation, and physical separation.

A filter must be designed with source and load impedances in mind. An LC filter can resonate if insufficient damping is present. Ferrite components are frequency- and current-dependent; their impedance curves and saturation behavior must be consulted rather than treating them as ideal resistors.

External cables are efficient antennas. Place transient protection at the connector, provide a short return path, and consider shield termination according to the system’s EMC and safety architecture. A shield connected with a long pigtail may perform poorly at high frequency because the pigtail adds inductance.

Regulatory requirements vary by product, environment, and jurisdiction. Designers should identify applicable standards early, such as standards relating to industrial equipment, information technology equipment, measurement systems, machinery, radio equipment, safety, and hazardous environments. The exact standard and test limits must be obtained from the current official edition or a competent compliance laboratory; a generic “EMC compliant” claim is not a substitute for product-specific evaluation.

8. Design for Manufacturability, Test, and Reliability

Design for manufacturability (DFM) adapts the design to the capabilities of the fabrication and assembly process. Important considerations include minimum trace and space, drill sizes, annular rings, solder-mask registration, component spacing, panelization, fiducials, stencil apertures, and thermal imbalance during reflow.

Design for assembly (DFA) favors standard packages, consistent orientation, adequate inspection access, and minimized manual operations. Avoid placing tall parts where they obstruct inspection or near board edges where depanelization may stress solder joints.

Design for test (DFT) includes accessible test points, programming headers or pads, boundary-scan provisions where appropriate, current-measurement links, and diagnostic firmware. A product that cannot be tested efficiently is expensive to manufacture and service.

Reliability analysis should consider overstress, wear-out, contamination, vibration, connector cycles, corrosion, and single-point failures. Failure Modes and Effects Analysis (FMEA) helps rank risks by severity, occurrence, and detectability. Protective measures should be prioritized for hazards involving fire, electric shock, uncontrolled motion, or loss of essential function.

9. Verification and Validation Workflow

Verification asks whether the design was built correctly against its specifications. Validation asks whether the resulting product meets its intended use. A disciplined workflow may include:

  1. Requirements review and traceability matrix.
  2. Schematic capture and electrical-rule checking.
  3. Simulation or analytical checks for critical circuits.
  4. Layout review using design rules and return-path inspection.
  5. Prototype inspection and controlled power-up.
  6. Functional, performance, thermal, and fault testing.
  7. Pre-compliance emissions and immunity testing.
  8. Design revision, documented corrective action, and regression testing.
  9. Production release with controlled bills of materials, drawings, firmware, and test procedures.

Power should be applied to a prototype with current limiting where practical. Check resistance to ground, polarity, regulator outputs, clock operation, reset behavior, and thermal rise before enabling high-power functions. Oscilloscope measurements require suitable probes and ground connections; a long probe ground lead can create ringing that does not exist in the circuit.

Illustrative Case: A 24 V Motor-Control PCB

Background

An illustrative mechatronics product controls a 24 V brushed DC motor using a microcontroller, a half-bridge power stage, current sensing, and a CAN interface. The board must operate continuously at 3 A motor current, tolerate a 30 V transient, and provide a 0–3.3 V analog current signal.

Problem

An initial prototype resets when the motor reverses direction. The ADC measurement also shows large spikes, and a laboratory radio receiver detects interference during PWM operation.

Analysis

The motor current changes rapidly during commutation and reversal. The high-current path shares part of the ground return with the microcontroller and ADC reference. The input capacitor is physically distant from the switching devices, creating a large high-di/dt loop. The motor cable is long and acts as an antenna. The ADC input has no defined bandwidth limit.

Approach and Solution

The design team first separated the power-stage, control, and interface regions. A continuous ground plane was retained, but the motor-current return was routed directly to the power-entry and switching region rather than through the controller area. Ceramic and bulk capacitors were placed close to the half-bridge supply pins. The gate-drive loop was reduced, and gate resistors were added to control edge rate.

A low-pass filter was added to the current-sense output. If the filter is treated as a first-order RC network, its cutoff frequency is:

fc = 1/(2πRC)

where R is resistance in ohms and C is capacitance in farads. The selected cutoff was made high enough for the control bandwidth but low enough to attenuate PWM-related ripple. A transient suppressor and reverse-polarity protection were added at the 24 V input. The motor connector received a defined return path and optional common-mode filtering.

The PCB was revised to provide thermal copper under the power devices and multiple thermal vias. Test points were added for supply voltage, gate signals, current-sense output, and controller reset. Pre-compliance scans were performed while varying motor speed, load, cable arrangement, and enclosure configuration.

Outcome

The reset problem was eliminated under tested reversal conditions, ADC noise was reduced, and radiated disturbance decreased sufficiently to provide useful margin in the laboratory pre-compliance test. The final design still required formal testing against the applicable product standards because pre-compliance measurements do not constitute certification.

Learning Points

The failure was not caused by one defective component. It resulted from an uncontrolled current-return path, excessive switching-loop area, inadequate local energy storage, and insufficient attention to cable coupling. EMC performance was improved primarily through layout and current-path control, not by adding an arbitrary number of filters.

Contemporary Developments and Professional Practice

Modern PCB design increasingly uses automated constraint management, field-solver-based impedance calculation, thermal simulation, and automated optical inspection. AI-assisted tools can suggest footprints, identify schematic inconsistencies, summarize datasheets, or flag unusual layout patterns. Such tools must be treated as assistants: engineers remain responsible for verifying pin assignments, ratings, interpretations, data provenance, and compliance claims.

Digital twins and hardware-in-the-loop testing allow control algorithms and plant models to be evaluated before full hardware is available. Advanced power modules, wide-bandgap semiconductors, high-density interconnects, and embedded sensors improve efficiency and compactness but increase switching speed, thermal density, and EMC difficulty.

Ethical practice requires honest reporting of test results, clear disclosure of limitations, protection of safety-critical functions, and control of design data. Engineers should not claim compliance based on incomplete testing or copy a reference layout without confirming that the operating conditions and manufacturing stack-up are equivalent.

Best-Practice Checklist

Before release, confirm that:

  • every requirement has an owner and verification method;
  • worst-case voltage, current, temperature, and transient conditions are evaluated;
  • component ratings include suitable derating;
  • high-di/dt loops are compact;
  • sensitive circuits have controlled return paths;
  • decoupling capacitors are physically close to their loads;
  • external interfaces include appropriate protection;
  • thermal paths and enclosure effects are considered;
  • PCB rules match the manufacturer’s capabilities;
  • test points and programming access are provided;
  • EMC sources, paths, and victims have been reviewed;
  • applicable safety and EMC standards are identified;
  • bills of materials, drawings, firmware, and test procedures are revision-controlled.

Chapter Summary

Electronic design is an iterative process that begins with measurable requirements and proceeds through architecture, schematic capture, component selection, PCB implementation, verification, and compliance evaluation. Good design controls current flow, return paths, parasitic effects, thermal behavior, and manufacturing variation from the beginning.

Ground planes and decoupling are effective only when their physical placement and current paths are appropriate. Signal integrity depends on reference planes, impedance, edge rate, and termination; power integrity depends on rail impedance, transient current, and converter-loop geometry. EMC problems are best analyzed as source–path–victim problems and addressed through a combination of source control, path filtering, shielding, grounding, and victim hardening.

Thermal calculations, DFM, DFT, safety analysis, and regulatory planning are not final-stage paperwork. They are design inputs. A professionally engineered PCB is therefore not merely electrically functional: it is robust, testable, manufacturable, serviceable, safe, and supported by evidence.

Key Terms

Requirements traceability: Linking each requirement to an implementation and verification method.

Schematic: A symbolic representation of electrical connectivity and function.

Derating: Operating a component below its maximum rated stress to improve reliability.

Decoupling: Local supply bypassing that reduces voltage disturbances caused by load transients.

Ground plane: A broad conductive PCB region used for reference and current return.

Return path: The physical route through which current flows back to its source.

Signal integrity: Preservation of signal amplitude, timing, and waveform quality.

Power integrity: Control of supply voltage variation, ripple, impedance, and current distribution.

High-di/dt loop: A circuit loop carrying rapidly changing current and therefore prone to inductive noise.

EMC: Electromagnetic compatibility between equipment and its environment.

EMI: Electromagnetic interference that disrupts equipment or exceeds emission limits.

Conducted emission: Electromagnetic disturbance traveling through conductors.

Radiated emission: Electromagnetic energy emitted through space.

Thermal resistance: Temperature rise per unit dissipated power, expressed in °C/W.

DFM: Design for manufacturability.

DFA: Design for assembly.

DFT: Design for test.

FMEA: Failure Modes and Effects Analysis.

Pre-compliance test: Engineering evaluation before formal certification testing.

Transient: A temporary voltage or current excursion caused by switching, faults, or environmental events.

Review Questions

Short Answer Questions

  1. Why should requirements be measurable and traceable in an electronic design project?
  2. What is the purpose of placing a decoupling capacitor close to an integrated-circuit supply pin?
  3. Distinguish conducted EMI from radiated EMI.
  4. Why can a long oscilloscope ground lead produce misleading ringing?
  5. What is the difference between verification and validation?

Long Answer Questions

  1. Explain how schematic partitioning and PCB placement can reduce interaction between a switching power stage and an analog measurement circuit.
  2. Discuss the advantages and limitations of a continuous ground plane compared with simplistic star-grounding rules.
  3. Describe a complete component-selection process for a power transistor in a motor-control application.
  4. Explain the source–path–victim model of EMC and provide practical measures for each part of the model.
  5. Discuss how DFM, DFA, DFT, thermal design, and regulatory planning influence PCB architecture.

Analytical / Application Questions

  1. A load draws 0.8 A for 5 µs from a local 10 µF capacitor while the regulator responds slowly. Estimate the ideal capacitor voltage change using ∆V = I∆t/C. State why the practical change may be larger.
  2. A resistor of 10 Ω carries 0.25 A continuously. Calculate its power dissipation and recommend design considerations beyond the nominal calculation.
  3. A motor-control board resets whenever a long motor cable is connected. Develop a structured investigation using the source–path–victim model, and propose at least four layout, filtering, protection, or firmware improvements.

Multiple Choice Questions with Answers

Question 1

Which activity should normally occur before detailed schematic capture?

A. Selecting a decorative enclosure color

B. Defining measurable requirements and system architecture

C. Ordering production quantities

D. Performing final EMC certification

Correct Answer: B. Defining measurable requirements and system architecture

Question 2

For a resistive component, which expression gives power dissipation under steady DC conditions?

A. P = I/R

B. P = IR²

C. P = I²R

D. P = R/I²

Correct Answer: C. P = I²R

Question 3

What is the main purpose of local decoupling capacitance?

A. To increase PCB mechanical strength

B. To supply transient current and reduce local rail disturbance

C. To eliminate all thermal losses

D. To replace every voltage regulator

Correct Answer: B. To supply transient current and reduce local rail disturbance

Question 4

Which layout feature generally reduces inductive voltage caused by rapidly changing current?

A. A long, narrow loop

B. A large switching-node area

C. A short, compact current loop

D. Routing across multiple plane splits

Correct Answer: C. A short, compact current loop

Question 5

A resistor of 10 Ω carries 0.25 A. What is its ideal power dissipation?

A. 0.025 W

B. 0.25 W

C. 0.625 W

D. 6.25 W

Correct Answer: C. 0.625 W

Question 6

Which statement about a PCB ground plane is most accurate?

A. It has zero impedance at all frequencies

B. It can provide a low-impedance return path, but placement and continuity remain important

C. It always increases electromagnetic emissions

D. It eliminates the need for decoupling capacitors

Correct Answer: B. It can provide a low-impedance return path, but placement and continuity remain important

Question 7

In the source–path–victim EMC model, a motor switching node is an example of a:

A. Victim

B. Regulatory limit

C. Noise source

D. Thermal interface

Correct Answer: C. Noise source

Question 8

The equation TJ = TA + PDθJA estimates:

A. Junction temperature from ambient temperature and dissipated power

B. Trace resistance from copper length

C. Capacitor ripple current from capacitance

D. Filter cutoff frequency from inductance

Correct Answer: A. Junction temperature from ambient temperature and dissipated power

Question 9

Which practice best supports design for test?

A. Removing all accessible measurement points

B. Providing test points and programming access

C. Using undocumented component substitutions

D. Hiding connector pin assignments

Correct Answer: B. Providing test points and programming access

Question 10

Why can a ferrite component not be treated as an ideal resistor in EMC design?

A. Its impedance depends on frequency and operating current

B. It has no electrical effect

C. It always behaves as an ideal capacitor

D. Its value is independent of temperature and current

Correct Answer: A. Its impedance depends on frequency and operating current

Analog and Digital Electronics
Chapter 13 of 15