Fase 4: Seguimiento

Since hidden behavioral characteristics of passive components exist, we now investigate how RF energy is developed within the PCB. Both passive and active digital components develop unwanted RF energy. The field of EMC is described by a series of complex mathematical formulas identified as Maxwell's equations. These equations are based on the physics of electromagnetics. Maxwell's four equations describe the relationship of both electric and magnetic fields. These equations are derived from

Ampere's law, Faraday's law, and two from Gauss's law. The formulas are complex and beyond the scope of this book, and are taught as an upper-division course in electrical engineering at colleges and universities.

Excellent reference material is provided in the References section; these works discuss how these integral and differential equations (calculus) are derived, as well as their relationship to both static and time-varying fields.

Knowledge of Maxwell's equations is not a prerequisite to designing a PCB for both signal integrity and EMC compliance. This is the primary reason why a detailed analysis of Maxwell is not presented in this book. What is required is a solid understanding of the fundamental concepts of complex physics, and application of these concepts, to solving difficult problems.

To briefly summarize Maxwell, these equations describe the root causes of how EMI is developed: time-varying currents. Static-charge distributions produce static electric fields, not magnetic fields. Constant current sources produce magnetic fields, not electric fields. Time-varying currents produce both electric and magnetic fields. Static fields store energy. This is the basic function of a capacitor: accumulation of charge and retention.

Constant current sources are a fundamental concept for the use of an inductor.

To "overly simplify" Maxwell, his four equations are associated to Ohm's law. The presentation that follows is a simplified discussion that allows us to visualize Maxwell in terms that are easy to understand. Although not mathematically perfect, this presentation concept is useful in presenting Maxwell to those with minimal exposure to EMC theory.

where V is voltage, I is current, R is resistance, Z is impedance (R + jX), and the subscript rf refers to radio frequency energy.

To relate Maxwell Made Simple to Ohm's law, if RF current exists in a PCB trace which has an impedance value, an RF voltage will be created that is proportional to the RF current present. Notice that in the electromagnetics model, R is replaced by Z, a complex quantity that contains both resistance (DC-real component) and reactance (AC-complex component). The

important item to note is "impedance." Impedance is the resistance to the flow of energy, in both the time and frequency domains. Voltage and current are metric units of measurements that describe the activity of electrons, electromagnetic potential, electrostatic fields, and the like.

For the standard impedance equation, various forms exist. For a wire, or a PCB trace, Eq. (2.2) is the most applicable impedance equation. Within this

(2.1)

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equation, we see both inductive and capacitive reactance.

When a component has a known resistive and inductive element, such as a ferrite bead-on-lead, a resistor, a capacitor, or other device with parasitic (hidden) components, Eq. (2.3) is applicable, as the magnitude change of impedance versus frequency must be considered.

For frequencies greater than a few kHz, the value of inductive reactance typically exceeds R. Current takes the path of least impedance, Z. Below a few kHz, the path of least impedance is resistive; above a few kHz, the path of least reactance is dominant. Because most circuits operate at frequencies above a few kHz, the belief that current takes the path of least resistance provides an incorrect concept of how RF current flow occurs within a transmission line structure or PCB trace.

Each trace has a finite impedance value. Trace inductance is only one reason RF energy is developed within a PCB. Even the lead-bond wires that connect a silicon die to its mounting pads may be sufficiently long to cause RF potentials to exist. Traces routed on a board can be highly

inductive, especially traces that are electrically long. Electrically long traces are those physically long in routed length such that the time for the round trip of the signal does not return to the source driver before the next edge-triggered event occurs, when viewed in the time domain. In the frequency domain, an electrically long transmission line (trace) is one that exceeds approximately ˣ/10 of the frequency that is present within the trace. If a RF voltage travels through an impedance, we end up with RF current, per Ohm's law. This RF current propagates and can cause noncompliance to emission requirements. These examples help us to understand Maxwell's equations and PCBs in extremely simple terms.

Another simplified explanation of how RF energy is developed within a PCB is shown in Figs. 2.2 and 2.3. According to Kirchhoff's and Ampere's laws, a closed-loop circuit must be present if the circuit is to work.

Kirchhoff's voltage law states that the algebraic sum of the voltage around any closed path in a circuit must be zero.

Figure 2.2: Closed-loop circuit.

Figure 2.3: Frequency representation of a closed-loop (2.2)

Get MathML

where XL = 2›fL (the component in the equation that relates only to a wire or a PCB trace)

Xc = 1/(2›fC) (not observed or present in a pure transmission line or free space.)

˰ = 2›f

(2.3)

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circuit.

Figure 2.2 presents a simplified circuit. There is both a signal path and a return path. Without a closed-loop circuit, a signal would never travel through the transmission line (PCB trace) from source to load. When the switch is closed, the circuit is complete.

Maxwell, Kirchhoff, and Ampere all state that if a circuit is to function or operate, a closed loop must be present. When a trace goes from a source to a load, a current return path must also be present. If a conductive return path is absent, free space becomes the return path.

Figure 2.3 is another representation of Fig. 2.2. The circuit on the left represents a low-frequency network with a direct path for both signal and return current. Every transmission line has a finite impedance value, which consists of both resistance and inductance. For this circuit, the total

impedance value is small. Current will return without difficulty. For the circuit on the right, the return path is not the same physical length as the source path. Additional impedance has been added to the transmission line due to this longer path. The longer the trace, the greater inductance

becomes. Using the impedance equation, Z = R + j2›fL, as the frequency of the circuit increases, the value of impedance, Z, will increase. With additional inductance, total impedance, Z, will also increase. Resistance is negligible for most applications and is usually ignored. For a very high-frequency signal with a significant amount of inductance, the value of Z can become very large. The impedance of free space is 377 ohms. It takes very little inductance, in the frequency range between 100 kHz and 1 MHz, to exceed 377 ohms. Because current (the DC element of the circuit) must return to its source to satisfy Ampere's law, the RF energy (the AC current element) will return through the lowest impedance path available. When the impedance of the return path is greater than 377 ohms, free space becomes the return and is observed as radiated EMI. The illustrations in Fig. 2.3 show both high and low in frequency applicatons.

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Table of Contents

2.8: RF CURRENT DENSITY DISTRIBUTION

2.9: GROUNDING METHODOLOGIES

2.10: GROUND AND SIGNAL LOOPS (EXCLUDING EDDY 2.13: SLOTS WITHIN AN IMAGE PLANE

Chapter 2 - Printed Circuit Board Basics

Printed Circuit Board Design Techniques for EMC Compliance: A Handbook for Designers, Second Edition by Mark I. Montrose

IEEE Press © 2000 Recommend this title?

2.3 MAGNETIC FLUX AND CANCELLATION