Lenz Law vs. Faraday's Law: How Do They Govern Crosstalk and EMI?

Key Takeaways

• Lenz’s law and Faraday’s law tell us two important things about the way a changing magnetic field interacts with a loop of conductor.

• These two fundamental physical laws come together to govern how magnetic fields are generated by conductors carrying DC or AC currents.

• Lenz’s law states the direction of an induced current, and Faraday’s law relates the magnitude of the induced back EMF to the rate of change in the inducing magnetic field.

Magnetic induction in a transformer is governed by Lenz’s law and Faraday’s law.

Inductors and transformers wouldn’t work if the fundamental laws of electromagnetism didn’t exist. We’d only have an electric field and no magnetic effects produced by moving currents. The two basic electromagnetic laws that describe the relationship between induced voltages and the magnetic field are Lenz’s law and Faraday’s law. At the PCB level, these two laws combine to produce inductive coupling between different circuits.

Flux and magnetic flux specifically affect electromagnetics directly, and to understand the relationship to matters like Faradays law and Lenz's law, you'll be looking at core subjects like electromagnetic induction or induced EMF, flux linkage, electric current and induced electric field, lorentz force, and magnetic field lines. Whether a uniform magnetic field is at play or a changing magnetic flux is at work in your wire loop or electric field at large, you'll want to be sure you have a good gauge of flux density and magnetic field strength. 

If the term “inductive coupling” sounds vague, just remember we’re talking about crosstalk, EMI, noise transfer, and any other way the magnetic field might induce noise in an electrical circuit. To better see and predict when a signal in one area of a PCB can induce noise in another area of a PCB, it pays to know something about the difference between Lenz’s law and Faraday’s law. Here’s how they differ and where they lead to crosstalk in a PCB layout.

Lenz’s Law vs. Faraday’s Law

These two fundamental physical laws define how the magnetic field interacts with a loop of conductor. Consider that we have two loops of conductor that are facing each other. One loop carries a current, which we’ll call the inducing current, while the other loop does not carry any current. By Ampere’s law, we know that the current in one loop generates a magnetic field. How does this magnetic field interact with the other loop? To get the answer, we need to look at the difference between Lenz’s law and Faraday’s law.

Faraday’s Law

Simply put, Faraday’s law states the following:

• Faraday's law: When a magnetic field is incident on a coil of conductor, the magnitude of the electromotive force (EMF) induced in the coil is directly proportional to the rate of change in the inducing magnetic field and dot product between the field direction and the axis of the coil.

This tells us something important about the conditions required for induction: The magnetic field generated by a current must be changing in time (either oscillating, rising, or falling) in order to induce a current in the second loop of conductor. This is normally seen in a basic experiment by moving a magnetic field toward and away from a loop of conductor, as shown in the image below.

Voltage and current are only induced in a circuit by a changing magnetic field.

Since the changing magnetic field induces a voltage, it also induces a current. Which direction does this current flow? For this, we need Lenz’s law.

Lenz’s Law

 Understanding electrical energy means understanding current direction and conducting loop as well as any changing flux, mechanical energy, or varying magnetic field in your product.  Lenz’s law is actually the counterpart to Faraday’s law in that it tells you the direction of an induced current, but not explicitly.

• Lenz's Law: When a magnetic field induces a current in a conducting coil, the induced current also generates its own magnetic field that points opposite to the inducing magnetic field.

This has an important consequence: The direction of the induced current is opposite the direction of the inducing current. If the inducing and induced fields are pointing in opposite directions, then the currents must also be pointing in opposite directions thanks to the definition of the right-hand rule. The direction of the induced magnetic field is shown in the image below, where the induced magnetic field created by the induced current is determined through the right-hand rule.

Lenz’s law tells you the direction of an induced current and voltage in a loop of conductor.

Together, these two laws tell us everything we need to know about the behavior of the electromagnetic field in a PCB. When we bring them together, we can now better understand how crosstalk, EMI, and noise coupling occur between different areas of a circuit board.

How These Laws Govern Inductive Crosstalk and EMI in a PCB

Obviously, we are dealing with inductive signal behavior, meaning we need to consider two possible effects involving induction in a PCB:

• Crosstalk: When a signal switches, the magnetic field generated by the switching current will induce a signal in a victim trace, which can then propagate along the interconnect and reach the receiver.

• Noise coupling: This is basically a form of crosstalk, where an oscillating signal is induced in a conductor; one common form is via-to-via noise coupling.

When these effects occur, Lenz’s law states that the induced signal creates its own magnetic field, and the direction of the induced magnetic field points in the opposite direction as the inducing magnetic field. Meanwhile, Faraday’s law states that the magnitude of the induced back EMF is larger when the inducing signal’s frequency is higher. These two laws together with Ohm’s law describe the behavior of inductive crosstalk entirely.

The above points apply to induced crosstalk between aggressor and victim traces, but it also applies to EMI induced in a current loop in a real PCB. Whenever there is a changing magnetic field incident parallel to a loop of conductor, then there will be an induced current. To reduce the magnitude of both effects, you have two options to adjust your trace geometry:

1. Use slightly wider traces

2. Place traces closer to their reference plane (i.e., use a thinner laminate for microstrip or stripline traces)

The right set of routing tools and trace design tools can help you maintain desired impedance while also helping you adjust trace dimensions to stay within required tolerances. You’ll also have the tools you need to analyze crosstalk within your completed PCB layout.  You'll also want to be sure that you find the proper differential form in your equations to tackle any challenge like mutual induction or abnormal electromagnetic induction states, electrolysis, and your various induced electromotive force. Finding the electromotive force, your induced voltage, and your circuits position in eddy currents are all vital for the integrity of your product from its copper wire to the board and package itself. 

Whether you’re worried about Lenz’s law vs. Faraday’s law, the best PCB layout and design software and complete set of analysis tools can help you understand how these two effects govern electromagnetic behavior in your PCB. Allegro PCB Editor includes the features you need for planning board layouts for any application, as well as advanced design verification tools and field solver utilities to analyze the behavior of your high speed and high frequency electronics.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts. To watch videos about related topics or see what's new with our suite of design and analysis tools, subscribe to our YouTube channel.