Technical Article

# What Is Mutual Inductance? A Guide for Circuit Designers

July 06, 2018 by Robert Keim

## Learn about mutual inductance and how it can influence an engineer’s approach to circuit and system design.

Learn about mutual inductance and how it can influence an engineer’s approach to circuit and system design.

### What Is Mutual Inductance?

If you’ve ever used a transformer, you’re familiar with mutual inductance. The name might be a bit misleading; it seems to refer to the sharing of inductance itself, as if two coils lose their own physical inductance properties when you arrange them in close proximity. I would say that mutual inductance refers not to the sharing of inductance but rather to the interaction of inductance: the electrical behavior of one coil influences the electrical behavior of a nearby coil.

There is no doubt that the transformer is a very important application of mutual inductance, but the phenomenon has various other implications that are relevant to just about anyone who works with electronic circuits and systems (i.e., not just transformer designers).

### Unintentional Transformers

Let’s start this section with a syllogism:

• Premise: A component consisting of two adjacent coils of wire is what we call a transformer.
• Premise: A discrete inductor is a coil of wire.
• Ergo, if we place discrete inductors in close proximity we are creating a transformer.

If you consider the extent to which current through a transformer’s primary winding affects the electrical conditions of the secondary winding, the problem readily becomes apparent: discrete inductors can be an effective means of coupling noise and interference from one signal to another. This is especially problematic nowadays when circuits are so compact.

For example, let’s say that you have a small board with a critical sensor signal that must be digitized. You decide to use an LC low-pass for the anti-aliasing filter. The power supply for this board is a switching regulator. In your mind you don’t establish a connection between the anti-aliasing filter and the power-supply circuitry, but since the final device needs to be not much larger than a matchbook, all the parts will end up jammed together on a tiny two-sided PCB.

Before you send the board off to fab, take a look at which components are where. Did the switcher’s inductor end up right next to the inductor in the anti-aliasing filter? Or maybe they are vertically adjacent, i.e., one inductor is on the top side directly above the other inductor on the bottom side? (The ground plane might reduce the effects of mutual inductance, but physically shielding high-frequency magnetic fields is not so easy.)

If your layout restrictions make it impractical to physically separate inductors, you can “magnetically separate” them by means of the relative orientation. Magnetic coupling is maximized when the coils are arranged in parallel. If you have two inductors, make one perpendicular to the other. If you have three inductors in close proximity, two can be perpendicular and the third can be at a 45° angle.

### Reducing Inductance

An interesting manifestation of the mutual inductance phenomenon occurs when two “sourcing” and “sinking” portions of a current path are in close proximity. By “sourcing” and “sinking” I mean that one portion of the path has current flowing in the outward direction (i.e., from the source to the load) and the other has current flowing in the inward direction (i.e., from the load back to the source). You can actually reduce the overall inductance of the current path by placing the sourcing and sinking conductors close to each other, and this lower inductance translates to better high-frequency performance.

### Reducing (Unwanted) Coupling

The lower-inductance arrangement discussed in the previous section also results in a physically smaller current loop, and this brings additional benefits. The mutual inductance between one current loop and a nearby current loop leads to unintentional coupling. This reminds me of the square-shaped magnetic loop antenna that came with an audio receiver that I had almost twenty years ago. From an electrical perspective, loop antennas are like coils that interact with the magnetic portion of the transmitted electromagnetic signal.

Large loops are good if you’re trying to listen to the radio, but not so good if you’re trying to maintain signal integrity in an electronic device. If you don’t want the signals from one subcircuit mixing with the signals in another subcircuit, you can reduce coupling by reducing mutual inductance, and you can reduce mutual inductance by forming a physically smaller current loop.

Have you ever wondered why cables sometimes include numerous ground connections? In some cases multiple ground wires are needed to safely carry all the return current, but in low-current applications they help to prevent excessive mutual-inductance-based coupling between adjacent conductors.

If there is a large distance between a conductor and the nearest return wire, this conductor’s current path will have a large loop area. The adjacent conductor will also have a loop area of similar size (slightly larger or slightly smaller, depending on where the return wire is). Consequently, the mutual inductance will be high. You can reduce the size of the loops by distributing ground wires throughout the cable, and if you really want to minimize mutual inductance you can pair every signal wire with a return wire.

### Conclusion

In this article we reviewed some practical implications of mutual inductance. You really can improve signal integrity and system reliability by keeping this phenomenon in mind as you are designing your PCBs and your interconnects, especially in this age of relentless miniaturization—as devices get smaller, less and less PCB real estate is available for ensuring adequate separation between current loops and inductive components. If you’d like to delve deeper into subtle issues related to PCB layout, I recommend two resources that helped me to formulate the information in this article: one is an app note from Maxim and the other is a book chapter published by Analog Devices.

• D
Diletante July 13, 2018

Thank you Robert for a very clear and logical exposition of the subject. A great starting point for going deeper.

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• J
james.le January 07, 2019

Hi there, I have a question. You said “An interesting manifestation of the mutual inductance phenomenon occurs when two “sourcing” and “sinking” portions of a current path are in close proximity” and then “You can actually reduce the overall inductance of the current path by placing the sourcing and sinking conductors close to each other”. I’ve quite confused. Can you explain a bit more pls? Sorry for my bad. Thanks a lot,

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• T
triman February 14, 2019

Hi Robert. Great article and I enjoy these summary type presentations. So, I was reading the part about “source” and “sink” and the direction of current. The part I was thinking about is that inductance is an AC effect and not DC. So constant current loops in either direction won’t contribute to mutual induction, right? The AC component from a SMPS superimposed on the DC will however contribute, but the raw AC component itself has no direction since it flows in both. In transformer terms, are you referring to the “dots” we see on the windings, which are related to the CW or CCW windings. But that would be a function of the inductors themselves, and not their placement in a “source” or “sink”.  Any further light on what you mean by source and sink and how this affects mutual inductance would be great.

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