3. Inductance 101

coilMy assistant, Todd Dixon, adjusts a
coil tap in a 50,000 watt AM phasor.divider(I’m having a contest with my cat to see how many different ways I can say, click any of these images for a larger picture.)

On This Page:
Stephen Meets Inductance
“He Hates This Energy!”
Simplifying The Math
Drink The Juice …
… And Spit It Out
In Sum


Stephen Meets Inductance

Back when giants walked the land and shadows fell only in bad places, a little kid named Stephen took a 120V AC transformer, stripped the primary leads and touched them to a 9V battery. Nothing seemed to happen —

Until I pulled the wires away. Then I got the taste knocked out my mouth.

It baffled me at the time, but now I know: a magnetic field formed inside the transformer. The primary coil stored energy. When I removed the battery, the magnetic field collapsed and that stored energy looked for somewhere to go. It found my fingers.

You can’t be an RF engineer without understanding inductance, and we love it. We see inductors as gentle creatures that eat harmonics and help us tune stuff.

Hah! They’re just lulling you into a false sense of security. In a switched mode power supply (SMPS), they reveal their true nature. You have been warned.

PlatypusAn inductor is like a platypus: sensitive to
electromagnetism and he’ll make you very
sorry if you bother him while he’s working.


“He Hates This Energy!”

If you try to use the hydraulic (or “waterflow”) analogy to describe a switched inductor, you’ll need a Rube Goldberg contraption with balloons, hamster wheels and jingly bells. (And a clown with an air horn.)

If you want a better animal analogy, forget the platypus (see above). Inductors are POO FLINGING MONKEYS.

Unlike capacitors, they’ll resist being “charged” in the first place. Once you finish annoying them, they’ll spit that juice back out as quickly as possible. If you try to impede them (with a high circuit resistance, for example), they simply jack the voltage as high as possible. (See above re: my fingers and that 9V battery.)

To formally describe their behavior requires a bunch of boring math. But to understand these things in switched service, you simply need to grasp how they “drink and spit.” More on that in a moment.

flip-off Pictured: A large inductor.


Simplifying The Math

I’m not going to worry about strict technical accuracy here.  (In case you haven’t noticed yet.) (If not, you may need more coffee.)

But you can thank me later: we’re going to simplify the math. The reason why it’s so hairy is because inductance reacts to changes. That’s why you have those little “di/dt” thingies and stuff in the Official Formulas(tm).

(Steady-state DC current just warms the coil and possibly pushes it closer to saturation.)

I want you to understand these devils intuitively. When you spot a coil in an SMPS, I want you to visualize the “pulsing” flow of current and the changes in voltage. (And the jingly bells.) (But no clowns with air horns. Or poo.)

big-inductor“CENTIMETERS, Smithers, centi –!”  (Face palm.)


Drink The Juice …

SMPS circuit analysis usually assumes ideal conditions: no losses, no resistance, and so on. That’s typical, of course. But actually, with well-chosen components and average switching frequencies, the reality comes close to the theory.

So: here’s the theory. In figure 1, we switch a voltage onto a coil. The current through the coil can’t rise instantaneously, because a magnetic field will form that opposes the change in current. It will rise (again, assuming ideal conditions) in a smooth, straight ramp shape. The rate of rise is determined by

A-s = V / L

… where “A-s” is change in amperes per second, “V” is volts and “L” is inductance in henries. As shown in figure 1, with 10V across 10 uH …

10 / .00001  = 1,000,000 amps per second.

Don’t run screaming into the shrubbery. That’s the rate of change (i.e., the “slope”) of the current. In a typical SMPS, we only do this for a very short time. 1,000,000 amperes per second works out to only 1 amp per microsecond.

(If you ever try to ram 1,000,000 amperes through anything for a full second, I’ll watch from a far away. Through binoculars. Wearing a helmet.)

1MegRiseFig 1: Don’t hold that
switch for very long.


… And Spit It Out

When you release that switch, the inductor instantly wants to spit … and things get weird.

Inductors are the opposite of capacitors when they release stored energy. Speaking generally, a cap wants to dump current, and the voltage across it decreases as you discharge. An inductor makes voltage as the current through the coil decreases, and the lower the load current, the higher the voltage.

If you have trouble picturing this in your mind, All About Circuits compares the inductive and reactive time constants with the old “rolling cart” analogy.

It gets better. When you release the switch, the polarity of the voltage reverses. In figure 2 (below), once the switch is released, the end of the coil that was positive now becomes negative. By simply rearranging the same components, we can get a positive (left side of figure 2) or negative (right side) output voltage.

(The voltage values may differ for the same switch “on” time, but that’s not the point.)

coil-polarityFig 2: Positive output on the left,
negative on the right. Science.


In Sum

I’ve only shown you one formula so far. Not bad, huh?

The key points made here are:

  1. Inductors are poo-flinging monkeys. Never forget.
  2. Inductors in SMPS service behave quite differently from what we’re used to.
  3. When you switch a fixed voltage onto an inductor, assuming ideal conditions, the coil current will rise at a rate that is determined only by the voltage and the inductance.
  4. When you release the applied voltage, an inductor will try to rid itself of stored energy as quickly as possible. The higher the resistance, the higher the voltage and the more rapidly the coil will “discharge.”
  5. Inductors are poo-flinging monkeys. (That needed repeating.)

Use the menu, or click here to begin our examination of honest-to-goodness, real-life SMPS circuits using poo-flinging inductors and MOSFET switches.

“You’re using  an  inductor to
control voltage? How quaint.