Surge Impedance: Why you see the spark when you unplug your iron

One morning last month started off over coffee with a Sherlock Ohms article in Design News Magazine titled Noise Messed With the Automation System …Hmmm, this looked interesting, so lets see what the problem was [annotated with my comments in blue]:

I manage the new product verification team for a small manufacturer of industrial automation equipment. We sell most of our products through partners who sell them as their own products. About six month ago, we had one of our partners come to us with an intermittent customer issue. The customer had one of our analog output (4-20mA) modules installed next to a relay module (made by our partner).

The analog module controlled the speed of a conveyor through an oven, and the relay module switched a contactor that controlled the heaters in the oven. The customer had installed a number of these systems at various locations with both AC and DC power to the heaters. [Hmmm, I'll bet this involves arcing when the load is switched off…]

After installation, the systems worked very well, but after about a month, only on the AC-powered systems, one channel of the analog output would go to 0 mA, stopping the conveyor and burning a lot of product. After a power cycle, the system would work again, but with a decreasing failure interval. Our module had been redesigned recently and the older version was not showing the problem at all. [Nothing here: Move along…]

Our partner asked us to try to duplicate the problem with our own equipment. They had managed to duplicate it on one system, but could not on another. One of my test engineers worked with the design engineer for two months trying various loads and accelerated switching rates [But what were the test conditions?! ], but he could not recreate the failure. It appeared that either our module was not the source of the problem, or no one understood the conditions of the failure very well. [As you'll see in my comment on the article, duplicated below, this was the problem.]

Our partner came back to us with more information on the system. They told us that they were able to demonstrate the failure regularly on two systems: one with a large contactor as a load, and another with a resistive load. [Gee, I'll bet this is switching transients from an inductive load, despite the "resistive load" he called it…] They also had a third system with a resistive load that would not show the failure. While reading the new data, I noticed that the test system they had managed to duplicate it on had a step down transformer between the relay and the resistive load (local power was 220V and the load was designed for 110V). [Like I said, inductive load!] All of the systems that showed the failure were switching a large inductive load with the relay, while those that worked properly were switching a resistive load directly… [Balance in two page article]

Ding Ding Ding!

It’s called surge impedance Zo, which is defined as √(L/C), where L is the inductance in Henrys, and C is the capacitance, which for a coil of wire in a transformer or motor is the interwinding stray capacitance (very small value). The back EMF is defined by
v= Zo(∂i/∂t),
…and it will have an oscillation frequency of
…and is typically in the tens to hundreds of kilohertz.When you open up the contacts supplying an inductive load,
∂i/∂t → ∞
v= Zo * ∞
…i.e. ∞ volts: You see this as the arc when you unplug an iron; and also when relay & motor starter contacts are switching off an inductive load.

This is also why contactors & motor starters have serious current deratings when switching off DC: Once the arc is established and current starts flowing through the ionized channel, there is no zero crossing to extinguish the arc, as occurs with AC.

When dealing with AC, you design using the peak (not RMS) value of the load current when calculating, because you don’t know where in the AC cycle the contacts will open.

Note: Those of you who are RF jocks will quickly recognize  Zo = √(L/C) as the equation for the characteristic impedance of a transmission line (like 75Ω RG11 coax): Yes, it’s the same thing. [Oh, and by the way, it applies not only to RF transmission lines, but also those big power transmission lines you see criss-crossing the country: They have a surge impedance too, and on this switchgear engineers keep close tabs.]

Zo(∂i/∂t) arcs aren’t necessarily confined to switches: This photo of a train shows the carbon pickup shoe arcing as it is bouncing over an expansion joint in the 600 volt third rail:

Arcing train pickup shoe

Arcing train pickup shoe: Click to enlarge


Now, you’re probably scratching your head wondering “what the hell does this have to do with my hearing aids (or CI’s)?!” The answer is not very much, except for two areas:

  • If you try to use a T-coil on a train or subway, you’ll get a large BANG! every time there’s an arc – Electrical noise is the fatal flaw of baseband induction “hearing loop” systems and the telecoils that enable them;
  • Direct Audio Input (DAI) is still used on CI’s and a few hearing aids: Unplugging the cables will cause switching transients; and depending on how robust the surge suppression is designed, it can cause the whole hearing aid or processor to fail.

Aren’t the fundamentals of Electrical Engineering fun?!

Fun Stuff added on March 27th 2014:

From Accidental Arcs: 8 Power Line Failures on Video, we have these awesome YouTube clips:

This video catches something rather interesting. Notice how the final explosion of electricity completely extinguishes the flame. Not unheard of but also not something many of us have actually seen:

You need to wait until about the 55 second mark to see the close-up of the arc jumping about 3 feet to the crane boom:

From 48th & Wells in Chicago, we have this shower of sparks:

And finally, ice can be quite a hazard, even without tree branches hitting the lines:


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About the author

Dan Schwartz

Electrical Engineer, via Georgia Tech


  1. William Hole
    April 22, 2013 at 10:25 am

    This is a terrific piece!
    BUT – in my experience, an iron (clothes or soldering) is a resistive load? So the inductance is upstream?
    Much appreciated


    • Dan Schwartz
      April 22, 2013 at 12:37 pm

      William, in fact there’s a lot of inductance in the heating coils of devices such as clothes irons & coffee pots. Also, you have stray shunt capacitance, usually interwinding capacitance. The surge impedance Zo is defined as √(L/C), where L is the inductance in Henrys, and C is the capacitance, which for a coil of wire in a transformer or motor is still a very small value. The back EMF v= Zo(∂i/∂t), and it will have an oscillation frequency 1/(2π√LC) and is typically in the tens to hundreds of kilohertz. When you open up the contacts supplying an inductive load ∂i/∂t → ∞ hence  v= Zo * ∞ i.e. ∞ volts: You see this as the arc when you unplug an iron; and also when relay & motor starter contacts are switching off an inductive load.

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