Quote of the Day

You know how an economist gets out of a 20-foot deep hole? He assumes the existence of a 20-foot long ladder.

— Unnamed politician giving his opinion on economists

## Introduction

I have been looking at different options for providing surge protection on some AC circuits. During my investigations, I started read about the surge protector shown in Figure 1, which is a commonly deployed unit that is well-thought of and has an excellent history in the field.

While reading about how these units worked, I noticed that the amount of surge voltage they let pass (called let-through voltage) is a function of the hookup wire length. The units are tested with a hookup length of 6 inches, and the user is warned that the let-through voltage increased by ~20 V per inch of additional wire. I became curious about the origin of this rule of thumb. In this post, I will show you how to calculate the rule of thumb for yourself.

While most of my surge stories are related to lightning strikes, I do have one story that shows that surges can occur for other reasons. One of our customers had one of our products on the same AC circuit as a very large copy machine – the largest I have every seen. This copy machine continuously generated enormous power surges that actually wore our surge protectors out. I resolved the issue by convincing the customer to put the copy machine on a different circuit, and the problem vanished.

## Background

### Definitions

- Let Through Voltage (
*V*)_{LT} - Voltage let-through refers to the amount of transient voltage passed through a power conditioning device to the load. A transient is a high amplitude, short duration spike or surge superimposed on the normal waveform. (Source)
- Self-Inductance (
*L*)_{Wire} - Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing. In the case of self-inductance, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self-induced. (Source)
- Metal Oxide Varistor (MOV)
- A varistor is an electronic component with an electrical resistance that varies with the applied voltage. A metal oxide varistor is a type of varistor that contains a ceramic mass of zinc oxide grains, in a matrix of other metal oxides (such as small amounts of bismuth, cobalt, manganese) sandwiched between two metal plates (the electrodes). The boundary between each grain and its neighbors forms a diode junction, which allows current to flow in only one direction. The mass of randomly oriented grains is electrically equivalent to a network of back-to-back diode pairs, each pair in parallel with many other pairs. When a small or moderate voltage is applied across the electrodes, only a tiny current flows, caused by reverse leakage through the diode junctions. When a large voltage is applied, the diode junction breaks down due to a combination of thermionic emission and electron tunneling, and a large current flows. The result of this behavior is a highly nonlinear current-voltage characteristic, in which the MOV has a high resistance at low voltages and a low resistance at high voltages. (Source)

### Lightning Surge Model

Figure 2 shows how a surge protector is rated. For the example I will work here, we will be using a 3000 A spice with an 8 μs rise time and 20 μs fall time.

Figure 3 shows what a typical surge spike looks when not driving the low-resistance of the MOV-based surge protector. The presence of a surge protector will put a large load on this waveform and dramatically reduce the peak level down to the let-through voltage. However, the current will surge up to 3000 A.

Figure 4 shows impact of the surge voltage looks like with different lead lengths. The amplitude reduction is dramatic.

### Video Briefing

Figure 5 shows a good demonstration of how a surge protector is built and how it works.

Figure 5: Good video briefing on Eaton Surge Protectors. |

### Installation Model

Figure 6 shows how the effect of lead wire inductance is modeled.

## Analysis

### Inductance Modeling

Figure 7 shows a commonly used formula for the self-inductance of a cylindrical wire.

I usually see the formula of Figure 7 expressed in terms of the ratio of dimensions, which I derive in Figure 8.

### Wire Dimension Modeling

Figure 9 shows how I used a formula from the Wikipedia to convert wire gauge values into metric diameters. I also put some check figures in my worksheet to show the accuracy of this formula, which is within 0.032% of true over the range of values for which I am interested.

### Let-Through Voltage Due to Lead Length Calculations

Figure 10 shows how to compute the surge voltage across the two lead wires. I am ignoring any contribution from ohmic losses – only inductive effects are modeled.

## Conclusion

I was able to show why the surge protector vendors often warn engineers that every inch of lead wire will increase the let-through voltage by 20 V per inch. This agrees with my constant admonishment to junior engineers about "keeping your leads short".