# Archive for December 17th, 2014

### Kenmore 158: Relay Transient Simulation

After having blown two ET227 transistors, I fiddled with some SPICE models to explore the ahem problem space. This seems to be the simplest model with all the relevant details:

Motor Transient – no NTC – schematic

A step change in the voltage source simulates the relay clicking closed with the AC line at a peak. R4 might resemble the total wiring resistance, but is more of a placeholder.

I measured 1 nF from each motor wire to the motor shell, so I assume a similar value from wire to wire across the winding. I can’t measure that, because, as far as my capacitance meters are concerned, the 40 Ω motor winding looks exactly like a resistor. R1 and L1 model the winding / commutator, but on the time scale we’re interested in, that branch remains an open circuit.

There’s no transistor model even faintly resembling a hulking ET227, so a current controlled current source must suffice. The 0 V `VIB` “source” in the base lead measures the base current for the CCCS labeled `ET227`, which applies a gain of 10 to that value and pulls that current from the collector node. R2 is the internal base-emitter resistor built into the ET227.

C2 is the 6 nF (!) collector-base capacitance I measured at zero DC bias on a good ET227. That’s much more than you’ll find on any normal transistor and I’m basically assuming it’s vaguely related to the Miller capacitance of small-signal fame. C3 is a similar collector-emitter capacitor; I can’t tell what’s going on under the hood without a whole lot of measurement equipment I don’t have.

Simple Transient Model – current pulse

Whenever you see a simulation result like that, grab your hat in both hands and hunker down; the breeze from the handwaving will blow you right off your seat.

The key unknown: the rise time of the voltage step as the relay contacts snap closed. Old-school mercury-wetted relay contacts have rise times in the low tens of picoseconds. Figuring dry high-power contacts might be 100 times slower gives a 1 ns rise time that I can’t defend very strongly; it seems to be in the right ballpark. The green trace shows the input voltage ramping to 180 V in 1 ns, which is pretty much an irresistible force.

The motor shunt capacitance forms a voltage divider with the parallel base and collector capacitors, so the collector voltage shouldn’t exceed 180 * (1/(1+3)) = 45 V. In fact, the blue trace shows the collector voltage remains very low, on the order of 10 V, during the whole pulse.

The red trace shows the collector current hitting 150 A during the entire input ramp, which is exactly what you’d expect from the basic capacitor equation: I = C dv/dt. The current depends entirely on the absurdly fast 180 V / 1 ns rate: if the relay rise time is actually smaller, the current gets absurdly higher.

The ET227 datasheet remains mute on things like junction capacitance, damage done by nanosecond-scale high-current pulses, and the like.

Absolutely none of those numbers have even one significant figure of accuracy, but I think the overall conclusion that I’m blowing junctions based on transient startup currents through the collector holds water.

Adding four of those NTC power thermistors seems in order. This picture also shows the snubber hanging from the back of the ET227, but I eventually took that off because the simulations show it’s not doing anything useful and it does resonate with the 120 Hz halfwave supply:

HV Interface – snubber and thermistors

The thermistors get comfortably warm after a few minutes and settle out around 1 Ω apiece. Adding 4 Ω to the simulation reduces the current to 30 A during a 1 ns ramp, which number obviously depends on all the assumptions mentioned above.

I’ve been running it like that for a few hours of start-stop operation and the ET227 lives on, so maybe I can declare victory.