Presumably the line terminals all act in parallel? (They're not drawn as a bus, so... But it would be weird if they're actually like separate cords, right?)
Then the 0.1 should act to bypass everything, and the high value resistor is just a bleeder so you don't get shocked when unplugging the cord and touching the blades.
That helps attenuate the switching noise, but doesn't prevent it.
What happens is:
First, the motor current needs to be significant, near a peak. This might be mostly real current (coincident with a voltage peak), or inductive (near voltage zero crossing). Those motors are likely quite inductive, so probably more the latter case, but it doesn't really matter. What does matter, is that there is also significant (leakage) inductance, of the winding with respect to any work it's doing, as this is the part that plays in the following situation.*
*That is, there is effectively a series inductance between the terminals, and whatever internal motor-physics-operation-stuff the motor is actually doing. The motor can be modeled as a Thevenin voltage source, where the voltage is the EMF associated with applied field and rotor motion, and the series impedance is winding resistance and leakage inductance. Which also means these limit how fast the motor can accelerate, max torque, that sort of thing, and indeed they do.
When current is near peak (or "significant" in any case), then when the contact is opened, the inductance discharges, causing voltage to flyback up to a peak determined by air breakdown voltage, and it rises at a rate determined by capacitance (stray capacitance in the wiring and winding).
Consider the contact for a moment. As it opens, microscopic points of contact gradually move apart and separate (and probably slide and drag on the surface for a bit, as well). When the last point separates, in the first, whatever, microseconds, where it's only a few nanometers away -- the voltage drop rises, current no longer flowing through the contact but now charging into stray capacitance instead.
As the contacts get further apart, gradually the breakdown voltage rises. You can imagine, if they separated fast enough, perhaps the breakdown voltage could rise fast enough as well, that breakdown never occurs, and a single flyback pulse and ringdown is experienced by the motor winding, all by itself.
This is actually designed to be the case, in archaic (points) ignition systems: the "condenser" slows the voltage rise, enough that the contact can open far enough to avoid breakdown. The ignition coil develops a high voltage (some hundreds on the primary, 10k's on the secondary), then finds a path through the spark plug. At least, when the system was working right... points were notoriously bad, subject to continuous mechanical and electrical wear.
We might not have that luxury here. We could add such a capacitor across the motor winding, and repeat the function here; but it might turn out that the switch doesn't open far enough, or fast enough, to avoid breakdown, or that the ringdown (even without sparking) is still enough noise to be annoying. Note that ringing is coupled through the motor's casing into nearby ground (or if ungrounded, then electrostatic fields to anything nearby), so we still get a common mode (flows through neutral alone, even without the hot wire connected) noise current, albeit much less than the direct route.
Ringdown is given by the high-frequency losses of the motor winding, its inductance, and the capacitor value. It's more-or-less a simple RLC parallel resonant circuit. You'd need to measure the R and L at the frequency, to solve for the waveform (peak amplitude, resonant frequency, damping rate), but this can be done with basic test equipment ("basic" as in scope and signal generator).
So that's kind of, your top example: simply slowing it enough that the switch doesn't spark (or as much). The capacitor is evidently on the wrong side, so I'm imagining it across the motor for sake of argument. (Across the line, it acts to reduce line impedance; more on that later.)
The middle example is snubbing the switch, typically with an R+C. Though the value is wrong; is it really 470k?
So, what happens when the switch breaks down?
The switch is full of air, which has the effect that, when breakdown occurs, the voltage drop suddenly (within <1ns) goes to maybe 10V (give or take spark length; we're talking quite short sparks here, so the voltage drop will be low), and remains conductive as long as sufficient current flows (holding current).
We're probably at less than that current, so we can assume the spark goes cold after a few microseconds, goes out, then we're back where we started: voltage is rising (into stray capacitances), and the motor inductance has discharged only incrementally (proportional to the area under the flyback pulse).
The effect is a relaxation oscillator, where the bias current is supplied from the motor inductance, the breakdown element is the switch airgap, and the capacitance being discharged is the strays of wiring and winding. (Note that the capacitance supplies holding current for some ns to µs, but eventually runs out.) In this case, the return path to ground, is the mains system itself -- discharging that capacitance into the supply transmits an electromagnetic pulse (EMP) of significant amplitude. Note that the spark risetime is extremely fast: under 1ns, so we really can speak in terms of a wavefront: mere 10s cm wide, propagating up the mains cable at a modest fraction of the speed of light (waves travel in cables somewhat slower, due to the dielectric). This is fast stuff!
This waveform is important enough, that it is included in EMC standards, such as IEC 61000-4-4 electrical fast transients / burst transients. The peak voltage can be several kV, the risetime a few ns, and the pulse energy comparable to ESD -- it can be destructive in its own right. Add to that, the fact that it repeats rapid-fire until the motor inductance has discharged to zero current: the sustained noise can disrupt communications between equipment (e.g. knocking out a USB, Ethernet, etc. packet in transit, or causing garbled data on less error-tolerant networks).
So that's what we're ultimately protecting against.
Note that, mains filtering is ineffective for two reasons:
1. If we simply put a shunt capacitor across the line (as C1), this reduces the line impedance for high frequencies, shunting the EFT -- instead of ~kV, maybe it's only 10s or 100s of V. But we cannot eliminate it this way, not without using a more complicated filter at least.
2. There is significant capacitance to ground, or whatever nearby metal there is -- and again, this is a very fast pulse, so it literally radiates out from the switch at light speed, washing around anything metallic nearby; and anything metallic provides a partial ground-return path for that wave to launch down the mains wires in parallel (common mode), so that any (differential mode) filter has no effect at all.
So we really are quite interested in preventing that noise in the first place!
If we put an R+C (that is, R in series with C) across the switch, with R dimensioned so that, even at peak maximum load current, the voltage drop is never more than switch breakdown voltage; and choose C = L / R^2, then: the resonant circuit is the series path between mains, snubber R+C, and motor R+L. (We can likely ignore stray (parallel) C here, because the snubber C will be much larger; or we can include it in a more complete model of the circuit, that's fine too.) Note that to solve for C, technically we should use the total loop R, not just the snubber's. (But if we don't have the R, L and C of the motor/wiring, it's safe enough to assume the snubber R is dominant. This isn't rocket surgery, being within a factor of 2 is more than good enough.)
Note that, for DPST switches, we don't in general know which contact will open first, so we need a snubber across each. If we did know, we could snub just the first, and by the time the other opens (probably some ~ms later -- mechanics are slow!), current is already ~zero so we don't care. But yeh, we don't know. Or it might even vary with wear, maybe one contact wears faster so opens sooner after a lot of use. So, safest to do both.
For small motors like these, likely the motor current isn't much over say 100mA, and if we want a peak voltage under 200V, that's 200V / 100mA = 2kohm. If the inductance is ballpark say 1H, then C ~ 0.25uF will do. Likely anything from 0.047 to 1uF will do. You often see pre-packaged components with 100R + (0.22 or 0.47uF) for exactly this purpose, and that will do a fine job as well.
Or for the 80W motor, that's maybe a few 100 mA peak, so will need a somewhat lower resistance, and more capacitance. That's fine too.
Interestingly, your middle example is right, in that the switch has an R+C across it; but wrong, in that 470k is wholly ineffective. Is the 'k' a misread? 470R would be in the right order of magnitude. Note that if it's an old type, it might have failed, measuring very different from its rating.
Finally, about the bottom example, the reversible motor -- it's not obvious that the capacitor is serving as a snubber, really. It could be for phasing, so that, actually your choice of a stepper may be much more accurate than you expected -- namely, the capacitor causes a phase shift between windings, so whichever winding is powered is reference, and the capacitor causes a lagging phase shift to the other. Thus creating a rotating magnetic field that spins the rotor, and that spin is CW / CCW depending on which winding is energized. Cool, huh?
Reflecting on the above analysis, if we consider each winding as an ideal motor in series with winding impedance, then we can realize, regardless of what each motor is doing internally (and, generally speaking, they'll be doing similar things, they're part of the same motor after all), we'll still have impedance facing the outside world -- basically, the winding R+L act in parallel with respect to the switch, assuming the capacitor between them is large enough to ignore for this purpose (which I'm guessing it is). So, we will still need the R+C snubber here. The effect of C3 is to couple both windings together at high frequencies -- one snubber should do the job for both windings.
TL;DR:
- Mechanical contacts open and close extremely quickly. Sub-ns quickly. Easily creating EMP that can travel along wires and disrupt nearby devices.
- Use the RLC equivalent circuit to solve for damping: R^2 = L/C. Add R to the loop as needed, to ensure damping. If you don't have exact values, crude assumptions are okay.
- Particularly for the snubber, place it across the contacts -- where the EMP is emitted -- and dimension R to avoid contact breakdown at peak current, if possible. R = Vbd / Ipk. Assume Ipk from sqrt(2) * Irms(max) of the motor.
Tim
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