## General Motion Control

# Evolution of the control electronics

**Bob Parente**| November 1, 2011

The last blog described how, by controlling the current magnitude in a stepper motor’s winding, we could create smaller steps or micro steps.

The motor that we’ve been “using” in our previous discussions is rated at one amp, one ohm and one millihenry, values that I picked out of the air to make this discussion simple.

Who remembers what the time constant (*t*) is for a resistor in series with a capacitor?

It’s *t* = RC. If you have a 1,000 ohm resistor in series with a 1 microfarad capacitor the *t* is 1 millisecond (msec.) If we applied 1 volt to this RC network at time = zero the voltage across the capacitor would rise to about 63% of its final value in one time constant, in our case 1 msec. It would be fully charged in five time constants, or 5 msec.

What does an RC network have to do with a stepper motor or micro stepping? Nothing,

I just remember the time constant of RC networks better than inductive ones and I’m assuming that you might too.

The point to all this is to ask the question: who remembers what the time constant is for a resistor in series with an inductor?

It’s *t* = L/R. The equivalent circuit for our motor has a one ohm resistor in series with a pure inductor of one millihenry. The time constant for this motor is 1 msec.

If we apply one volt to the motor winding at time = zero the current in the winding will rise to 63% of its final value (one amp) in one msec. It will reach its final value in 5 time constants or 5 msec. It’s the same idea as the capacitor except that we’re looking at the current going into the inductor as opposed to the voltage across the capacitor

Why current into the inductor? Because it’s the current that generates the motor’s torque and the inductor that we are talking about is really one of the motor’s winding.

Is everybody with me so far? Good!

Take a look at the unipolar drive circuit in Figure 1

For the two-on full step mode Q1 & Q2 can never be on at the same time. If Q1 turns on then Q2 turns off. The same goes for Q3 and Q4 and we still have a four step sequence that we had before, except we’re using only half the motor’s winding at a time.

Let’s assume that the applied voltage in figure 1 is one volt, the series resistors that are shown in the schematic are zero ohms and that the power transistors are ideal and have zero voltage drop across them when they are on. Each time one of the transistors turns on it takes 5 msec for the current in the motor winding to get to one amp. If the step rate is slow enough (greater than 5 msec per step) then the current will always reach one amp and the motor will produce its maximum torque. However, if the step rate is faster than 5 msec the current doesn’t have the time to reach its maximum value and the torque will fall off as the motor step rate increases because the torque is proportional to the winding’s current..

Let’s raise the applied voltage to two volts and make the series resistors one ohm.

When a transistors turn on we have two volts applied across two one-ohm resistors (one external to the motor and one internal) in series. This limits the current to one amp. The same as before, so why do this? The benefit is a decrease in the time constant. The *t* for the circuit has now become L/2R. We just lowered 5*t* from 5 msec to 2.5 msec.

Raise the applied voltage to 48 volts and increase the resistor value to 47 ohms. We still have one amp in the motor winding, but now the *t* value is L/48R and 5t is 0.104 msec.

This unipolar drive using a series resistor to limit the current is know as an L over R (L/R) drive with its name derived from the inductive time constant. This type of drive was prevalent in the last century. They’re still available from some manufactures today and are very simple and reliable. Some automotive applications use motors with windings rated at 12 volts and operate them directly from the battery with no series resistors.

The generic “unipolar” name comes from the fact that current in the windings always flows in “one” direction when the appropriate power transistors are on.

One of the down sides to this design is that power loss in the series resistor. One amp and 47 ohms produces 47 watts of wasted power and heat. And there are two of them, one for each phase. Another down side is that the drive uses only half of each winding and produces about 40% lower torque than other drive technologies that use the full winding.

Our next blog will look at bipolar chopper drives.

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