### General Motion Control

# Stepper motor basics: Half and Micro stepping

**Bob Parente**| August 31, 2011

In the last posting we explored the two-on full stepping sequence. In this edition we will look at how we can control the motor current to allow us to divide the full 1.8° steps in to 0.9° half steps, and even smaller increments called microsteps. The half step sequence produces a finer step resolution of 0.9 degree steps or 400 half-steps per revolution.

But this time, instead of changing phase B’s current direction, we’ll just turn it off as shown in Figure 2

And the shaft moves only 0.9 degrees or half the full step distance, hence the name “half step.” (Complicated, huh?)

What do we do to make it move to the 1.8 degree position?

We just do what we did in the full-step mode and that is turn on phase B in the opposite direction as shown in Figure 3

You have the idea, right?

The whole half-step sequence is shown in Figure 4.

Just by turning the appropriate phase off before reversing the current we can generate four extra steps and create an eight step sequence giving us 400 steps per revolution. Let’s call this a “coarse microstepping” and extend what we learned about the half-step sequence to microstepping.

The “current probe” view of Figure 4 is shown in Figure 5.

Does that waveform look familiar?

I’ll give you a hint in Figure 6.

I’ve superimposed a sine wave over phase A’s current and a cosine wave over B’s.

So what happens if we control the phase current level as we take steps instead of turning the current full-on or off?

The current in phase A follows a sine wave and the current in phase B follows a cosine wave, with the 0, 90, 180, 270 and 360 (or 0 again) electrical-current degrees being the same as the mechanical step positions 8, 2, 4, 6 & 8 respectively in figure 4. It’s okay, go back and look at figures 4 & 6 and line up those five points on the sine and cosine wave and verify that the current direction and magnitude of figure 6 match the steps in Figure 4. We need to have a good understanding of what was just said. I’ll wait.

To keep things reasonably simple, I’ll describe the current conditions in both phases for a four micro step sequence that takes us from zero to 90 electrical-current degrees and covers the shaft movement of 1.8 degrees or just one full step.

To start with we have no current in phase A (sine 0 = 0 and cosine 90 = 1) and 100% current in phase B (see Table 1)

Step# | Current magnitude angle | Phase A current direction | Phase B current direction | Shaft position |

1 | 0.0° | OFF | 100% | 0° |

2 | 22.5° | 38.3% | 92.4% | 0.45° |

3 | 45.0° | ON | ON | 0.9° |

4 | 67.5° | 92.4% | 38.3% | 1.35° |

5 | 90.0° | 100% | OFF | 1.8° |

Table 1: Microstepping sequence

Step number one in Table 1 is the same current condition as step 8 in Figure 4.

Now, instead of turning phase A on full we increment it up slightly to 38.3% (sine 22.5^{o}) of its rating and decrease the current in phase B to 92.4% (cosine 22.5^{o}) of its rating.

These current levels define step two and it moves the shaft 0.45 degrees.

Continuing with the third step, we have phase A and B both at 70.7% of their rated current (sine 45^{o} and cosine 45^{o}) and the shaft moves to the 0.90 degrees.

Step four continues with the sine and cosine of 67.5 degrees and a shaft position of 1.35 degrees. The finally step five, where we have the sine and cosine of 90 degrees and phase A’s current is full on and phase B’s current is completely off. Exactly the same as step two in the half-step sequence of Figure 4. We had to take four steps to get there, not two.

We’ve just created a four-step micro-step resolution or 800 steps per revolution. (See Figure 7.)

Microstepping is giving us finer and finer resolutions. Generate sine and cosine waves that take 256 steps instead of four to go from zero to 90 electrical-degrees and we have a step motor control that can generate 51,200 steps in one revolution (256 x 200 = 51,200 steps/rev.)

Next posting we’ll play with some numbers to show how technology has improved the stepper motor’s capability and show how micro stepping can generate the same the torque as the two-on full step sequence and where you might get in trouble thinking that it does that all the time.