Stepper motors provide unique high-torque and positioning characteristics, along with the ability to hold a load at a specific rotational angle. Furthermore, these motors can be implemented as part of an open-loop positioning system without the additional costs associated with feedback circuitry. Stepper motors are susceptible to vibration that could prove problematic at certain rotational speeds, especially when using lower resolution stepping algorithms.

For example, using a two-phase bipolar stepping motor, a common practice is to implement a two-phase-on switching algorithm that energizes both phases simultaneously for each full step. Current direction in each phase is alternately changed from step-to-step, providing 41 percent more torque over full-stepping methods that energize one winding at a time. Problems may arise, as the rotor will tend to oscillate briefly on each step as a result of a number of system dynamics — including kinetic energy (momentum) — that cause the rotor to overshoot the detent position. The rotor, in an attempt to minimize reluctance, must then correct itself and travel in the opposite direction. Momentum will cause the rotor to overshoot once again and the process repeats until energy dissipates.

What makes matters worse is that, as the step rate increases, there is a frequency at which this oscillation and the next step pulse in the sequence will coincide. This leads to missed steps, as the rotor never truly comes to rest at the previous detent position. The consequences of a missed step could range from simple vibration and noise issues to the catastrophic failure of an application, especially if the motor is used as part of an open-loop system.

Modern hybrid stepping motors minimize the effects of overshoot by implementing teeth on both a permanent-magnet rotor and stators that can commonly reduce step angles to 0.9 and 1.8 degrees. The distributed tooth construction dramatically increases magnetic field concentration, thereby increasing available torque. These motors, when used in conjunction with advanced stepping algorithms such as microstepping, can reduce noise and vibration while increasing rotational resolution.

Microstepping smoothes the rotor’s rotation by dividing each full step by 4/8/16/32 smaller steps (typically, divisions of the full-step angle greater than 32 microsteps do not improve rotor motion). The method discussed in this article accomplishes this microstepping by varying the current in each phase in a sinusoidal fashion called Sine/Cosine microstepping. Two variations of a Sine/Cosine microstepping technique are shown in Figure 1.

A two-phase stepper motor is used as an example here, with the current in both windings separated by a 90-degree phase difference. It is important to note here that 360 degrees, or one complete electrical cycle, differs from a 360-degree mechanical rotation of the rotor. The diagrams shown in Figure 1 reveal one full step actually represents 90 degrees of electrical angle. The instantaneous current in each winding is calculated as follows:

**Equation 1:**

I_{A} = I_{PEAK} * sin ?

I_{B} = I_{PEAK} * cos ?

where:

I_{A} = instantaneous current in Winding A

I_{B} = instantaneous current in Winding B

I_{PEAK} = manufacturer’s specified maximum current rating per winding

? = electrical angle

On the right side of Figure 1, page M11, are the associated current-phase diagrams, with the x-axis representing the current in Winding A and the y-axis the current in Winding B. The length of each phasor represents the resulting vector sum of both currents at a given electrical angle, as calculated using Equation 2.

Equation 3 demonstrates the length of each phasor is also proportional to the torque at a given angle.

**Equation 3:**

T_{A} = H * sin ?

T_{B} = H * cos ?

where:

T_{A} = instantaneous torque in Winding A

T_{B} = instantaneous torque in Winding B

H = manufacturer’s specified maximum holding torque

The first method shown in Figure 1 maintains a constant torque (all phasors the same length) throughout rotor rotation, by constantly varying the current in both windings. A second method implements a high-torque microstepping algorithm. Here, the peak current level in one winding is maintained while the current in the other winding is gradually dropped to zero, reversed and then ramped up again. This sequence is then repeated for the other winding. Referring to the associated phasor diagram, note the effect on the torque. With the current in one winding held at its maximum while the other transitions, phasor length dynamically changes to provide higher average torque than generated in the first method. Note in particular the thicker phasors on the associated diagram at steps ½ (45 degrees), 1½ (315 degrees), 2½ (225 degrees) and 3½ (135 degrees). These points indicate the maximum torque positions in the algorithm, which naturally occur when both phases are energized to their maximum rated current. Note these are the full-step points corresponding to the detent positions used by the two-phase-on, full-step switching algorithm discussed earlier.

A variety of methods can be used to dynamically change the current in each winding to implement High-Torque Sine/Cosine microstepping. The method described in this article utilizes a PIC16HV616 microcontroller (MCU) and associated peripherals.

The Enhanced Capture/Compare/PWM (ECCP) peripheral is capable of generating a Pulse-Width-Modulated waveform with a software-programmable duty cycle. This peripheral also features a half-bridge output mode that can modulate two pins simultaneously. Varying the duty cycle of a PWM output pin connected to the drive circuitry of a winding will vary the current in the winding proportionally, as shown in Equation 4.

**Equation 4:**

I_{WINDING} = Duty Cycle x I_{PEAK}

For example, if a 3-V stepper motor has a rated current of 0.5A, modulating a 3-V supply with a 50-percent duty cycle across the coil results in an average current of 0.25A.

To implement the high-torque method, firmware on the PIC16HV616 utilizes a look-up table of duty cycles to produce sinusoidal current transitions with the number of table values corresponding to the number of microsteps. Since each full step represents 90 degrees of electrical angle, an eight-microsteps/full-step algorithm can be calculated as per Equation 5 to generate the table values shown in Table 1, below.

**Equation 5:**

90°/8 = 11.25°/step

Duty Cycle (step #) = (sin (step # * 11.25)) * 100 (to obtain duty cycle in %)

Example:

Calculate Step 2 Duty Cycle

Duty Cycle (step 2) = (sin (2*11.25°))*100 = 38% (rounded to a whole number)

Two complete full steps are shown. The first half of the table varies the duty cycle to the drive circuitry of Winding A, transitioning the current across the coil from 0 to I_{PEAK} while maintaining a maximum current in Winding B. At the end of the first eight microsteps, 90 degrees of electrical angle or one full step has been completed. In the next eight microsteps, the current in Winding A is now held, while the current in Winding B is decreased by simply reversing the order of the duty-cycle values used to ramp Winding A in the previous 90 degrees of transition.

An example circuit diagram using the PIC16HV616 is shown in Figure 2, page M13.

The 8-bit PIC16HV616 MCU features a permanent internal 5-V shunt regulator that can help limit external regulation components while allowing higher supply voltages to be used, optimizing the current and therefore the torque generated by the winding. The size of the required external current-limiting resistor (R_{REG}) is determined using equations provided in the PIC16HV616 datasheet.

The drive circuit consists of AND and NAND buffer ICs to interface the high side of each H-Bridge with the PWM output

pins P1A and P1B and four General Purpose I/O PORT pins RA5 (CTRLB1), RA4 (CTRLB2), RC3 (CTRLA1) and RC2 (CTRLA2). Driving a PORT pin HIGH will configure the coil current direction by turning on the associated n-channel MOSFET while enabling the signal present on the PWM pin. The PWM output pins are configurable as either input or output. When configured as an output, the PWM waveform is present on the pin. When configured as an input, the PWM pin is in a high-impedance state, allowing the pull-up resistors connected to the pin to clamp the line HIGH.

To implement the first eight microsteps shown in Table 1, page M12, the RC3 pin connected to CTRLA1 is driven HIGH, turning on the lower right n-channel MOSFET on the Winding A bridge. The P1A pin is configured as an output and firmware begins stepping through the look-up table, changing the duty cycle of the PWM output to the values calculated at each step. The Winding B current is held at a maximum with firmware driving the CTRLB1 pin HIGH and configuring the P1B pin as a high-impedance input. The 10-K resistor connected to P1B clamps the line HIGH and maximum current flows across the winding. The remainder of the algorithm is simply a variation on these steps.

High-Torque microstepping provides a means of electronically damping the stepper motor’s response through overshoot suppression. The application example easily accomplishes the task by implementing a PIC16HV616 microcontroller along with some common peripherals. Integrating an embedded solution into the design further adds a level of intelligence that can accommodate more advanced drives incorporating current limiting techniques or even modify the behavior of the drive as system dynamics change. In this way, designers now have a few extra tools at their disposal to help take full advantage of the benefits associated with this truly unique motor.