Pulse width modulation is a form of signal communication that transposes a signal from analog to digital form. Analog signals with changing amplitude and frequency pass through a comparator and are compared to a carrier signal, typically a triangular waveform. When the analog signal's magnitude exceeds that of the carrier, the PWM circuit produces high output. Conversely, when the analog signal is less than the carrier signal magnitude, PWM circuits produce low output. Thus, a series of equally spaced pulses, the widths of which correspond to the analog and carrier's relative amplitudes, define the output. (See Fig. 1.)
Microcontrollers and DSPs often incorporate such PWM conversion circuits as onchip peripherals to drive electromechanical components like brakes and motors. Not all chips employ the same switching methods, however, making it necessary to thoroughly study the differences before settling on a commercial PWM IC for a particular application.
Switching methods
Most dc and sixstep brushless motor drives adopt switch configurations shown in Fig. 2. Here, each terminal connects to a pair of switches and operates at one of three conditions: High (with the top switch on and bottom switch off), Low (with the top switch off and bottom switch on), or Off — with both switches off. If both switches in the same phase turn on, the bus voltage can shortcircuit, causing a “shootthrough” condition. To avoid this, most PWM chips wait or pause from 100 nsec to 3 µsec after powering off one switch and turning on another. In brushless and dc motors, there are four switching states that system engineers (and circuit designers) must be concerned with:

During driving, one phase is high, while the other is low. In this state, called the “D” state, applying voltage shortcircuits the windings to the low or highside terminal. Permanent magnet motors then determine current from the previous state: If the prior stage contains negative current, voltage is decreasing. As voltage changes in such a highly inductive circuit, so does current — but at a much slower rate.

Two states correspond to short circuit conditions. In the “Sh” state, where the short circuit is high, two phases short to the highside bus. Similarly, the “Sl” state corresponds to two phases shorting to the lowside bus.

During regeneration, the “R” state, one phase is high, while the other is low.
Driving and regeneration are opposite states: Power flows from the dc link to the motor during driving, and travels in the reverse for regeneration. Regardless of the state, total current appears as torque. In Figs. 3 to 8, the PWM switching frequency of each mode is 20 kHz and Aphase line current is set to 1 A = 100 mV. Figs. 3A through 8A show brushed dc motor operation at various switching schemes, while Figs. 3B through 8B represent a brushless motor.
PWM Scheme Zero: Twoquadrant switching
In this scheme, permanently turning on switch S_{b}' while S_{a} pulsewidth modulates sends positive Aphase voltage to the motor. In this setup, when both S_{a} and S_{b}' are on (in other words, during driving), current I_{a} increases and drives the motor forward. With both switches off, current freewheels, slowly decaying through winding and switch resistance. This happens through an antiparallel diode of S_{b} and the conducting transistor S_{a} — the state that shortcircuits to high. Turning on S_{a}' permanently while modulating switch S_{b} applies negative Aphase voltage and drives the motor backward. Note that only two switchings occur in a PWM period.
Since current raises temperature and increases power supplied to the motor (especially when moving a load) Scheme Zero is the best and simplest of all possibilities. It switches the least number of times per cycle and operates in quadrant zero or two. This means that applications without braking capabilities — such as fans and pumps — benefit from singleside driving. The required switching sequence in one PWM period to provide 30% bus voltage is 70% short circuit to low and 30% driving.
In Scheme Zero, only highside switches modulate. This is advantageous for small bus capacitance requirements and low switching losses. One drawback: The motor cannot change direction quickly (twoquadrant operation), as it relies on mechanical friction to decelerate. Fig. 3 indicates a 20mV peaktopeak current ripple (or 0.2A ripple) for approximately two electrical cycles.
PWM Scheme One: Fourquadrant switching, simultaneous
Here, pulse width modulating S_{a} and S_{b}' simultaneously applies positive Aphase voltage. When both S_{a} and S_{b}' turn on (during driving) current Ia increases and drives the motor forward, just as in scheme Zero. Motor current during the PWM off period decays rapidly through two antiparallel diodes of S_{a}' and S_{b}, and reverse application of bus voltage (for regeneration) ensues. Modulating S_{a}' and S_{b} applies negative Aphase voltage and reverses rotation.
Unlike Scheme Zero, two simultaneous switchings of two transistors occur in a single PWM period. The switching sequence to produce 30% of the bus voltage is 35% regeneration and 65% driving, resulting in positive bus voltage 30% (65% to 35%) of the period. When using Scheme One, the size requirement on bus capacitance is very large and switching losses are high.
Fig. 4 shows 32mV peaktopeak current ripple. A shunt regulator or power supply with bidirectional flow is used, due to the rising bus voltage during regeneration. Although this adds cost and complexity, the energy from braking (friction) must dissipate; otherwise, voltage increases and blows the drive.
PWM Scheme Two: Fourquadrant switching, simultaneous, complementary
This mode (see Fig. 5) operates similarly to Scheme One, except that its switching states S_{b} and S_{a}' complement S_{a} and S_{b}' . However, there are two distinct differences: First, current changes direction within a given period, offering finer control at around zero current. Second, current during regeneration flows through the MOSFETs (instead of the antiparallel diode) to achieve lowerconduction loss. This technique is called “synchronous rectification” and is employed in many MOSFETbased power converters. By using MOSFETs with low conduction resistance, conduction losses are less than a diode's.
PWM Scheme Three: Fourquadrant, nonsimultaneous
This scheme is also similar to Scheme One (see Fig. 6) except that each phase switches at different times. The switching of Sb' is the same as S_{a}, but with a halfperiod delay for a total of four switchings (as opposed to two) in one period. To produce 30% of the bus voltage: short circuit to low (35%) while driving (15%) and short circuit to high (35%) while driving (15%). Regeneration occurs when the duty of S_{a} is less than 50%. To produce regeneration for 30% of the time, short circuit to low 35% with regeneration (15%) and short circuit to high (35%) with regeneration (15%). Due to nonsimultaneous switching, the current ripple's frequency is twice the switching frequency.
PWM Scheme Four: Fourquadrant, nonsimultaneous, complementary
This mode, represented in Fig. 7 operates similarly to Scheme Three and also displays a halfcycle delay. However its switching states, S_{b} and S_{a}' , complement S_{a} and S_{b}' . Here too, conduction losses can be reduced. Scheme Four is also comparable to the PWM waveforms of sinusoidal PWM, as seen in Fig. 8.
Advantages and disadvantages
Switching schemes in most dedicated brushlessmotor control chips are either fixed to Scheme Zero, or selectable from two schemes (Zero or One). Currently, no dedicated control chips offer Schemes Three and Four. However, both can be implemented with additional hardware circuits employed with the motor control chip or with a DSPbased design. Commercial motor control boards let users select their desired switching scheme for testing. The resulting data then informs users of whether or not they are working with an appropriate switching scheme, and if they can improve total power loss in motors and drives.
The best switching scheme depends on the application's requirements. Split switching schemes (Schemes Three and Four) suit lowinductance, highcurrent motors with pronounced PWM current ripple better than simultaneous switching schemes (Schemes One and Two). Their efficiency at low speeds and light loads significantly improves because of the current ripple's dependence on supply voltage and motor inductance. Application examples include batteryoperated motors in power tools, automotive motors, and slotless motors.
Compared to Schemes One and Three, Schemes Two and Four (complementary switching) minimize conduction losses (synchronous rectification using MOSFETs) and offer fine current control. In simultaneous switching schemes (Schemes One and Two) power flows repetitively between the motor and dc link, a characteristic demanding capacitors with a high bus capacitance and low effective series resistance. Oftentimes, these schemes produce higher electromagnetic interference. For all other schemes, a freewheeling state (with a short circuit to high or low) is introduced after an active drive or regeneration state.
When twoquadrant operation meets the performance goal (as in fans and pumps) Scheme Zero provides the most cost effective and efficient solution, since it switches the least number of times per PWM cycle. Scheme Four is very similar to sinusoidal operation except that it uses sixstep commutation. A synchronous regulator drives the system and enables the motor to run more efficiently. This efficiency depends on currentloop tuning. Compared to sinusoidal drives, sixstep drives produce excessive torque ripple at six times the electrical line frequency and its harmonics. This ripple produces audible noise and increases system loss. However, while sinusoidal drives reduce torque, they also increase resolution feedback and current. Given the limitations of fixed designs, perhaps the most flexible motor controller is one based on a digital signal processor that selects a preprogrammed switching scheme for optimal power and operation. These preprogrammed schemes can be optimized for system efficiency, drive losses, and related sizing/cooling issues: motor losses and torque ripple, PWM noise and electromagnetic interference, and bus capacitor size.
This topic was also presented at a PE Technology Conference in Rosemont, Ill. For more information, call (703) 3272797.
TOPICS OF DISCUSSION
 Switching methods
 PWM Scheme Zero: Twoquadrant switching
 Scheme One: Fourquadrant switching, simultaneous
 Scheme Two: Fourquadrant switching, simultaneous, complementary
 Scheme Three: Fourquadrant nonsimultaneous
 Scheme Four: Fourquadrant nonsimultaneous, complementary
 Advantages and disadvantages