Building on the fundamentals of BLDC motor operation and control covered in Part 1, Part 2 and Part 3 in this series, let's now turn our attention to putting this knowledge to work, shifting from the earlier six-step 120-degree modulation to an examination of 180-degree modulation.

We will also discuss sinusoidal modulation including an example of code used to generate a sine wave as well. Later we will discuss open-loop V/f control and closed-loop control, as well as a few last words on vector control.

180-degree modulation
Recall that for six-step 120-degree modulation, power switches are turned on and off so that the current passes through two coils, as shown in Figure 28. Every 60 degrees we switch connections so that the current flowing from coil U to V now flows from U to W. This switching effectively keeps the V coil free of current for the next 60 degrees. During this period when no current flows in the V coil, the back-EMF signal generated by the rotor's magnetic field can be detected in the V coil. The progression of six-step coil energization is shown in Figure 29, below.

Figure 29. Progression of six coil energization steps.

Another way to understand 120-degree modulation is to look at the timing of Up, Vp, and Wp during electrical rotation. Each phase is energized for a time that corresponds to 120 degrees of electrical rotation. Phase Up is on for 120 degrees; Vp is on for the next 120 degrees; and finally Wp is on for the rest of the cycle. Lower switches are turned on and off to provide the path for current flow. In this scheme, there is a period of 120 degrees of rotation in which, for example, phase U does not create any torque on the rotor. Effectively each coil is utilized at only 2/3 of its capacity.

However, if we could use each coil for the entire electrical period, we would be able to generate more torque on the rotor. So, rather than turning on Up for 120 degrees of rotation and then waiting another 60 degrees before turning on Un, what if we could keep Up on for an entire 180 degrees of rotation with no long wait period before turning Un on?

This modulation scheme is viable, but only if we provide enough transition time between the act of turning Up off and turning Un on to protect the switches from a short circuit. If we turn Un on before Up has been properly turned off, we risk creating a short circuit that can explode the power switches. The transition time required to safely implement this 180-degree modulation scheme is known as dead time.

Figure 30. 180 degree modulation scheme using three coils at a time

Effectively with 180-degree modulation we are passing the current through all three coils at all times, inserting a small transition time to protect the power switches each time the direction of the current is switched.

For the first 60 degrees, current flows in from Up and from Wp and exits the Vn coil as shown in Figure 30, above. The Wn coil is no longer free, as it now also passes the current. Next we switch Wp and Wn so that the current direction changes, and for the next 60 degrees, current flows in from Up and exits the Vn and Wn coils.

We continue in a similar fashion for the next four steps. In this way, the coils are utilized fully at all times to create torque on the rotor. Note that the ability to detect back-EMF is greatly diminished because of the short dead time.

Generally we say that with 180-degree modulation, there is no back-EMF detection. This statement is correct for all practical purposes. The dead-time requirement also affects the MCU timers, as a dead-time register must be used to insert the proper delay before each phase can be turned on.

We can contrast 120-degree modulation with 180-degree modulation as follows. The 120-degree technique uses only 2/3 of the electrical period to create torque and rotate the motor, whereas the 180-degree modulation scheme uses the entire electrical period.

Torque created using 120-degree modulation contains ripples, because torque is applied to a coil for the first 120 degrees, is not applied for the next 60 degrees, and then is applied again for 120 degrees. However, because 180-degree modulation does away with the long (60-degree) wait period, the current flow is smooth and torque ripples are mostly eliminated. Moreover, 180-degree modulation makes possible various other modulation strategies such as sine modulation, quasi-sine modulation, and space vector modulation.

Let's consider the example of a timer with a dead-time register. The Renesas M16C/Tiny series microcontroller unit (MCU) has a special 3-phase timer, shown in Figure 31, below, which inserts the dead time required between turning the Up and Un power switches on and off.

Timer channel B2 generates the carrier frequency and Timer channels A1, A2, and A4 are used with buffers to set the pulse width modulation (PWM) values for on and off counts. The first buffer holds the value that turns on the output when a compare match occurs. The second buffer holds the value to turn off the output on a compare match.

When the dead-time register is programmed with a value, two internal signals—P for Up and N for Un—are modified by inserting the dead-time count in the compare match. Then, negative signal N is turned off for Un, dead time is inserted, and positive signal P is turned on for Up. Thus our internal timer hardware makes sure that the upper and lower switches are protected properly.

Figure 31. MI6C 3-phase time automatically inserts dead time

The dead-time register is programmed once at the beginning of operation, and the count value is dependent on the characteristics of the power switches. Two internal buffer bits—Di0 and Di1—are programmed to generate a specific high or low output on the compare match. The compare-match output is high if the bits Di0 and Di1 are set to 0,1. The output is low if these bits are set to 1,0. For the second buffer, the bits are DiB0 and DiB1.

By changing the bits properly, a center-aligned or edge-aligned PWM output can be generated easily. Since each channel has a set of buffer bit settings, designers can change the behavior of any channel at will.

The MCU's 3-phase timer is quite versatile in its ability to generate various modulation schemes. It can generate 180-degree, sine wave, quasi-sine wave, space vector, or any custom modulation scheme. It can also generate 120-degree modulation with 60-degree or 120-degree modulation time. It can modulate the upper switches only, the lower switches only, both switches together, or one at a time every 60 degrees. Because the phase timer has dual buffers—the first buffer for the rising-edge compare match and the second buffer for the falling-edge compare match—dual sampling of the angle is possible for better sine-wave generation.

Sine-wave generation Using the MCU's 180-degree modulation capability, we can generate a sine-wave output easily. In this case, instead of a 360-degree electrical cycle period, we employ a period called the carrier-wave-frequency period. During this period, we calculate sine of the angle and set the PWM accordingly. The basic steps to generate this sine-wave output, illustrated in Figure 32 below, are as follows:

1. Select a carrier wave frequency f_c such as 20kHz or 16kHz.
2. Select the voltage V0 and frequency f of the output wave.
3. Compute the phase angle of the voltage at every carrier-wave period.
4. Look up the corresponding sine value from the table.
5. Multiply the sine value with the modulation ratio to generate the PWM value.
6. Transfer the PWM values to the registers.

Figure 32. Basic steps of sinewave generation.

The basic formulas are listed below.

Let's examine in detail the steps for sine-wave generation. Three values are required—the carrier frequency fc, the sine wave frequency f, and the voltage level V0. We will use fc =10kHz, f =50 Hz, and V0=100 % of the possible DC bus voltage. The maximum voltage level is Vdc and the minimum voltage is zero, thus implying

V_max = V_dc and V_min = 0.

The sine wave is generated from a center value to a maximum value V0 and then to a minimum value -V0. Therefore the center value is Vdc/2 computed as

(Vmax + Vmin)/2 = ½ Vdc.

Note that V0 (at maximum 100%) is also ½ Vdc. In our case, Vdc = 160 volts; therefore, V0 = 80 volts and the center point is also 80 volts. The sine wave is now calculated as

½ Vdc + ½ Vdc * Sin (theta).

We can write this as,

Vpwm = ½ Vdc + ½ Vdc * Sin (theta).

We will get Vpwm = Vmax at 90 degrees and Vpwm = Vmin at 270 degrees as expected.

The angle traversed every carrier frequency is now

theta = 2f / fc = 360 * 50 / 10000 = 360 / 200 = 1.8 degrees.

Also,

t = 1/fc = 1/10000 = 100 µs period,
Max PWM count = t * counting frequency, and
PWM max = t * 20MHz = 100 * 20 = 2000.

Because we are using a center-edged PWM generation timer, the timer's B2 channel is ½ of this value. The timer B2 period is 1000 counts, and the first PWM for the rising edge is

PWM1 = 500 + 500 * Sin (theta).

We can compare this to

½ Vdc + ½ Vdc * Sin (theta).

The second PWM for the falling edge is

PWM2 = 1000 -  PWM1.

At 90 degrees, the sine of the angle is 1. We must therefore get the maximum number of counts. At 270 degrees, the sine of the angle is -1 and we must get the minimum number of counts.

In summary, to generate a sine wave, we begin with theta=0 and then set the timer channel B2 to a value of 1000 counts for the count down. We set the interrupt at every second underflow, which is the completion of the triangular center-edge waveform.

In the interrupt routine, we compute the angle, look up the sine table, and multiply by the voltage value to compute the PWM1 value. We check this value for maximum and minimum bounds and then compute PWM2. We will examine the code for this procedure in the next section.

You probably noticed that we performed a sine-table lookup in generating PWM. How do we create this sine table? Since the MCU performs all calculations in integer arithmetic, we must use a scaled value for the sine table. We also must use a scaled value for the voltage.

Using Microsoft Excel, we can create a sine table with one-degree resolution similar to the one in Figure 33, below. We start at zero degrees and advance the table by one degree for each entry, using the sine of the average angle for the index. All sine values are computed in floating values, as shown in the third column.

Figure 33. Sine wave table and its graph with integer values

We then convert these values to 2^13 format - that is, value 1 is represented by 2^13 = 8192. Next we take the floor value of the calculation to get the sine value in integer format. For the U value, we continue with the angle computation, and for the V and W values, we add a 240-degree and 120-degree offset, respectively, for the lookup process. Then we plot the three values to see if correct sine waves result.

Several important points should be noted. Applying a dynamically changing PWM voltage to the stator results in sine-wave voltage and current passing through the stator. This action requires a carrier frequency. We select the value of the carrier frequency based on how precise and accurate the applied sine wave must be and how large a table our MCU's memory can handle. Typical carrier frequency values falls in range of 2 to 20kHz.

However, many designers want to avoid the audible frequency range, so they select values of or above 16kHz. Because a single PWM signal cannot create negative current, a lower power switch is used to enable the current to flow in the opposite direction. Positive and negative PWM output switches are required. To protect these switches, dead time must be inserted between positive and negative signals, as we have discussed previously. Hardware-based dead time is more accurate than software based dead time and reduces CPU bandwidth usage.

With sine-wave implementation, we can improve control performance and efficiency. However, this process requires a true 3-phase timer unit with dead time insertion for proper operation. Sine-wave modulation is compared to trapezoidal modulation in Figure 34, below.

Figure 34. Comparison of 120 deg trapezoidal and 180 deg Sine wave modulation.

Sine-wave generation example Now let's consider how to code a device for sine-wave generation. We begin with a motor-control reference platform, shown in Figure 35. This platform consists of two boards—a Starter Kit Plus (SKP) and a Power Board. A Renesas M16C/28 series MCU, an LCD, and LEDs are mounted on the SKP. The power board has AC-to-DC conversion and an integrated power module (IPM) with six power switches plus drivers built in. The IPM uses a heat sink, as Figure 35 below shows.

Figure 35. Power and MCU board for controlling the motor.

To measure the motor position and current in the U and V phases, the power board provides a Hall-sensor input, an encoder input, and two DCCT devices. Three back-EMF resistor ladders plus a fourth resistor ladder for measuring the Vbus are also implemented on the board, too. A precision shunt resistor on the low voltage side is also included to measure the overall current or to perform a one-shunt current detection technique for current measurements. Together these elements allow us to run various BLDC algorithms.

Figure 36. Test set-up with Bodine motor.

Our test set-up consists of a Bodine BLDC motor with two pole pairs, as shown in Figure 36, above. The MCU is used to generate a sine-wave PWM series of various frequencies, and the current waveforms are captured by the DCCT sensors. The basic sine wave is generated as follows.

When the interrupt is entered, the MCU's firmware checks the validity of the new frequency update. If the update is true, the new frequency is commanded and the delta theta for angle computation is updated. Delta theta is presented in 2^6 format, so delta theta = 64 means 1 degree, and delta theta = 96 means 1.5 degree.

The firmware then integrates the total angle, denoted as sinpt_sum, by adding the delta theta value. If the resulting sinpt_sum is greater than 360 degrees ( 23040 using 2^6 format), then roll-over has occurred and the sinpt_sum must be corrected to a new value by subtracting 23040. Then, sinpt_sum is scaled back by a 2^6 value to get an index in the sine table. This index is called sin_pt in our code.

The constants C4_DAT and C2_DAT in our code are based on carrier frequency and represent ¼ and ½ counts for the carrier-frequency time period. For example, assume that the carrier frequency is 10kHz. Thus, the time period is 100 microoseconds. Counting at 20MHz, it represents 2000 counts. It follows that C4_DAT = 500 and C2_DAT = 1000 counts. Using the C4_DAT constant, three PWM values are computed, as shown in Listing 1, below.

As you can see, sin_pt is used as an index for the sine table. Voltage is represented by the variable tqdat, and the entire multiplication is scaled by 2^19 because sine values are given in 2^13 format and voltage values in 2^6 format. For V and W values, offset_v and offset_w variables are used. To rotate the motor forward, V and W must have offsets of 240 and 120, respectively. To rotate the motor in reverse, V and W must have offsets of 120 and 240. Notice that this procedure is not unlike running the six-step state table in reverse order.

Next, PWM values for U, V and W are checked for PWM_MIN and PWM_MAX to protect the timer operations, and code is developed to reduce the execution time. A PWM2 value is computed using the constant C2_DAT, again to minimize the execution. Finally the six timer registers are loaded, with ta4 and ta41 representing the PWM1 and PWM2 for U phase.

Figure 37. Current wave forms using DCCT sensors at 40 and 60 Hz sinewave.

Since we have two buffers, we can integrate the angle for the first-half period and use the first index for PWM1. Then we can integrate the angle for the second-half period and use that index for PWM2. Although this method doubles the number of sine lookups and thus increases execution time, it also provides a higher-resolution sine wave.

Figure 38. PWM output with 10kHz filtering.

As Figure 37 above shows, we capture the current waveforms at 40Hz and 60Hz using DCCT sensors with 10kHz filtering. As Figure 38 above shows, we capture the PWM output from the MCU with 10kHz filtering to view the PWM. We see that the DCCT current waveforms and PWM output are sinusoidal and represent proper fidelity.

Yashvant Jani is director of application engineering for the system LSI business unit at Renesas Technology America.