May 2003
 SENSOR 
 TECHNOLOGY AND DESIGN 
Table of Contents

A Digitally Programmable
Pulse-Width-Modulation Converter

A digital technique for converting a 0%–100% PWM signal to a different maximum-to-minimum duty cycle offers linearity and temperature characteristics superior to those achieved by conventional analog conversion methods.

Asad M. Madni, Jim B. Vuong, and Philip T. Vuong
BEI Technologies, Inc.

Most modern sensors provide their outputs in two basic forms, analog and digital. Among the formats for digital outputs are:

  • Serial and parallel data derived from A/D converters
  • Pulse frequency representing the analog sensor output, derived from voltage-to-frequency converters
  • Pulse-width-modulated output (PWM), where the duty cycle of the pulse represents the sensor output

Although several PWM circuits have been developed that provide 0%–100% duty cycle to represent the sensor’s full-scale output, specialized applications require the start and stop duty cycles to be very specific, e.g., 5%–95% to represent the total output. This article describes a circuit design technique that produces a programmable PWM output. Although designed for 5%–95% duty cycle range for a noncontact angular position sensor (NCAPS) [1,2], the technique can be adapted to any start or stop duty cycle for virtually any sensor.

Theory of Operation
In general, it is relatively straightforward to convert the output of an analog sensor to a PWM signal by comparing the analog output voltage of the sensor to a triangular wave (see Figure 1).

figure
Figure 1. An analog sensor output may be easily converted to a PWM signal.

For example, when a 5%–95% PWM is desired, all it takes is to precisely adjust the offset and limit the gain of the sensor’s output amplifier to correspond to the desired minimum and maximum values. However, if a sensor’s natural output is a PWM signal, as is true of the NCAPS, then it is a different story.

The NCAPS is an angular position sensor based on a transceiver concept. Its output is generated by comparing the phase information that is proportional to the angular position of a rotor (coupler) to a fixed reference phase signal. The difference between these two signals generates a PWM output (see Figure 2).

figure
Figure 2. A noncontact angular position sensor uses phase information to generate a PWM signal.

It should be noted, however, that the output waveform is dependent on the type of phase detection technique used. For example, edge detection will generate a PWM with sawtooth characteristics; an exclusive OR will generate a triangular PWM. Since the output PWM signal is proportional to the position of the rotor/coupler, a 0%–100% PWM signal represents the angular position of 0°–360°.

Either an analog or a digital method can be used to convert a 0%–100% PWM signal into a different start-and-stop value (in this case, 5%–95%). In the analog approach, the PWM signal must be converted into a analog signal by using a simple RC circuit or an active low-pass filter circuit; the analog signal is then compared to a triangular waveform to generate the final 5%–95% signal. It should be noted, though, that this method can adversely effect the sensor’s linearity due to the PWM-to-analog conversion and the temperature susceptibility of the analog components. The digital method, on the other hand, can be immune to these problems. A block diagram of a digitally programmable PWM converter is shown in Figure 3.

figure
Figure 3. A digitally programmable PWM converter uses standard digital ICs.

The converter’s major components are counters and comparators. Counters are used to digitize the pulse width of the signal, and comparators to create the required signal in digital form. To convert the incoming PWM signal (fi) to a desired PWM signal output, it is necessary to count the pulse width of the incoming signal with a faster and known frequency (f1). It then can be used to derive a new PWM signal output with the same frequency as the input signal, but with (P1%–P2%) duty cycle. The calculation for frequency f1 is given by:

equation (1)

The total number of counts (x1) for COUNTER1, COUNTER2, and COUNTER4 is:

equation (2)

and the total number of counts (x2) for COUNTER3 is:

equation (3)

where:

P1   =   minimum % duty cycle of the output PWM signal
P2   =   maximum % duty cycle of the output PWM signal

equation

= period of the system clock

equation

= period of the input PWM signal

The relationship between the input and output duty cycle is given by the following transfer function:

equation (4)

where:

Pin   =   % duty cycle of the input PWM signal
Pout   =   % duty cycle of the output PWM signal

When an external PWM signal of frequency fi, with a 0%–100% duty cycle, is fed to the converter, COUNTER1 is triggered; it begins counting at the rising edge of this signal and stops counting at the falling edge. When the PWM signal goes low, it will latch the current value (k1) of COUNTER1 through latch1 and reset COUNTER1 as well. The latched value is compared with the output value of COUNTER2 through the A comparator in order to generate an internal 0%–100% duty cycle PWM signal with frequency f1. This internal PWM signal is further decoded by COUNTER3.

The rising edge of f1 triggers COUNTER3 to start counting, and when it goes low it latches the current value (k1') of COUNTER3 through LATCH2 and resets COUNTER3 as well. This latched value corresponding to the duty cycle of f1 is added to a P1 set value using an adder, and the resultant sum (k2) is compared to the output value of COUNTER4. When the sum is greater than the current value of COUNTER4, the output of the B comparator will stay high; otherwise it will be low until COUNTER4 overflows.

The value of COUNTER4 always contains an additional count corresponding to the P1 PWM set value so that it can maintain the minimum and maximum duty cycles (P1 and P2) for the output PWM signal. In other words, the output duty cycle is a proportional value between the sum of the current count of COUNTER3 and P1 set value to the total number of counts of COUNTER4. In this manner, the converter will generate a PWM signal that has the same frequency as the input PWM signal (i.e., fi) with P1–P2 duty cycle. A timing diagram of converting a 1% and 99% PWM input signal is shown in Figures 4 and 5.

figure
Figure 4. The converter generates a PWM signal that has the same frequency as the input PWM signal (shown here for 1% PWM input).

figure
Figure 5. The converter generates a PWM signal for a 1%-99% PWM input (shown here for 99% PWM input).

Illustration of a Typical Conversion
Consider converting a 2 kHz 0%–100% PWM signal to a 2 kHz 5%–95% PWM signal. First, you need to select a clock source (CLK1) as reference for COUNTER1, COUNTER3, and COUNTER4; (e.g., CLK1 = 8 MHz). If an 80 MHz crystal oscillator with frequency f is chosen as the system clock for the converter, then a divider of 10 is needed to obtain CLK1:

CLK1 = f/10 = 80 MHz / 10 = 8 MHz (5)

To measure the pulse width of a 2 kHz PWM signal with COUNTER1, we need to determine the number of counts for the counter. If CLK1 is 8 MHz, then the period is t0 = 0.125 µs (1/8 MHz). A 2 kHz signal has a period t1 = 500 µs (1/2 kHz), so the total number of counts needed for COUNTER1, COUNTER2, and COUNTER4 is x1 = t1/t0 = 500/0.125 = 4000. The total number of counts for COUNTER3 is x2 = x1 × (P2 – P1) = 4000 × (0.95 – 0.5) = 3600. The calculation for frequency f1 equals 1/[(P2P1) × t1] = 1/[(0.95 – 0.5) × 500 µs] = 2.22 kHz.

Since a counter with 4000 counts is used to decode the 2 kHz PWM signal, a second counter with the same counting value must also be used for decoding the 2.22 kHz PWM signal. To match a 2.22 kHz PWM signal with a 2 kHz PWM signal in the same manner, a clock source with CLK2= 4000 × f1 = 4000 × 2.22 kHz = 8.88 MHz is applied to this counter. After all, a 12-bit counter
figure
Figure 6. The input vs. output PWM duty cycle characteristic of the converter is linear.
(4096) is selected for COUNTER1, COUNTER2, COUNTER3, and COUNTER4 to achieve a total 3600 counts as well as 4000 with clock source 8.88 MHz and 8 MHz, respectively. The characteristic of the input vs. output PWM duty cycle is shown in Figure 6.

Summary
A digital technique for converting a 0%–100% PWM signal to a different P1%–P2% PWM signal has been presented. While the design was developed to convert to a 5%–95% PWM output, the technique is applicable and programmable for any values of P1–P2. Among the advantages the digital approach provides over conventional analog conversion methods are improved linearity and temperature characteristics.

Acknowledgment
The authors wish to thank Linet Aghassi for her help in the preparation of this manuscript.

References
1. Asad M. Madni, Jim B. Vuong, and Roger F. Wells. March 2001. “The Next Generation of Position Sensing Technology, Part 1: Theory and Design,” Sensors, Vol. 18, No. 3:42-55.

2. ———. April 2001. “The Next Generation of Position Sensing Technology, Part 2: Differential Displacement and Linear Capabiities,” Sensors, Vol. 18, No. 4: 61-65.


Dr. Asad M. Madni, a member of the Sensors Editorial Advisory Board, is President and Chief Operating Officer; Jim B. Vuong is Senior Staff Engineer; and Philip T. Vuong is Project Engineer, BEI Technologies, Inc., Sylmar, CA; 818-364-7215, bei1madni@aol.com (Madni); jvuong@bei-tech.com (J. Vuong); pvuong@bei-tech.com (P. Vuong).

MORE!
For further reading on this and related topics, see these Sensors articles.

"The Next Generation of Position Sensing Technology," Part 1 and Part 2, March and April 2001
"Creating a PWM Output Sensor Using a Field-Programmable Analog Array," "Working at High Speed: Multimegahertz 16-Bit A/D Conversion," May 1998
"Voltage-to-Current Conversion of a Pressure Sensor," April 1998
"Signal Conditioning a Pressure Sensor with a Field-Programmable Analog Array," November 1997





 
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