# Basic Pulse Width Modulation

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1 EAS 199 Fall 211 Basic Pulse Width Modulation Gerald Recktenwald v: September 16, Basic PWM Properties Pulse Width Modulation or PWM is a technique for supplying electrical power to a load that has a relatively slow response. The supply signal consists of a train of voltages pulses such that the width of individual pulses controls the effective voltage level to the load. Both AC and DC signals can be simulated with PWM. In these notes we will describe the use of PWM on an Arduino for controlling LEDs and DC motors. The PWM pulse train acts like a DC signal when devices that receive the signal have an electromechanical response time that is slower than the frequency of the pulses. For a DC motor, the energy storage in the motor windings effectively smooths out the energy bursts delivered by the input pulses so that the motor experiences a lesser or greater electrical power input depending on the widths of the pulses. For an LED, using PWM causes the light to be turned on and off at frequency than our eyes can detect. We simply perceive the light as brighter or dimmer depending on the widths of the pulses in the PWM output. Figure 1 shows a voltage signal comprised of pulses of duration τ o that repeat every units of time. The output of a PWM channel is either V s volts during the pulse or zero volts otherwise. If this signal is supplied as input to a device that has a response time much larger than, the device will experience the signal as an approximately DC input with an effective voltage of V eff = V s τ o (1) The ratio τ o / is called the duty cycle of the square wave pulses. The effective DC voltage supplied to the load is controlled by adjusting the duty cycle. 2 Using PWM on an Arduino An Arduino Uno has 14 digital input/output (I/O) pins 1. Conventional, i.e., not PWM, operation of the digital I/O pins is controlled with the pinmode, digitalread and digitalwrite functions. The pinmode function is used to configure a pin as an input or output. When a digital I/O pin is configured as an input, digitalread reads the state of the pin, which will be either HIGH or LOW. In an Arduino sketch, HIGH is a predefined constant that is evaluated as true in a conditional 1 τ o V s... Figure 1: Nomenclature for definition of PWM duty cycle.

2 EAS 199 :: Basic PWM Output 2 int PWM_out_pin = 9; // Must be one of 3, 5, 6, 9, 1, or 11 // for Arduino Uno void setup() { pinmode(pwm_out_pin, OUTPUT); void loop() { byte PWM_out_level; PWM_out_level =... // Code logic to set output level analogwrite( PWM_out_pin, PWM_out_level); Listing 1: Skeleton of an Arduino sketch to demonstrate the use of pinmode and analogwrite in controlling PWM output. expression, and is equivalent to a numerical value of 1. Electrically, a value of HIGH means the pin voltage is close to 5 V. Similarly, the constant LOW is interpreted as false in conditional expressions, it is numerically equivalent to, and electrically the pin voltage is. When a digital I/O pin is configured for output, digitalwrite is used to set the pin voltage to HIGH or LOW. On an Arduino Uno, PWM output is possible on digital I/O pins 3, 5, 6, 9, 1 and 11. On these pins the analogwrite function is used to set the duty cycle of a PWM pulse train that operates at approximately 5 Hz 2. Thus, with a frequency f c = 5 Hz, the period is = 1/f c 2 ms. As with conventional digital I/O, the pinmode function must be called first to configure the digital pin for output. The skeleton of a sketch in Listing 1 shows the basic code components for using PWM on an Arduino. Two integer variables, PWM_out_pin and PWM_out_level are used to indicate the pin number and output level respectively. In the setup function, the statement pinmode(pwm_out_pin, OUTPUT); configures the PWM_out_pin for output. The OUTPUT symbol is a constant defined by the Arduino programming tools (the IDE or Integrated Development Environment). The statement analogwrite( PWM_out_pin, PWM_out_level); sets the PWM_out_pin pin to the value of the PWM duty cycle and hence the effective voltage according to Equation (1). The parameter that sets the duty cycle is an 8-bit unsigned integer, i.e., a value in the range PWM_out_level 255. The digital output voltage of an Arduino Uno is either V or 5 V. Thus, in Equation (1), V s = 5 V. The PWM output level specified with the analogwrite is an 8-bit value that corresponds to an effective voltage range of to 5 V. Figure 2 depicts the relationships between the PWM output parameters. The quantities in Figure 2 are linearly related. Thus, PWM_out_level = 255 τ o = 255 V eff V s Remember that the second input to analogwrite is an unsigned 8-bit value, so PWM_out_level should be an byte variable type. Since V s = 5 V always, for routine calculations, we can use the simple formula PWM_out_level = V eff (2) 2 See and

4 EAS 199 :: Basic PWM Output 4 // File: Blink.pde // File: Blink_dim.pde // // // Turns on an LED on for one second, // Turns on an LED on for one second, // then off for one second, repeatedly. // then off for one second, repeatedly. // For digital I/O the brightness is set // Use PWM to control variable level of // to maximum during the "on" phase. // brightness of the "on" phase. // Use pins be, 1,..., 13 for digital I/O // Use pins 3, 5, 6, 9, 1 or 11 for PWM int LED_pin = 11; int LED_pin = 11; // must be in the range <= level <= 255 int level = 2; void setup() { void setup() { pinmode(led_pin, OUTPUT); pinmode(led_pin, OUTPUT); void loop() { void loop() { digitalwrite(led_pin, HIGH); analogwrite(led_pin, level); delay(1); delay(1); digitalwrite(led_pin, LOW); analogwrite(led_pin, ); delay(1); delay(1); Listing 2: Arduino using PWM to control the brightness of an LED. The Blink dim.pde program on the right hand side of Listing 2 uses the analogwrite function to supply a variable voltage level to the LED. Example 3.2 PWM Control of LED Brightness In this example, the brightness of the LED is set to three levels in an endlessly repeating sequence. This allows us to verify that the PWM control of brightness is working as it should. The LED circuit is the same. Digital output 5V Digital output Figure 3: Electrical circuit for the basic blink program on the left, and the transistor-controlled blink program. Note that the program to drive these two circuits can be identical as long as the same digital output pin is used for both circuits.

5 EAS 199 :: Basic PWM Output 5 // File: LED_three_levels.pde // // Use PWM to control the brightness of an LED // Repeat a pattern of three brightness levels int LED_pin = 11; // must be one of 3, 5, 6, 9, 1 or 11 for PWM void setup() { pinmode(led_pin, OUTPUT); // Initialize pin for output void loop() { int dtwait = 1; // Pause interval, milliseconds int V1=2, V2=22, V3=12; // 8-bit output values for PWM duty cycle analogwrite(led_pin, V1); delay(dtwait); analogwrite(led_pin, V2); delay(dtwait); analogwrite(led_pin, V3); delay(dtwait); Listing 3: Arduino using PWM to control the brightness of an LED. The LED three levels.pde sketch in Listing 3 causes an LED to glow at three different brightess levels specified by the variables V1, V2 and V3. Each level is held for a time interval specified by the dtwait variable. Example 3.3 Transistor-based PWM Control of LED Brightness The Arduino digital output pins can supply a maximum current of 4 ma. In many applications, higher current loads need to be switched. For modestly larger current loads, say up to 1A, simple NPN transistors can be used. For higher currents, MOSFETs or relays are necessary. In this example, the basic principle of using a transistor to switch a load is demonstrated. The load is an LED, which does not need a transistor for switching. The Arduino sketch is the same as in the preceding examples. The only difference is in the electrical circuit, where the PWM output pin is tied to the base of an NPN transistor, as shown in the right half of Figure 3. Continue Writing Here:

6 EAS 199 :: Basic PWM Output 6 Example 3.4 PWM Control of a DC Motor DC motor circuit: Transistor control; Diode snubber Sketch 3.3 Hardware Limits Each digital output pin of an Arduino Uno can supply no more than 4 ma. To drive modestly higher current loads, the PWM output can be used with a transistor that switches the load. That strategy works with small DC motors. For example, a P2N2222 transistor from ON Semiconductor has a current limit of 6 ma, a factor of 3 higher than a digital pin of an Arduino. Controlling higher power AC or DC loads introduces the potential for electrical hazards, and should not be attempted without substantial experience and abundant safety precautions. A MOSFET (Metal Oxide Field Effect Transistor) device can be used to control DC loads at higher currents. Arduino shields using MOSFET controls can be purchased from Sparkfun 3 or other vendors. One solution for controlling resistive AC loads such as heaters is a product called the Power- SwitchTail, which is available from the manufacturer (http://powerswitchtail.com/) or Adafruit (http://www.adafruit.com/products/268). 3.4 Further Reading The Secrets of Arduino PWM on the official Arduino web site 4 explains some of the low-level details of Arduino PWM, and how to take fine level control over the PWM outputs. 3 See, e.g., the Power Driver Shield or the mini FET Shield http: //www.sparkfun.com/products/ V Orient the diode so + that the black stripe is at the same voltage as the positive motor motor terminal control pin 33Ω Collector. Connect to negative terminal of motor Base. Connect to motor control pin on Arduino Emitter: Connect to ground Figure 4: Electrical circuit for using PWM to control the speed control of a DC motor.

7 EAS 199 :: Basic PWM Output Study Questions 1. What is the effective voltage V eff for V s = 5V and duty cycles of 25 percent, 38 percent, and 64 percent? 2. A small DC motor is connected to digital output pin 7 of an Arduino Uno. What are the Arduino commands to set the effective output voltage to 2V, 3V, and 4.5V? Only write the analogwrite( ) command.

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