# Arduino Tutorial 8: Understanding Pulse Width Modulation (PWM) and the Arduino Analog Write Command

In Lesson 7, we learned how we can get in-between voltages from the Arduino pins using the analogWrite command. Actually, this command only approximates analog voltages, and does not produce actual analog signals. It works by quickly turning the voltage to the pin on and off. For example, if you ask for 2.5 volts, it will quickly switch the pin on, with it on 50% of the time and off 50% of the time. Similarly, if you asked for 1 volt, it is really switching 5 volts on and off quickly. For this case, it would be on 20% of the time and off 80% of the time. This technique is called Pulse Width Modulation. In this video we show you the actual waveforms coming from the analogWrite command on an oscilloscope. If you want to follow this lesson at home, you can get the Arduino kit we are using HERE.

# Beaglebone Black LESSON 12: Control a Servo from Python Using PWM

This lesson will show how to use Python running on the Beaglebone Black to control the position of a servo. First, I am using a small servo that I have verified can be powered from the Beaglebone Black without drawing too much current. All servos are different, so if you are unsure of the current requirements of your servo, it is safest to power it from an external 5 Volt power source. You can still control it through the control line connected to the Beaglebone Black, just make sure the servo and Beaglebone have a common ground.

Most all servos have three wires; Power, Control, and Ground. For my servo, Control is Yellow, Power is Red, and Ground is Black. If you have a different servo, check the data sheet to see what colors are Control, Power and Ground on your servo. Note we are using pin P9_2 as ground, P9_7 as 5V power, and P9_14 as our control pin.

We will be controlling the position of the servo using PWM. We will have to play around with our individual servo to determine precisely what signal pulse width will result in the servo being in the full left position, and what pulse width will result in the servo being in the full right position.

For most servos, full left is somewhere around 1 milliseconds, and the pulse width that will give us full right position is about 2 milliseconds. These are ballpark numbers, and we will have to play around with things to find the exact values for our servo.

We will set up a 50 Hz PWM signal. A 50 Hz signal has a period of:

period = 1/frequency = .02 seconds = 20 miliseconds.

Hence, if we want to get to about the full left position we would want a duty cycle of about 5%. Because 20 milliseconds x .05 = 1 milliseconds. This one millisecond pulse width should put the servo about in the full left position. Similarly for the full right position, we would want a duty cycle of 10%, because that would give us a pulse width of 2 milliseconds, since:

PulseWidth = Period x DutyCycle

PulseWidth = 20 x .1 = 2 milliseconds.

We can use the following code to determine precisely for our servo what dutyCycle will give the precise full left and full right positions.

For my servo, running a 50 Hz PWM singnal, I find that a duty cycle of 2% puts it in the full left position and a duty cycle of 12% puts it in the full right position.

Now we would like to be able to just specify an angle we want and have it go to that angle. If we want an angle of 0 degrees we would apply a 2% duty cycle. This value is for my servo. You will have to play around with your servo and the code above to find what this number is for you. But for me, I have the point:

(0,2)

That is to say when I desire an angle of 0 on the servo, I should apply a dutyCycle of 2 to the PWM pin. Similarly, when I desire 180 degrees, I should apply a dutyCycle of 12. (Again, this number might vary for your servo). For my servo, I get the point:

(180, 12)

We can fit a line to these points, which would then allow us to calculate the dutyCycle for any desired angle. The slope from the two points above would be:

m=(y2-y1)/(x2-x1)=(12-2)/(180-0) = 10/180= 1/18

Using the point slope form of the line, we would get

y-y1 = m (x- x1)

y – 2 = 1/18( x – 0)

y= 1/18*x + 2

Now putting in our actual variable names we get:

dutyCycle = 1/18*desiredAngle + 2

You can develop the same type equation just using the values suitable for your servo from the experiment above.

Now we can use this code to smoothly move the servo to any desired position.

# Beaglebone Black LESSON 7: Create a Dimable LED Circuit with PWM in Python

In this lesson we will explore how to use the PWM commands we learned in the last lesson to control the brightness of LEDs in a circuit. (If you do not have a Beaglebone Black yet, you can pick one up HERE.) In order to proceed with this project, you should hook the following circuit up to your Beaglebone Black.

Note that we are using pins “P9_14” and “P9_22” which are good working PWM pins. Note the current limiting resistors are 330 ohm. Always connect the long leg of the LED towards the control voltage.

The video steps you through the code to control the LED brightness.

# Beaglebone Black LESSON 6: Control PWM Signals on Output Pins from Python

In Lesson 4 and Lesson 5 we showed how to do digital writes to the GPIO pins using Python. (If you have not picked up your Beaglebone Black Rev. C yet, you can get one HERE) With digital writes, we could generate an output of 3.3 volts or 0 volts. For many applications, we would like analog output, or the in between voltages. The Beaglebone Black, as with most microcontrollers, can not produce true analog output. However, for many applications, an analog output can be simulated by creating a fast on/off sequence where the analog value is simmulated by controlling the ratio of on time and off time. This technique is called Pulse Width Modulation, or more simply, PWM. Consider a 3.3 volt signal, which is turning on and off with a frequency of 50 Hz.  A 50 Hz signal has a Period of: Period=1/frequency=1/50=.02 seconds, or 20 milliseconds. If during that 20 millisecond period, the signal was “High” for 10 milliseconds, and “Low” for 10 milliseconds, the signal would act like a 1.65 volt analog signal. The output voltage therefor could be considered the rail voltage (3.3 volts) multiplied by the duty cycle (percentage of time the signal is high.

For the Beaglebone Black, only certain pins can be used for PWM signals.

In the chart above, the purple pins are suitable for PWM output. You can see there are 7 pins which can produce PWM signals. In this lesson we show you how to control those pins.

In order to control PWM signals, we are going to use Python and the Adafruid_BBIO Library. Recent versions of Beaglebone Black Rev. C are shipped with the library already part of the operating system. If you are getting errors indicating that you do not have the library, update your operating system to the latest Debian image for the Beaglebone Black.

In order to use PWM in Python, you must load the Adafruit Library. If you have the recent versions of Debian Wheezy for the Beaglebone black, the library will already be on your system. If you do not do an update and upgrade on your operating system.

To begin with, you will need to load the library.

Next up, you will need to start the PWM on the pin you are using. We will use pin “P8_13”. Remember you must use one of the purple colored pins on the chart above. We start the PWM with the following command:

This command puts a 1000 Hz signal (Period of 1 mSec) on pin P8_13, with a duty cycle of 25%. This should yield a simulated analog voltage of .84 volts.

We can change the duty cycle after this initial setup with the command:

This command would change the duty cycle to 90%, which would simulate a voltage of 3.3 * .9 =  2.97 volts.

You can also change the frequency of the signal using the command:

This would change the frequency to 100 Hz (Period of 10 mSec). Changing the frequency does not really affect the net result of PWM in most applications, although it does matter for many servo applications.

After you are done, you can stop the PWM with the command:

And always remember to clean up after yourself with:

Play around with the Python Program below. Connect a DVM to your Beaglebone Black, and measure the DC voltage at the output pin. The DVM should show your anticipated voltages.

Considering that the simulated analog voltage V=3.365 X Duty Cycle, how would modify the program above to ask the user for the Voltage he desires, and then calculate the duty cycle that would give that voltage. Your assignment is to modify the program above where the user inputs desired voltage, and DC is calculated. Use a DVM to check your results