Analog and Digital Signals

In this post we are going discuss something which is used in all the electronics and computers which is the Pulse Width Modulation and the concepts related to it.

Logic level is the voltage level that a particular device communicates with. A common logic level that a micro-controller uses is 5V. An analog varies from 0V to 5V for example as a sine wave. So, at any point of time we can get any value between 0 and 5 volts in the case of the analog signal. On the other hand digital signal can have only two values 0V or 5V just like the on or off.

Analog to Digital
Digital signals are more efficient since the analog signals have a lot of noise in them. So, we usually convert the analog to digital. The analog to digital converter on the Arduino is of 10-bit which means we have 2^10 = 1024 resolutions. Thus the analogRead() reads the analog value from 0 to 5 volts and assigns it a digital value from 0 to 1023. Whereas the digitalRead() reads either high (1) or low (0). The analogWrite() is 8-bit resolution and takes values from 0 to 255.


Digital to Analog (PWM)
The conversion of the digital to the analog is done using the pulse width modulation (PWM) . To do so we modulate the digital signal at a particular duty cycle. Since the device takes time to respond, it averages out the signal and we get the analog output. LEDs respond very quickly to the changing voltage but when we modulate the LED, its our eyes which average out the signal since they are no t fast enough to discern the difference.

Hence by changing the time that  signal is on versus the time that the signal is off , we can simulate a range of voltages between o and 5 volts. The duty cycle represents how much of the time is the signal high in one cycle. It is a ratio of the time that the signal is high to the total time in one cycle.The output voltage is determined by multiplying the maximum voltage ( usually 5V ) and the duty cycle. For example the duty cycle of 50% gives us the output analog voltage of 2.5V which is analogWrite(127).

Duty cycle frequency is the number of duty cycles that occurs every second. For example if there is one duty cycle in one second we have frequency 1Hz. Here is how the brightness of a LED varies as the duty cycle changes.


Bit-banging PWM 
We can even manually implement the PWM on any digital pin by turning it on and off. We make use of our knowledge that delay() function maintains the current state for a milli-second i.e. delay(1000) delays for 1 second.

Following is a code for the generation of 25% duty cycle @ 10Hz
 
void setup() {

  pinMode(13,OUTPUT);
}

void loop() {

  digitalWrite(13,HIGH);
  delay(25);
  digitalWrite(13,LOW);
  delay(75);
}
Food for thought : The analog reading ( value 0-1023 ) is taken from the analog pin of the Arduino. Whereas the digital reading ( 0 or 1 ) can be taken from any of the pin. The digitalWrite( high or low ) can be given from any of the pins but the analogWrite (0-255) can only be given from the PWM pins !

Comments

Post a Comment

Popular posts from this blog

The move_base ROS node

Image
move_base package provides the move_base node which is a major element of ROS Navigation stack. It moves the robot from its current position to a goal position. When path planning is done, the user gives uses the 2D Nav Goal in RVIZ to specify the goal position and orientation. This position (x,y,z) and orientation(x,y,z,w) are actually published in move_base/goal topic. The move_base node links together a global and local planner to accomplish its global navigation task. The Global Planner It is in charge of calculating the safe path in order to arrive at goal pose. Note that the path is calculated before the robot starts moving so it will not take into account the laser readings while moving i.e. unscanned obstacles that are not in the map. Navfn Planner The Navfn planner is the most commonly used global planner for ROS Navigation. It uses Dijkstra's algorithm in order to calculate the shortest path between the initial pose and the goal pose. Carrot Planner This plann
Read more

Three Wheeled Omnidirectional Robot : Motion Analysis

Image
A Three-wheeled omnidirectional robot is capable to moving in any given direction without rotating by giving velocities to the three wheels in a certain ratio. All motors are situated at an angle of 120 degrees from each other. f B ,  f L ,  f R  are for back , left and right wheel respectively. a x  and a y  are accelerations in X R  and Y R  axis in Robot frame and w is the angular velocity in Robot frame. Hence putting the values of alpha and making it into a matrix form we get : As we need to obtain the f values, we will invert the matrix. We need  a x  , a y  and w is the world frame, so we apply transformation. The transformation angle is    α 1  = 30 degrees.  Putting this in the previous equation, Multiplying the two matrices, we get the final relation as : For example, if you want to move the robot along X axis(world frame), put  a x W  = 1 , a y W  = 0 , w = 0 You will get the ratio of velocities as : 1 : -2 : 1 .
Read more

Overview of ATmega328P

Image
While reading about the ATmega328, I came a across a lot of stuff which I would like to share here. There is a humongous amount of information available in its datasheet. Introduction ATmega328 is a single chip micro-controller created by Atmel. It has a In-System Self-programmable Flash memory of 32 KB, SRAM of 2 KB (2048 bytes) and EEPROM of 1 KB (1024 bytes). It has a 8-bit AVR CPU type which means they can process data in 8-bit chunk as its data bus is 8-bit wide.   It contains 23 general purpose I/O pins and 32 general purpose working registers. It has 32 single-byte registers and 8-bit RISC (reduced instruction set computer) devices and hence the name 328. The P is for ' picoPower '. It has 3 flexible timer/counter with compare modes, internal and external interupts , 6-channel 10-bit A/D converter , programmable watch dog timer with internal oscillator and 5 software selectable power saving modes. Digital communication peripherals include 1-USART, 2-SPI and 1-I
Read more