Pulse Modulation

It is a technique used in communication systems to send information by modifying pulses. It's divided into two main categories: Analog Pulse Modulation, which includes methods like PAM, PWM, and PPM, and Digital Pulse Modulation, such as Delta Modulation (DM). These techniques change aspects of the pulse—like its amplitude, width, or position—or use digital encoding to represent the original signal. Pulse modulation is commonly used in areas like telecommunications, audio transmission, remote controls, and power electronics (such as motor control and light dimming). Its advantages include reducing noise, making transmission more efficient, and allowing for easy multiplexing, which makes it a crucial part of modern communication.

1.0Definition of Pulse Modulation

• It is a technique used to encode information into a series of pulses by varying one or more characteristics—such as amplitude, width, or position—of the pulses, allowing the transmission of analog or digital signals over communication channels. It is used for both analog and digital signal transmission.
• Pulse modulation refers to the process of modulating a signal by varying discrete pulse parameters—such as amplitude (PAM), duration or width (PWM), or timing (PPM)—in accordance with the message signal. It also includes digital techniques like Delta Modulation (DM), making it suitable for digital communication systems

2.0Types of Modulation

3.0Types of Pulse Modulation

4.0Analog Pulse Modulation

Analog Pulse Modulation (APM) is a modulation technique where an analog signal is encoded by varying a specific characteristic of a periodic pulse, such as its amplitude, width, or position, to represent the information. The key types of Analog Pulse Modulation include:

1. Pulse Amplitude Modulation (PAM): 

• The amplitude of each pulse varies in proportion to the instantaneous amplitude of the analog signal.
• It is a method where the amplitude of a pulse carrier is directly tied to the changing amplitude of the message signal. Essentially, the PAM signal mirrors the fluctuations of the original message, capturing its entire waveform. In regular PAM, the signal is sampled at the Nyquist rate, which allows it to be reconstructed accurately by running it through a low-pass filter (LPF) with the right cutoff frequency. This process helps retrieve the original signal with very little distortion.

Note: Though the PAM signal is passed through an LPF, it cannot recover the signal without distortion. Hence to avoid this noise, flat-top sampling is done as shown in the following figure. 

Flat-top sampling involves representing the sampled signal as pulses with constant amplitude, maintaining the same value as the original analog signal. The pulse tops remain flat, simplifying circuit design.

2. Pulse Width Modulation (PWM): 

• The width (duration) of each pulse is varied in adherence with the instantaneous amplitude of the analog signal.
• Pulse Width Modulation (PWM), also known as Pulse Duration Modulation (PDM) or Pulse Time Modulation (PTM), is an analog modulation technique where the duration, width, or timing of the pulse carrier varies in fraction to the instantaneous amplitude of the message signal. In this method, the pulse width changes while the amplitude remains constant. To maintain a constant amplitude, amplitude limiters are used, which clip the signal to a desired level, helping to reduce noise. The following figures illustrate the different types of Pulse Width Modulation.

There are three variations of Pulse Width Modulation (PWM):

1. The leading edge of the pulse remains constant, while the trailing edge varies according to the message signal.
2. The trailing edge of the pulse remains constant, while the leading edge varies with the message signal.
3. The center of the pulse remains fixed, while both the leading and trailing edges adjust according to the message signal.
4. Pulse Position Modulation (PPM):

• The position or timing of each pulse within a fixed time frame is adjusted based on the instantaneous amplitude of the analog signal.
• Pulse Position Modulation (PPM) is an analog modulation technique where the amplitude and width of the pulses remain constant, but the position of each pulse, relative to a reference pulse, varies as per the instantaneous value of the message signal. To ensure proper synchronization between the transmitter and receiver, synchronizing pulses (or sync pulses) are transmitted. These pulses help maintain the correct positioning of the signal pulses. The following figures illustrate how Pulse Position Modulation works.

Pulse Position Modulation (PPM) is based on the Pulse Width Modulated (PWM) signal. In this method, the trailing edge of each PWM pulse serves as the starting point for the corresponding PPM pulse. Therefore, the position of each PPM pulse is directly proportional to the width of the PWM pulses.

5.0Evaluation between PAM, PWM, and PPM 

6.0Digital Pulse Modulation

Pulse Code Modulation

• Pulse Code Modulation (PCM) is a type of digital pulse modulation technique. Unlike analog modulation methods such as PAM, PWM, and PPM, PCM is more complex because the message signal undergoes several processing steps. In PCM, the analog input signal is converted into a binary sequence composed of 1s and 0s.
• The output of a PCM system is a stream of binary numbers, each representing the approximate amplitude of the initial analog signal at specific sampling instances. These values are obtained by sampling the signal and quantizing the amplitude into discrete levels, which are then encoded into binary form.
• PCM effectively represents the analog message signal using a sequence of coded pulses, where the signal is discretized in both time and amplitude. As a result, instead of a traditional pulse train, PCM generates a digital representation of the signal

Elements of a PCM System

The basic operation in the transmitter of a PCM system are : 

1. Sampling: It involves measuring the amplitude of an analog signal at uniform time intervals. As per the Nyquist Theorem, the sampling rate must be at least twice the signal's elevated frequency to enable accurate reconstruction.

• Nyquist Theorem: A signal can be accurately reconstructed from its samples if it is sampled at a rate at least twice the elevated frequency present in the signal. fs ≥ 2 ✕ fmax

2. Quantizing: It is the process of approximating each sampled value to the nearest value within a set of fixed discrete levels. Since real-world signals have infinite precision, quantizing limits the number of amplitude levels to a finite set. This introduces a small error known as quantization noise, but it enables digital representation.
3. Encoding: It is the process of converting each quantized value into a binary code (a series of 0s and 1s).Each unique quantized level is assigned a binary word. This digital output is what gets transmitted through the communication channel.

Delta Modulation

• Delta Modulation is a type of digital modulation where the input signal is sampled at a much elevated rate than the Nyquist rate, and the difference between successive samples is encoded using small step sizes, denoted by Δ (delta). Instead of encoding the absolute value of each sample, DM encodes only the change in amplitude.
• It is a simplified version of Differential Pulse Code Modulation (DPCM) and is often referred to as a 1-bit DPCM system, since it uses just one bit to indicate whether the signal has increased or decreased.

Key Features of Delta Modulation

• Uses over-sampling to take advantage of signal correlation.
• Very simple quantization process.
• The sampling rate is significantly higher than the Nyquist rate.
• Moderate signal quality compared to more complex techniques.
• Both modulator and demodulator are simple in design.
• Produces a staircase-like approximation of the original waveform.
• Uses a very small step size (Δ) for finer resolution.
• Bit rate is adjustable based on system requirements.
• Offers simpler implementation and lower cost.

Block Diagram Delta Modulation

The Delta Modulator consists of a 1-bit quantizer, a delay element, and two summing circuits. The simplified structure of the delta modulator is shown in the block diagram below.

x(nTs) = over sampled input  

ep(nTs) = summer output and quantizer input 

 eq(nTs) = quantizer output = v(nTs) 

$\hat{x}(nTs)$ = output of delay circuit  

u(nTs) = input of delay circuit