Mathematical Expression for Pulse Amplitude Modulation
A modulation method used in signal processing and telecommunications is pulse amplitude modulation, or PAM. It involves modulating the amplitude of a sequence of pulses in accordance with the modulating signal’s amplitude.
A periodic train of signals is the unmodulated carrier signal in pulse modulation. Thus, the following is a description of the pulse train.
up(t)=[Tex]\sum_{K=-\infty}^{\infty} A rect \frac{t-KTs}{\tau}[/Tex]
The unmodulated pulse amplitude is represented by the letter “A” in the pulse train.
τ stands for pulse width.
“Ts” is a symbol for the periodic time of the pulse trains.
The modulating signal in PAM allows for the modification of the signal amplitudes. Here, the modulating signal, such as m(t), PAM, can be obtained by multiplying the modulating signal by the carrier signal. The output is a collection of pulses that can have their signal amplitudes adjusted using the modulating signal.
The pulse train’s periodic time is called the sampling period.
Fs = 1/Ts
This is an explanation of the equation for natural pulse amplitude modulation:
[Tex]up(t)=a_0+\sum_{n=1}^{Z}a_n cos \frac{2 \pi nt}{T_s}[/Tex]
[Tex]=a_0+a_1cos\frac{2 \pi nt}{Ts}+a_2cos \frac{4 \pi nt}{Ts}+…[/Tex]
The modulated pulse train can be described like
E(t) = m(t) +Up(t)
= a0 m(t) + a1 m(t) cos2πnt/Ts + a2 m(t) cos4πnt/Ts+….
Pulse Amplitude Modulation
Pulse Amplitude Modulation (PAM) is a key modulation technique used in digital communication for transmitting analog data and is one of the most widely used types of analog-to-digital conversion. Its process is simple where the amplitude of a sequence of pulses changes with the instantaneous amplitude of the analog message signal. The analog signal that is to be modulated is sampled by a sequence of pulses that are amplitude-modulated on the carrier to produce the amplitude-modulated pulses.
The analog signal is sampled at regular intervals to enable the amplitude of pulses due to be produced by the carrier to be varied. The sampled values are quantized to a specific number of quantization levels or discrete levels whereupon the process is repeated. Due to its simplicity of implementation and analysis, PAM is often employed in many applications including digital communication, audio transmission, and instrumentation among others. One of the biggest drawbacks of PCM is its sensitivity towards channel errors, as poor-quality channels will introduce noise and distortion, particularly over larger distances and lower data rates.
Table of Content
- What is PAM?
- PAM Block Diagram
- Types
- Mathematical expression
- Construction
- PAM Circuit
- Solved Examples on PAM
- Applications
- Advantages
- Disadvantages