# Pulse Amplitude Modulation

Today communication is the heart of technology. Communication is achieved over a transmitter and a receiver through signals. These signals carry the information through modulation. Pulse Amplitude Modulation is one of the kinds of modulation techniques used in signal transmission. Pulse amplitude modulation is the simplest form of modulation. It is an Analog to digital conversion method where the message information is encoded in the amplitude of the series of signal pulses. This article discusses an overview of pulse amplitude modulation which is known as PAM.

## What is Pulse Amplitude Modulation?

Pulse amplitude modulation is the basic form of pulse modulation. In this modulation, the signal is sampled at regular intervals and each sample is made proportional to the amplitude of the modulating signal. Before we study in detail PAM lets us know the concepts of modulation.

#### What is Modulation?

Modulation is a process of changing the characteristics of a carrier signal like amplitude, frequency, and width, etc. It is the process of adding information to the carrier signal. A carrier signal is a steady waveform with constant amplitude and frequency.

Modulation is normally applied to electromagnetic signals like radio laser and optical signals. The Audio, video, images, and text data are added to the carrier signal for transmission over telecommunication.

### Types of Modulation

Modulation is categorized into two types depending on the type of signal.

• Continuous-wave Modulation
• Pulse Modulation

Continuous-wave modulation and Pulse modulation are further categorized as shown below.

#### Continuous-wave Modulation

In continuous wave modulation signal is used as a carrier signal which modulates the message signal. There are three parameters that can be altered to achieve modulation namely, frequency, amplitude and phase. Thus, there are three types of modulations.

1. Amplitude Modulation
2. Frequency Modulation
3. Phase Modulation

#### Pulse Modulation

Pulse modulation is a technique in which the signal is transmitted with the information by pulses. This is divided into Analog Pulse Modulation and Digital Pulse Modulation.

Analog pulse modulation is classified as

• Pulse Amplitude Modulation (PAM)
• Pulse Width Modulation (PWM)
• Pulse Position Modulation (PPM)

Digital modulation is classified as

### Pulse Amplitude Modulation

Pulse amplitude modulation is a technique in which the amplitude of each pulse is controlled by the instantaneous amplitude of the modulation signal. It is a modulation system in which the signal is sampled at regular intervals and each sample is made proportional to the amplitude of the signal at the instant of sampling. This technique transmits the data by encoding in the amplitude of a series of signal pulses.

There are two types of sampling techniques for transmitting a signal using PAM. They are:

1. Flat Top PAM
2. Natural PAM

#### Flat Top PAM

The amplitude of each pulse is directly proportional to modulating signal amplitude at the time of pulse occurrence. The amplitude of the signal cannot be changed with respect to the analog signal to be sampled. The tops of the amplitude remain flat.

#### Natural PAM

The amplitude of each pulse is directly proportional to modulating signal amplitude at the time of pulse occurrence. Then follows the amplitude of the pulse for the rest of the half-cycle.

In Pulse modulation, the unmodulated carrier signal is a periodic train of signals. So the pulse train can be described like the following.

Where ‘A’ is the unmodulated pulse amplitude

‘τ’ is pulse width

The pulse trains periodic time can be denoted as ‘Ts’

In PAM, the signal amplitudes can be changed based on the modulating signal. Here, the modulating signal like m(t), PAM can be achieved through multiplying the carrier signal with the modulating signal. The o/p is a set of pulses, where the amplitudes of signals can be changed on the modulating signal.

The specific type of PAM can be referred to as normal PAM, as the pulses follow the outline of the modulating signal. The pulse train works like a periodic switching signal toward the modulator. Once it is switched ON, and then allows the samples of modulating signals to supply toward the output. The pulse train’s periodic time is called the sampling period.

Fs = 1/Ts

The natural pulse amplitude modulation equation can be described as the following.

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+….

In the above equation, the modulated signal includes modulating signal that is multiplied through the dc term like ‘a0’a sequence of DSBSC based components which results from the harmonics within the pulse signal.

To stop the low-edge of the DSBSC range from overlapping through the less frequency range, the division ∆ among these should not below zero. So

W + ∆ = fs – W, with ∆ ≥ 0

fs ≥ 2W

This statement is compulsory on the sampling frequency which states that the sampling frequency should be as a minimum double the maximum frequency within the modulating signal.

If the sampling state is not met the spectra overlap parts, then such overlap is permitted to arise the spectra can no longer be divided through filtering. As the maximum frequency components within the DSBSC range come out within the less frequency fraction of the spectrum, so this effect is known as aliasing.

To evade aliasing, first, the modulation signal can be passed throughout an anti-aliasing filter to cut off the signal spectrum at W value.

The ‘fs’ (sampling frequency) = 2W which is called the Nyquist Frequency due to its wideband nature, pulse amplitude modulation includes an extremely limited range of applications for direct signal transmission. It is used in instrumentation systems & in ADC for computer interfacing.

### How PAM Signal is generated?

The generation of PAM can be done based on the following block diagram of pulse amplitude modulation.

The basic type of pulse modulation is known as PAM or Pulse amplitude modulation, where the signal can be sampled at regular intervals & every sample can be made relative to the modulating signal’s amplitude on the sampling moment.

The above block diagram of PAM shows the PAM signal generation from the sampler where the sampler includes two inputs namely sampling/carrier signal and modulating signal. Therefore the signal amplitude is relative to the modulating signal through where the data can be carried. So, this is the PAM signal. The spectrum of the PAM signal is shown in the above waveforms which include the message & the sampling signals where the carrier train of signals using the waveform plotted within the time field.
Pulse Modulation is mainly used for transmitting analog data like data otherwise continuous speech signal.

Circuit Design of Pulse Amplitude Modulation

A PAM is generated from a pure sine wave modulating signal and a square wave generator which produces the carrier pulse and a PAM modulator circuit.

A sine wave generator is used which is based on the Wien Bridge Oscillator circuit. This can produce distortion less sine wave at the output. The circuit is designed such that the amplitude and the frequency of the oscillator can be adjusted using a potentiometer.

The frequency can be varied by varying the potentiometer R2 and the amplitude of the adjusted using the potentiometer R. The frequency of the sine wave generated is given by

F = 1/(2π√R1R2C1C2)

The square wave is generated using op-amp based astable circuit. The op-amp is used to reduce the complexity of generating the square wave. The ON time and the OFF time of the pulse can be made identical and the frequency can be adjusted without changing them.

The time period of the pulses generated depends on the value of the resistance R and the capacitance C. The period of the op-amp astable circuit is given by

T = 2.2RC

### Types of Pulse Amplitude Modulation

Pulse amplitude modulation is categorized into two types

1. Single Polarity PAM
2. Double Polarity PAM

Single polarity PAM is a situation where a suitable fixed DC bias is added to the signal to ensure that all the pulses are positive.

Double polarity PAM is a situation where the pulses are both positive and negative.

In some pulse amplitude modulations, the amplitude of each pulse can be directly proportional to instant modulating amplitude once the pulse takes place. In another type of PAM, each signal’s amplitude can be inversely proportional toward instant modulating amplitude once a pulse occurs.

In other systems, every pulse’s intensity mainly depends on specific modulating signal characteristics excluding strength like instant phase otherwise frequency.

The capability of using stable amplitude pulses is the main benefit of pulse modulation. As PAM does not use stable amplitude signals, it is not frequently used. Once it is used, then the frequency of pulse changes the carrier.

It is very simple to produce & demodulate a pulse amplitude modulation. The signal conversion is a generator that can be done toward PAM that is fed to a single input of an AND-gate.

Signals at the sampling frequency are given toward the other i/p of the AND gate, to open it throughout the required time intervals. After that, the output of the logic gate includes pulses at the sampling rate, which is equivalent in amplitude toward the signal voltage at every second, then the signals are passed throughout a network that is in pulse shape, which provides them a plane top.

### Demodulation of PAM

For the demodulation of the PAM signal, the PAM signal is fed to the low pass filter. The low pass filter eliminates the high-frequency ripples and generates the demodulated signal. This signal is then applied to the inverting amplifier to amplify its signal level to have the demodulated output with almost equal amplitude with the modulating signal.

### Pulse Amplitude Modulation Circuit using 555 Timer

The pulse amplitude modulation circuit using a 555 timer is shown below. The pulse amplitude modulation can be generated through 555IC by connecting one NPN transistor at the output. The connection of this IC can be done in the astable mode for producing a pulse train so that samples of the audio signal can be obtained.

The frequency of this must be a minimum double to the audio signal. Generally, it is 8 KHz as the audio signal is equal to 3.4 KHz however for enhanced quality this circuit uses 32 KHz. The output of the pulse train can be given to the base terminal of the NPN transistor. This transistors collector terminal is connected through a low-frequency audio signal using a positive clamper that is connected with the C1 capacitor & D1 diode.

The level of the audio signal can be shifted with a positive clamper above 0V, So the o/p at the collector terminal of the transistor is the pulse amplitude modulation signal. The signal amplitude which is generated through IC555 changes in accordance with the instant amplitude of the data signal.

The advantages of pulse amplitude modulation include the following.

• It is a simple process for both modulation and demodulation.
• Transmitter and receiver circuits are simple and easy to construct.
• PAM can generate other pulse modulation signals and can carry the message at the same time.
• The data can be transmitted quickly, efficiently, and effectively through usual copper wires in high volume.
• The FM available is infinite; therefore the development of PAM can be done frequently to permit enhanced data throughput over accessible networks.
• It is the simplest type of modulation
• For all types of digital modulation methods, it is the base and simple method for both modulation & demodulation.
• For both the transmission as well as reception, it doesn’t require complex circuitry. The circuit design of the Transmitter & receiver is very simple.
• This modulation can generate other types of pulse modulation signals & also carries the message at the same time.

The disadvantages of pulse amplitude modulation include the following.

• Bandwidth should be large for transmission PAM modulation.
• Noise will be great.
• Pulse amplitude signal varies so the power required for transmission will be more.
• For transmitting PAM signal, BW must be large
• The frequency changes based on the message or modulating signal because of these changes within the frequency of the signal, intrusions will be there.
• For this modulation, noise immunity is low as compared to other types. So it is nearly equivalent to AM.
• Once pulse amplitude signal changes then the required power for transmission is high and even to get the PAM, more power is necessary.

Applications of PAM

• It is used in Ethernet communication.
• It is used in many micro-controllers for generating control signals.
• It is used in Photo-biology.
• It is used as an electronic driver for LED lighting.
• PAM is used in the Ethernet network which is used to connect two systems & used to transfer data among these systems. So PAM is used in Ethernet communications.
• The control signals can be generated in various microcontrollers by using PAM
• This modulation technique is mostly used in digital data transmission & applications changed by PCM &PPM. Mostly all phone modems which are faster above 300 bit/s utilize QAM (quadrature amplitude modulation).