Chapter 2: Amplitude Modulation Transmission

EET-223: RF Communication Circuits

Walter Lara

Introduction

• As see before, modulation is needed to:

– Avoid interference since intelligence signals are at approximately the same frequency

– Avoid impractical large antennas since intelligence signals have low frequencies

• Problem: how to put intelligence signal onto a carrier (high frequency) signal for transmission

• Simplest solution: put intelligence into carrier’s amplitude

AM Fundamentals

• Combining (“mixing”) the intelligence and carrier signals can be done:

– Using linear device (e.g. resistor) – simple addition, but not suitable for transmission (receiver cannot detect intelligence)

– Non-linear device (e.g., BJT or OpAmp) – method used in practice

• Non-linear mixing results on:

– DC Component

– Components at original frequencies (intelligence & carrier)

– Components at sum & difference of original frequencies

– Harmonics of original frequencies

AM Fundamentals – Cont’d

• Only the following components resulting from non-linear mixing are used on an AM waveform:

– Carrier frequency (fc)

– Lower-side frequency (fc - fi)

– Upper-side frequency (fc + fi)

Figure 2-1 Linear addition of two sine waves.

Figure 2-2 Nonlinear mixing.

AM Waveforms

• An AM modulated signal can be expressed as:

e(t) = (Ec + Ei sin wit) sin wct

where:

Ec = peak value of carrier signal

Ei =peak value of intelligence signal

wc= angular frequency of carrier signal

wi = angular frequency of intelligence signal

• It can be demonstrated that:

e(t)= Ec sin wct + (Ei/2)cos (wc - wi)t - (Ei/2)cos (wc + wi)t

Figure 2-3 AM waveform under varying intelligence signal (ei) conditions.

Figure 2-4 Carrier and side-frequency components result in AM waveform.

Figure 2-5 Modulation by a band of intelligence frequencies.

Figure 2-6 Solution for Example 2-1.

Percentage Modulation

• Aka Modulation Index or Modulation Factor

• Measure of extend to which carrier voltage is varied by intelligence

• Defined as: %m = Ei / Ec * 100

– Ei: Peak value of intelligence signal

– Ec: Peak value of carrier signal

• Can also be computed using the peak-to-peak value of the AM waveform (see Fig. 2-8)

– Convenient in graphical (oscilloscope) solutions.

Figure 2-8 Percentage modulation determination.

Overmodulation

• Overmodulation is a condition that occurs when an excessive intelligence signal overdrives an AM modulator making %m > 100% (because Ei > Ec)

• Modulated carrier amplitude reach value greater than double of unmodulated value

• It produces a distortion known as sideband splatter, which results on transmission at frequencies outside the allocated range

• It is unacceptable because it causes severe interference with other stations and causes a loud splattering sound to be heard at the receiver.

Figure 2-9 Overmodulation.

AM Analysis

• Recall:

e(t) = (Ec + Ei sin wit) sin wct

= Ec sin wct + (Ei/2)cos (wc - wi)t + (Ei/2)cos (wc + wi)t

• Since Ei = m Ec , then:

e(t) = Ec sin wct + (mEc/2) cos (wc - wi)t

+ (mEc/2) cos (wc + wi)t

• Therefore, the side-frequency amplitude is:

ESF = mEc/2

Why is important to use a high %m?

• The higher m, the more transmitted power gets to our sidebands, which contain the intelligence.

• The total power can be computed as:PT = PC + 2PSF = PC (1 + m2 / 2)

Where:

PC : carrier power

PSF : single sideband power

• The total current can be computed as:

IT = Ic 𝟏 +𝒎𝟐/𝟐

• The power efficiency can be computed as:Efficiency = 2PSF / PT = m2 / (2 + m2)

AM Transmitter System

• Refer to block diagram at Fig. 2-18 (next slide).

• Main components are:– Oscillator: generates carrier signal at high accuracy (crystal-

controlled)

– Buffer Amplifier: provides high impedance load to oscillator to minimize drift

– Intelligence Amplifier: amplifies the signal from input transducer

– Modulated Amplifier (aka Modulator): generates modulated/mixed signal

– Linear Power Amplifier: amplifies modulated signal on high-power (commercial) systems

Figure 2-18 Simple AM transmitter block diagram.

Trapezoidal Patterns

• Method to check proper modulation of AM signal– More revealing than viewing signal on scope

• Procedure:– Put scope in XY Mode

– Put AM signal on vertical

– Put intelligence signal on horizontal (through RC phase-shift network

• Possible Results (see Fig 2-23):– Top & bottom straight lines: proper modulation

– Single vertical line: no intelligence (carrier only)

– Concave curvature: poor linearity on modulation stage

– Convex curvature: improper bias or low carrier signal

– Half oval with inner Y : improper phase relationships

Figure 2-23 Trapezoidal pattern connection scheme and displays.

Spectrum Analyzers

• Show plot of amplitude vs frequency

• Swept-tuned (superhetereodyne) Analyzer – uses analog frequency sweep, can go up to GHz range

• Fourier Analyzer – digitizes waveform and uses FFT algorithms. Limited to ~40 MHz (EET Labs)

• Vector Signal Analyzer (VSA) – uses analog front-end and digitizes after down-convertion.

– Best of both worlds, but expensive

– Can measure Total Harmonic Distortion (THD)

Figure 2-24 Spectrum analysis of AM waveforms.

Figure 2-25 Spectrum analyzer and typical display. (Courtesy of Tektronix, Inc.)

Figure 2-25 (continued) Spectrum analyzer and typical display. (Courtesy of Tektronix, Inc.)

Relative Harmonic Distortion (RHD)

• Ratio of fundamental with respect to the largestundesired harmonic

– The greater, the better

• Can be computed (in dB) as:

RHD = 𝟐𝟎 𝒍𝒐𝒈 𝑽𝟏/𝑽𝟐Where:

V1: desired component (fundamental frequency)

V2: largest undesired harmonic component

Figure 2-26 Relative harmonic distortion.

Total Harmonic Distortion (THD)

• Ratio of power from unwanted harmonics to desired frequency components– The greater, the worst– More descriptive distortion spec than RHD

• Occurs in amplifiers and non-linear devices

• Can be computed as:

THD = (𝑽𝟐𝟐 + 𝑽𝟑

𝟐 + 𝑽𝟒𝟐 + …)/𝑽𝟏

𝟐

Where:

V1: desired component (fundamental frequency)

V2, V3, … : undesired harmonic components