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### Transcript of AM Modulation

EECE377 EE477/540Lecture #6. Section 2.1-2.2 (Overview, AM Modulation) February 3, 2006

Contents Essential points of Review Section Signals time-domain waveform: Acos(2fct) Fourier transform: A[(f-fc)+(f+fc)]/2 Magnitude spectrum, bandwidth, power Transfer function, convolution Y(f)=H(f)G(f)

Ideal filter: LPF, BPF

This class Section 2.1: overview of continuous wave modulation Section 2.2: AM modulation

2.1 Overview of Continuous Wave Modulation Definitions Continuous wave (CW) modulation A nick name for analog modulation, where both the message signal and the transmitted signal are analog signals Two classes: amplitude modulation, angle modulation

Modulating signal (wave), Modulated signal (wave) Modulating signal: another name for the message signal, or the signal to be modulated Modulated signal: the signal to be transmitted, or the signal obtained after modulation

Baseband, Passband Baseband: refers to the signals and systems before modulation, which have frequencies/bandwidth much lower than the carrier frequency Passband: refers to the signals and systems after (including) modulation, which have frequencies/bandwidth around the carrier frequency Baseband signal: is usually the modulating signal, or message signal Passband signal: is usually the modulated signal, or transmitted signal

What is modulation? Change baseband signal into passband signal (shift frequency of message signal from low to high) Change some characteristics of a carrier according to a message signal Add the message information into the carrier General form of modulated signal:

s (t ) = A(t ) cos[2 f ct + (t )] where cos(2 f ct) : carrier f c : carrier frequency s( t) : modulate d signal

Message signal m(t) embedded in Amplitude A(t) or phase (t )

Message signal m(t) modifies: amplitude A(t ) : AM linear modulation phase (t ) : PM Non-linear modulation d (t ) Frequency : FM f (t ) = dt Example 5.1 Compare signal waveformsmessage signal: m(t ) = cos(2 t ). carrier: c(t ) = cos(2 10t ).

List of modulation methods we will learn Amplitude modulation methods and applications AM (amplitude modulation): AM radio, short wave radio broadcast, CB radio DSBSC (double sideband suppressed carrier modulation): data modem, Color TVs color signals SSB (single sideband modulation): telephone VSB (vestigial sideband modulation): TV picture signal

Angle modulation methods and applications FM (frequency modulation): FM radio broadcast, TV sound signal, analog cellular phone PM (phase modulation): not widely used, except in digital communication systems (but that is different)

Checkpoints for studying each modulation1. 2. 3. 4. Modulated signal (time-domain) Spectrum (frequency-domain) Parameters: bandwidth, power, Modulator and demodulator (Principles, block diagrams or circuits) 5. Major properties (advantages/disadvantages over other modulations)

2.2 AM Modulation AM The amplitude of carrier wave is varied about a mean value, linearly with message signal

Modulated signal Carrier: c(t ) = Ac cos(2 fc t ) Message signal: m(t ) AM modulated signal

s (t ) = Ac [1 + ka m(t )]cos(2 fc t )

Important Parameters

s (t ) = Ac [1 + ka m(t )]cos(2 fc t )

i) amplitude sensitivity: ka ii) percentage modulation: max ka m (t ) 100

A good AM requires:1) carrier frequency: f c ? W (message signal bandwdith) 2) percentage modulation: ka m(t ) < 1, for any t .

Note: if ka m(t ) < 1, then [1 + ka m(t )] > 0. If (2) is violated: over modulation percentage modulation >=100 causes envelope distortion

Example 5.2 AM signals. Modulate a 1 Hz single-tone sinusoidal message signal onto a 10 Hz carrier. Examine the over-modulation case.

Spectrum of AM signalS ( f ) = FT[ Ac cos(2 fc t )] + FT[ Ac ka m(t ) cos(2 fc t )] Ac ka Ac = [ ( f f c ) + ( f + fc )] + [ M ( f fc ) + M ( f + fc )] 2 2

where M ( f ) = FT[m(t )]

Bandwidth of AM signal BT = 2W AM signals bandwidth is twice message bandwidth This is also transmitted signal bandwidth Negative frequency contents of m(t) becomes visible in positive frequency fc f fc + W Upper sideband (USB): f c W f fc Lower sideband (LSB):

Transmission power:PT = PM + Pcarrier = PUSB + PLSB + Pcarrier

Exercise 5.3 For the AM signal spectrum pictured in the figure below, calculate The message signal frequency fm The magnitude of the upper sideband The bandwidth Percentage modulation

Exercise 5.4 A single-tone modulated signal is shown below. The envelope has maxima 18 and minima 2. What is the carrier amplitude Ac? What is the percentage modulation?

max kam t 100 ()

Exercise 5.5 An AM modulation with carrier frequency fc=540 kHz, carrier amplitude Ac=20. Message signal is single tone with fm=10kHz, whose amplitude Am can make the carrier amplitude changing +/-7.5 around Ac=20 20. What is percentage modulation? Find the modulated signal.

Exercise 5.6 The first channel in AM broadcast has carrier fc=540 kHz. FCC standards admit maximum message signal frequency fm=W=5 kHz. Determine Frequency limits for the upper and lower sidebands Transmission bandwidth Sketch the spectrum of AM signal.

Conclusions Overview of continuous wave modulations Concepts List of modulation techniques checkpoints for study them

AM modulation Signal waveform, spectrum Parameters, bandwidth