Analog Signals No. 1Seattle Pacific University

Band Limited Signals:Sending Analog Data with Band Limited Signals

Based on Chapter 5 of William Stallings, Data and Computer Communication

Kevin BoldingElectrical Engineering

Seattle Pacific University

Analog Signals No. 2Seattle Pacific University

Pulse Trains vs. Band-Limited SignalsPulse Trains consume the

entire bandwidth of the transmission medium

Band-Limited signals are waves (compositions of sine waves) and constrained to a specified band of a medium’s bandwidth

Line coding uses pulse trains to send digital data

Band-limited signals may be used to send analog or digital data

Analog Signals No. 3Seattle Pacific University

Modulation

Modulation is the process ofcombining a signal waveand a carrier wave

Carrier wave has frequency fc, which must be greater than the modulating wave’s frequency, fm

Modulation allows the engineer to move the base frequency of a band

Allows the use of higher-frequency media

Makes frequency-division multiplexing possible

Analog Signals No. 4Seattle Pacific University

Amplitude ModulationGenerate a signal by modulatingthe amplitude of the carrier with the signal wave

tftxnts ca 2cos)](1[)(

Carrier Signal

Modulation Index

)(tx

tfc2cos

Analog Signals No. 5Seattle Pacific University

Multiplying Sine/Cosine Waves

If the signal x(t) is a single cosinewave, we get (with a modulationindex of 1):

tftfts cx 2cos]2cos1[)(

tfc2cos

tftftfts cxc 2cos2cos2cos)(

tfftfftfts xcxcc )(2cos2

1)(2cos

2

12cos)(

Carrier Difference

Sum

tf x2cos1

fcfc- fx fc+ fx0

pwr

f

SpectrumAnalyzer view

)(ts

Analog Signals No. 6Seattle Pacific University

AM Signal Spectrum

• Modulating signal covers a band from 0Hz to B

• Carrier signal is concentrated at Fc

• Combined signal has bandwidth of 2B, centered at Fc

• Includes a large amount of power at Fc

• Sending just one sideband reduces the bandwidth to B

• Filtering out the carrier reduces the power required

0 Fc-B

S(f)

fFc Fc+B

Upper sideband

Lower sideband

0 B

M(f)

fFc

Signal Carrier

0 Fc-B

S(f)

fFc Fc+B

Single Sideband

CarrierFc

BandpassFilter

(Fc to Fc+B)

SignalBW: B

Analog Signals No. 7Seattle Pacific University

Power of an AM Signal

2

12a

ct

nPP

Carrier Power

Total Power

Note: Largest practical modulation index is 1

Modulation Index

Analog Signals No. 8Seattle Pacific University

AM Detection

• To Detect (Demodulate) an AM Signal:

Vin Vout

• Rectify it to remove the negative portion of the waveform

• Low pass filter using a simple RC filter

Analog Signals No. 9Seattle Pacific University

Frequency/Phase ModulationGenerate a signal by modulatingthe frequency/phase of the carrier with the signal wave

)](2cos[)( ttfAts cc

Angle Offset Carrier )(tx

tfc2cos

)()( txnt p

)()( txnt f

For phase modulation:

For frequency modulation:

Carrier

Signal

Signal

Analog Signals No. 10Seattle Pacific University

FM/PM Signal Spectrum

• FM/PM frequencies vary according to an analog signal

• Analog signal --> Unlimited precision

• Unlimited bandwidth needed

• Some practical limits

• Maximum frequency deviation F is proportional to maximum amplitude in the modulating signal

• Carson’s rule for FM bandwidth requirement:

BFBT 22 works well