Modulasi

Modulasi

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Introduction• Baseband signal = electrical replica of the message itself,

such baseband signal is not suitable for transmission over the transmission medium

• Carrier signal = another electrical signal is used to carry the baseband signal

• Modulation = Process that modify carrier signal according to the input signal

• Modulation leads to frequency “translation”• Modulation Method

AM, FM, PAM, PCM, etc.• Reason for modulation : for ease of radiation/reception, for

frequency translation to assigned band, and for multiplexing

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Isyarat Sinus

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Amplitude Modulation[AM]• Amplitude of a sinusoidal carrier is made to change according to the “instantaneous”

value of message• In general, the modulating signal such as voice or music is a complex waveform consist

of bands of frequency, thus the modulated AM wave consists of two sidebands for frequency

• Great disadvantage: In the a-m receiver, interference has the same effect on the r-f signal as the intelligence being transmitted because they are of the same nature and inseperable.

• There are various forms of AM1. Double sideband - suppressed carrier [DSB-SC]2. Single sideband - suppressed carrier [SSB-SC]3. Double sideband - full carrier [DSB-FC] (envelope AM)

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Amplitude Modulation[AM

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Percentage of Modulation • In amplitude modulation, it is common practice to express the degree to

which a carrier is modulated as a percentage of modulation. • When the peak-to-peak amplitude of the modulationg signal is equal to the

peak-to-peak amplitude of the unmodulated carrier, the carrier is said to be 100 percent modulated.

• The actual percentage of modulation of a carrier (M) can be calculated by using the following simple formula M = percentage of modulation

– M= ((Emax - Emin) / (Emax + Emin)) * 100

– where Emax is the greatest and Emin the smallest peak-to-peak amplitude of the modulated carrier.

• For example, assume that a modulated carrier varies in its peak-to-peak amplitude from 10 to 30 volts. – M = ((30 - 10) / (30 + 10)) * 100 = (20 / 40) * 100 = 50 percent.

• This formula is accurate only for percentages between 0 and 100 percent

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Percentage of Modulation

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• This results in a distorted signal, and the intelligence is received in a distorted form.

• Therefore, the percentage of modulation in a-m systems of communication is limited to values from 0 to 100 percent.

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Side Bands • When the outputs of two oscillators beat together, or hetrodyne, the two

original frequencies plus their sum and difference are produced in the output. This heterodyning effect also takes place between the a-f signal and the r-f signal in the modulation process and the beat frequencies produced are known as side bands.

• Assume that an a-f signal whose frequency is 1,000 cps (cycles per second) is modulating an r-f carrier of 500 kc (kilocycles). The modulated carrier consists mainly of three frequency components: the original r-f signal at 500 kc, the sum of the a-f and r-f signals at 501 kc, and the difference between the a-f and r-f signals at 499 kc.

• The component at 501 kc is known as the upper sideband, and the component at 499 kc is known as the lower side band. Since these side bands are always present in amplitude modulation, the a-m wave consists of a center frequency, an upper side-band frequency, and a lower side-band frequenmcy.


Side Bands• The carrier with the two sidebands, with the

amplitude of each component plotted against its frequency, is represented in figure.

• The modulating signal, fA, beats against the carrier, fC, to produce upper side band fH and lower side band fL.

• The modulated carrier occupies a section of the radio-frequency spectrum extending from fL to fH, or 2 kc.

• To receive this signal, a receiver must have r-f stages whose bandwidth is at least 2 kc. When the receiver is tuned to 500 kc, it also must be able to receive 499 kc and 501 kc with relatively little loss in response.


Side Bands


Side Bands• The audio-frequency range extends approximately from 16 to 16,000 cps. • To accommodate the highest audio frequency, the a-m frequency channel

should extend from 16 kc below to 16 kc above the carrier frequency, with the receiver having a corresponding bandwidth.

• Therefore, if the carrier frequency is 500 kc, the a-m channel should extend from 484 to 516 kc. (Double Side Band)

• This bandwidth represents an ideal condition; in practice, however, the entire a-m bandwith for audio reproduction rarely exceeds 16 kc.

• For any specific set of audio-modulating frequencies, the a-m channel or bandwidth is twice the highest audio frequency present.


Side Bands• The r-f energy radiated from the transmitter antenna in the form of a

modulated carrier is divided among the carrier and its two side bands. With a carrier componet of 1,000 watts, an audio signal of 500 watts is necessary for 100-percent modulation. Therefore, the modulated carrier should not exceed a total power of 1,500 watts. The 500 watts of audio power is divided equally between the side bands, and no audio power is associated with the carrier.

• Since none of the audio power is associated with the carrier component, it contains none of the intelligence. From the standpoint of communication efficiency, the 1,000 watts of carrier-component power is wasted. Furthermore, one side band alone is sufficient to transmit intelligence.

• It is possible to eliminate the carrier and one side band, but the complexity of the equipment needed cancels the gain in efficiency.


Double sideband Full carrier

• Full AM contains TWO sidebands, hence it is known as Double Sideband Full Carrier [DSB-FC]

• Information is carried by two (duplicating) sidebands [as such one is redundant]

• Hence, it is possible to transmit with only one of the sidebands which is known as Sinble Sideband

• Envelope AM or Full-AM requires two times bandwidth of SSB-AM

• Full-AM wasteful on part of transmitting power, but requires simple demodulation circuit on the receiver side (e.g. in case of millions receivers of broadcasting radio)


DSBFC tAtAtX ccmmAM coscos1

ttAAtA cmcmcc coscoscos carrier DSB-SC

0 +Fc-Fc


DSBFCMessage, m(t)

Message + d.c., 1+m(t)

Envelope modulated signal tAtmtx cc cos1


Demodulation DSBFCHalf-wave rectifier circuit + LPF

LPFRC

RC time constant RCt RC

f 1

RC f RC f


Diagonal Clipping• In the design of an envelope detector, the RC

time constant of the LPF is a critical parameter• Too small a value of RC time constant results to

too much ripple

• Too large a RC make it unable to follow fast fall in modulating signal envelope

RC f

RC f


Double sideband suppressed carrier

tAtm mm cos

tAtX ccc cos

Let Message signal

Carrier signal

mc mc FF then

tm

tX c

tXtmtX cAM


DSBSC tXtmtX cAM

ttAA ccmm coscos

ttAAmcmc

cm coscos2

BABABA coscos21coscos

tjtjtjtjcm mcmcmcmc eeeeAA 4


Demodulation [DSB-SC]XAM(t)

Carrier replicaXC(t)

LPF message

ttAAtX cCmmAM coscos

tAtX ccc cos

tAttAAty ccccmm coscoscos

2

2cos1cos;coscos 222 ttAA cmcm

tAtA cc

mm 2cos12

cos2

tAtAtAAc

cmmmm

c 2cos2

coscos2

22

LPFY(t) tAAtZ mm

c cos2

2

message DSB-SC


Single sideband suppressed carrier

• The main advantages of SSB-SC are

1. Only half of the bandwidth is required, hence the effective channel capacity is doubled

2. Smaller transmitter results from suppressing the carrier (containing 66.7% of the power), and one other sideband (another 16.7%)

3. Better SNR [Signal to Noise Ratio]Note : Smaller the bandwidth - Higher SNR Remember!! Noise Power : Pn = kTB


SSBSC• Converting DSB-SC to SSB-SC can be achieved in a

number of ways1.By Filtering

The high-pass filter must change from Full attenuation to Zero attenuation over a range of carrier frequency, hence the carrier frequency can be kept reasonably low

2.MixerDue to the limitation of real filters available, in practice two frequency translations are necessary to obtain SSB-SC at the desired tramsmitter frequency


SSBSCHPFDSB-SC SSB-SC

0DSB-SC

0SSB-SC

ttAASCDSB mcmccm coscos

2:

tAASCSSB mccm cos

2:


Demodulation [SSB-SC]

XAM(t)

Carrier replicaXC(t)

LPF Z(t)Y(t)

ttAAtY cmccm coscos

2)(

2

ttAAmcm

cm 2coscos4

2

BABABA coscos21coscos


Power Relationship

Root Mean Square value [rms]

tAtAtX ccmmAM coscos1

ttAAtA mcmccm

cc coscos2

cos

2cA

sidebandsAA cm 222

rms value

Power into 1 ohm of resistancecarrier

Two sidebandsR

VP2

2

2cA

2

84

2222cmcm AAAA


Power Relationship AMLet Am=1; total transmitted Power:

43

42

222ccc

totalAAAP

%7.6632

432

2

2

c

c

total

carrier

AA

PP

%7.1661

438

2

21

c

c

total

sideband

AA

PP

DSBFC


Power Relationship AM• Double Sideband Suppressed Carrier has the

potential to save up to 66.7% of power ((Ptotal-Pcarrier)/Ptotal)

• Single Sideband Suppressed Carrier can save up to 83.3% of power (100 – 16.7). That is one sideband contains 16.7% of the transmitting power


Phase Modulation • the frequency or phase of the carrier can be varied to

produce a signal bearing intelligence. • The process of varying the frequency in accordance

with the intelligence is frequency modulation, and the process of varying the phase is phase modulation.

• When frequency modulation is used, the phase of the carrier wave is indirectly affected. Similarly, when phase modulation is used, the carrier frequency is affected


Phase Modulation

• The starting point for measuring time is chosen arbitrarily, and at 0 time, curve A has some negative value. If another curve B, of the same frequency is drawn having 0 amplitude at 0 time, it can be used as a reference in describing curve A.


Vector Representation




Vector Representation• For each cycle of the modulating signal, the relative

phase of the carrier is varied between the values of (f+Df) and (f-Df).

• These two values of instantaneous phase, which occur at the maximum positive and maximum negative values of modulation, are known as the phase-deviation limits.

• The upper limit is +Df; the lower limit is -Df.





Frequency Modulation[FM]The carrier frequency fi is made to vary according tothe instantaneous amplitude of the message

tmkff fci cf Unmodulated carrier

fk Modulation constant, frequency deviation constant

freq.

m(t)

fc

Vmax

tmkff fci

f : max. frequency deviation, fd

slopek f fmax


FM

Message

Unmodulated carrier

FM signal


FM Signal Analysis

dtdff

dtd

212

tAtm cos

ttwheretA cos

tmkff fci sincedtd

21

tmkfdtd

fc 22

tmkfdtd

fc 22

dttmktft fc 22

t

fc dttmktf0

22cos



Multiplexing• Multiplexing is a process of combining

serveral information channels so as to share a common Transmission Channel, without mutual interference

• FDM [Frequency Division Multiplexing] is a method of multiplexing based on frequency translation consideration

• TDM [Time Division Multiplexing] is another mean of multiplexing based on time allocation consideration


Frequency Division Multiplexing[FDM]

LPFf2

LPFf1

LPFf3

SSBmod

SSBmod

SSBmod

fc1

fc2

fc3

MUX

O/P X(t)

To band limiteach input signalto avoid interference ffc1 fc2 fc3fc1+f1 fc2+f2 fc3+f3

Guardband


CCITT FDM HierachyChannel 1ch 4kHz

Group 12ch 48kHz

Super group 60ch 240kHz

Master group 300ch 1.2MHz

Super Master group 900ch 3.6MHz

Date post:	22-Nov-2014
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