communication system Chapter 4

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Communication System Communication System Ass. Prof. Ibrar Ullah

BSc (Electrical Engineering)

UET Peshawar

MSc (Communication & Electronics Engineering)

UET Peshawar

PhD (In Progress) Electronics Engineering

(Specialization in Wireless Communication)

MAJU Islamabad

E-Mail: [email protected]

Ph: 03339051548 (0830 to 1300 hrs)

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Chapter-4 Amplitude Modulation

1. Bandwidth and baseband

2. Amplitude modulation

3 Quadrature amplitude modulation

4. Single side band Modulation

5. Vestigial side band Modulation

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Baseband and carrier Communication

• The bandwidth B represents a measure of frequency range. • It is typically measured in Hz with 1 Hz = 1/sec.• The bandwidth of a signal indicates the frequency range in which the

signal‘s Fourier transform has a power above a certain threshold (typically half of the maximum power)

• Often the frequency f = / 2 is used instead of the angular frequency .

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Baseband and carrier Communication

• The term baseband designates a frequency range starting at 0 Hz• Example of a baseband signal spectrum:

• In baseband communication baseband signals are sent without any shift in the range of frequencies

• Any communication that uses modulation of a high-frequency carrier signal is called carrier communication

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Amplitude Modulation (DSB)

•Amplitude modulation (AM) varies the amplitude of a carrier signal according to a modulating signal m(t).

• The modulated signal is

)cos( cctwA

)cos()( twtm c

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Amplitude Modulation (DSB) cont…

Frequency-Shifting Property of Fourier transform:

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• This type of modulation shifts the spectrum of m(t) to the carrier frequency.

If

)()(2

1cos)( ccc wwMwwMtwtm

)()( wMtm

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•This modulation shifts the frequency spectrum to the right and the left by • The modulated signal is composed of two parts, above and below

– the upper sideband (USB) containing the frequencies |w| > | |

– the lower sideband (LSB) containing the frequencies |w| < | |

•The modulated signal in this scheme does not have a discrete component of the carrier frequency for this reason this is called double-sideband suppressed carrier (DSB-SC) modulation

)()(2

1cos)( ccc wwMwwMtwtm

cwcw

cw

cw

cw

cw

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B Vs cw•If the bandwidth of the original signal m(t) is 2 B, then the bandwidth of the modulated signal will be 4 B, consisting of

– the upper sideband (USB) containing the frequencies |w| > | |

– the lower sideband (LSB) containing the frequencies |w| < | |

cw

cw

To avoid overlap of the two spectral parts, wc > 2B must be fulfilled

(if c < 2B , the information of m(t) will be partly lost in the process of modulation)

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Spectrum

Spectrum of the DSB-SC signal m(t)cos10,000t

)cos()cos(2

1coscos

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Spectrum


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Spectrum


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Modulation / Demodulation

Modulation

Demodulation

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Demodulation

• The process of receiving the original signal from the modulated signal is called demodulation.

• Demodulation is similar to modulation and can be performed by multiplying the modulated signal again with the carrier signal )cos( tw

c

The resulting signal

)2cos()()(21cos)()( 2 twtmtmtwtmte

cc

It has the Fourier transform

)2()2(41)(2

1)(cc

wwMwwMwMwE

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Demodulation

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Modulators

Multiplier modulators:

•Modulation is achieved directly by multiplying m(t) by using an analog multiplier.

•The output is proportional to the product of two input signals.

•Difficult to maintain linearity and are expansive.

twccos

Better to avoidBetter to avoid

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Modulators (cont…)

Nonlinear modulators:

Modulation is achieved by using nonlinear devices such as semiconductor diode or a transistor

NL: Two identical nonlinear elements

NL: Two identical nonlinear elements

Let output characteristics of NL be approximated by the power series as:

Where x(t) and y(t) are input & output

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Changing inputs

Gives:

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•Spectrum m(t) is centered at the origin, while of m(t)coswct is centered at +-wc

•The signal is ready for transmission but we do not need the m(t) part of z(t)

•Z(t) is passed through a band-pass filter tuned to wc , the signal m(t) is suppressed while 4bm(t)coswct passed unharmed.

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Summary nonlinear modulator:

•Two inputs m(t) and coswct

•The summer output does not contain one of the input coswct

•Circuits which have this characteristic are called balanced circuits.

•The previous circuitry is an example of balanced modulators.

This circuit is balanced to only one input carrier, the other input m(t) still appear at the filter input, which must reject it…….for that reason it is called a single balanced modulator

This circuit is balanced to only one input carrier, the other input m(t) still appear at the filter input, which must reject it…….for that reason it is called a single balanced modulator

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Modulators (cont…)Modulation through any periodic signal:

Modulated signal can not only be obtained by a pure sinusoid but by any periodic signal.of fundamental frequency wc. E.g:

Trigonometric Fourier seriesTrigonometric Fourier series

Spectrum of the modulated signal is the spectrum M(w) shifted to

If we pass this modulated signal through band-pass filter of bandwidth 2B tuned to wc

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Modulators (cont…)Modulation through any periodic signal:

Modulated signal can not only be obtained by a pure sinusoid but by any periodic signal.of fundamental frequency wc. E.g:

Trigonometric Fourier seriesTrigonometric Fourier series

Spectrum of the modulated signal is the spectrum M(w) shifted to

If we pass this modulated signal through band-pass filter of bandwidth 2B tuned to wc

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Switching Modulators

Multiplication operation of modulation can be replaced by switching operation. If we a periodic signal having Fourier series as:

carrier

Modulated signal

Now consider a periodic square pulse train with Fourier series as

....7cos

7

15cos

5

13cos

3

1cos

2

2

1)( twtwtwtwtw

cccc

From example 2.8From example 2.8

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The modulated signal m(t)w(t) is given by

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Switching ModulatorsModulated signal m(t)w(t) consists of the component m(t) plus infinite numbers of modulated signals with carrier frequencies ,.....5,3,

cccwww

The spectrum of m(t)w(t) consists of M(w) and M(w) shifted to,.....5,3,

cccwww

As we are interested in modulated component only. To separate this component from others we pass m(t)w(t) through a bandpass filter of bandwidth 2BHz, centered at

gives the required modulated signal

twtmc

cos)(

cw

twtmc

cos)(2

Therefore the multiplication of a signal by a square pulse train is is reality a switching operation means turning off and on signal m(t) periodically and can be accomplished by switching element controlled by w(t)

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Diode bridge modulator:

Consider the following electronic switch circuit driven by to produce the switching action

twAc

cos

4321,, DDDD and

are matched pairs

During the next half cycle d is positive with respect to c, all the diodes open, terminal a & b are open.

When terminal c is positive with respect to d, all the diodes conduct, terminal a & b are effectively shortened.

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Therefore the the circuit act as a desired electronic switch, where the terminal a & b open and close periodically with the carrier frequency . When is applied across the terminal ab

To obtain m(t)w(t) we may place terminal ab in series or in parallel as:

cf twA ccos

Series-bridge diode modulator Shunt-bridge diode modulator

Switching on and off m(t) for each cycle of the carrier, resulting in the switched signal m(t)w(t) and passing through bandpass filter gives the desired signal:

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Ring modulator:

Consider the following circuit

During the positive half cycle of the carrier D1 & D3

conduct and D2 & D4 are open, hence terminal a is connected to c & b to d

During the negative half cycle of the carrier D1 & D3 are open and D2 & D4 conduct, hence terminal a is connected to d & b to c

Output is proportional to m(t) during positive cycle &

-m(t) during negative cycle

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The Fourier series of bipolar square wave is given by:

Example 2.8 p-52Example 2.8 p-52

Gives modulated signal as:

Filtering this signal to bandpass filter tuned to wc gives the required modulated signal:

In this circuit there are two inputs m(t) and coswct, the input of the final bandpass filter does not contain either of the inputs……

this circuit is an example of double balanced modulator

In this circuit there are two inputs m(t) and coswct, the input of the final bandpass filter does not contain either of the inputs……

this circuit is an example of double balanced modulator

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Problem 4.2-4

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Problem 4.2-4

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Problem 4.2-4

At point b

At point c

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Problem 4.2-4

The minimum value of wc is to avoid overlapping

Will not work

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Problem 4.2-4

This may be verified that the identity for contains a term when n is odd. This is not true when n is even. Hence, the system works for a carrier only when n is odd.

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Example 4.2

Frequency mixer or converter:

Frequency mixer or converter is used to change the carrier frequency of the modulated signal m(t)coswct to some other frequency wl

Can be achieved by multiplying m(t)coswct by

where or

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Example 4.2

In both cases the filter tuned to Wl will pass the term m(t)coswlt and suppress the other term and giving the required output

m(t)coswct (the carrier frequency is translated to wl from wc)

Frequency mixing or frequency conversion is also known as heterodyning.

All the modulators discussed previously can be used for frequency mixing.

Frequency selected as operation called up-conversion Frequency selected as operation called down-conversion

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Amplitude Modulation (AM)

For DSB-SC a receiver must generate a carrier in frequency and phase synchronism with the carrier at the transmitter.

Problem:

Transmitter and receiver may be located thousands of miles away, this call for a sophisticated receiver and could be costly.

Solution:

Transmit a carrier Acoswct along with the modulated signal m(t)coswct so no need to generate a carrier at the receiver.

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This type of modulation is called amplitude modulation and denoted by and is given by:

)(tAM

It has the Fourier spectrum

The spectrum of is the same as m(t)coswct plus two additional impulses at )(tAM

c

w

•DSB-SC signal m(t)coswct and AM signal are identical with A+m(t) as modulating signal instead of m(t)

•To sketch ,we sketch A+m(t) & -(A+m(t) ) and fill in between the carrier frequency.

)(tAM

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Amplitude Modulation (AM)As we sketch A+m(t) & -(A+m(t) ):

Consider two cases:

0)( tmA and 0)( tmA

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Amplitude Modulation (AM)For simple envelope detection for AM signal is:

A = 0, also satisfies the condition. In this case there is no need to add carrier, because the envelope of DSB-SC signal m(t)coswct is m(t)

Such a DSB-SC signal can be detected by envelope detection

Assume for all t

Let mp is the peak amplitude (positive or negative) of m(t)

Then

Hence the condition is equivalent to

Thus the minimum carrier amplitude required for the envelope detection is mp

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We define the modulation index as:A = carrier amplitude

mp = constant of m(t)

As A is the carrier amplitude and there is no upper bound on A,

This is the condition for the viability of demodulation of Am signal by an envelope detector

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Example 4.4 p-164

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Sideband and carrier power:

There is a disadvantage of envelope detection in terms of power waste, as the carrier term does not contain any information

The carrier power Pc is given by

The sideband power Ps is given by

Hence the power efficiency is given by:

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For the special case of tone modulation:

Hence

twAtm mcos)( and

With condition Thus under best condition only one third of the transmitted power is used for

carrying message, for practical signals the efficiency is even worst

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Generation of AM signals

• Am signals can be generated by any DSB-SC modulators.

• The input should be A + m(t) instead of just m(t).

• The modulating circuit do not have to be balanced because there is no need to suppress the carrier

Switching action is provided by a single diode and controlled by with

Switching action is provided by a single diode and controlled by with twc ccos

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Generation of AM signals

The diode opens and short periodically with infect multiplying the input signal by w(t).

The diode opens and short periodically with infect multiplying the input signal by w(t).

/bbThe voltage across is:

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Demodulation of AM Signals

The AM signal can be demodulated coherently by a locally generated carrier. E.g.

twtwtmA cc coscos)( No benefit of sending carrier on the channelNo benefit of sending carrier on the channel

There are two well known methods of demodulation of AM signals:

1) Rectifier detection 2) Envelope detection

Rectifier detector:

AM signal is applied to a diode and resistor circuit, the negative part of the the AM wave will be suppressed.

The output across the resistor is the half wave rectified version of the AM signal means multiplying AM with w(t).

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Rectifier Detector

)(cos)( twtc

wtmAvR

...5cos

5

13cos

3

1cos

2

2

1cos)( t

cwt

cwt

cwt

cwtmA

otherTermstmA )(1

The rectified output VR

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Rectifier Detector (cont…)

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Envelope Detector

In an envelope detector, the output follows the envelope of the modulated signal.

The following circuit act as an envelope detector:

• During the positive cycle of the input signal, the diode conducts and the capacitor C charges up to the peak voltage of the input signal.

•When input signal falls below this peak value, the diode is cut off. (because the diode voltage which is nearly the peak voltage is greater than the input signal voltage causing the diode to open ).

•At this stage the capacitor discharge at the slew rate (with a time constant RC)

• during the next positive cycle the process repeats.

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Envelope Detector (cont…)

During each positive cycle the capacitor charges up to the peak voltage of the input signal and then decays slowly until the next positive cycle.

This behavior of the capacitor makes output voltage Vc(t) follow the envelope of the input signal.

Capacitor discharges during each positive peaks causes a ripple signal of frequency wc at the output

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The ripple can be reduced by increasing the time constant RC so the capacitor discharges very little between positive peaks of the input signals

Making RC too large, makes capacitor voltage impossible to follow the envelope.

Conditions:

RC should be large compared to 1/wc, but should be small compared to

Where B is the highest frequency in m(t)

B21

Also requires a condition which is necessary for well defined envelope.

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The envelope detector output is with a ripple of frequency wc

The DC term A can be blocked by a capacitor or a simple RC high pass filter, and the ripple may be reduced further by another low-pass RC filter.

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Quadrature Amplitude Modulation

The DSB signals of AM require twice the bandwidth required for the baseband signal!

Idea: Try to send two signals m1(t) and m2(t) simultaneously by modulating them with two carrier signals of same frequency but shifted in phase by –/2

The combined signal is twtmtwtmtmtm cc sin)(cos)()()( 2121

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Quadrature Amplitude Modulation (cont…)

Both modulated signals occupy the same band

• At the receiver the two baseband signals can be separated by using a second carrier that is shifted in phase by –/2

• The first signal m1(t) can be detected by a multiplication with 2cos(ct) followed by a low-pass filter

The second signal x2(t) can be detected accordingly by a multiplication with sin(ct) followed by a low-pass filter

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Quadrature Amplitude Modulation (cont…)

• Thus, two baseband signals, each of bandwidth B, can be simultaneously transmitted over a channel with bandwidth 2B

• This principle is called quadrature amplitude modulation (QAM), because the carrier frequencies are in phase quadrature.

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Amplitude Modulation (Single Sideband SSB)

• The DSB spectrum has two sidebands: USB and LSB

• Both USB and LSB contain complete information of the baseband signal.

• A scheme in which only one sideband is transmitted is known as single-sideband ( SSB) transmission.

• In SSB transmission the required bandwidth is half compared to DSB signal.

• An SSB signal can be coherently (synchronously) demodulated. E.g.

For example multiplying USB signal by shifts its spectrum to the left and right by wc

twccos

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Single Sideband SSB (cont..)

Low pass filtering will give the required baseband signal at the receiver.

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Single Sideband SSB (cont..)

Time domain representation of SSB signals:

twtmtwtmt chcSSB sin)(cos)()(

Where minus sign applies to USB and the plus sign applies to LSB

Hilbert Transform of m(t)

and delays the phase of each component by

Hilbert Transform of m(t)

and delays the phase of each component by

)(tmh

2

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Example 4.7 p-174

Tone Modulation:

Find for a simple case of tone modulation, that is, when the modulating signal is a sinusoid

)(tSSBtwtm mcos)(

Solution:


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Example 4.7 p-174

Hence

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Example 4.7 p-174

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Generation of SSB Signals

Two methods are generally used to generate SSB signals.

1) Sharp cutoff filters

2) Phase shifting networks

Selective Filtering Method:

• In this method the DSB-SC signal is passed through a sharp cutoff filter to eliminate the undesired sideband.

• To obtain USB , the filter should pass all components above wc, attenuated and completely suppress all components below wc

• Such an operation requires an ideal filter that is practically not possible.

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Generation of SSB Signals

• This method of generating SSB signal can be used when there is some separation between the passband and stopband.

• In some application this can be achieved e.g. voice signals

Voice signals spectrum shows little power content at the origin. Thus filtering the unwanted sideband is relatively easy.

Tests have shown that frequency components below 300Hz are not important.

Tests have shown that frequency components below 300Hz are not important.

600Hz transition region around the cutoff frequency wc , makes filtering easy and minimize the channel interference

600Hz transition region around the cutoff frequency wc , makes filtering easy and minimize the channel interference

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Generation of SSB Signals(cont…)

Phase-Shift Method:


The basis of this method is the following equation

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Generation of SSB Signals(cont…)

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communication system Chapter 4