Chapter 2 Part Ii Anas

COMMUNICATION SYSTEM EECB353 Chapter 2 Part II AMPLITUDE MODULATION

Anas Bin Muhamad Bostamam Dept of Electrical Engineering Universiti Tenaga Nasional http://metalab.uniten.edu.my/~shafinaz

AM Voltage Distribution 

Mathematically an unmodulated carrier can be described as:

vc (t ) = Ec sin( 2πf c t ) where vc(t) = time-varying voltage for the carrier



Ec

= peak carrier amplitude (volts)

fc

= carrier frequency (hertz)

But Vmax = Ec + Em , then the instantaneous modulated amplitude:

vam (t ) = [ Ec + Em sin( 2πf mt )][sin(2πf c t )] where

[ Ec + Em sin(2πf mt )]

= amplitude of modulated wave

Em

= peak change in the amplitude of the envelope (volts)

fm

= frequency of the modulating signal (hertz) 2

AM Voltage Distribution Em = mEc

vam (t ) = [ Ec + mEc sin( 2πf mt )][sin(2πf c t )] = [1 + m sin( 2πf mt )][ Ec sin( 2πf c t )] [1 + m sin( 2πf mt )] [ Ec sin( 2πf c t )]

= constant + modulating signal = unmodulated carrier

vam (t ) = Ec sin( 2πf c t ) + [mEc sin( 2πf m t )][sin(2πf c t )] mEc mEc = Ec sin( 2πf ct ) − cos[2π ( f c + f m )t ] + cos[2π ( f c − f m )t ] 2 2 Carrier Signal

Upper side freq signal

Lower side freq signal 3

AM Voltage Distribution Vam = Ec sin( 2πf ct ) − 

mEc mEc cos[2π ( f c + f m )t ] + cos[2π ( f c − f m )t ] 2 2

Notes from DSBFC eqn,

Vam

 Amplitude

of the carrier Ec is unaffected by the modulation process  Amplitude of the upper (Eusf) and lower side frequencies (Elsf )depend on both carrier amplitude, Ec and coefficient of modulation,m.

Voltage Spectrum for AM DSBFC wave 4

Example 3 

One input to a conventional AM modulator is a 500kHz carrier with an amplitude of 20Vp. The second input is a 10kHz modulating signal that is of sufficient amplitude to cause a change in the output wave of ± 7.5Vp. Determine a. b. c. d. e. f. g.

Upper and lower side frequencies. Modulation coefficient and percent modulation Peak amplitude of the modulated carrier and the upper and lower side frequency voltages. Maximum and minimum amplitudes of the envelope. Expression for the modulated wave. Draw the output spectrum. Sketch the output envelope.

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Example 4 

If the modulated wave has the equation, vam (t ) = 150 sin( 2π 250t ) − 60 cos(2π 282t ) + 60 cos(2π 218t )V find (a) the carrier freq (b) the usf and lsf (c) the modulating signal freq (d) the peak amplitude of the carrier signal (e) the upper and lower side signal peak amplitude (f) the change In peak amplitude of the modulated wave (g) the coefficient of modulation.

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AM Power Distribution 

The average power dissipated in a load by unmodulated carrier is equal to the rms carrier voltage, Ec squared divided by the load resistance, R.



Mathematically, power in unmodulated carrier, Pc is: Pc =

( Ec ( rms ) ) 2 R

=

2 )2

( Ec R

Ec 2 = 2R

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AM Power Distribution 

The upper and lower sideband powers: Pusb

(mEc 2) 2 m 2 Ec = Plsb = = 2R 8R

2

where mEc/2 is the peak voltage of usf and lsf. Then, 2 m 2  Ec  m 2 Pusb = Plsb = Pc  = 4  2R  4 

Total transmitted power in DSBFC AM envelope: Pt = Pc + Pusb + Plsb m2 m2 = Pc + Pc + Pc 4 4  m2  m2  = Pc + Pc = Pc 1 + 2 2  

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AM Power Distribution Pt = Pc + Pusb

 m2  m2 m2 m2  + Plsb = Pc + Pc + Pc = Pc + Pc = Pc 1 + 4 4 2 2  

Power Spectrum for AM DSBFC wave

Note:  Carrier power in the modulated signal is the same in the unmodulated signal i.e carrier power is unaffected by the modulation process. The total power in an AM envelope increase with modulation (i.e as m ↑, Pt ↑).  Major disadvantage of AM DSBFC is most of the power is wasted in the carrier. (It does not contain info, info is contained in the sidebands). 9

Efficiency of AM 

Efficiency, E is defined as the percentage of total power that conveys information i.e it is the percentage of total transmitted power that is in the sidebands.

PSBs Pusb + Plsb Efficiency, E = = PT Pc + Pusb + Plsb

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Example 

Draw the power spectrum for a given expression and determine the modulation index and efficiency. (Assume R=1Ω)

m(t ) = 20 sin 300πt − 6 cos 320πt + 6 cos 280πt

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Example 

Determine the maximum sideband power if the carrier output is 1 kW and calculate the total maximum transmitted power.

Since

ESF = mEc/2,

It is obvious that the max SB power occurs when m = 1 or 100%, and also when m = 1, each side freq is ½ the carrier amplitude. Since power is proportional to the square of voltage, each SB has ¼ of the carrier power i.e ¼ x 1kW, or 250W. Therefore, total SB power is 250W x 2 = 500W. And the total transmitted power is 1kW + 500W = 1.5kW 12

Importa nce of High- percent age Modul ati on m

Pc

P1SB

PSBs

PT

E

1.0

1kW

250W

500W

1.5kW

0.3

0.5

1kW

62.5W

125W

1.125kW

0.1

Table: Effective transmission at 50% versus 100% modulation Notes  Even though the total transmitted power has only fallen from 1.5kW to 1.125kW, the effective transmission has only ¼ the strength at 50% modulation as compared to 100%.  Because of these considerations, most AM transmitter attempts to maintain between 90 and 95 percent modulation as a compromise between efficiency and the chance of drifting into overmodulation. 13

Example 

A DSBFC AM Signal with a 1kW carrier was modulated to a depth of 60%. How much power is contained in the upper sideband? Given

Pc = 1kW

but, total power

then, Pusb = Plsb

m2 0.6 2 = Pc = (1k ) = 90W 4 4

 0 .6 2   = 1180W Pt = 10001 +  2  

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Exercise The total power of an AM transmitter is measured to be 850W. What is the total output sideband power if it has a percent modulation of 100%? Calculate the efficiency.

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Example 5 

For an AM DSBFC wave with a peak unmodulated carrier voltage Vc = 10Vp, a load resistance RL = 10 Ω, and a modulation coefficient, m = 1, determine     

Powers of the carrier and the upper and lower sidebands. Total sideband power. Total power of the modulated wave. Draw the power spectrum. Repeat steps (a) to (d) for a modulation index, m = 0.5.

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Example 6 A 1.5MHz carrier signal is modulated with 3.4kHz modulating signal. The modulated carrier voltage is 28Vmax and 14Vmin across a 100Ω resistive load impedance. Determine: a) Peak amplitude of the unmodulated carrier. b) Coefficient of modulation c) Carrier power. d) Sideband power e) Total power f) Upper and lower sideband frequencies. g) Bandwidth.

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