Amplitude Modulation Part 1

AMPLITUDE MODULATION


Modulation – the process of impressing low-frequency information signals onto a high-frequency carrier signal.

Demodulation – the reverse process where the received signals are transformed back to their original form.


Amplitude Modulation- the process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of the modulating signal.- inexpensive, low-quality form of modulation that is used for commercial broadcasting of both audio and video signals.- also used for two-way mobile radio communications.


AM Modulators- non-linear devices with two inputs and one output- the information acts on or modulates the RF carrier- the output is called an AM envelope

Modulator

VC

VM

Output


VC (t) = EC sin (2fCt)

VM (t) = EM sin (2fmt)

VAM (t) = [EC +EM sin (2fmt)] [sin(2fCt)]

AMPLITUDE MODULATIONAM Envelope


AM Frequency Spectrum and Bandwidth Non-linear mixing Complex wave

DC voltage Carrier Frequency Sum and Difference FrequenciesCarrier

Am

plit

ud

e

LSB USB

LSF USFfc fc + fm(max)fc - fm(max)

Frequency

B = 2fm(max)


Coefficient of Modulation – used to describe the amount of amplitude change present in an AM modulator.

Percent Modulation – the coefficient of modulation stated as a percentage.

- gives the percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal.


m = Em / EcWhere: m – modulation coefficient

(unitless) Em – peak change in the

amplitude of the output waveform voltage (volts)

Ec – peak amplitude of the unmodulated carrier voltage (volts)

M = Em / Ec x 100%


Em = ½ (Vmax - Vmin)

Ec = ½ (Vmax +Vmin) Vmin = Ec – Em

Vmax = Ec + Em

½ (Vmax – Vmin) (Vmax – Vmin)M =½ (Vmax +Vmin)

x 100% =(Vmax + Vmin)

x 100%


Em = EUSF + ELSF ELSF = EUSF

ELSF = EUSF = Em/2

= ½(Vmax-Vmin)/2

= ¼(Vmax – Vmin)

Where: EUSF = peak amplitude of the upper side frequency (volts)

ELSF = peak amplitude of the lower side frequency(volts)


Conditions of Coefficient of Modulation:m = value is usually between 0 and 1

m 1 : if the amplitude of the modulating voltage is higher than the carrier voltage

: causes severe distortion of the modulated waveform

: overmodulation


m 1 : no distortion will occur : amplitude of the modulating signal is less than the carrier amplitude

m 1 : ideal condition for AM : generates output at the

receiver without distortion


AM Voltage DistributionVc(t) = Ec sin(2fct)

V1 = Ec + Em

V1 = Ec + Em sin(2fmt)

V2 = V1sin(2fct)

Vam(t) = [Ec + Em sin(2fmt)][sin (2fct)] Amplitude of the

modulated wave

Peak change in the amplitude of the envelope Frequency of the modulating

signal


but: Em = mEcVam(t) = [Ec + mEc sin(2fmt)][sin (2fct)]

Vam(t) = [1 + m sin(2fmt)][Ecsin (2fct)]

Amplitude of the modulated wave

Constant + modulating signal

Unmodulated carrier


Vam(t) = [Ec + mEc sin(2fmt)][sin (2fct)]

But: sin A sin B = cos(A-B)/2 – cos (A+B)/2

Vam(t) = Ecsin (2fct) – mEc/2 cos [2(fc+fm)t] + mEc cos [2(fc -fm)t] Lower Side frequency

SignalCarrier Signal Upper Side frequency

Signal

fLSF fUSFfc

Ec

mEc/2 mEc/2

Frequency(Hz)

Am

plit

ude(

V)


AM Power Distribution- the power dissipated is equal to the

voltage squared, divided by the resistance.PC = (0.707 EC)2/R

PC = EC2/2R

Where: Pc = carrier power(watts) Ec = peak carrier voltage (volts) R = load resistance (ohms)


PUSB = PLSB = (mEC/2)2/2R

= m2EC

2 / 8R

= m2/4 (EC2/2R)

= m2PC/4

Where: PUSB = upper sideband power (watts)

PLSB = lower sideband power (watts)

Peak Voltage


PT = PC + PLSB + PUSB

PT = PC + m2PC/4 + m2PC/4

PT = PC + m2PC/2

PT = PC ( 1 + m2/2)

fLSF fUSFfcFrequency(Hz)

Pow

er(

watt

s)

Pc = EC2/2R

m2PC/4 m2PC/4


AM Current Calculations

Where: Pt = total transmit power(watts) Pc = carrier power (watts) It = total transmit current (amperes) Ic = carrier current (amperes) R = antenna resistance (ohms

PT

PC=

IC2IC2RIT2R IT2

= = 1 + m2/2


ITIc

1 + m2/2=

IT = IC

(1 + m2/2)


Modulation by a Complex Information SignalVam(t) = sin (2fct) + ½ cos [2(fc-fm1)t]- ½ cos[2(fc+fm1)t]

+ ½ cos [2(fc-fm2)t]- ½ cos[2(fc+fm2)t]

mt = m12 + m2

2 + m32 +…+

mn2

Total Coefficient of Modulation

Coefficient of modulation for inputs 1,2,3..,n


Examples:1. A modulated carrier wave has maximum and

minimum amplitudes of 750mV and 250mV. Calculate the value of percentage modulation.

2. A 10MHz sinusoidal carrier wave of amplitude 10mV is modulated by a 5kHz sinusoidal audio signal wave of amplitude 6mV. Find the frequency components of the resultant modulated wave and their amplitudes.


3. An audio signal given by 15 sin2(2000t) amplitude modulates a sinusoidal carrier wave 60 sin2(100000t). Determine(a) modulation index (b) percent of modulation (c) frequency of signal and carrier (d) frequency spectrum of the modulated wave.

4. A bandwidth of 15MHz is available for AM transmission. If the maximum audio signal frequency used for modulating the carrier is not to exceed 15kHz, how many stations can broadcast within this band simultaneously without interfering with each other?


5. In a broadcasting studio, a 1000kHz carrier is modulated by an audio signal of frequency range 100-5000Hz. Find the (a) width or freq. range of sidebands (b) max and min freq of USB (c) max and min freq of LSB (d) width of the channel

6. The tuned circuit of the oscillator in an AM transmitter uses a 40H coil and a 1nF capacitor. If the carrier wave produced by the oscillator is modulated by an audio freq up to 10kHz, calculate the freq band occupied by the sidebands and the channel width.


7. The total power content of an AM wave is 2.64kW at a modulation factor of 80%. Determine the power content of (a) carrier and (b) each sidebands.

Date post:	18-Nov-2014
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Amplitude Modulation Part 1

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