amplitude modulation part 1
TRANSCRIPT
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AMPLITUDE MODULATION
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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.
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AMPLITUDE MODULATION
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.
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
VC (t) = EC sin (2fCt)
VM (t) = EM sin (2fmt)
VAM (t) = [EC +EM sin (2fmt)] [sin(2fCt)]
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AMPLITUDE MODULATIONAM Envelope
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AMPLITUDE MODULATION
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)
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AMPLITUDE MODULATION
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.
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AMPLITUDE MODULATION
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%
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AMPLITUDE MODULATION
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%
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AMPLITUDE MODULATION
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)
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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)
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AMPLITUDE MODULATION
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)
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
ITIc
1 + m2/2=
IT = IC
(1 + m2/2)
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AMPLITUDE MODULATION
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
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AMPLITUDE MODULATION
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.
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AMPLITUDE MODULATION
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?
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AMPLITUDE MODULATION
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.
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AMPLITUDE MODULATION
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.