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Modulation Index & AM Modulation Index & AM Power SignalsPower Signals

MODULATION INDEXMODULATION INDEX Modulation index, mModulation index, m is defined as a parameter, which is defined as a parameter, which

determines the amount of modulation.determines the amount of modulation. For AM, it is defined as a measure of the extent which a For AM, it is defined as a measure of the extent which a

carrier voltage is varied by the modulating signal.carrier voltage is varied by the modulating signal. For proper AM to occurFor proper AM to occur

VVmm V Vcc

Modulation index, or in percentage , Modulation index, or in percentage ,

By this definition, we could distinguished three different By this definition, we could distinguished three different types of amplitude modulation.types of amplitude modulation.– Under modulated AM for Under modulated AM for m < m < 11– Ideal AM for Ideal AM for m = m = 11– Over modulated AM for Over modulated AM for m > m > 11

100%m

c

VM x

V

c

m

V

Vm

m < m < 11 : under modulation : under modulation– VVmm < V < Vcc

– signal strength obtained at the receiver is not signal strength obtained at the receiver is not exactly the same as the signal strength at the exactly the same as the signal strength at the transmitter.transmitter.

– No distortion to the signal, just reduced signal No distortion to the signal, just reduced signal strength.strength.

Figure 2.4 m < 1, under modulation.

m=1m=1 : ideal modulation : ideal modulation– VVmm = V = Vcc

– will produce greatest output at the receiver will produce greatest output at the receiver without distortionwithout distortion

– maximum info signal amplitude is transmittedmaximum info signal amplitude is transmitted– more info signal power is transmitted more info signal power is transmitted

producing stronger, more intelligible signalproducing stronger, more intelligible signal– hard to achieve especially when the hard to achieve especially when the

modulating signal amplitude varies randomly modulating signal amplitude varies randomly over a wide range – only the peak of the signal over a wide range – only the peak of the signal will produce 100% modulation.will produce 100% modulation.

Figure 2.5 m = 1, ideal modulation.

m > m > 11 : over modulation : over modulation

– VVmm > V > Vcc

– cause distortioncause distortion– negative peaks have been clipped off.negative peaks have been clipped off.– The original shape of the signal is destroyed.The original shape of the signal is destroyed.

Figure 2.6 m > 1, over modulated AM

Modulation index can be calculated directly from the AM wave. Modulation index can be calculated directly from the AM wave. Figure 2.7(a) shows the measurement of modulation index using the Figure 2.7(a) shows the measurement of modulation index using the minimum and maximum value while Figure 2.7(b) using peak-to-minimum and maximum value while Figure 2.7(b) using peak-to-peak value.peak value.

max

max min

max min

max min

2

2

m c

c c

c c

m

c

V V Vm

V V

V V V V

V VV

V VV

Figure 2.7(a) Measuring m using max and min value mc

mc

VVV

VVV

Or

min

max

Figure 2.7(b) Measuring m using peak-to-peak value and the form of trapezoidal

A B

%100% xAB

ABm

max min

max min

max min

max min

p p p p

p p p p

V Vm

V V

V Vm

V V

Example 2.3Example 2.3

A carrier signal with a peak voltage of 2.0V A carrier signal with a peak voltage of 2.0V is amplitude modulated with a 10kHz sine is amplitude modulated with a 10kHz sine wave. The modulation voltage has an wave. The modulation voltage has an effective value of 750mV. Compute the effective value of 750mV. Compute the following:following:

a.a. The percent modulation, The percent modulation, mmb.b. The instantaneous voltage of the positive The instantaneous voltage of the positive

and negative envelope when the 10kHz and negative envelope when the 10kHz sine has completed 68µs of its cycle.sine has completed 68µs of its cycle.

c.c. Illustrate the resulting AM waveformIllustrate the resulting AM waveform

AnswersAnswers

a.a. Modulation indexModulation index

b.b. Voltage at t = 68µsVoltage at t = 68µs

Therefore the negative envelope is -1.04VTherefore the negative envelope is -1.04V

1.414 750100% 100% 53.04%

2.0m

c

V x mVm x x

V V

sin 2

(1 sin 2 )

2.0(1 0.5304sin 2 .10kHz.68μs)

=1.04V

env c m m

m

V V V f t

Vc m f t

POWER FOR AMPOWER FOR AM The equation of amplitude modulation and the definition The equation of amplitude modulation and the definition

of modulation index can be combined to show the of modulation index can be combined to show the amount of power in a carrier and total signal:amount of power in a carrier and total signal:

index modulation

powercarrier

power ed transmitttotal

m

P

P

c

T

21

2mPP cT

AM POWER TRANSMISSIONAM POWER TRANSMISSION

We have seen that the power in AM is equal to We have seen that the power in AM is equal to the carrier power and the sideband power. the carrier power and the sideband power.

Total transmitted power, Total transmitted power, PPTT is equal to the sum of is equal to the sum of the carrier power (the carrier power (PPCC) and both of the sidebands ) and both of the sidebands ((PPUSBUSB, P, PLSBLSB))

2 2 2( ) ( ) ( )

2 2 2

2 2 2

0.707 0.707 0.707

2 2 2

T C USB LSB

C rms USB rms LSB rms

C USB LSB

C USB LSB

P P P P

V V V

R R R

V V V

R R R

V V V

R R R

The term The term RR correspond to the correspond to the fact that antenna (which is a fact that antenna (which is a load) will have its own load) will have its own impedance and dissipate impedance and dissipate power for a resistor is power for a resistor is

In the previous discussion, In the previous discussion, we assume the impedance of we assume the impedance of the antenna is unity the antenna is unity ((RR = 1) = 1)..

From the sideband voltageFrom the sideband voltage

2 2

2rmsV V

PR R

21

44

24242

2

2

22

22222

mP

Pm

Pm

P

R

Vm

R

Vm

R

VP

VmVV

c

ccc

cccT

cUSBLSB

Upper and lower sidebands power are Upper and lower sidebands power are equal, thereforeequal, therefore

2

2

2 2 2 2

22

22

4 2 8

m

LSB USB

c

c c

V

P PR

mV

R

m V m V

R R

If If m = m = 11,,

In practice, carrier signal will be modulated In practice, carrier signal will be modulated by several signals simultaneously. The total by several signals simultaneously. The total modulation index or effective modulation modulation index or effective modulation index has to be calculated.index has to be calculated.

3 2,

2 31 1

,3 6

T C C T

sidebands T LSB USB T

P P P P

P P P P P

for m < 1 , PLSB + PUSB are even less !!

2 20.751 400 1

2 2

512.5

T C

mP P

W

A A 400 W400 W carrier is modulated to a depth carrier is modulated to a depth of of 75%.75%. Calculate the total power in the Calculate the total power in the modulated wavemodulated wave

Solution:Solution:



An AM broadcast station’s peak carrier voltage An AM broadcast station’s peak carrier voltage of of 2 2 kVkV has been amplitude modulated to an has been amplitude modulated to an index of 75% with a index of 75% with a 2 2 kHzkHz test tone. The station test tone. The station broadcast frequency is broadcast frequency is 810810 kHzkHz. Compute the . Compute the following:following:

1.1. The lower and upper sidebands frequencies, The lower and upper sidebands frequencies, ffLSBLSB and and ffUSBUSB

2.2. The peak modulation voltage, The peak modulation voltage, VVmm

3.3. The peak lower and upper sideband voltages, The peak lower and upper sideband voltages, VVLSBLSB and and VVUSBUSB

4.4. The maximum signal amplitude, The maximum signal amplitude, VVmaxmax

Example 2.6Example 2.6A spectrum analyzer with an input impedance of A spectrum analyzer with an input impedance of 50 50 is used is used to measure the power spectrum of an AM signal at the output to measure the power spectrum of an AM signal at the output of a preamplifier circuit. The AM signal has been modulated of a preamplifier circuit. The AM signal has been modulated with a sine wave. The effective power with a sine wave. The effective power PPCC is is 745 745 mWmW, and each , and each sideband, sideband, PPUSBUSB and and PPLSBLSB is is 125125 mWmW. Compute the following:. Compute the following:

1.1. The total effective power, The total effective power, PPTT

2.2. The peak carrier voltage, The peak carrier voltage, VVCC

3.3. The modulation index, The modulation index, mm, and the percentage of , and the percentage of modulation index modulation index MM

4.4. The modulation voltage The modulation voltage VVmm

5.5. The lower and upper sideband voltages, The lower and upper sideband voltages, VVLSBLSB and and VVUSBUSB

6.6. Sketch the waveform that you would see with an Sketch the waveform that you would see with an oscilloscope if it were placed in parallel with the oscilloscope if it were placed in parallel with the spectrum analyzerspectrum analyzer

MODULATION BY SEVERAL MODULATION BY SEVERAL SINE WAVESSINE WAVES

In practice, modulation of a carrier by a several In practice, modulation of a carrier by a several sine waves simultaneously is the rule rather than sine waves simultaneously is the rule rather than exception.exception.

To calculate the resulting power To calculate the resulting power

– Let VLet V11, V, V22 and V and V33 etc. be the amplitude of the etc. be the amplitude of the information signals, the resultant voltages, Vinformation signals, the resultant voltages, VTT becomesbecomes

– dividing both sides by Vdividing both sides by VCC

2 2 21 2 3 .........TV V V V

2 2 2

31 2 ..........T

C C C C

VV V V

V V V V

The equation of the The equation of the total current and total current and carrier current is carrier current is derived from the total derived from the total power equation :-power equation :-

2 2 21 2 3

2

that is

..........

12

T

TT C

m m m m

mP P

2

22 2

2

2

12

12

12

12

T C

T C

T

C

T T

C

mP P

mI R I R

I m

I

I mor

I

(4.26)


Q. The antenna current of an AM transmitter Q. The antenna current of an AM transmitter is 12A when unmodulated but increases to is 12A when unmodulated but increases to 13A when modulated. Calculate the index 13A when modulated. Calculate the index percentage.percentage.

A. 59%A. 59%


Q. The antenna of an AM transmitter is Q. The antenna of an AM transmitter is 8 8 AA when only the carrier is sent, but when only the carrier is sent, but it increases to it increases to 8.93 8.93 AA when the carrier when the carrier is modulated by a single sine wave. is modulated by a single sine wave. Find the percentage of modulation Find the percentage of modulation and the antenna current when the and the antenna current when the percentage of modulation changes to percentage of modulation changes to 0.80.8..

AM CircuitsAM Circuits

AM CIRCUITSAM CIRCUITS

2 ways to produce AM :-2 ways to produce AM :- Analog MultiplicationAnalog Multiplication

– multiply carrier by a gain or attenuation factor multiply carrier by a gain or attenuation factor that varies with the modulating signal.that varies with the modulating signal.

– eg. : analog multipliereg. : analog multiplier Non-linear MixingNon-linear Mixing

– linearly mix or algebraically add the carrier and linearly mix or algebraically add the carrier and modulating signal and then apply the modulating signal and then apply the composite signal to a nonlinear device or circuitcomposite signal to a nonlinear device or circuit

– eg. : the simplest circuit is a resistive mixing eg. : the simplest circuit is a resistive mixing network + diode rectifier + LC tuned circuitnetwork + diode rectifier + LC tuned circuit

Analog MultiplicationAnalog Multiplication

AM is produced by multiplying the carrier by a factor AM is produced by multiplying the carrier by a factor = 1 + modulating sine wave.= 1 + modulating sine wave.

Device like amplifiers or voltage dividers (PIN diodes) Device like amplifiers or voltage dividers (PIN diodes) can create the gain or attenuation that varies with can create the gain or attenuation that varies with the modulating signal and hence produces the AM by the modulating signal and hence produces the AM by passing the carrier through the device.passing the carrier through the device.

( sin 2 )(sin 2 )

( sin 2 )(sin 2 )AM c m m c

c c m c

v V V f t f t

V mV f t f t

)2sin1(2sin tfmtfVv mccAM

Non-Linear MixingNon-Linear Mixing

Linearly mix the carrier and modulating Linearly mix the carrier and modulating signals.signals.

A composite voltage is used to vary the A composite voltage is used to vary the current in the nonlinear device.current in the nonlinear device.

The current is proportional to the The current is proportional to the nonlinear device but not vary linearly with nonlinear device but not vary linearly with the applied voltage.the applied voltage.

Nonlinear device Nonlinear device – FETs, diodes & BJTsFETs, diodes & BJTs– Square law responseSquare law response

Continue..Continue.. Figure 2.8 – Square law response Figure 2.8 – Square law response

curvecurve– Current in the device is proportional to Current in the device is proportional to

the square of the input voltage.the square of the input voltage.– Squaring the sum of the carrier and Squaring the sum of the carrier and

modulating signals produces the modulating signals produces the classic AM equation.classic AM equation.

Figure 2.9 – AM with diodeFigure 2.9 – AM with diode– the simplest circuit is a the simplest circuit is a

resistive mixing network resistive mixing network + diode rectifier + LC + diode rectifier + LC tuned circuit.tuned circuit.

– LC filters the unwanted LC filters the unwanted higher order harmonics.higher order harmonics.

a = constant

i = av2

Vm(t)

Vc(t)

R1

R2

R3

D AM output

L C

Diode ModulatorDiode Modulator

■ It is the oldest and the It is the oldest and the simplest modulatorsimplest modulator

consist of :consist of :– resistive mixing resistive mixing

networknetwork– diode rectifierdiode rectifier– LC tuned circuitLC tuned circuitVm(t)

Vc(t)

R1

R2

R3

D AM output

L C

Figure 2.10 Diode modulatorFigure 2.11 Waveform in the diode modulator

Carrier signal is applied to one input resistorCarrier signal is applied to one input resistor Modulating signal is applied to other input resistorModulating signal is applied to other input resistor The mixed signal appear across The mixed signal appear across RR33 The signal are linearly mixed The signal are linearly mixed algebraically added algebraically added Resultant wave : modulating signal seems riding on Resultant wave : modulating signal seems riding on

the carrier signalthe carrier signal The positive going pulses are applied to the parallel The positive going pulses are applied to the parallel

tune circuit, which will resonate at carrier frequencytune circuit, which will resonate at carrier frequency LL and and CC repeatedly exchange causing an oscillation at repeatedly exchange causing an oscillation at

resonant frequency resonant frequency it will create a –ve half cycle for it will create a –ve half cycle for every +ve inputevery +ve input pulsespulses

Most commonly used in low power AM transmitterMost commonly used in low power AM transmitter Carrier signal is applied to the emitter of a Carrier signal is applied to the emitter of a

transmitter through transmitter through TT11

Modulating signal is applied to the collectorModulating signal is applied to the collector Also called collector modulationAlso called collector modulation QQ11 is a class C base amplifier is a class C base amplifier Collector bias is developed by Collector bias is developed by VVcccc through through RR22 and and

the small DC resistance of the small DC resistance of LL11.. Base bias is also developed by Base bias is also developed by VVcccc and and RR22 through through

the voltage divider network of the voltage divider network of RR11 and and RR33

CC33 compensate for temperature variation compensate for temperature variation

TransistorTransistor ModulatorModulator

R2R1L1

C1

C6C5

C4

C3

C2

C7

T1Vc(t)

L2 output AMsignal

Q1

VccVm(t)

R3

Figure 2.12 Transistor modulator

CC44 prevents prevents acac signal from reaching the power signal from reaching the power supplysupply

The output signal is developed across the high The output signal is developed across the high acac resistance of resistance of LL11

Since Since QQ11 is is biased class C, onlybiased class C, only the amplified the amplified +ve pulses+ve pulses of the carrier signal will appear on of the carrier signal will appear on the outputthe output

-ve pulses are developed in the same manner as -ve pulses are developed in the same manner as in the diode modulator in the diode modulator a pie filter circuit a pie filter circuit consisting of consisting of LL22 and and CC66/ C/ C77 is resonant at the carrier is resonant at the carrier frequency and adds to the –ve pulsesfrequency and adds to the –ve pulses

CC55 is the coupling capacitor and prevents the is the coupling capacitor and prevents the dcdc bias on the collector from reaching the outputbias on the collector from reaching the output

LL22 is in parallel to is in parallel to CC66 and and CC77 making a tank circuit making a tank circuit that is resonant at the carrier frequencythat is resonant at the carrier frequency

This circuit also can operate as an impedance This circuit also can operate as an impedance matching circuit.matching circuit.

Other Examples of ModulatorsOther Examples of Modulators

R1

R2

L2

C2

C4 C5

C3

Q1

L1

Q2

C1

Vcc

Vm(t)

Vc(t)

Output AMsignal

Figure 2.13 Series Modulator

Fig. 2.14 PIN diode modulator

Linear Integrated Circuit AM Linear Integrated Circuit AM ModulatorsModulators

Use a unique arrangement of transistors and FETs Use a unique arrangement of transistors and FETs to perform signal multiplication to perform signal multiplication ideally suited ideally suited to generate AM waveforms.to generate AM waveforms.

ICs can perfectly match current flow, amplifier ICs can perfectly match current flow, amplifier voltage gain, and temperature variations.voltage gain, and temperature variations.

Also offer excellent frequency stability, Also offer excellent frequency stability, symmetrical modulation characteristic, circuit symmetrical modulation characteristic, circuit miniaturization, fewer components, temperature miniaturization, fewer components, temperature immunity and simplicity of design and immunity and simplicity of design and troubleshooting.troubleshooting.

Disadvantages of ICs on the other hand are low Disadvantages of ICs on the other hand are low output power, relatively low usable frequency output power, relatively low usable frequency range, susceptibility to fluctuation in the dc power range, susceptibility to fluctuation in the dc power supply, eg. XR-2206supply, eg. XR-2206

FIGURE 2.15 XR-2206: (a) Block diagram; (b) schematic diagram; (c) output voltage-versus-input voltage curve

FIGURE 2.16 Linear integrated-circuit AM modulator

SINGLE SIDEBAND SINGLE SIDEBAND SUPPRESSED SUPPRESSED

CARRIERSCARRIERS

Suppressed CarriersSuppressed Carriers In Fig. 2.17, the center In Fig. 2.17, the center

spectrum is removed or spectrum is removed or reduced, hence the whole reduced, hence the whole signal becomes double signal becomes double sideband suppressed sideband suppressed carrier or DSB-SCcarrier or DSB-SC

Total transmitted power is Total transmitted power is in the sidebands.in the sidebands.

Instead of 2/3 of power Instead of 2/3 of power lost in the carrier, almost lost in the carrier, almost all being the available all being the available power is used in the power is used in the sidebands.sidebands.

LSB USB

f

ASuppressed

carrier - absent

Fig. 2.17 DSB AM in the frequency domain

The algebraic sum of the 2 sinusoidal sidebands.The algebraic sum of the 2 sinusoidal sidebands. During the modulation, the carrier is suppressed, During the modulation, the carrier is suppressed,

but the 2 sidebands remains (refer Fig. 2.17).but the 2 sidebands remains (refer Fig. 2.17). Repetition rate is determined by the RF carrier Repetition rate is determined by the RF carrier

wave.wave. Amplitude is controlled by the level of Amplitude is controlled by the level of

modulating signal.modulating signal. Output takes the shape of the modulating signal Output takes the shape of the modulating signal

except with alternating +ve and –ve polarities except with alternating +ve and –ve polarities that corresponds to the polarity of the carrier that corresponds to the polarity of the carrier signal.signal.

Phase transition.Phase transition. Generated using balance modulator.Generated using balance modulator.

DSB-SCDSB-SC

Figure 2.18 DSBSC generation

Figure 2.19 Block diagram of balanced modulator

Figure 2.20 (a) The (magnitude) spectrum of a DSB SC AM signal for a sinusoid message signal and (b) its lower and (c) upper sidebands.

Example 2.9Example 2.9 For a 100W total available power in the sidebands, For a 100W total available power in the sidebands,

compare the power in the sidebands when the compare the power in the sidebands when the modulation is standard AM with m = 100%, vs a modulation is standard AM with m = 100%, vs a SC design where 90% of the carrier power is SC design where 90% of the carrier power is suppressed. How many times greater is the suppressed. How many times greater is the sideband power in the suppressed carrier case?sideband power in the suppressed carrier case?

For m = 1, PFor m = 1, PTT = P = PCC(1+m(1+m22/2) = P/2) = PCC(3/2)(3/2) PPCC = 66.7W & P = 66.7W & PSB SB =100 – 66.7 =33.3W=100 – 66.7 =33.3W DSB-SC PDSB-SC PCC = 66.7W x 0.9 = 60.0W (reduced) = 66.7W x 0.9 = 60.0W (reduced) New PNew PSB SB =33.3W +60.0W = 93.3W=33.3W +60.0W = 93.3W The power ratio = PThe power ratio = PSBnewSBnew/ P/ PSBoldSBold = 2.8 = 2.8 In dB = 4.5 dBIn dB = 4.5 dB Means in AM info transmitted only 33.3% but in Means in AM info transmitted only 33.3% but in

DSB-SC is 93.3%.DSB-SC is 93.3%.


Q.Q. A 500 W DSB-SC system with 100% modulation A 500 W DSB-SC system with 100% modulation suppresses 50% of the carrier and the suppresses 50% of the carrier and the suppressed carrier power goes to the suppressed carrier power goes to the sidebands. How much power is in the sidebands. How much power is in the sidebands and how much is in the carrier? By sidebands and how much is in the carrier? By how many dB has the sideband power how many dB has the sideband power increased?increased?

R.R. With 100% modulation, final Pc = 500W and With 100% modulation, final Pc = 500W and total Psb = 250W, if Pc is diverted to SB, the total Psb = 250W, if Pc is diverted to SB, the new Pc = 500 – 250 = 250W and the new Psb new Pc = 500 – 250 = 250W and the new Psb = 250 +250 = 500W. The increase in power is = 250 +250 = 500W. The increase in power is 500/250 = 2 = 3dB.500/250 = 2 = 3dB.

Figure 2.21(a) A time-domain display of a DSB SC AM Figure 2.21(a) A time-domain display of a DSB SC AM signal (b) A frequency-domain display of a DSB AM signalsignal (b) A frequency-domain display of a DSB AM signal

Advantages of DSBSC compared to AMAdvantages of DSBSC compared to AM– power conservation power conservation can be allocated to can be allocated to

both sidebands both sidebands longer distance longer distance– easy to generateeasy to generate

Disadvantages of DSBSC compared to Disadvantages of DSBSC compared to AMAM– Rarely used because the signal is difficult to Rarely used because the signal is difficult to

recover at the receiver recover at the receiver requires carrier requires carrier reinsertion reinsertion complex circuitry complex circuitry

– Take the same BW as in AM Take the same BW as in AM not efficient not efficient

Single SidebandSingle Sideband

In DSB, info is transmitted twice, once in In DSB, info is transmitted twice, once in each sidebandeach sideband

One sideband may be suppressed One sideband may be suppressed SSBSC / SSBSSBSC / SSB

In SSB, when no info or modulating signal In SSB, when no info or modulating signal is present, no RF signal is transmittedis present, no RF signal is transmitted

In a standard AM transmitter, carrier is still In a standard AM transmitter, carrier is still transmitted even though it may not be transmitted even though it may not be modulatedmodulated

Refer Figure 2.22 and 2.23.Refer Figure 2.22 and 2.23.

Figure 2.22 SSB signal with carrier

Figure 2.23 SSB signal without carrier


Q. Given Q. Given ffcc = 14.3 MHz and = 14.3 MHz and ffmm = 2 kHz, what is the = 2 kHz, what is the frequency of the signal if it is being SSB frequency of the signal if it is being SSB modulated?modulated?

A. After SSB modulation, the modulated signal is at A. After SSB modulation, the modulated signal is at f = ff = fcc + f + fmm

= = 14.30214.302 MHz MHz USBUSB oror

f = ff = fcc – f – fmm

= = 14.29814.298 MHz MHz LSB either one. LSB either one.

*most signals are not pure sine wave, eg. Voice,*most signals are not pure sine wave, eg. Voice, it will create it will create a complex SSB signal which varies in frequency and a complex SSB signal which varies in frequency and amplitude over a narrow spectrum defined by the voice amplitude over a narrow spectrum defined by the voice signal BW.signal BW.

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