Amplitude Modulation

AMPLITUDE MODULATION Lecture Notes by:

Engr. Analene M. Nagayo

Modulation Theory What is MODULATION? - A process by which a low frequency signal is made to change a property of a higher frequency signal to allow effective transmission and reception of the desired information. - A process of imposing information contained in lower-frequency signal onto a higher frequency signal. -The low frequency signal is called the modulating signal and the high frequency signal is called the carrier. Why modulate? 1.) Direct transmission of low-frequency information signal would cause to interference problem since the resulting radio waves would all be at the same frequency range. 2.) Transmitting low-frequency information signal in free space is not practical since it will require a very high antenna.

Modulation Theory Types of Modulation A. Analog Modulation I. Amplitude Modulation II. Angle Modulation a.) Frequency Modulation b.) Phase Modulation

Vm(t )  Vm sin 2fmt

B. Digital Modulation

Vc(t )  Vc sin 2fct

Amplitude Modulation What is AMPLITUDE MODULATION? -Type of analog modulation wherein the amplitude of the carrier signal is varied or changed according to the instantaneous amplitude of the modulating signal.

- Process of modulation wherein the information is imposed on the carrier, causing the amplitude of the carrier to vary in accordance with the modulating signal. Note that the carrier frequency remains constant during the modulation process.

Amplitude Modulation MATHEMATICAL DESCRIPTION OF AN AM SIGNAL Let:

VAM (t )  A sin 2fct where: VAM is the Amplitude Modulated signal A is the instantaneous amplitude of the AM signal

A  Vc  Vm sin 2fmt

Vm   A  Vc  1  sin 2fmt  Vc  

Vm   V AM ( t )  Vc  1  sin 2fmt  sin 2fct Vc  

but Vm / Vc is the modulation index, m.

Amplitude Modulation V AM (t )  Vc  1  m sin 2fmtsin 2fct

V AM (t )  [Vc  mVc sin 2fmt] sin 2fct

V AM (t )  Vc sin2fct  mVc sin 2fmt sin 2fct Let : Note: sin X sin Y 

1 1 cos(X - Y) - cos(X  Y) 2 2

V AM (t )  Vc sin 2fct 

VC (rms ) 

Vc 2

X  2fct and Y  2fmt

mVc mVc cos2(fc - fm)t cos2(fc  fm)t 2 2

VUSB(pk)  VLSB(pk) 

mVc ; 2

VUSB(rms )  VLSB(rms ) 

mVc 2 2

Amplitude Modulation

Amplitude Modulation FREQUENCY SPECTRUM OF AN AM SIGNAL

BANDWIDTH = 2 fm

PERCENT MODULATION, %M AND MODULATION INDEX, m - show the relationship between amplitudes of the modulating signal and carrier. Also referred to as modulation factor or depth of modulation.

Vm Vc Vm %M  x 100 Vc m

Amplitude Modulation

m

Vmax - Vmin Vmax  Vmin

where: Vmax is the maximum peak value of the AM wave Vmin is the minimum peak value of the AM wave

Amplitude Modulation Three (3) degrees of modulation : a) Undermodulation - %M < 100%, m < 1, Vm < Vc (practical)

b) 100% modulation - m = 1, Vm = Vc (ideal)

c) Over modulation – %M > 100%, m > 1, Vm > Vc (with distortion)

Amplitude Modulation POWER CONTENT OF AN AM SIGNAL

PT  Pc  PLSB  PUSB m2 PLSB  PUSB  Pc 4

PT  Pc 

2

2

m m Pc  Pc 4 4

Where: PT = total transmitted power or total modulated power in Watts PLSB, PUSB = lower and upper sideband power in Watts Pc = unmodulated carrier power in Watts. Carrier power remains the same, regardless of percent modulation.

 m2  PT  Pc 1   2  

Amplitude Modulation CALCULATION OF VOLTAGE IN AM SYSTEMS

m2 v T  Vc 1  2 where: vT = total transmitted voltage or total voltage of the modulated wave Ic = unmodulated carrier voltage m = modulation index

Amplitude Modulation CALCULATION OF CURRENTS IN AM SYSTEMS

I T  Ic

m2 1 2

where: IT = total transmitted current or total current of the modulated wave Ic = unmodulated carrier current m = modulation index

EFFICIENCY OF TRANSMISSION -ratio of the total sideband power to the total transmitted power

%  (eta) 

PSB P P x 100  USB LSB x 100  %PSB PT PT

m2 %  (eta)  x 100 2 2m

m2Pc m2Pc m2Pc where: PSB  PUSB  PLSB    4 4 2

Amplitude Modulation MODULATION BY A COMPLEX INFORMATION SIGNAL OR BY SEVERAL INFORMATION SIGNAL

The total modulating signal, Vm t  Vm12  Vm 22  Vm 32  ...... The total modulation index, mt 

m12  m22  m32  ......

 mt 2  The total transmitted power, PT  Pc 1  2    mt 2Pc The total sideband power, PS Bt  2

Amplitude Modulation FORMS OF AMPLITUDE MODULATION TRANSMISSION 1. Double Sideband, Full Carrier Transmission (DSBFC) or A3 - Standard AM transmission - Component of the AM wave being transmitted: USB, LSB and carrier signal - In conventional AM systems, at least two thirds of the transmitted power is in the carrier. There is no information in the carrier; the sidebands contain the information. Also the information contained in the upper sideband is identical to the information contained in the lower sideband.

PT  Pc  PLSB  PUSB 2. Double Sideband, Suppressed Carrier Transmission (DSBSC) - Component of the AM wave being transmitted: USB and LSB signals - Produced by balanced modulator

PT  PLSB  PUSB

Amplitude Modulation 3. Single sideband, Full Carrier Transmission or H3E emission - Form of amplitude modulation in which the carrier is transmitted at full power, but only one sideband is transmitted

PT  Pc  PLSB or PT  Pc  PUSB 4. Single Sideband, Suppressed Carrier Transmission (SSBSC) or J3E emission - Form of amplitude modulation in which the carrier is totally suppressed and only one sideband is transmitted. - It reduces the amount of power and bandwidth necessary to transmit a given amount of information. - Used for radio communication.

PT  PLSB or PT  PUSB 5. Single sideband, Reduced Carrier Transmission or R3E - Form of amplitude modulation in which one sideband is totally removed and the carrier voltage is reduced to approximately 10% of its unmodulated amplitude

Amplitude Modulation 6. Two independent sidebands, with an attenuated or suppressed carrier Transmission or B8E - Also known as ISB (independent sideband emission). - A form of amplitude modulation in which a single carrier frequency is independently modulated by two different modulating signals. - Used for HF point to point radiotelephony 7. Vestigial Sideband Transmission or C3F - Used for TV video transmission - A form of amplitude modulation in which the carrier and one complete sideband are transmitted, but only part of the second sideband is transmitted. - Picture carrier and only a small vestige of the lower sideband is transmitted to conserve bandwidth. 8. Amplitude Compandored Single Sideband (ACSSB) - recently developed AM system in which the speech signal is compressed at the transmitter and expanded at the receiver.

Amplitude Modulation PERCENTAGE POWER SAVING

Power saved during suppression % POWER SAVING  x 100 Total power without suppression SINGLE SIDEBAND TRANSMITTER RATING

 VPK    2 PEP   R

2

Where: PEP = peak envelope power (W) Vpk = peak voltage (V) R = load resistance (ohms)

SAMPLE PROBLEM: 1. An audio signal whose mathematical representation is 25 sin 21000t modulates a carrier described as 75 sin 2150000t. Determine the following: a) sketch of the modulating signal b) sketch of the carrier c) sketch of the AM wave d) modulation index and percent modulation e) instantaneous voltage equation of the AM signal f) frequency spectrum of the AM signal g) bandwidth 2. An antenna transmit an AM signal having a total power content of 15KW. Determine the power being transmitted at the carrier and at each sideband when the %M is 85% and find the efficiency of transmission. 3. An AM signal contains 4000W at the carrier frequency and 1000 W in each of its sidebands. Determine the following: a) total power of the AM signal b) %M and m c) total power of the AM signal when the %M is changed to 70% 4. When a broadcast transmitter is 50% modulated, its total antenna current is 12 A. What is the carrier unmodulated current? What will be the total modulated current when the modulation depth is increased to 0.9?

5. A certain transmitter radiates 9KW with the carrier unmodulated, and 12KW when the carrier is sinusoidally modulated. Calculate the modulation index. If another sine wave, corresponding to 30% modulation, is transmitted simultaneously, determine the total modulation index and total radiated power. 6. The antenna current of an AM broadcast transmitter, modulated to a depth of 40% by an audio signal, is 10 A. It is increased to 12 A as a result of the simultaneous modulation by another sine wave. Determine the following: a) Carrier current b) Total modulation index c) Modulation index due to the second wave 7. A SSB transmission contains 800W. This transmission is to replaced by a DSBFC AM signal with the same power content. Determine the power being transmitted at the carrier and at each sideband when the %M is 85%. Find the efficiency of transmission. 8. A SSB signal contains 10KW. How much power is contained in the sideband and how much at the carrier? 9. A 500 W carrier is modulated to a depth of 75%. Calculate the total power in the modulated wave in the following form of AM transmission. a) DSBFC b) DSBSC c) SSBFC d) SSBSC

REFERENCES Electronic Communication Systems Through Advanced by W. Tomasi  Communication Electronics by L. Frenzel  Lecture Notes in Principles of Communication by A.H. Ballado and M.M. Sejera  Electronic Communication Systems by G. Kennedy 