MODULATION (AM/FM)

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

MODULATION - The process of imposing information contained in a lower frequency electronic signal onto a higher frequency signal. - The higher frequency signal is called the CARRIER and the lower frequency signal is called the MODULATING SIGNAL. Note: If the information is imposed on the carrier by causing its amplitude to vary in accordance with modulating signal, the method is called AMPLITUDE MODULATION. ADVANTAGES OF TRANSMITTING HIGHER FREQUENCY SIGNAL 1. If all radio stations broadcast simultaneously at audio frequencies they could not be distinguished from one another, and only jumbled mess would received. 2. It is found that antennas on the order of magnitude of 5 miles to 5000 miles are necessary for audio frequency transmission.

ADVANTAGE OF AM

DISADVANTAGE OF AM

Usable with very simple modulators and demodulators.

Poor performance in the presence of noise and inefficient use of transmitter power

APPLICATIONS OF AM 1. Broadcasting in the medium and high frequency bandwidth. 2. Aircraft communications in the VHF frequency range. 3. Citizen’s Band (CB) radio. Note: An AM signal can be produced by using the instantaneous amplitude of the information signal (baseband or modulating signal) to vary the peak amplitude of a higher frequency signal.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

FULL CARRIER TIME DOMAIN Amplitude modulation is created by using instantaneous modulating signal to vary the amplitude of the modulated signal:

V(t) = [Ec + em] sin wct Where:

V(t) Ec em wc t

= = = = =

instantaneous amplitude of the modulated signal in volts peak amplitude of the carrier in volts instantaneous amplitude of the modulating signal in volts radian frequency of the carrier time in seconds

If the modulating (baseband) signal is a sine wave:

V(t) = [Ec + Em sin wmt] sin wct Where:

Em wm

= peak amplitude of the modulating signal in volts = radian frequency of the modulating signal

EXAMPLE: A carrier wave with an RMS voltage of 2V and a frequency of 1.5MHz is modulated by a sine wave with a frequency of 500Hz and amplitude of 1V RMS. Write the equation for the resulting signal.

Solution: fc = 1.5MHz

fm = 500Hz

Ec = 2V / 0.707 = 2.83V

Amplitude = 1V / 0.707 = 1.4V

V(t) = [Ec + Em sin wmt] sin wct V(t) = [2.83 + 1.4 sin (2π500) t] [sin(2π500) V(t) = [2.83 + 1.4 sin (3.14x103t] [sin 9.4x106 t] V

w = 2πf = 2π500

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

MODULATION INDEX, m The amount by which the signal amplitude is changed in modulation depends on the ratio between the amplitudes of the modulating signal and the carrier.

m = Em/Ec

PERCENT MODULATION, M

M = m • 100 OVER MODULATION -

Creates side frequencies further from the carrier. These spurious frequencies are known as SPLATTER, and they cause the modulated signal to have increased bandwidth.

-

Creates distortion in the demodulated signal and may result in the signal occupying a larger bandwidth than normal since spectrum space is tightly controlled by law, over modulation of an AM transmitter is actually illegal and means must be provided to permit it. Therefore, for full carrier AM, the modulation index must be in the range from 0 to 1.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

MODULATION INDEX FOR MULTIPLE MODULATION FREQUENCIES -

When there are two or more sine waves of different uncorrelated frequencies (i.e., frequencies that are not multiples of each other) modulating a single carrier, m is calculated by using the equation:

Where:

mT = total resultant modulation index m1m2 = modulation indices due to the individual modulating components

EXAMPLE: Find the modulation index if a 10V carrier is amplitude modulated by 3 different frequencies with amplitudes of 1V, 2V and 3V respectively

Solution: Ec Em1 Em2 Em3

= = = =

10V 1V 2V 3V

m1 = (1/10) = .1 m2 = (2/10) = .2 m3 = (3/10) = .3

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

FULL CARRIER FREQUENCY DOMAIN Note: Although both the carrier and the modulating signal may be sine waves, the modulated waveform is not a sine wave.

fLSB = fc - fm fUSB = fc + fm

EXAMPLE: a. A 1MHz carrier with an amplitude of 1V peak is modulated by a 1KHz signal with m=0.5. Sketch the voltage spectrum. b. An additional 2KHz signal modulates the carrier with m=0.2. Sketch the voltage spectrum.

Solution: a.

fc = 1MHz fm = 1KHz fLSB = fc–fm = 0.999MHz fUSB = fc+fm = 1.001MHz

b.

fUSB = 1MHz + 2KHz = 1.002MHz fLSB = 1MHz – 2KHz = 0.998MHz mEc/2 = 0.1V

Ec = 1V mEc/2 = 0.25V

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

BANDWIDTH Signal bandwidth is one of the most important characteristics of any modulated scheme. In general, a narrow bandwidth is desirable in any situation where spectrum space is limited; a narrow bandwidth allows more signals to be transmitted simultaneously than does a wider bandwidth. It also allows a narrow bandwidth to be used in the receiver.

B = 2Fm Where:

B Fm

= bandwidth in Hz = highest modulating frequency in Hz

POWER RELATIONSHPS Power is important in any communication scheme, because the crucial signal to noise ratio at the receiver depends as much on the signal being large as on the noise power being small. The power that is most important however, is not the total signal power but only that portion that is used to transmit information. Note: Since the carrier in an AM signal remains unchanged with modulation, it contains no information. Its only function is to aid in demodulating the signal at the receiver. This makes AM inherently wasteful of power, compared with some other modulation schemes.

ec = Ec sin wct Where:

ec Ec

= instantaneous carrier voltage = peak carrier voltage

More formulas:

PT = PC + PUSB + PLSB

PUSB = PLSB = m2PC / 4

PT = Pc [(1+m2) / 2]

PC = Ec2 / R

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

EXAMPLE1: A bandwidth of 20MHz is to be considered for the transmission of AM signals. If the highest audio frequencies used to modulate the carriers are not to exceed 3KHz, how many stations could broadcast within this band simultaneously without interfering with one another?

Solution: No. of stations No. of stations

= B/2Fm = 20MHz / 6KHz = 3.33x103 = 3,333 stations

EXAMPLE2: An amplitude wave has a power content of 800M at its carrier frequency. Determine the power content of each of the sidebands for a 90% modulation.

Solution: PUSB PUSB

= m2PL / 4 = (0.92 • 800W) / 4 = 162W

EXAMPLE3: Determine the power content of the carrier frequency of each of the sidebands for an AM signal having a percent modulation of 80% and a total power of 2500W.

Solution: PT = Pc [1 + (m2/2)] 2500 = Pc [1 + (0.82/2)] Pc = 1893.94W

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

Note: Under 100% modulation (optimum condition), only 1/3 of the power transmitted is located in the sidebands, 2/3 of the power is located at the carrier frequency. No information is contained at the carrier frequency. All information is contained within the upper and lower sidebands. In reality, the two sidebands contain identical information. Note: Schemes have been devised for making better use of the available power being transmitted. These schemes include suppressed-carrier transmission, double sideband transmission and single sideband transmission. SUPRESSED CARRIER:

DOUBLE SIDEBAND:

SINGLE SIDEBAND:

Note: In each of these schemes, the power is placed where the information is. An additional advantage of the Single Sideband (SSB) scheme is that only half as much bandwidth is required for the transmission and therefore twice as many stations can transmit simultaneously. In SSB transmission, amount of power and bandwidth are reduced. BALANCED MODULATOR – circuit used to suppress a carrier signal.

ANGLE MODULATION (FM/AM) USES OF FM (Frequency Modulation) 1. Used extensively for radio broadcasting 2. Used for sound signal in television 3. Used for two way fixed and mobile radio systems 4. Used for satellite communication 5. Used for cellular telephone systems

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

USE OF PM (Phase Modulation) 1. Used extensively in data communications Note: The most important advantage of FM or PM over AM is the possibility of a greatly improved signal to noise ratio. FREQUENCY MODULATION - Was originally developed to cope with undesirable noise which competed with the desired signal when AM was used. Most noise appeared as an additional amplitude modulation on the signal. - When frequency modulating a carrier, information is placed on the carrier by varying its frequency while holding its amplitude fixed. CARRIER SIGNAL: SIGNAL:

MODULATING SIGNAL:

MATHEMATICAL DESCRIPTIONS OF: a) CARRIER:

b) MODULATING OR AUDIO SIGNAL:

c) CARRIER FREQUENCY, f:

MODULATED:

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

CARRIER SWING = = total variation in frequency from the lowest value to the highest value. 88-108MHz = FMbroadcast band Note: 75KHz = maximum 25KHz = maximum

for FM broadcast for sound portion of television broadcast

PERCENT MODULATION, M

-

Ratio of actual frequency deviation to the maximum allowable frequency deviation. Thus, 100% modulation corresponds to 75KHz for the commercial FM broadcast and 25KHz for television.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

SIDEBANDS Note: In amplitude modulated wave, it has only two side frequencies for each modulating frequencies. The FM signal has infinite number of side frequencies spaced far apart on both sides of the resting frequency.

Note: Most of the side frequencies do not contain significant amounts of power. Note:

fa max

= frequency of the modulating signal

CENTER FREQUENCY AND BANDWIDTH ALLOCATIONS Each commercial FM broadcast station in the 88 to 108MHz band is allocated a 150 KHz channel plus a 25KHz guard band at the upper and the lower edges of the station allocation by the FCC. Thus, a total channel width of 200 KHz is provided to each station in the commercial FM broadcast band. Note: In addition to this large bandwidth and guard band combination, only alternate channels are assigned within any particular geographic area. Note: Assigning only alternate channels in any given geographic area limits the possibility interface.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

NARROWBAND FM

WIDEBAND FM

mf < π/2

mf > π/2

DEVIATION RATIO - The worst case modulation index, in which the maximum permitted frequency deviation and the maximum permitted audio frequency used is called deviation ratio.

Example: A 107.6MHz carrier is frequency modulated by a 7KHz sine wave. The resultant FM signal has a frequency deviation of 50KHz a. Find the carrier swing of the FM signal b. Determine the highest and lowest frequencies attained by the modulated signal c. What is the modulation index of the FM wave?

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

FM RECEIVER

THE LIMITER Its purpose is to clip all amplitude variations which may exist in the signal as it reaches this part of the system. Note: Clipping removes any AM noise which may have become part of the signal. Clipping by the limiter eliminates noise but does not affect the information content of the signal because the information is contained in the frequency variations, not in the amplitude variations. THE DE-EMPHASIS NETWORK Note: The pre-emphasis network causes the higher frequency information content of the audio signal at the transmitter to be amplified more than the lower frequency information. The de-emphasis network causes the higher frequency information content of the audio signal at the transmitter to be amplified more than the lower frequency information. The reason for the inclusion of such system is to reduce frequency modulated noise which enters the transmitted signal while EN ROUTE from the transmitter to the receiver as well as any such noise which may enter at the front end of the receiver.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

AM-FM RECEIVERS All radio receivers perform these 3 basic functions: 1. SELECTION - It allows the receiver to select one frequency while rejecting other frequencies. This is done by tuning the receiver to the frequency of the desired carrier. This function is performed through combinations of inductances and capacitances, where the oscillating frequency can be determined by:

2. AMPLIFICATION - The incoming signal may be weak as such, amplification must take place between the input of the receiver and its output. This is usually called the gain of the receiver.

3. DETECTION - The purpose of a detector in the receiver is to remove the desired information from the carrier and convert it into a form that will actuate the output device such as the loudspeaker.

ECEG07 – PRINCIPLES OF COMMUNICATION MIDTERM. JUNE302011.

AM vs FM

Note: The transmitted signal will travel along the transmission medium. Noise affects the signal being transmitted. In AM, the changes in amplitude cannot be removed and doing so would also remove the original information. In FM, changes in amplitude of the signal due to noise can be removed upon receiving the signal. The signals caused by noise are negligible on the receiving site because in FM receivers, a limiter is incorporated in the system to remove any changes in amplitude of the received signal. The limiter does not disturb the original modulating frequency. A good example of noise free reception of FM compared to AM is in TV sets. The sound being transmitted is in FM, while the picture is in AM. Note: It is advantageous to use FM because FM is relatively immune from one noise interference; it has better noise rejection and better utilization of transmitter power. AM is inefficient in utilizing system power and is susceptible to noise in the system.