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## CHAPTER 2

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**CHAPTER 2**AMPLITUDE MODULATION (AM)**Principles of AM**• Definitions: • The process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of modulating signal (information) • A process of translating information signal from low band frequency to high bandfrequency.**Cont’d…**• Information signal cannot travel far. It needs carrier signal of higher frequency for long distance destination. • Inexpensive, low quality form of modulation**Cont’d…**• Amplitude of the carrier signal varies with the information signal. • The modulated signal consist of carrier signal,upper sideband and lower sideband signals • The modulated AM signal (figure 1 & figure 2) needs to go through demodulation process to get back the information signal.**The AM Envelope**• AM double-sideband full carrier (AM DSBFC) is the most commonly used and the oldest and simplest form of AM modulation. • Sometimes called conventional AM or simply AM. • The outline of the positive and negative peaks of the carrier frequency re-create the exact shape of the modulating signal known as envelope. • Note that the repetition rate of the envelope is equal to the frequency of the modulating signal.**AM Frequency Spectrum and Bandwidth**• An AM modulator is a non-linear device. • Nonlinear mixing results in a complex output envelope consists of the carrier frequency and the sum (fc + fm) and difference (fc – fm) frequencies (called cross-products). • The cross-products are displaced from the carrier frequency by fm on both sides of it. • AM modulated wave contains no frequency component of fm.**Bandwidth (BW)**• The BW of an AM DSBFC wave is equal to the difference between the highest upper side frequency and lowest lower side frequency: • BW = [fc + fm(max)] – [fc – fm(max)] = 2fm(max) • For efficiency transmission the carrier and sidebands must be high enough to be propagated thru earth’s atmosphere.**Example 1**• For a conventional AM modulator with a carrier freq of fc = 100 kHz and the maximum modulating signal frequency of fm(max = 5 kHz, determine: • Freq limits for the upper and lower sidebands. • Bandwidth. • Upper and lower side frequencies produced when the modulating signal is a single-freq 3-kHz tone. • Draw the output freq spectrum.**Modulation Index and Percent of Modulation**• Used to describe the amount of amplitude change (modulation) present in an AM waveform. • Percentage modulation (%m) is simply the modulation index (m) stated as a percentage. • More specifically percent modulation gives the percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal.**Cont’d…**• Mathematically, the modulation index is • And the percentage of modulation index is m = modulation index Em = peak change in the amplitude output waveform (sum of voltages from upper and lower side frequencies) Ec = peak amplitude of the unmodulated carrier**Cont’d…**• If the modulating signal is a pure, single-freq sine wave and the process is symmetrical then the modulation index can be derived as follows: • Therefore,**Cont’d…**• Since the peak change of modulated output wave Em is the sum of the usf and lsf voltages hence, • Then Eusf = peak amplitude of the upperside frequency (volts) Elsf = peak amplitude of the lower side frequency (volts)**Cont’d…**• From the modulated wave displayed in the previous slide, the maximum and minimum values of the envelope occurs at +Vmax = Ec + Eusb + Elsb +Vmin = Ec – Eusb – Elsb -Vmax = -Ec - Eusb - Elsb -Vmin = -Ec + Eusb + Elsb**Modulation Index for trapezoidal patterns**• Modulation index, m can be calculated using the equation: m = Emax – Emin/ Emax + Emin = Em / Ec = (A - B) / (A + B)**Cont’d…**• For proper AM operation, Ec > Em means that 0≤ m ≤ 1. • If Ec < Em means that m > 1 leads to severe distortion of the modulate wave. • If Vc = Vm the percentage of modulation index goes to 100%, means the maximum information signal is transmitted. In this case, Vmax = 2Vc and Vmin = 0.**Example 2**• Suppose that Vmax value read from the graticule on an oscilloscope screen is 4.6 divisions and Vmin is 0.7 divisions. Calculate the modulation index and percentage of modulation.**Example 3**• For the AM waveform shown in Figure below, determine • Peak amplitude of the upper and lower side frequencies. • Peak amplitude of the unmodulated carrier. • Peak change in the amplitude of the envelope. • Modulation index. • Percent modulation.**The Mathematical Representation and Analysis of AM**• Representing both the modulating signal Vm(t) and the carrier signal Vc(t) in trigonometric functions. • The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals**Cont’d…**• Substituting Vm = mVc gives: Constant + mod. signal Unmodulated carrier**Cont’d…**• The constant in the first term produces the carrier freq while the sinusoidal component in the first term produces side bands frequencies Carrier frequency signal (volts) Upper side frequency signal (volts) Lower side frequency signal (volts)**Cont’d…**• From the equation it is obvious that the amplitude of the carrier is unaffected by the modulation process. • The amplitude of the side frequencies depend on the both the carrier amplitude and modulation index. • At 100% modulation the amplitudes of side frequencies are each equal to one-half the amplitude of the carrier.**Generation of AM DSBFC envelope showing the time-domain of**the modulated wave, carrier&sideband signals**Example 4**• One input to a conventional AM modulator is a 500-kHz carrier with an amplitude of 20 Vp. The second input is a 10-kHz modulating signal that is of sufficient amplitude to cause a change in the output wave of ±7.5 Vp. Determine • Upper and lower side frequencies. • Modulation index and percentage modulation. • Peak amplitude of the modulated carrier and the upper and lower side frequency voltages. • Maximum and minimum amplitudes of the envelope. • Expression for the modulated wave.**AM Power Distribution**• In any electrical circuit, the power dissipated is equal to the voltage squared (rms) divided by the resistance. • Mathematically power in unmodulated carrier is Pc = carrier power (watts) Vc = peak carrier voltage (volts) R = load resistance i.e antenna (ohms)**Cont’d**• The upper and lower sideband powers will be • Rearranging in terms of Pc,**Cont’d…**• The total power in an AM wave is • Substituting the sidebands powers in terms of PC yields • Since carrier power in modulated wave is the same as unmodulated wave, obviously power of the carrier is unaffected by modulation process.**Power spectrum for AM DSBFC wave with a single-frequency**modulating signal**Cont’d…**• With 100% modulation the maximum power in both sidebands equals to one-half the carrier power. • One of the most significant disadvantage of AM DSBFC is with m = 1, the efficiency of transmission is only 33.3% of the total transmitted signal. The less wasted in the carrier which brings no information signal. • The advantage of DSBFC is the use of relatively simple, inexpensive demodulator circuits in the receiver.**Example 5**• For an AM DSCFC wave with a peak unmodulated carrier voltage Vc = 10 Vp, a load resistor of RL = 10 and m = 1, determine • Powers of the carrier and the upper and lower sidebands. • Total sideband power. • Total power of the modulated wave. • Draw the power spectrum.**Transmitter Efficiency**Transmitter efficiency, תּ = average power from sideband/total power absorbed. = m²/ ( 2+m² )**Modulation by a complex information signal**• Previous examples are all using a single frequency modulation signal. In practice, however, modulating signal is very often a complex waveform made up from many sine waves with different amplitudes and frequencies. • Example: if a modulating signal contains three frequencies(fm1, fm2, fm3), the modulated signal will contain the carrier and three sets of side frequencies, spaced symmetrically about the carrier:**Cont’d..frequency spectrum for complex information signal**fc Fc-fm3 Fc-fm2 Fc-fm1 Fc+fm1 Fc+fm2 Fc+fm3**Cont’d..modulation index for complex information signal**• When several frequencies simultaneously amplitude modulate a carrier, the combined coefficient of modulation is defined as: mt=total modulation index/coefficient of modulation m1, m2, m3, mn= modulation index/coefficient of modulation for input 1, 2 ,3 , n**Cont’d..Power calculation for complex information signal**• The combined coefficient of modulation can be used to determine the total sideband power and transmitted power, using:**Example 6**• For an AM DSBFC transmitter with an unmodulated carrier power, Pc= 100W that is modulated simultaneously by three modulating signals, with coefficients of modulation m1=0.2, m2= 0.4, m3=0.3, determine: • Total coefficient of modulation • Upper and lower sideband power • Total transmitted power