AMPLITUDE MODULATION (AM) CHAPTER 2 AMPLITUDE MODULATION (AM)

Types of communication In simplex communications, the information travels in one direction only. E.g. radio/TV broadcasting In duplex communications, information travels in two-way: it can be further categorized into half duplex and full duplex. Half duplex- only one party transmit at a time (e.g. walkie-talkie). Full duplex – each party can transmit and receive simultaneously (e.g. cell-phone).

TYPES OF COMMUNICATIONS TX Channel RX Simplex: One-way Duplex: Two-way Half duplex: Alternate TX/RX Full duplex: Simultaneous TX/RX TX RX Channel(s) TX RX

COMMUNICATIONS SIGNAL VARIATIONS Baseband - The original information signal such as audio, video, or computer data. Can be analog or digital. Broadband - The baseband signal modulates or modifies a carrier signal, which is usually a sine wave at a frequency much higher than the baseband signal.

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 band frequency.

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.

Cont’d…

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.

The Generation of AM Envelope

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.

Frequency spectrum of an AM DSBFC Wave

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.

Solution : Frequency limits for the lower sideband Frequency limits for the upper sideband b) Bandwidth

Solution : c) Upper side frequency : Lower side frequency:

Solution : d) Output frequency 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

Determining modulation index from Vmax and Vmin

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…

% modulation of AM DSBFC envelope

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.

Solution: Modulation index, m 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.

AM Envelope for Example 3

Peak amplitude of upper side & lower side frequencies Solution : Peak amplitude of upper side & lower side frequencies b) Peak amplitude of unmodulated carrier c) Peak change in the amplitude of the envelope

Solution : d) Coefficient of modulation, m e) 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

Voltage spectrum for an AM DSBFC wave

Example 4 Carrier=Ecsin(225t) Modulating signal=Emsin(25t) Determine the expression for the modulated wave.