CHAPTER 2 AMPLITUDE MODULATION AM DEMODULATION AMPLITUDE MODULATION
- Slides: 41
CHAPTER 2 AMPLITUDE MODULATION (AM) & DEMODULATION
AMPLITUDE MODULATION (AM) Sub-topics: l Modulation Techniques: An Overview l AM Principles l The AM Envelope l AM Frequency Spectrum and Bandwidth l Modulation Index and Percent of Modulation l The Mathematical Representation and Analysis of AM l AM Power Distribution l Various types of AM Methods or Schemes
Modulation Techniques: An overview Communications electronics is largely the study of various modulation techniques and the modulator and demodulator circuits. It covers transmission, reception and processing the information between two or more locations. l Two basic types of electronic communications systems: analog (energy Tx and Rx in analog form) and digital (energy Tx and Rx in digital form). l
Cont’d… l Direct transmission Vs. Broadband transmission. ¡ ¡ ¡ l Telephone sys Video over coaxial cable Long-distance communication? ? It is often impractical to propagate info signals over a metallic systems or fiber cables or thru earth’s atmosphere directly, hence necessary to encode the info onto a higher-freq carrier signal.
Generic Block Diagram of a Comm. System
Definition Modulation is a process of changing some property (amplitude, frequency or phase) of the higher frequency signal in accordance with the information signal. l The information signal (voice, video or digital data) is usually called the modulating signal and the higher frequency being modulated is called the carrier (usually a sine wave) or modulated wave. l
Why modulation is necessary in communications? It is extremely difficult to radiate low-freq signals thru earth’s atmosphere (atm) in the form of EM energy: antenna length. l Signal propagates with greater efficiency at higher frequencies. l The information signals always occupy the same freq band: interference, use multiplexing. l ¡ ¡ A standard voice-quality transmission – 3 k. Hz Microwaves and satellite radio – 30 MHz
AM Principles l Amplitude modulation (AM) is a process of changing the amplitude of the high frequency carrier in proportion with the instantaneous value of the modulating signal. l AM is a process of translating information signal from low band frequency to high band frequency. l AM is a linear analog modulation process
Cont’d… Inexpensive, low quality form of modulation l Applications of AM: l ¡ ¡ Commercial broadcasting – audio & video signals Two way mobile radio communication Amplitude of the carrier signal varies with the information signal. An increase in the modulating signal amplitude causes the amplitude of the carrier to increase. l The modulated signal consist of carrier signal, upper sideband lower sideband signals. l
The AM Envelope AM double-sideband full carrier (AM DSBFC) is the most commonly used and the oldest and simplest form of AM modulation. l Sometimes called conventional AM or simply AM. l The outline of the positive and negative peaks of the carrier frequency re-create the exact shape of the modulating signal is known as envelope. l Note that the repetition rate of the envelope is equal to the frequency of the modulating signal. l
AM Generation Waveforms
AM Frequency Spectrum and Bandwidth An AM modulator is a non-linear device. l 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). l The cross-products are displaced from the carrier frequency by fm on both sides of it. l AM modulated wave contains no frequency component of fm. l
Frequency spectrum of an AM DSBFC Wave
Bandwidth (BW) l The BW of an AM DSBFC wave is equal to the difference between the highest upper side frequency and lowest lower side frequency: l BW = [fc + fm(max)] – [fc – fm(max)] l = 2 fm(max) l For efficiency transmission the carrier and sidebands must be high enough to be propagated thru earth’s atm.
Example 1 For a conventional AM modulator with a carrier freq of fc = 100 k. Hz and the maximum modulating signal frequency of fm(max) = 5 k. Hz, determine: a) Freq limits for the upper and lower sidebands. b) Bandwidth. c) Upper and lower side frequencies produced when the modulating signal is a single-freq 3 k. Hz tone. d) Draw the output freq spectrum. l
Modulation Index and Percent of Modulation Used to describe the amount of amplitude change (modulation) present in an AM waveform. l Percentage modulation (%m) is simply the modulation index (m) stated as a percentage. l Moe specifically percent modulation gives the percentage change in the amplitude of the output wave when the carrier is acted on by a modulating signal. l
Cont’d… l Mathematically, the modulation index is m = modulation index Vm = peak change in the amplitude output waveform (sum of voltages from upper and lower side frequencies) Vc = peak amplitude of the unmodulated carrier l And the percentage of modulation index is
Determining modulation index from Vmax and Vmin
Cont’d… l 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: l Therefore,
Cont’d… l Since the peak change in of modulated output wave Vm is the sum of the usf and lsf voltages hence, l Then Vusf = peak amplitude of the lower side frequency (volts) Vlsf = peak amplitude of the upper side frequency (volts)
Cont’d… l From the modulated wave displayed in the previous slide, the maximum and minimum values of the envelope occurs at +Vmax = Vc + Vusb + Vlsb +Vmin = Vc – Vusb – Vlsb -Vmax = - Vc - Vusb - Vlsb -Vmin = - Vc + Vusb + Vlsb
% modulation of AM DSBFC envelope
Cont’d… l For proper AM operation, Vc ≤ Vm means that 0≤ m ≤ 1. l If Vc > Vm means that m > 1 leads to severe distortion of the modulate wave. l If Vc = Vm the percentage of modulation index goes to 100%, means the maximum information signal is transmitted. In this case, Vmax = 2 Vc and Vmin = 0.
Example 2 l Suppose that Vmax value read from the graticule on an oscilloscope scree is 4. 6 divisions and Vmin is 0. 7 divisions. Calculate the modulation index and percentage of modulation.
Example 3 l a) b) c) d) e) 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
The Mathematical Representation and Analysis of AM Representing both the modulating signal Vm(t) and the carrier signal Vc(t) in trigonometric functions. l The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals. l
Cont’d… l Substituting Vm = m. Vc gives: Constant + mod. signal Unmodulated carrier
Cont’d… l 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… l From the equation it is obvious that the amplitude of the carrier is unaffected by the modulation process. l The amplitude of the side frequencies depend on the both the carrier amplitude and modulation index. l 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 and sideband signals
Voltage spectrum for an AM DSBFC wave
Example 4 l a) b) c) d) e) One input to a conventional AM modulator is a 500 -k. Hz carrier with an amplitude of 20 Vp. The second input is a 10 -k. Hz 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. l Mathematically power in unmodulated carrier is l Pc = carrier power (watts) Vc = peak carrier voltage (volts) R = load resistance i. e antenna (ohms)
Cont’d l The upper and lower sideband powers will be l Rearranging in terms of Pc,
Cont’d… l The total power in an AM wave is l Substituting the sidebands powers in terms of PC yields l 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. l 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. l The advantage of DSBFC is the use of relatively simple, inexpensive demodulator circuits in the receiver. l
Example 5 l a) b) c) d) 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.
Amplitude modulation with digital signal Digital signal i. e binary data may also used to amplitude modulate a carrier. l Figure below shows a binary signal modulating a sine wave carrier. l In Amplitude Shift Keying (ASK), carrier switches between two different levels. Binary ‘ 1’ produces a maximum carrier amplitude and binary ‘ 0’ produces a lower-value carrier. l A special case of ASK is On-off Keying (OOK) in which the carrier is simply switched on and off. l
Amplitude modulation of a carrier with binary information: ASK and OOK
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