CHAPTER 4 AMPLITUDE MODULATION AM PART 1 Prepared
- Slides: 58
CHAPTER 4 AMPLITUDE MODULATION (AM) PART -1 Prepared by Dr M. Murugappan
HEA 01 Define, explain and analyze amplitude modulation (AM), modulation index, spectral analysis, bandwidth calculation and power analysis of AM Discuss and analyze double sideband suppressed carrier (DSBSC) and single sideband suppressed carrier (SSBSC) resistive sensors Discuss and analyze AM modulator and demodulator circuit Evaluate noise in analogue communication system
Topics Covered Amplitude Modulation (AM) Concepts Modulation Index (MI) and Percentage of Modulation Sidebands and the Frequency Domain AM Power Single-Sideband Modulation
Recall Modulation Principles of AM Why we need modulation? › Information signal cannot travel far. It needs carrier signal of higher frequency for long distance destination. Definition – Amplitude Modulation: › 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… The instantaneous value of the carrier amplitude changes in accordance with the amplitude and frequency variations of the modulating (information) signal. Inexpensive, low quality form of modulation
Contd…. Figure 1: The modulating or information signal. Figure 3: Principle of Amplitude Modulation Figure 2: The modulated carrier signal.
The Generation of AM Envelope
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 (information) signal is known as envelope. Note that the repetition rate of the envelope is equal to the frequency of the modulating signal.
Cont’d… Figure 4: Examples of AM Modulated signals
The Mathematical Representation and Analysis of AM • Representing both the modulating signal Em(t) and the carrier signal Ec(t) in trigonometric functions. The AM DSBFC modulator must be able to produce mathematical multiplication of these two analog signals The sine wave carrier can be expressed as ec = Vc sin 2πfct Vc is peak value of the unmodulated carrier • A sine wave modulating signal can be expressed as em = Vm sin 2πfmt Vm is peak value of information signal
Contd… Instantaneous value of either top or bottom voltage envelope is e 1 = Vc + em = Vc + Vm sin 2πfmt Instantaneous value of complete modulated wave can be expressed as e 2 = e 1 sin 2πfct
Contd… Substitute v 1 in v 2 e 2 = [Vc + Vm sin (2πfmt)] sin (2πfct) = Vc sin (2πfct) + Vm sin (2πfmt) sin (2πfct) The second part of the right hand side of the equation is characteristic of AM.
Contd… Figure 5: Amplitude modulator showing input and output signals.
Contd… Vm = m. Vc , so e 2 = [Vc + m. Vc sin (2πfmt)] sin (2πfct) = [1 + m sin (2πfmt)] Vc sin (2πfct) The term in square bracket is modulating signal + constant. The term outside bracket is carrier signal.
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.
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 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. the
Cont’d… 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 And the percentage of modulation index is
Determining modulation index from Vmax and Vmin Figure 6: Determine the Modulation index for the above AM Modulated Wave
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) Figure 7: Trepezoidal representation of AM signal
% 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 Ec = Em the percentage of modulation index goes to 100%, means the maximum information signal is transmitted. In this case, Emax = 2 Ec and Emin = 0.
AM Frequency Spectrum Amplitude of the carrier signal varies with the information signal. When the carrier signal is added with modulating signal through non-linear device (modulator), it gives three outputs › Lower side band frequency (LSB) › Carrier signal frequency › Upper Side Band frequency (USB) The Sum and Differences of Carrier signal frequency and modulating signal frequency produces USB and LSB, respectively.
Contd… Nonlinear mixing results in a complex output envelope consists of the carrier frequency (fc) 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.
Contd… Observing an AM signal on an oscilloscope, you see only amplitude variations of the carrier with respect to time. A plot of signal amplitude versus frequency is referred to as frequency-domain display. A spectrum analyzer is used to display the frequency domain as a signal.
Contd… Figure 8: Frequency spectrum of Amplitude Modulated DBFC Wave
Contd… Figure 9: The AM wave is the algebraic sum of the carrier and upper and lower sideband sine waves. (a) Intelligence or modulating signal. (b) Lower sideband. (c ) Carrier. (d ) Upper sideband. (e ) Composite AM wave.
Contd… Figure 10: The relationship between the time and frequency domains.
Contd… Figure 11: AM DSBFC Modulated Signal frequency spectrum
Bandwidth (BW) Bandwidth is the difference between the upper and lower sideband frequencies. BW = f. USB−f. LSB 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)] BW = 2 fm(max) For efficient signal transmission, the carrier and sidebands must be high enough to be propagated through the earth’s atmosphere.
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.
Example 2 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 a) Upper and lower side frequencies. b) Modulation index and percentage modulation. c) Peak amplitude of the modulated carrier and the upper and lower side frequency voltages. d) Maximum and minimum amplitudes of the envelope. e) Expression for the modulated wave.
AM Power In radio transmission, the AM signal is amplified by a power amplifier. A radio antenna has a characteristic impedance that is ideally almost pure resistance. The AM signal is a composite of the carrier and sideband signal voltages. Each signal produces power in the antenna. Total transmitted power (PT) is the sum of carrier power (Pc ) and power of the two sidebands (PUSB and PLSB).
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 Figure 12: AM DSBFC Modulated Signal Power Spectrum
AM Power (Alternative Derivation) When the percentage of modulation is less than the optimum 100, there is much less power in the sidebands. Output power can also be calculated by using the formula PT = (IT)2 R where IT is measured RF current and R is antenna impedance. IT can be expressed as where IC is the unmodulated carrier current
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.
Transmitter Efficiency Transmitter efficiency: It’s the ratio of average side band powers to the total power absorbed. % TE= m²/ ( 2+m² ) X 100
Example-1 Given the unmodulated carrier current of an AM transmitter is 10 A, antenna load impedance is 50 Ω and percentage of modulation is 85%. What is total AM transmitted power?
Example-1 Given the unmodulated carrier current of an AM transmitter is 10 A, antenna load impedance is 50 Ω and percentage of modulation is 85%. What is total AM transmitted power? Solution: = 11. 67 A PT = (11. 67)2(50) = 6809 W
Example-2 For an AM DSCFC wave with a peak unmodulated carrier voltage Vc = 10 Vp, a load resistor of RL = 10 and m = 1, determine a) Powers of the carrier and the upper and lower sidebands. b) Total sideband power. c) Total power of the modulated wave. d) Draw the power spectrum. e) Repeat the steps (a) to (d) for a modulation index m=0. 5.
Example-2 For an AM DSCFC wave with a peak unmodulated carrier voltage Vc = 10 Vp, a load resistor of RL = 10 and m = 1, determine a) Powers of the carrier and the upper and lower sidebands. b) Total sideband power. c) Total power of the modulated wave. d) Draw the power spectrum. e) Repeat the steps (a) to (d) for a modulation index m=0. 5. Solutions m=1; Pc = 5 W Pusb=Plsb= 1. 25 W Pt-sb= 2. 5 W Pt= 7. 5 W m=0. 5; Pc = 5 W Pusb=Plsb= 0. 3125 W Pt-sb= 0. 625 W Pt= 5. 625 W
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 m 1, m 2, m 3, mn= modulation index/coefficient of modulation for input 1, 2 , 3 , n
Example-3 For an AM DSBFC transmitter with an unmodulated carrier power, Pc= 100 W that is modulated simultaneously by three modulating signals, with coefficients of modulation m 1=0. 2, m 2= 0. 4, m 3=0. 3, determine: a) Total coefficient of modulation Upper and lower sideband power Total transmitted power b) c)
Sideband Modulation In amplitude modulation, two-thirds of the transmitted power is in the carrier, which conveys no information. Signal information is contained within the sidebands. Single-sideband (SSB) is a form of AM where the carrier is suppressed and one sideband is eliminated. Conventional form of AM is called double-sideband full carrier (DSBFC).
Double Sideband Modulation The first step in generating an SSB signal is to suppress the carrier, leaving the upper and lower sidebands. This type of signal is called a double-sideband suppressed carrier (DSB-SC) signal. No power is wasted on the carrier. A balanced modulator is a circuit used to produce the sum and difference frequencies of a DSB-SC signal but to cancel or balance out the carrier. DSB is not widely used because the signal is difficult to demodulate (recover) at the receiver.
Double Sideband Modulation DSB-SC consist of the product of the modulating signal and carrier signal. EDSB-SC = Ec. Em = Ec sin (2πfct) Em sin (2πfmt) using trigonometry identity, EDSB-SC = Ec. Em [ 1 cos 2π(fc-fm)t 2 cos 1 2π(fc+fm)t] 2 The signal consist of two waveform with sideband frequencies (no carrier). If no modulating signal (Em =0) there will be no modulated signal produced.
Double Sideband Modulation Figure 13: A frequency-domain display of DSB signal.
Single-Sideband Modulation
Single-Sideband Modulation One sideband is all that is necessary to convey information in a signal. A single-sideband suppressed carrier (SSSC) signal is generated by suppressing the carrier and one sideband.
Single-Sideband Modulation SSB signals offer four major benefits: 1. Spectrum space is conserved and allows more signals to be transmitted in the same frequency range. 2. All power is channeled into a single sideband. This produces a stronger signal that will carry farther and will be more reliably received at greater distances. 3. Occupied bandwidth space is narrower and noise in the signal is reduced. 4. There is less selective fading over long distances.
Single-Sideband Modulation Signal Side Band Power Considerations ◦ In SSB, the transmitter output is expressed in terms of peak envelope power (PEP), the maximum power produced on voice amplitude peaks. ◦ PEP is given by PEP = Vrms 2/R ◦ Example : A voice signal produces 360 V peak-to-peak signal across 50 Ω load. PEP = [(360/2)0. 707]2 50 = 324 W
Single-Sideband Modulation Disadvantages of DSB and SSB › Single and double-sideband are not widely used because the signals are difficult to recover (i. e. demodulate) at the receiver. › A low power, pilot carrier is sometimes transmitted along with sidebands in order to more easily recover the signal at the receiver.
Sideband Modulation Applications of DSB and SSB ◦ Two-way communication in military and radio amateurs (ham radio). ◦ Transmit two-channel stereo signal. ◦ Transmit color information for TV picture. ◦ A vestigial sideband signal (VSB) is produced by partially suppressing the lower sideband. This kind of signal is used in TV transmission.
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