 # Principles Of Communication Engineering

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Principles Of Communication Engineering

Chapter 2 Amplitude Modulation

Topics Covered in Chapter 2
2-1: AM Concepts 2-2: Modulation Index and Percentage of Modulation 2-3: Sidebands and the Frequency Domain 2-4: Single-Sideband Modulation 2-5: AM Power

2-1: AM Concepts In the modulation process, the voice, video, or digital signal modifies another signal called the carrier. In amplitude modulation (AM) the information signal varies the amplitude of the carrier sine wave. The instantaneous value of the carrier amplitude changes in accordance with the amplitude and frequency variations of the modulating signal. An imaginary line called the envelope connects the positive and negative peaks of the carrier waveform.

2-1: AM Concepts Figure 1-1: Amplitude modulation. (a) The modulating or information signal.

2-1: AM Concepts Figure 1-2: Amplitude modulation. (b) The modulated carrier.

2-1: AM Concepts In AM, it is particularly important that the peak value of the modulating signal be less than the peak value of the carrier. Vm < Vc Distortion occurs when the amplitude of the modulating signal is greater than the amplitude of the carrier. A modulator is a circuit used to produce AM. Amplitude modulators compute the product of the carrier and modulating signals.

1-1: AM Concepts Figure 1-3: Amplitude modulator showing input and output signals.

2-2: Modulation Index and Percentage of Modulation
Figure 1-5: AM wave showing peaks (Vmax) and troughs (Vmin).

2-2: Modulation Index and Percentage of Modulation
The modulation index (m) is a value that describes the relationship between the amplitude of the modulating signal and the amplitude of the carrier signal. m = Vm / Vc This index is also known as the modulating factor or coefficient, or the degree of modulation. Multiplying the modulation index by 100 gives the percentage of modulation.

2-2: Modulation Index and Percentage of Modulation
The modulation index is commonly computed from measurements taken on the composite modulated waveform. Using oscilloscope voltage values: Vm = Vmax − Vmin 2 The amount, or depth, of AM is then expressed as the percentage of modulation (100 × m) rather than as a fraction.

Determining modulation index from Vmax and Vmin
EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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 EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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, EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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 upper side frequency (volts) Elsf = peak amplitude of the lower side frequency (volts) EKT343 –Principle of Communication Engineering

2-2: Modulation Index and Percentage of Modulation
Overmodulation and Distortion The modulation index should be a number between 0 and 1. If the amplitude of the modulating voltage is higher than the carrier voltage, m will be greater than 1, causing distortion. If the distortion is great enough, the intelligence signal becomes unintelligible.

2-2: Modulation Index and Percentage of Modulation
Overmodulation and Distortion Distortion of voice transmissions produces garbled, harsh, or unnatural sounds in the speaker. Distortion of video signals produces a scrambled and inaccurate picture on a TV screen.

2-2: Modulation Index and Percentage of Modulation
Figure 1-4: Distortion of the envelope caused by overmodulation where the modulating signal amplitude Vm is greater than the carrier signal Vc.

2-3: Sidebands and the Frequency Domain
Side frequencies, or sidebands are generated as part of the modulation process and occur in the frequency spectrum directly above and below the carrier frequency.

2-3: Sidebands and the Frequency Domain
Sideband Calculations Single-frequency sine-wave modulation generates two sidebands. Complex wave (e.g. voice or video) modulation generates a range of sidebands. The upper sideband (fUSB) and the lower sideband (fLSB) are calculated: fUSB = fc + fm and fLSB = fc − fm

2-3: Sidebands and the Frequency Domain
Figure 1-6: 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.

2-3: Sidebands and the Frequency Domain
Frequency-Domain Representation of AM 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. Bandwidth is the difference between the upper and lower sideband frequencies. BW = fUSB−fLSB = [fc + fm(max)] – [fc –fm(max) ] = 2fm(max)

2-3: Sidebands and the Frequency Domain
Figure 1-8: The relationship between the time and frequency domains.

2-3: Sidebands and the Frequency Domain
Frequency-Domain Representation of AM 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.

EKT343 –Principle of Communication Engineering
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. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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. EKT343 –Principle of Communication Engineering

AM Envelope for Example 3
EKT343 –Principle of Communication Engineering

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 EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Cont’d… Substituting Vm = mVc gives: Constant + mod. signal Unmodulated carrier EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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) EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Generation of AM DSBFC envelope showing the time-domain of the modulated wave, carrier & sideband signals EKT343 –Principle of Communication Engineering

Voltage spectrum for an AM DSBFC wave
EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
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. EKT343 –Principle of Communication Engineering

2-3: Sidebands and the Frequency Domain
Pulse Modulation When complex signals such as pulses or rectangular waves modulate a carrier, a broad spectrum of sidebands is produced. A modulating square wave will produce sidebands based on the fundamental sine wave as well as the third, fifth, seventh, etc. harmonics. Amplitude modulation by square waves or rectangular pulses is referred to as amplitude shift keying (ASK). ASK is used in some types of data communications.

2-3: Sidebands and the Frequency Domain
Figure 1-11: Frequency spectrum of an AM signal modulated by a square wave.

2-3: Sidebands and the Frequency Domain
Figure 1-12: Amplitude modulation of a sine wave carrier by a pulse or rectangular wave is called amplitude-shift keying. (a) Fifty percent modulation. (b) One hundred percent modulation.

2-3: Sidebands and the Frequency Domain
Pulse Modulation Continuous-wave (CW) transmission can be achieved by turning the carrier off and on, as in Morse code transmission. Continuous wave (CW) transmission is sometimes referred to as On-Off keying (OOK). Splatter is a term used to describe harmonic sideband interference.

2-4: Single-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.

2-4: Single-Sideband Modulation
DSB Signals 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 (DSSC) signal. No power is wasted on the carrier. A balanced modulator is a circuit used to produce the sum and difference frequencies of a DSSC signal but to cancel or balance out the carrier. DSB (or DSSC) is not widely used because the signal is difficult to demodulate (recover) at the receiver.

2-4: Single-Sideband Modulation
Figure 1-16: A frequency-domain display of DSB signal.

2-4: Single-Sideband Modulation
SSB Signals 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.

2-4: Single-Sideband Modulation
SSB Signals SSB signals offer four major benefits: Spectrum space is conserved and allows more signals to be transmitted in the same frequency range. 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. Occupied bandwidth space is narrower and noise in the signal is reduced. There is less selective fading over long distances.

2-4: Single-Sideband Modulation
Disadvantages of DSSC and SSBSC Single and double-sideband SC’s 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.

2-4: Single-Sideband Modulation
Signal Power Considerations In SSB, the transmitter output is expressed in terms of peak envelope power (PEP), the maximum power produced on voice amplitude peaks. Applications of DSB and SSB A vestigial sideband signal (VSB) is produced by partially suppressing the lower sideband. This kind of signal is used in TV transmission.

2-5: 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).

2-5: AM Power When the percentage of modulation is less than the optimum 100, there is much less power in the sidebands. Output power can be calculated by using the formula PT = (IT)2R where IT is measured RF current and R is antenna impedance

2-5: AM Power The greater the percentage of modulation, the higher the sideband power and the higher the total power transmitted. Power in each sideband is calculated PSB = PLSB = PUSB = Pcm2 / 4 Maximum power appears in the sidebands when the carrier is 100 percent modulated.

EKT343 –Principle of Communication Engineering
AM Power Review: conventional AM(DSB-FC) Frequency spectrum: Bandwidth=2 x fmmax Total Power=Pcarrier +Pusb +Plsb fc fc+fm fc-fm EKT343 –Principle of Communication Engineering

DSB FULL CARRIER

Two major Drawbacks of DSBFC
Large power consumption, where carrier power constitutes >2/3 transmitted power.{remember : carrier does not contain any information} Utilize twice as much bandwidth – both the upper and lower sideband actually contains same information (redundant). Thus, DSBFC is both power and bandwidth inefficient EKT343 –Principle of Communication Engineering

Double side band suppressed carrier(DSB-SC)
Frequency spectrum: Bandwidth:2 x fmmax Total Power= Pusb + Plsb fc fc+fm fc-fm EKT343 –Principle of Communication Engineering

Single-Sideband (SSB)
The carrier is transmitted at full power but only one sideband is transmitted requires half the bandwidth of DSBFC AM Carrier power constitutes 80% of total transmitted power, while sideband power consumes 20% SSBFC requires less total power but utilizes a smaller percentage of the power to carry the information EKT343 –Principle of Communication Engineering

Single Side Band Full Carrier (SSB-FC)
Frequency spectrum: Bandwidth=fmmax Total Power=Pcarrier +Pusb fc fc+fm fc-fm EKT343 –Principle of Communication Engineering

AM Single-Sideband Suppressed Carrier (SSBSC)
The carrier is totally suppressed and one sideband is removed requires half the bandwidth of DSBFC AM Considerably less power than DSBFC and SSBFC schemes Sideband power makes up 100% of the total transmitted power The wave is not an envelope but a sine wave at frequency equal to the carrier frequency ±modulating frequency (depending on which sideband is transmitted) EKT343 –Principle of Communication Engineering

Single Side band Suppress Carrier (SSB-SC)
Frequency spectrum: Bandwidth=fmmax Total Power=+Pusb fc fc+fm fc-fm EKT343 –Principle of Communication Engineering

AM Single-Sideband Reduced Carrier (SSBRC)
One sideband is totally removed and the carrier voltage is reduced to approximately 10% of its unmodulated amplitude requires half the bandwidth of DSBFC AM Less transmitted power than DSBFC and SSBFC but more power than SSBSC As much as 96% of the total transmitted power is in the sideband The output modulated signal is similar to SSBFC but with reduced maximum and minimum envelope amplitudes EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Comparison of time domain representation of three common AM transmission systems: EKT343 –Principle of Communication Engineering Tomasi Electronic Communications Systems, 5e

EKT343 –Principle of Communication Engineering
Example 5 For an AM DSCFC wave with a peak unmodulated carrier voltage Vc = 10Vp, frequency of 100kHz, a load resistor of RL = 10 , frequency of modulating signal of 10kHz and m = 1, determine the following Powers of the carrier and the upper and lower sidebands. ii) Total power of the modulated wave. iii) Bandwidth of the transmitted wave. iv) Draw the power and frequency spectrum. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Example 5..cont’d Solution for DSBFC; i) ii) iii) Bandwidth=2xfmmax=2(10kHz)=20kHz EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Example 5..cont’d For the same given values, determine questions (ii)-(iv) for a AM DSB-SC, AM SSB-FC and AM SSB-SC systems. Determine also the percentage of power saved in each of the system design. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Example 5..cont’d Solution: For DSB-SC ii) iii)Bandwidth=2xfmmax=2(10kHz)=20kHz iv) 110kHz 90kHz EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Example 5..cont’d Solution:For SSB-FC ii) iii)Bandwidth=fmmax=10kHz iv) 100kHz 110kHz fc-fm EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Example 5..cont’d Solution:For SSB-SC ii) iii)Bandwidth=fmmax=10kHz iv) fc-fm fc 110kHz EKT343 –Principle of Communication Engineering

Exercises 1. An audio signal 15sin2π (1500t ). Amplitude modulates a carrier 60sin2π (100000t). Sketch the audio signal Sketch the carrier Construct the modulated wave Determine the modulation index and percent modulation What are the frequencies of the audio signal and the carrier f) What frequencies would show up in the spectrum analysis of the modulated wave.

Exercises 2. The total power content of an AM wave is 600W. Determine the percent modulation of the signal if each of the sidebands contains 75W. 3. Determine the power content of the carrier and each of the sidebands for an AM signal having a percent modulation of 80% and the total power of 2500W

Methods of Generating SSB
i) Filtering method A filter removes the undesired sideband producing SSB. Quartz crystal filters are the most widely used sideband filters since they are very selective and inexpensive. ii) Phasing method A balanced modulator eliminates the carrier and provides DSB. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Filtering method Filter response curve Sideband filter Balanced modulator Carrier oscillator Microphone Audio amplifier Linear Antenna Upper sidebands DSB signal SSB Lower EKT343 –Principle of Communication Engineering

Phasing methods-using two balance modulator
Another way to produce SSB uses a phase shift method to eliminate one sideband. Two balanced modulators driven by carriers and modulating signals 90º out of phase produce DSB. Adding the two DSB signals together results in one sideband being cancelled out. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Phasing method..cont’d Balanced Modulator 1 Modulator 2 Phase shifter + Information signal Carrier signal Output Signal, aot Am cos wmt Am cos (wmt + 90) Ac cos (wct + 90) A2(t) A1(t) EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Phasing method..cont’d Cos 90 = 0 EKT343 –Principle of Communication Engineering

Power consumption - Much less total transmitted power is necessary to produce the same quality signal as achieved with DSBFC AM Bandwidth conservation Selective fading - carrier phase shift and carrier fading can not occur, thus smaller distortion is expected. Noise reduction - thermal noise power is reduced Disadvantages Complex receivers Tuning difficulties – requires more complex and precise than DSB With DSB, the carrier and two sidebands may propagate through the channel by different paths and experience different transmission impairment called as selective fading EKT343 –Principle of Communication Engineering

VESTIGIAL SIDEBAND (VSB)
VSB is similar to SSB but it retains a small portion (a vestige) of the undesired sideband to reduce DC distortion. VSB signals are generated using standard AM or DSBSC modulation, then passing modulated signal through a sideband shaping filter. Demodulation uses either standard AM or DSBSC demodulation. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Cont’d Also called asymmetric sideband system. Compromise between DSB & SSB. Easy to generate. Bandwidth is only ~ 25% greater than SSB signals. Derived by filtering DSB, one pass band is passed almost completely while just a trace or vestige of the other sideband is included. EKT343 –Principle of Communication Engineering

EKT343 –Principle of Communication Engineering
Cont’d AM wave is applied to a vestigial sideband filter, producing a modulation scheme – VSB + C Mainly used for television video transmission. VSB Frequency Spectrum fc LSB MSB Carrier VSB EKT343 –Principle of Communication Engineering