Amplitude & Frequency Modulation Techniques - Essay Example

Table of Contents Objectives………………………………………………………………. 2 2. Introduction ……………………………………………………………. 2 3. Amplitude Modulation………………………………………………….. 3 3.1 AM Mathematical Analysis……………………………………….. 3 3.2 AM Modulation Index…………………………………………….. 4 3.3 AM Spectrum and Bandwidth……………………………………. 5 3.4 AM Power Relations………………………………………………. 6 3.5 AM Demodulation Circuits……………………………………….. 7 3.6 Double Sideband Suppressed Carrier (DSBSC) and Single Sideband (SSB) AM……………………………………… 8 3.7 Practical AM Modulation and Demodulation Circuits…………. 9 3.8 Advantages and Disadvantages of AM Modulation…………… 10 3.9 MATLAB/ SIMULINK Simulation Results for AM……………… 11 4. Frequency Modulation………………………………………………….. 19 4.1 FM Mathematical Analysis………………………………………. 19 4.2 FM Power Relations……………………………………………… 20 4.3 FM Spectrum……………………………………………………… 20 4.4 Carson’s Rule……………………………………………………… 22 4.5 FM Modulator Implementation…………………………………… 23 4.6 FM Demodulator Implementation………………………………… 23 4.7 Practical FM Modulation and Demodulation Circuits…………... 24 4.8 Advantages of FM Modulation……………………………………. 25 4.8.1 Noise Immunity……………………………………………… 25 4.8.2 Capture Effect………………………………………………... 25 4.8.3 Transmitter Efficiency………………………………………. 25 4.9 Disadvantages of FM Modulation………………………………… 25 4.9.1 Excessive Bandwidth Use…………………………………. 25 4.9.2 Circuit Complexity…………………………………………… 25 4.9.3 MATLAB/ SIMULINK Simulation Results for FM………… 26 5. Conclusions…………………………………………………………….. 30 6. References……………………………………………………………… 31 7. Appendix………………………………………………………………… 32 ABSTRACT This report details the theory and mathematical formulation behind Amplitude Modulation and Frequency Modulation. MATLAB/ SIMULINK software development tool will be used to investigate the parameters affecting the performance of AM and FM modulators and 
demodulators. The comparison of the two modulation techniques and their applications will also be discussed at the end of the report. INTRODUCTION The objective of this report is to investigate the Amplitude Modulation and Frequency Modulation techniques in time and 
frequency domains using MATLAB/SIMULINK software development tools. Modulator schemes will be set up for the following modulation techniques: 
Double Sideband Amplitude Modulation (DSBAM), Double Sideband Suppressed Carrier Amplitude Modulation (DSBSCAM), Single Sideband Amplitude Modulation (SSBAM) and Frequency Modulation (FM). Demodulator schemes for DSBAM and FM modulation techniques will also be set up. 
 AMPLITUDE MODULATION In amplitude modulation or AM, the amplitude of the carrier wave is varied by the modulating or information signal. The carrier is always the higher frequency signal while the modulating signal can be an audio or video signal (Hammer et. al, 1977). The basic form of amplitude modulation is Double Sideband or DSB. It can be represented by the following equation: Eq. 3.1 Basic AM Signal (Hammer et. al, 1977) The following figures show the block diagram of a DSB AM modulator with the corresponding waveforms of the modulating signal and output DSB signal. Fig. 3.1 DSB AM Modulator System Diagram (Rice and Long, 1997) Fig. 3.2 Waveform of DSB Modulating Signal (Kennedy and Davis, 1993) Fig. 3.3 Waveform of Output DSB Signal (Kennedy and Davis, 1993) If a DC bias “A” is added to the modulating signal before the modulation process, the resultant signal will be what is termed as AM (Amplitude Modulation), which is the type commonly used in radio broadcasting. Figure 3.4 shows a sample AM signal with a corresponding modulating signal. The AM signal can be represented by the following equation: Eq. 3.2 AM Signal showing Carrier and Sideband component (Hammer et. al, 1977) Based on Figure 3.4, a parameter termed as modulation index can be derived: Eq. 3.3 AM Modulation Index (Rice and Long, 1997) This parameter has a minimum value of zero. For values less than or equal to 1, the envelope of the AM signal is always positive. For values more than 1, the AM signal will experience zero crossings resulting to phase shifting at each crossing (Hammer et. al, 1977). Fig. 3.4 Modulating Signal and AM Waveform (Kennedy and Davis, 1993) AM Spectrum The spectrum of an AM signal can be represented by the following equation and figure: Eq. 3.4 AM Signal Spectrum (Hammer et. al, 1977) Fig. 3.5 AM Signal Spectrum (Hammer et. al, 1977) The center of the spectrum is the frequency of the AM signal with sidebands at the left and the right – Lower Sideband (LSB) and Upper Sideband (USB). Take note that the bandwidth required for AM is twice the bandwidth of the modulating signal (Hammer et. al, 1977). AM Transmitted Power The transmitted power of an AM signal can be represented by the following: Eq. 3.5 AM Transmitted Power (Hammer et. al, 1977) In simpler terms, the total power of an AM signal is the sum of the carrier power plus the power of the two sidebands. Pt = Pc + PLSB + PUSB Eq. 3.6 AM Transmitted Power (Kennedy and Davis, 1993) If the modulation index is equal to 1, it is interesting to note that the following power relation will be obtained: Pt = 1.5Pc Efficiency From the transmitted power equation, we can also derive the formula for efficiency. This parameter is the percentage of the power used for transmitting information contained in the modulating signal over total power utilized (including that for the carrier). Eq. 3.7 AM Efficiency (Rice and Long, 1997) AM Demodulation The system diagram of an AM signal demodulator is shown in Figure 3.6. The demodulator output contains a constant DC component that is later removed in succeeding stages after the demodulator. Fig. 3.6 AM Demodulator System Diagram (Rice and Long, 1997) If the modulation index is equal to or less than 1, an AM signal can be demodulated by a simple and practical circuit called an envelope detector. Take note that this circuit will not work for AM signals with modulation indices more than 1. Figure 3.7 shows a diode with an RC circuit. The diode produces the rectified half-wave AM signal while the RC circuit smoothens this signal to approximate the original modulating signal. Fig. 3.7 Simple AM Envelope Detector (Kennedy and Davis, 1993) Single Sideband Modulation The other types of amplitude modulation are Double Sideband Suppressed Carrier (DSBSC) and Single Sideband (SSB). In both types of modulation, the carrier is removed by the use of a balanced modulator. In SSB, the process is taken another step further by the removal of one of the sidebands by using a filter (see Figure 3.8). The logic behind these techniques is the carrier actually contains no information and the sidebands that contain the information are just mirror of each other. The primary advantage of SSB over standard AM is obvious, it requires lesser power and just half the bandwidth (Hammer et. al, 1977). Fig. 3.8 SSB Modulator System Diagram (Rice and Long, 1997) Fig. 3.9 SSB Spectrum (Hammer et. al, 1977) Practical AM Modulator Circuit Fig. 3.10 LM1496 Balanced Modulator (J. B. Calvert, 2001) A practical AM modulator can be made from the LM1496. The carrier signal, which can be generated from an RF generator, is fed to two differential amplifiers (Q1 to Q4) in antiphase mode. The total current for these differential amplifiers are then supplied by a differential amplifier made from Q5 and Q6, which is fed by the modulating signal. The gain of a differential amplifier is proportional to its current, so the lower amplifier controls the gain of the upper amplifiers, which will be proportional to the signal input. The resultant amplitude modulated carrier can be taken from either pin 6 or 12 (J. B. Calvert, 2001). Practical AM Demodulator Circuit Fig. 3.11 Square-Law Detector (J. B. Calvert, 2001) The above circuit is an example of a transistor square-law detector. The AM signal is fed to the base while the output message signal is extracted at the collector (J. B. Calvert, 2001). Advantages and Disadvantages of Amplitude Modulation AM is easy to generate and requires simpler circuits. It is also easy to receive and demodulate that translates to simple and inexpensive AM receivers. This is the reason why AM has become popular in sound broadcasting and is widely used worldwide. A modified form of AM, Single Sideband (SSB) is also widely used in point-to-point long-distance communication. The primary disadvantage of AM compared to FM is it is more affected by noise. The decoded information in AM is the envelope of the AM signal that is dependent on the modulating signal. Atmospheric and man-made noise can ride on this envelope, thus introducing noise to the decoded signal (Kennedy and Davis, 1993). MATLAB/ SIMULINK Simulation Results for AM DSBAM Modulator Simulation Fig. 3.12 Block Diagram of Double Sideband AM (DSBAM) Modulator. Fig. 3.13 Temporal representation of Message Signal of 5 Hz (Top) and Double Sideband AM (DSBAM) output waveform (Bottom). Carrier Signal is 100 Hz. Fig. 3.14 Spectral representation of Double Sideband AM (DSBAM) output waveform. Carrier Signal is 100 Hz. DSBSCAM Modulator Simulation Fig. 3.15 Block Diagram of Double Sideband Suppressed Carrier AM (DSBSCAM) Modulator. Fig. 3.16 Temporal representation of Message Signal of 5 Hz (Top) and Double Sideband Suppressed Carrier AM (DSBSCAM) output waveform (Bottom). Carrier Signal is 100 Hz. Fig. 3.17 Spectral representation of Double Sideband Suppressed Carrier AM (DSBSCAM) output waveform. SSBAM Modulator Simulation Fig. 3.18 Block Diagram of Single Sideband AM (SSBAM) Modulator. Fig. 3.19 Temporal representation of Message Signal of 2 Hz (Top) and Single Sideband AM (SSBAM) output waveform (Bottom). Carrier Signal is 100 Hz. Fig. 3.20 Spectral representation of Single Sideband AM (SSBAM) output waveform. DSBAM Demodulator Simulation Fig. 3.21 Block Diagram of Double Sideband AM (DSBAM) Demodulator. Fig. 3.22 Temporal representation of Message Signal of 5 Hz (Top), Double Sideband AM (DSBAM) modulated waveform (Middle) and Double Sideband AM (DSBAM) demodulated waveform (Bottom). Carrier Signal is 100 Hz. Fig. 3.23 Spectral representation of Double Sideband AM (DSBAM) output waveform. FREQUENCY MODULATION Frequency modulation (FM) is a type of angle modulation that can be represented by the following: Eq. 4.1 FM Signal (Hammer et. al, 1977) In this type of modulation, the frequency of the carrier wave is varied by the modulating or information signal. The corresponding frequency deviation constant can be represented by the following: Eq. 4.2 FM frequency Deviation (Hammer et. al, 1977) Figure 4.1 is an illustration of how angle modulated signals are formed. Here, a step modulating signal was used to simplify explanation. The waveform of the carrier signal is shown and the resultant frequency modulated signal and phase modulated signal (another type of angle modulation). Fig. 4.1 Illustration of modulating signal, carrier signal and resultant FM and PM signals (Kennedy and Davis, 1993) Transmitted Power The transmitted power for an FM signal can be represented by the following equation: Eq. 4.3 FM Transmitted Power (Hammer et. al, 1977) The approximation is due to the fact that the frequency deviates slowly in relation to the carrier frequency. It should also be noted that the modulated FM signal has a constant amplitude and all power are useful compared to AM, where much power is wasted in transmitting the carrier (Kennedy and Davis, 1993). FM Spectrum The FM spectrum is illustrated in Figure 4.2. This is a sample FM signal that contains a carrier (at center of spectrum) and four pairs of sidebands. Fig. 4.2 FM Spectrum (Hammer et. al, 1977) FM Average Power As shown in the above diagram, a signal that is angle modulated can contain power over an infinite number of bandwidths. However, there are only a few sideband pairs that have significant power components and the power becomes insignificant as sideband frequencies move further away from the carrier frequency (Hammer et. al, 1977). The average power in an FM modulated signal can be expressed in the following equation: Eq. 4.4 FM Average Power (Rice and Long, 1997) FM Modulation Index  is referred to as the modulation index in frequency modulation and can represented by the following equation: Eq. 4.5 FM Modulation Index (Hammer et. al, 1977) The relationship of the modulation index  to amplitude, which is represented by J can be shown by the following graph: Fig. 4.3 Bessel Function Graph (Kennedy and Davis, 1993) For values of  less than 1, what is produced is known as narrow band FM. This type of modulation is utilized in two-way radio communication that only requires small frequency deviations. The relationship of  to bandwidth can be approximated based on the above equations as follows: Eq. 4.6 Relationship of FM Modulation Index to Bandwidth (Rice and Long, 1997) Carson’s Rule For non-sinusoidal modulation, bandwidth can also be approximated by what is known as Carson’s rule. This is expressed by the following equation: Eq. 4.7 Carson’s Rule (Rice and Long, 1997) where D is the deviation ratio represented by the following equation: Eq. 4.8 FM Deviation Ratio (Rice and Long, 1997) FM Modulator Frequency modulation can be implemented by the use of a voltage controller oscillator or VCO (see Figure 4.4). The input signal m(t) is utilized to vary the frequency of the output signal. Fig. 4.4 FM Modulator Diagram (Hammer et. al, 1977) FM Demodulator An FM signal can be demodulated by the use of a combination of a differentiator and an envelope detector (see Figure 4.8). The FM input signal is approximated by the differentiator and the output is fed to an envelope detector, which extracts the envelope to recover the original signal m(t) - (Hammer et. al, 1977). Fig. 4.5 FM Demodulator Diagram (Rice and Long, 1997) Practical FM Modulator Circuit Fig. 4.6 XR2206 Function Generator (J. B. Calvert, 2001) The XR-2206 is a function generator that provides a square wave or a sine wave at an open-collector output. The output frequency can be modulated by an external voltage using the circuit shown at the left. R is the normal timing resistor, while RC handles the modulating current. The formula for the frequency is shown in the figure (J. B. Calvert, 2001). Practical FM Demodulator Circuit Fig. 4.7 Ratio Detector (J. B. Calvert, 2001) The above circuit is an example of a ratio detector. The input FM signal is fed to the primary of the transformer. The signal that goes directly to the center tap of the secondary splits equally there, and is rectified by the diodes to create equal voltages across the two capacitors to ground, in a kind of voltage doubler action (J. B. Calvert, 2001). Advantages of Frequency Modulation 1. Noise Immunity. The amplitude of an FM signal is kept constant and information is extracted in the receiver based on the variations in its frequency. This characteristic provides immunity to noise and interference during transmission. FM receivers also have a circuit known as a limiter. This is a special type of IF amplifier is used to limit noise peaks present in the FM signal prior to detection (Kennedy and Davis, 1993). 2. Capture Effect. This is an inherent noise suppression characteristic of FM. If two FM stations are operating on the same frequency, an FM receiver will only demodulate the stronger signal (Kennedy and Davis, 1993). 3. Power Efficiency. In FM, the efficiency is generally improved by increasing the number of modulation indices. For AM, the maximum efficiency possible without distortion is only 33% (at modulation index = 1). FM has almost limitless number of modulation indices and the power of the sidebands are just fractions of the total power in an FM signal (Kennedy and Davis, 1993). Disadvantages of Frequency Modulation 1. Excessive Bandwidth Utilization. Since there is no natural limit to the modulation indices in FM as compared to FM, the tendency is to increase it resulting to excessive bandwidth requirement. This may not be possible in actual communication systems because of telecom regulation issues (Kennedy and Davis, 1993). 2. Circuit Complexity. FM has inherent advantages over AM in terms of noise immunity and power efficiency. But in order to implement these advantages, more complex circuits are required in both the transmitter and the receiver. The direct method of generating FM using a VCO require sophisticated feedback control for it to be used in practical applications. The alternative method Armstrong System is even more complex because a PM signal should first be generated before an FM signal is produced. The re is also a need for baseband frequency-correction circuits (pre-emphasis and de-emphasis) because of limited frequency deviation possible in Armstrong systems (Kennedy and Davis, 1993). MATLAB/ SIMULINK Simulation Results for FM FM Modulator Simulation Fig. 4.8 Block Diagram of FM Modulator. Fig. 4.9 Temporal representation of Message Signal of 5 Hz (Top) and FM output waveform (Bottom). Carrier Signal is 100 Hz. Fig. 4.10 Spectral representation of FM output waveform. FM Demodulator Simulation Fig. 4.11 Block Diagram of FM Demodulator. Fig. 4.12 Temporal representation of Message Signal of 5 Hz (Top) and FM output waveform (Bottom). Carrier Signal is 100 Hz. Fig. 4.13 Spectral representation of FM output waveform. CONCLUSIONS Amplitude Modulation and Frequency Modulation work in the same principle that in both modulation techniques, a characteristic of a carrier signal is varied by the message signal. The difference lies in the manner how the carrier wave is modulated. In AM, the amplitude of the carrier signal is varied by the modulating signal. In FM, it is the frequency of the carrier signal that is varied. The above discussion was verified using MATLAB/SIMULINK software development tool. Modulator schemes were set up for Double Sideband Amplitude Modulation (DSBAM), Double Sideband Suppressed Carrier Amplitude Modulation (DSBSCAM), Single Sideband Amplitude Modulation (SSBAM) and Frequency Modulation (FM). Demodulator schemes were also set up for DSBAM and FM modulation techniques. The following results were observed: - In all types of AM, the message signal varies the amplitude of the carrier signal. Adding a DC bias to the message signal creates the basic DSBAM signal. - In both DSBSCAM and SSBAM, the carrier is removed by the use of a balanced modulator. In SSBAM, one of the sidebands is removed by using a filter. The logic behind these AM modulation techniques is the carrier contains no information and both the upper and lower sidebands contain identical information. - In FM, the message signal varies the frequency of the carrier signal while the amplitude remains constant. The main advantage of FM over AM is it is more immune to noise and interference based on the fact that the FM signal conveys information through changes in frequency. AM is susceptible to these signal anomalies because they can ride on the AM signal during transmission. AM conveys information through changes in amplitude. Another advantage of FM over AM is it is more efficient in terms of power and bandwidth usage. This is due to the inherent characteristic of FM to be modulated with a larger amount of frequency deviation. It is therefore possible to allocate bigger baseband bandwidth to a modulating signal, such as an audio signal. These are the reasons why frequency modulation is preferred in FM commercial broadcasting, which caters more to the music industry that requires higher fidelity audio than AM radio. AM on the other hand is a simpler modulation technique that requires simpler transmitters and receivers. A far larger number of AM broadcast receivers are used worldwide because they are inexpensive to manufacture. There is also a technique in AM that make it possible to save significantly in power and bandwidth if the carrier and one of its sidebands is suppressed before transmission. There is a trade off though in the cost of transmitters and receivers that make this type of AM more applicable for point-to-point communication links rather than in broadcasting. REFERENCES [1] Hammer, I. W. et. al, “Reference Data for Radio Engineers”, 6th ed., Indianapolis, Howard W. Sams & Co., Inc., 1977. [2] G. Kennedy and B. Davis, “Electronic Communications Systems”, 4th ed., Lake Forest, Macmillan/ McGraw-Hill, 1993. [3] Wikibooks.org,, “Communication Systems/ Amplitude Modulation”, [Online] Available at: http://en.wikibooks.org/wiki/Communication_Systems/Amplitude_Modulation [Accessed 26 December 2008]. [4] Wikibooks.org,, “Communication Systems/ Frequency Modulation”, [Online]. Available at: http://en.wikibooks.org/wiki/Communication_Systems/Frequency_Modulation [Accessed 27 December 2008]. [5] M. Rice and D. Long, , “Introduction to Analog and Digital Communication Theory”, Electrical and Computer Engineering Department Brigham Young University, 1997. [Online]. Available at: http://www.ee.byu.edu/class/ee444/ComBook/ComBook/ComBook.html [Accessed 28 December 2008]. [6] Tom Nguyen, “Matlab/ Simulink – A Tutorial”, [Online]. Available at: http://edu.levitas.net/Tutorials/Matlab/Simulink/index.html [Accessed 28 December 2008]. [7] J. B. Calvert, “Amplitude Modulation and Superheterodynes”, 2001 [Online], Available at: http://mysite.du.edu/~etuttle/electron/elect17.html APPENDIX List of Abbreviations AM – Amplitude Modulation DSBAM – Double Sideband Amplitude Modulation DSBSCAM - Double Sideband Suppressed Carrier Amplitude Modulation FM – Frequency Modulation LPF – Low-Pass Filter LSB – Lower Sideband SSBAM – Single Sideband Amplitude Modulation USB – Upper Sideband List of Symbols Ac = Carrier Amplitude c = Carrier Frequency  = AM Modulation Index  = Pi = 3.14159 E = AM Power Efficiency  = Phase Kf = FM Frequency Deviation Constant fd = FM Frequency Deviation  = FM Modulation Index Read More