Modulation and Demodulation.pdf

SD 274: Digital Communication and Signal Processing INTRODUCTION TO MODULATION TECHNIQUES LECTURE 3 Dr. E. Effah  Introduction to Modulation and Demodulation The purpose of a communication system...

SD 274: Digital Communication and Signal Processing INTRODUCTION TO MODULATION TECHNIQUES LECTURE 3 Dr. E. Effah  Introduction to Modulation and Demodulation The purpose of a communication system is to transfer information from a source to a destination. In practice, problems arise in baseband transmissions, the major cases being: Noise in the system – external noise and circuit noise reduces the signal-to-noise (S/N) ratio at the receiver (Rx) input and hence reduces the quality of the output. Such a system is not able to fully utilise the available bandwidth, for example telephone quality speech has a bandwidth ≃ 3kHz, a co-axial cable has a bandwidth of 100's of Mhz. Radio systems operating at baseband frequencies are very difficult. Not easy to network.  Components of Digital Communication System The Source encoder ( or Source coder) converts the input i.e. symbol sequence into a binary sequence of 0‟s and 1‟s by assigning code words to the symbols in the input sequence. For eg. :-If a source set has hundred symbols, then the number of bits used to represent each symbol will be 7 because 27=128 unique combinations are available. The important parameters of a source encoder are block size, code word lengths, average data rate, and the efficiency of the coder (i.e. actual output data rate compared to the minimum achievable rate). At the receiver, the source decoder converts the binary output of the channel decoder into a symbol sequence. The decoder for a system using fixed–length code words is quite simple, but the decoder for a system using variable–length code words will be very complex. Source coding aims to remove the redundancy in the transmitting information, so that the bandwidth required for transmission is minimized. Based on the probability of the symbol code word is assigned. The higher the probability, the shorter the codeword. Ex: Huffman coding.  Components of Digital Communication System CHANNEL ENCODER / DECODER: Error control is accomplished by the channel coding operation that consists of systematically adding extra bits to the output of the source coder. These extra bits do not convey any information but help the receiver to detect and/or correct some of the errors in the information-bearing bits. There are two methods of channel coding: 1. Block Coding: The encoder takes a block of „k‟ information bits from the source encoder and adds „r‟ error control bits, where „r‟ is dependent on „k‟ and the error control capabilities desired. 2. Convolution Coding: The information-bearing message stream is encoded continuously by continuously interleaving information bits and error control bits.  Components of Digital Communication System CHANNEL ENCODER / DECODER: The Channel decoder recovers the information bearing bits from the coded binary stream. Error detection and possible correction is also performed by the channel decoder. The important parameters of coder / decoder are: Method of coding, efficiency, error control capabilities and complexity of the circuit.  Components of Digital Communication System The Modulator converts the input bit stream into an electrical waveform suitable for transmission over the communication channel. Modulator can be effectively used to minimize the effects of channel noise, to match the frequency spectrum of transmitted signal with channel characteristics, to provide the capability to multiplex many signals. DEMODULATOR: The extraction of the message from the information bearing waveform produced by the modulation is accomplished by the demodulator. The output of the demodulator is bit stream. The important parameter is the method of demodulation. L = length of Antenna  Components of Digital Communication System CHANNEL: The Channel provides the electrical connection between the source and destination. The different channels are: Pair of wires, Coaxial cable, Optical fibre, Radio channel, Satellite channel or combination of any of these. The communication channels have only finite Bandwidth, non- ideal frequency response, the signal often suffers amplitude and phase distortion as it travels over the channel. Also, the signal power decreases due to the attenuation of the channel. The signal is corrupted by unwanted, unpredictable electrical signals referred to as noise. The important parameters of the channel are Signal to Noise power Ratio (SNR), usable bandwidth, amplitude and phase response and the statistical properties of noise.  Components of Digital Communication System Encryptor: Encryptor prevents unauthorized users from understanding the messages and from injecting false messages into the system. MUX : Multiplexer is used for combining signals from different sources so that they share a portion of the communication system. DeMUX: DeMultiplexer is used for separating the different signals so that they reach their respective destinations. Decryptor: It does the reverse operation of that of the Encryptor.  RECAP: Digital-to-analog conversion Digital-to-analog conversion is the process of changing one of the characteristics of an analog signal (carrier signal) based on the information in digital data. Digital /Analog converter Analog /Digital converter  Why we need digital modulation - Digital modulation is required if digital data has to be transmitted over a medium that only allows analog transmission. - Modems in wired networks. - Wireless must use analogue sine waves. 12 Analogue Modulation Techniques with some Derivatives and Familiar Applications Digital Modulation Techniques with some Derivatives and Familiar Applications Types of digital-to-analog conversion 1 6 Modulation & Demodulation Radio Carrier Carrier Channel Baseband Synchronization/ Modulation Detection/ Decision Data in Data out  Modulation Modulation : process (or result of the process) of translation the baseband message signal to bandpass (modulated carrier) signal at frequencies that are very high compared to the baseband frequencies. Demodulation is the process of extracting the baseband message back the modulated carrier. An information-bearing signal is non- deterministic, i.e. it changes in an unpredictable manner.  What is Modulation? In modulation, a message signal, which contains the information is used to control the parameters of a carrier signal, so as to impress the information onto the carrier. The Messages The message or modulating signal may be either: analogue – denoted by m(t) digital – denoted by d(t) – i.e. sequences of 1's and 0's The message signal could also be a multilevel signal, rather than binary; this is not considered further at this stage. The Carrier The carrier could be a 'sine wave' or a 'pulse train'. Consider a 'sine wave' carrier: vc (t ) = Vc cos(ωc t + φc ) If the message signal m(t) controls amplitude – gives AMPLITUDE MODULATION AM If the message signal m(t) controls frequency – gives FREQUENCY MODULATION FM If the message signal m(t) controls phase- gives PHASE MODULATION PM or M  Considering now a digital message d(t): If the message d(t) controls amplitude – gives AMPLITUDE SHIFT KEYING ASK. As a special case it also gives a form of Phase Shift Keying (PSK) called PHASE REVERSAL KEYING PRK. If the message d(t) controls frequency – gives FREQUENCY SHIFT KEYING FSK. If the message d(t) controls phase – gives PHASE SHIFT KEYING PSK. In this discussion, d(t) is a binary or 2 level signal representing 1's and 0's The types of modulation produced, i.e. ASK, FSK and PSK are sometimes described as binary or 2 level, e.g. Binary FSK, BFSK, BPSK, etc. or 2 level FSK, 2FSK, 2PSK etc. Thus there are 3 main types of Digital Modulation: ASK, FSK, PSK.  Why Carrier? Effective radiation of EM waves requires antenna dimensions comparable with the wavelength: – Antenna for 3 kHz would be ~100 km long – Antenna for 3 GHz carrier is 10 cm long Sharing the access to the telecommunication channel resources  NOTE: Bit rate, N, is the number of bits per second (bps). Baud rate is the number of signal elements per second (bauds). In the analog transmission of digital data, the signal or baud rate is less than or equal to the bit rate. S=Nx1/r bauds Where r is the number of data bits per signal element. Example 1: An analog signal carries 4 bits per signal element. If 1000 signal elements are sent per second, find the bit rate. Solution: In this case, r = 4, S = 1000, and N is unknown. We can find the value of N from  Example 2: An analog signal has a bit rate of 8000 bps and a baud rate of 1000 baud. How many data elements are carried by each signal element? How many signal elements do we need? Solution: In this example, S = 1000, N = 8000, and r and L are unknown. We find first the value of r and then the value of L.  Modulation Process f = f (a1 , a2 , a3 ,...an , t ) (= carrier) a1 , a2 , a3 ,...an (= modulation parameters) t (= time) Modulation implies varying one or more characteristics (modulation parameters a1, a2, … an) of a carrier f in accordance with the information-bearing (modulating) baseband signal. Sinusoidal waves, pulse train, square wave, etc. can be used as carriers  Amplitude Shift Keying (ASK) Baseband Data 1 0 0 1 ASK modula ted signal Acos(t) Acos(t) Pulse shaping can be employed to remove spectral spreading ASK demonstrates poor performance, as it is heavily affected by noise, fading, and interference  Amplitude Shift Keying (ASK) In ASK the amplitude of the carrier signal is varied to represent binary 1 or 0. Carrier signal is a high-frequency signal that acts as a basis for the information signal. Both frequency and phase remain constant while the amplitude changes. The peak amplitude of the signal during each bit duration is constant, and its value depends on the bit (0 or 1). 26  Binary ASK (BASK) or On Off Keying (OOK) - Although we can have several levels of signal elements, each with a different amplitude, ASK is normally implemented using only two levels. This is referred to as binary amplitude shift keying. - In ON-OFF Keying: bit 0 is represented by the absence of a carrier and bit 1 is represented by the presence of a carrier. 27  Pros and Cons - Pros: ASK transmitter and receiver are simple to design. ASK needs less bandwidth than FSK. - Cons: ASK transmission can be easily corrupted by noise. - Application: Early telephone modem (AFSK). ASK is used to transmit digital data over optical fiber. 28  Frequency Shift Keying (FSK) Baseband Data 1 0 0 1 BFSK modulat ed signal f1 f0 f0 f1 where f0 =Acos(c-)t and f1 =Acos(c+)t Example: The ITU-T V.21 modem standard uses FSK FSK can be expanded to a M-ary scheme, employing multiple frequencies as different states  FSK (Frequency Shift Keying) The frequency of the carrier signal is varied to represent binary 1 or 0. Both peak amplitude and phase remain constant while the frequency changes. The frequency of the signal during each bit duration is constant, and its value depends on the bit (0 or 1). 30  FSK Modulator - One way to think about binary FSK (or BFSK) is to consider two carrier frequencies Switch between two oscillators accordingly 31  ASK and FSK Amplitude Shift Keying Frequency Shift Keying (ASK) (FSK) Very simple. Needs larger bandwidth. Low bandwidth More error resilience than requirements. AM. Very susceptible to interference  Phase Shift Keying (PSK) Baseband Data 1 0 0 1 BPSK modulated signal s1 s0 s0 s1 where s0 =-Acos(ct) and s1 =Acos(ct) Major drawback – rapid amplitude change between symbols due to phase discontinuity, which requires infinite bandwidth. Binary Phase Shift Keying (BPSK) demonstrates better performance than ASK and BFSK BPSK can be expanded to a M-ary scheme, employing multiple phases and amplitudes as different states  Phase Shift Keying In phase shift keying, the phase of the carrier is varied to represent two or more different signal elements (Both peak amplitude and frequency remain constant). In binary PSK, we have only two signal elements: one with a phase of 0°, and the other with a phase of 180°. 34  Bandwidth of Binary PSK PSK is less susceptible to noise than ASK. PSK is superior to FSK because we do not need two carrier signals. The implementation of BPSK :  the signal element with phase 180° can be seen as the complement of the signal element with phase 0°. 35  Digital Modulation Summary Amplitude Shift Frequency Shift Phase Shift Keying Keying (ASK) Keying (FSK) (PSK) Very simple. Needs larger More complex. bandwidth. Low bandwidth More error Robust against requirements resilience than AM. interference. Very susceptible to interference 36 Digital Modulation Summary 37  Multiplexing Multiplexing is a modulation method that improves channel bandwidth utilization. For example, a co-axial cable has a bandwidth of 100's of Mhz. Baseband speech is only a few kHz  1) Frequency Division Multiplexing FDM This allows several 'messages' to be translated from baseband, where they are all in the same frequency band, to adjacent but non overlapping parts of the spectrum. An example of FDM is broadcast radio (long wave LW, medium wave MW, etc.)  2) Time Division Multiplexing TDM TDM is another form of multiplexing based on sampling which is a modulation technique. In TDM, samples of several analogue message symbols, each one sampled in turn, are transmitted in a sequence, i.e. the samples occupy adjacent time slots.  Radio Transmission Aerial dimensions are of the same order as the wavelength, , of the signal (e.g. quarter wave /4, /2 dipoles).  is related to frequency by c where c is the velocity of an electromagnetic wave, and c = λ= f 3x108 m/sec in free space. 3 x10 8 For baseband speech, with a signal at 3kHz, (3x103Hz) λ= = 105 metres or 100km. 3 x10 3 Aerials of this size are impractical although some transmissions at Very Low Frequency (VLF) for specialist applications are made. A modulation process described as 'up-conversion' (similar to FDM) allows the baseband signal to be translated to higher 'radio' frequencies. Generally 'low' radio frequencies 'bounce' off the ionosphere and travel long distances around the earth, high radio frequencies penetrate the ionosphere and make space communications possible. The ability to 'up convert' baseband signals has implications on aerial dimensions and design, long distance terrestrial communications, space communications and satellite communications. Background 'radio' noise is also an important factor to be considered. In a similar content, optical (fibre optic) communications is made possible by a modulation process in which an optical light source is modulated by an information source.  Networks A baseband system which is essentially point-to-point could be operated in a network. Some forms of access control (multiplexing) would be desirable otherwise the performance would be limited. Analogue communications networks have been in existence for a long time, for example speech radio networks for ambulance, fire brigade, police authorities etc. For example, 'digital speech' communications, in which the analogue speech signal is converted to a digital signal via an analogue-to-digital converter give a form more convenient for transmission and processing.  What is Modulation? In modulation, a message signal, which contains the information is used to control the parameters of a carrier signal, so as to impress the information onto the carrier. The Messages The message or modulating signal may be either: analogue – denoted by m(t) digital – denoted by d(t) – i.e. sequences of 1's and 0's The message signal could also be a multilevel signal, rather than binary; this is not considered further at this stage. The Carrier The carrier could be a 'sine wave' or a 'pulse train'. Consider a 'sine wave' carrier: vc (t ) = Vc cos(ωc t + φc ) If the message signal m(t) controls amplitude – gives AMPLITUDE MODULATION AM If the message signal m(t) controls frequency – gives FREQUENCY MODULATION FM If the message signal m(t) controls phase- gives PHASE MODULATION PM or M  Considering now a digital message d(t): If the message d(t) controls amplitude – gives AMPLITUDE SHIFT KEYING ASK. As a special case it also gives a form of Phase Shift Keying (PSK) called PHASE REVERSAL KEYING PRK. If the message d(t) controls frequency – gives FREQUENCY SHIFT KEYING FSK. If the message d(t) controls phase – gives PHASE SHIFT KEYING PSK. In this discussion, d(t) is a binary or 2 level signal representing 1's and 0's The types of modulation produced, i.e. ASK, FSK and PSK are sometimes described as binary or 2 level, e.g. Binary FSK, BFSK, BPSK, etc. or 2 level FSK, 2FSK, 2PSK etc. Thus there are 3 main types of Digital Modulation: ASK, FSK, PSK.  Multi-Level Message Signals As has been noted, the message signal need not be either analogue (continuous) or binary, 2 level. A message signal could be multi-level or m levels where each level would represent a discrete pattern of 'information' bits. For example, m = 4 levels  In general n bits per codeword will give 2n = m different patterns or levels. Such signals are often called m-ary (compare with binary). Thus, with m = 4 levels applied to: Amplitude gives 4ASK or m-ary ASK Frequency gives 4FSK or m-ary FSK Phase gives 4PSK or m-ary PSK 4 level PSK is also called QPSK (Quadrature Phase Shift Keying).  Consider Now A Pulse Train Carrier pt E ,0 t where p t 0, t T E 2E n and p t sinc cos n T T n 1 2 The 3 parameters in the case are: Pulse Amplitude E Pulse width vt Pulse position T Hence: If m(t) controls E – gives PULSE AMPLITUDE MODULATION PAM If m(t) controls t - gives PULSE WIDTH MODULATION PWM If m(t) controls T - gives PULSE POSITION MODULATION PPM In principle, a digital message d(t) could be applied but this will not be considered further.  What is Demodulation? Demodulation is the reverse process (to modulation) to recover the message signal m(t) or d(t) at the receiver. Summary of Modulation Techniques 1 Summary of Modulation Techniques 2 Summary of Modulation Techniques with some Derivatives and Familiar Applications Summary of Modulation Techniques with some Derivatives and Familiar Applications Summary of Modulation Techniques with some Derivatives and Familiar Applications 2  FURTHER ON ANALOGUE MODULATION Modulation Types AM, FM, PAM Modulation Types AM, FM, PAM 2 Modulation Types (Binary ASK, FSK, PSK) Modulation Types (Binary ASK, FSK, PSK) 2 Modulation Types – 4 Level ASK, FSK, PSK Modulation Types – 4 Level ASK, FSK, PSK 2  Analogue Modulation – Amplitude Modulation Consider a 'sine wave' carrier. vc(t) = Vc cos(ct), peak amplitude = Vc, carrier frequency c radians per second. Since c = 2fc, frequency = fc Hz where fc = 1/T. Amplitude Modulation AM In AM, the modulating signal (the message signal) m(t) is 'impressed' on to the amplitude of the carrier.  Message Signal m(t) In general m(t) will be a band of signals, for example speech or video signals. A notation or convention to show baseband signals for m(t) is shown below  Message Signal m(t) In general m(t) will be band limited. Consider for example, speech via a microphone. The envelope of the spectrum would be like:  Message Signal m(t) In order to make the analysis and indeed the testing of AM systems easier, it is common to make m(t) a test signal, i.e. a signal with a constant amplitude and frequency given by mt V m cos m t  Schematic Diagram for Amplitude Modulation VDC is a variable voltage, which can be set between 0 Volts and +V Volts. This schematic diagram is very useful; from this all the important properties of AM and various forms of AM may be derived.  Equations for AM From the diagram v s (t ) = (VDC + m(t ))cos(ωc t ) where VDC is the DC voltage that can be varied. The equation is in the form Amp cos ct and we may 'see' that the amplitude is a function of m(t) and VDC. Expanding the equation we get: v s (t ) = VDC cos(ωc t )+ m(t )cos(ωc t )  Equations for AM Now let m(t) = Vm cos mt, i.e. a 'test' signal, v s (t ) = VDC cos(ωc t )+Vm cos(ωm t )cos(ωc t ) Using the trig identity cosAcosB = 1 cos( A + B )+ cos( A − B ) 2 Vm V we have v s (t ) = VDC cos(ωc t )+ cos((ωc + ωm )t )+ m cos((ωc − ωm )t ) 2 2 Components: Carrier upper sideband USB lower sideband LSB Amplitude: VDC Vm/2 Vm/2 Frequency: c c + m c – m fc fc + fm f c + fm This equation represents Double Amplitude Modulation – DSBAM  Spectrum and Waveforms The following diagrams represent the spectrum of the input signals, namely (VDC + m(t)), with m(t) = Vm cos mt, and the carrier cos ct and corresponding waveforms.  Spectrum and Waveforms The above are input signals. The diagram below shows the spectrum and corresponding waveform of the output signal, given by Vm Vm vs t V DC cos c t cos c m t cos c m t 2 2  Double Sideband AM, DSBAM The component at the output at the carrier frequency fc is shown as a broken line with amplitude VDC to show that the amplitude depends on VDC. The structure of the waveform will now be considered in a little more detail. Waveforms Consider again the diagram VDC is a variable DC offset added to the message; m(t) = Vm cos mt  Double Sideband AM, DSBAM This is multiplied by a carrier, cos ct. We effectively multiply (VDC + m(t)) waveform by +1, -1, +1, -1,... The product gives the output signal vs t V DC m t cos c t Double Sideband AM, DSBAM  Modulation Depth Consider again the equation v s (t ) = (VDC + Vm cos(ωm t ))cos(ωc t ) , which may be written as   v s (t ) = VDC 1+ cos(ωm t )cos(ωc t ) Vm   VDC  The ratio is Vm Vm defined as the modulation depth, m, i.e. Modulation Depth m = VDC VDC From an oscilloscope display the modulation depth for Double Sideband AM may be determined as follows: Vm VDC 2Emax 2Emin  Modulation Depth 2 2Emax = maximum peak-to-peak of waveform 2Emin = minimum peak-to-peak of waveform 2 Emax − 2 Emin Modulation Depth m = 2 Emax + 2 Emin Vm This may be shown to equal as follows: VDC 2 Emax 2 V DC V m 2 Emin 2 V DC V m 2VDC + 2Vm − 2VDC + 2Vm 4Vm Vm m= = = 2VDC + 2Vm + 2VDC − 2Vm 4VDC VDC Double Sideband Modulation 'Types' There are 3 main types of DSB Double Sideband Amplitude Modulation, DSBAM – with carrier Double Sideband Diminished (Pilot) Carrier, DSB Dim C Double Sideband Suppressed Carrier, DSBSC The type of modulation is determined by the modulation depth, which for a fixed m(t) depends on the DC offset, VDC. Note, when a modulator is set up, VDC is fixed at a particular value. In the following illustrations we will have a fixed message, Vm cos mt and vary VDC to obtain different types of Double Sideband modulation. Graphical Representation of Modulation Depth and Modulation Types. Graphical Representation of Modulation Depth and Modulation Types 2.  Graphical Representation of Modulation Depth and Modulation Types 3 Note then that VDC may be set to give the modulation depth and modulation type. DSBAM VDC >> Vm, m  1 DSB Dim C 0 < VDC < Vm, m > 1 (1 < m < ) DSBSC VDC = 0, m =  The spectrum for the 3 main types of amplitude modulation are summarised  Bandwidth Requirement for DSBAM In general, the message signal m(t) will not be a single 'sine' wave, but a band of frequencies extending up to B Hz as shown Remember – the 'shape' is used for convenience to distinguish low frequencies from high frequencies in the baseband signal.  Bandwidth Requirement for DSBAM Amplitude Modulation is a linear process, hence the principle of superposition applies. The output spectrum may be found by considering each component cosine wave in m(t) separately and summing at the output. Note: Frequency inversion of the LSB the modulation process has effectively shifted or frequency translated the baseband m(t) message signal to USB and LSB signals centred on the carrier frequency fc the USB is a frequency shifted replica of m(t) the LSB is a frequency inverted/shifted replica of m(t) both sidebands each contain the same message information, hence either the LSB or USB could be removed (because they both contain the same information) the bandwidth of the DSB signal is 2B Hz, i.e. twice the highest frequency in the baseband signal, m(t) The process of multiplying (or mixing) to give frequency translation (or up-conversion) forms the basis of radio transmitters and frequency division multiplexing which will be discussed later.  Power Considerations in DSBAM 2  V pk  Remembering that Normalised Average Power = (VRMS)2 =    2 we may tabulate for AM components as follows: vs (t ) = VDC cos(ωc t )+ m cos((ωc + ωm )t )+ m cos((ωc − ωm )t ) V V 2 2 Component Carrier USB LSB Amplitude pk VDC Vm Vm 2 2 Power 2 2 2  Vm  Vm  Vm  2 2 VDC Vm Total Power PT =   =   = 2 2 2 8 2 2 8 Carrier Power Pc Power + PUSB 2 VDC 2 2 m VDC 2 m 2VDC + PLSB 2 8 8  Power Considerations in DSBAM From this we may write two equivalent equations for the total power PT, in a DSBAM signal 2 2 2 2 2 2 2 2 V V V V V VDC m 2VDC m 2VDC PT = DC + m + m = DC + m and PT = + + 2 8 8 2 4 2 8 8 2 m2 m2  m2  The carrier power Pc = V DC i.e. PT = Pc + Pc + Pc or PT = Pc 1+  2 4 4  2  Either of these forms may be useful. Since both USB and LSB contain the same information a useful ratio which shows the proportion of 'useful' power to total power is m2 Pc PUSB 4 m2 = = PT  m2  4 + 2m 2 Pc 1 +   2   Power Considerations in DSBAM For DSBAM (m  1), allowing for m(t) with a dynamic range, the average value of m may be assumed to be m = 0.3 Hence, m2 = (0.3) = 0.0215 2 4 + 2m 2 4 + 2(0.3)2 Hence, on average only about 2.15% of the total power transmitted may be regarded as 'useful' power. ( 95.7% of the total power is in the carrier!) m2 1 Even for a maximum modulation depth of m = 1 for DSBAM the ratio = 4 + 2m 2 6 i.e. only 1/6th of the total power is 'useful' power (with 2/3 of the total power in the carrier).  Example Suppose you have a portable (for example you carry it in your ' back pack') DSBAM transmitter which needs to transmit an average power of 10 Watts in each sideband when modulation depth m = 0.3. Assume that the transmitter is powered by a 12 Volt battery. The total power will be m2 m2 PT = Pc + Pc + Pc 4 4 m2 4(10 ) 40 where Pc = 10 Watts, i.e. Pc = = = 444.44 Watts 4 m 2 (0.3)2 Hence, total power PT = 444.44 + 10 + 10 = 464.44 Watts. Hence, battery current (assuming ideal transmitter) = Power / Volts = 464.44 amps! 12 i.e. a large and heavy 12 Volt battery. Suppose we could remove one sideband and the carrier, power transmitted would be 10 Watts, i.e. 0.833 amps from a 12 Volt battery, which is more reasonable for a portable radio transmitter.  Single Sideband Amplitude Modulation One method to produce signal sideband (SSB) amplitude modulation is to produce DSBAM, and pass the DSBAM signal through a band pass filter, usually called a single sideband filter, which passes one of the sidebands as illustrated in the diagram below. The type of SSB may be SSBAM (with a 'large' carrier component), SSBDimC or SSBSC depending on VDC at the input. A sequence of spectral diagrams are shown on the next page. Single Sideband Amplitude Modulation  Single Sideband Amplitude Modulation Note that the bandwidth of the SSB signal B Hz is half of the DSB signal bandwidth. Note also that an ideal SSB filter response is shown. In practice the filter will not be ideal as illustrated. As shown, with practical filters some part of the rejected sideband (the LSB in this case) will be present in the SSB signal. A method which eases the problem is to produce SSBSC from DSBSC and then add the carrier to the SSB signal. Single Sideband Amplitude Modulation  Single Sideband Amplitude Modulation with m(t) = Vm cos mt, we may write: vs (t ) = VDC cos(ωc t )+ cos((ωc + ωm )t )+ m cos((ωc − ωm )t ) Vm V 2 2 The SSB filter removes the LSB (say) and the output is Vm vs (t ) = VDC cos(ωc t )+ cos((ωc + ωm )t ) 2 Again, note that the output may be For SSBSC, output signal = SSBAM, VDC large V SSBDimC, VDC small v s (t ) = m cos((ωc + ωm )t ) SSBSC, VDC = 0 2  Power in SSB  m2  From previous discussion, the total power in the DSB signal is PT = Pc 1+  2 2  2  m m = PT = Pc + Pc + Pc for DSBAM. 4 4 Hence, if Pc and m are known, the carrier power and power in one sideband may be determined. Alternatively, since SSB signal = Vm vs (t ) = VDC cos(ωc t )+ cos((ωc + ωm )t ) 2 then the power in SSB signal (Normalised Average Power) is 2  V  2 2 2 V V V PSSB = DC +  m  = DC + m 2 2 2 2 8 2 2 VDC V Power in SSB signal = + m 2 8  Demodulation of Amplitude Modulated Signals There are 2 main methods of AM Demodulation: Envelope or non-coherent Detection/Demodulation. Synchronised or coherent Demodulation.  Envelope or Non-Coherent Detection An envelope detector for AM is shown below: This is obviously simple, low cost. But the AM input must be DSBAM with m 1, the distortion below occurs  Small Signal Operation – Square Law Detector For small AM signals (~ millivolts) demodulation depends on the diode square law characteristic. The diode characteristic is of the form i(t) = av + bv2 + cv3 +..., where v = (VDC + m(t ))cos(ωc t ) i.e. DSBAM signal.  Small Signal Operation – Square Law Detector a(VDC + m(t ))cos(ωc t )+ b((VDC + m(t ))cos(ωc t )) +... 2 i.e. ( 2 2 2 ) = aVDC + am(t )cos(ωc t )+ b VDC + 2VDC m(t )+ m(t ) cos (ωc t )+... ( ) 12 = aVDC + am(t )cos(ωc t )+ bV DC + 2bV DC m(t )+ bm (t )  + cos(2ωc t ) 2 2 1   2  2bV DC m(t ) bm (t )2 2 2 = aV DC + am (t )cos(ωc t ) + bV DC + + + b VDC cos(2ωc t )+... 2 2 2 2 'LPF' removes components. 2 + bV DC m(t ) i.e. the output contains m(t) bV DC Signal out = aVDC + 2  Synchronous or Coherent Demodulation A synchronous demodulator is shown below This is relatively more complex and more expensive. The Local Oscillator (LO) must be synchronised or coherent, i.e. at the same frequency and in phase with the carrier in the AM input signal. This additional requirement adds to the complexity and the cost. However, the AM input may be any form of AM, i.e. DSBAM, DSBDimC, DSBSC or SSBAM, SSBDimC, SSBSC. (Note – this is a 'universal' AM demodulator and the process is similar to correlation – the LPF is similar to an integrator).  Synchronous or Coherent Demodulation If the AM input contains a small or large component at the carrier frequency, the LO may be derived from the AM input as shown below.  Synchronous (Coherent) Local Oscillator If we assume zero path delay between the modulator and demodulator, then the ideal LO signal is cos(ct). Note – in general the will be a path delay, say , and the LO would then be cos(c(t – ), i.e. the LO is synchronous with the carrier implicit in the received signal. Hence for an ideal system with zero path delay Analysing this for a DSBAM input = (VDC + m(t ))cos(ωc t ) Synchronous (Coherent) Local Oscillator VX = AM input x LO = (VDC + m(t ))cos2 (ωc t ) = (VDC + m(t ))cos(ωc t )  cos(ωc t ) = (VDC + m(t )) 1 + 1 cos(2ωc t ) 2 2  VDC VDC m(t ) m(t ) Vx = + cos(2ωc t )+ + cos(2ωc t ) 2 2 2 2 We will now examine the signal spectra from 'modulator to Vx' Synchronous (Coherent) Local Oscillator (continued on next page)  Synchronous (Coherent) Local Oscillator and Note – the AM input has been 'split into two' – 'half' has moved or shifted up to  m(t )  V m(t ) 2 fc  cos(2ωc t )+ VDC cos(2ωc t ) and half shifted down to baseband, DC and  2  2 2  Synchronous (Coherent) Local Oscillator The LPF with a cut-off frequency  fc will pass only the baseband signal i.e. VDC m(t ) Vout = + 2 2 In general the LO may have a frequency offset, , and/or a phase offset, , i.e. The AM input is essentially either: DSB (DSBAM, DSBDimC, DSBSC) SSB (SSBAM, SSBDimC, SSBSC)  1. Double Sideband (DSB) AM Inputs The equation for DSB is (VDC + m(t ))cos(ωc t ) where VDC allows full carrier (DSBAM), diminished carrier or suppressed carrier to be set. Hence, Vx = AM Input x LO V x = (VDC + m(t ))cos(ωc t ).cos((ωc + Δω )t + Δφ ) Since cosAcosB = 1 cos( A + B )+ cos( A − B ) 2 Vx = (VDC + m(t )) cos((ω + ωc + Δω )t + Δφ )+ cos((ωc + Δω )t + Δφ − ωc t ) c 2 V m(t )  Vx =  DC + cos((2ωc + Δω )t + Δφ )+ cos( Δωt + Δφ )  2 2  VDC V Vx = cos((2ωc + Δω )t + Δφ )+ DC cos( Δωt + Δφ ) 2 2 m(t ) m(t ) + cos((2ωc + Δω )t + Δφ )+ cos( Δωt + Δφ ) 2 2  1. Double Sideband (DSB) AM Inputs The LPF with a cut-off frequency  fc Hz will remove the components at 2c (i.e. components above c) and hence m(t ) cos(ωt + φ) VDC Vout = cos(t + φ) + 2 2 VDC m(t ) Obviously, if Δω = 0 and Δφ= 0 we have, as previously Vout = + 2 2 Consider now if  is equivalent to a few Hz offset from the ideal LO. We may then say V m(t ) Vout = DC cos( Δωt )+ cos( Δωt ) 2 2 The output, if speech and processed by the human brain may be intelligible, but would include a low frequency 'buzz' at , and the message amplitude would fluctuate. The requirement  = 0 is necessary for DSBAM.  1. Double Sideband (DSB) AM Inputs Consider now if  is equivalent to a few Hz offset from the ideal LO. We may then say V m(t ) Vout = DC cos( Δωt )+ cos( Δωt ) 2 2 The output, if speech and processed by the human brain may be intelligible, but would include a low frequency 'buzz' at , and the message amplitude would fluctuate. The requirement  = 0 is necessary for DSBAM. Consider now that  = 0 but   0, i.e. the frequency is correct at c but there is a phase offset. Now we have VDC m(t ) Vout = cos( Δφ )+ cos( Δφ ) 2 2 'cos()' causes fading (i.e. amplitude reduction) of the output.  1. Double Sideband (DSB) AM Inputs The 'VDC' component is not important, but consider for m(t), π π m(t )  π  if Δφ = (90 ), cos  = 0 i.e. Vout = 0 cos  = 0 2   2 2 2 π m(t ) if Δφ = (1800), cos(π ) = −1 i.e. Vout = cos(π ) = −m(t ) 2 2 The phase inversion if  =  may not be a problem for speech or music, but it may be a problem if this type of modulator is used to demodulate PRK π However, the major problem is that as  increases towards the signal strength 2 π output gets weaker (fades) and at the output is zero 2  1. Double Sideband (DSB) AM Inputs If the phase offset varies with time, then the signal fades in and out. The variation of amplitude of the output, with phase offset  is illustrated below Thus the requirement for  = 0 and  = 0 is a 'strong' requirement for DSB amplitude modulation.  2. Single Sideband (SSB) AM Input The equation for SSB with a carrier depending on VDC is Vm VDC cos(ωc t )+ cos(ωc + ωm t ) 2 i.e. assuming m(t ) = Vm cos(ωm t )   Vx = VDC cos(ωc t )+ cos(ωc + ωm )t cos((ωc +  )t + Δφ) Hence Vm  2  cos((2ωc + Δω )t + Δφ )+ DC cos( Δωt + Δφ ) = VDC V 2 2 + m cos((2ωc + ωm + Δω )t + Δφ )+ m cos((ωm − Δω )t − Δφ ) V V 4 4  2. Single Sideband (SSB) AM Input The LPF removes the 2c components and hence cos( Δωt + Δφ )+ cos((ωm − Δω )t − Δφ ) VDC Vm 2 4 VDC Vm Note, if  = 0 and  = 0, + cos(ωm t ) ,i.e. m(t ) = Vm cos(ωmt ) has been 2 4 recovered. Consider first that   0, e.g. an offset of say 50Hz. Then cos( Δωt )+ m cos((ωm − Δω )t ) VDC V Vout = 2 4 If m(t) is a signal at say 1kHz, the output contains a signal a 50Hz, depending on VDC and the 1kHz signal is shifted to 1000Hz - 50Hz = 950Hz.  2. Single Sideband (SSB) AM Input The spectrum for Vout with  offset is shown Hence, the effect of the offset  is to shift the baseband output, up or down, by . For speech, this shift is not serious (for example if we receive a 'whistle' at 1kHz and the offset is 50Hz, you hear the whistle at 950Hz ( = +ve) which is not very noticeable. Hence, small frequency offsets in SSB for speech may be tolerated. Consider now that  = 0,  = 0, then VDC V Vout = cos( Δφ )+ m cos(ωm t − Δφ ) 2 4  2. Single Sideband (SSB) AM Input This indicates a fading VDC and a phase shift in the output. If the variation in  with time is relatively slow, thus phase shift variation of the output is not serious for speech. Hence, for SSB small frequency and phase variations in the LO are tolerable. The requirement for a coherent LO is not as a stringent as for DSB. For this reason, SSBSC (suppressed carrier) is widely used since the receiver is relatively more simple than for DSB and power and bandwidth requirements are reduced.  Comments In terms of 'evolution', early radio schemes and radio on long wave (LW) and medium wave (MW) to this day use DSBAM with m < 1. The reason for this was the reduced complexity and cost of 'millions' of receivers compared to the extra cost and power requirements of a few large LW/MW transmitters for broadcast radio, i.e. simple envelope detectors only are required. Nowadays, with modern integrated circuits, the cost and complexity of synchronous demodulators is much reduced especially compared to the additional features such as synthesised LO, display, FM etc. available in modern receivers. Amplitude Modulation forms the basis for: Digital Modulation – Amplitude Shift Keying ASK Digital Modulation – Phase Reversal Keying PRK Multiplexing – Frequency Division Multiplexing FDM Up conversion – Radio transmitters Down conversion – Radio receivers