DIGITAL Counications Contents Introduction to Counication Systes Analogue Modulation AM, DSBSC, SB, SSB, FM, PM, Narrow band FM, PLL Deodulators, and FLL Loops Sapling Systes Tie and Frequency Division ultiplexing systes, Nyquist Principle, PAM, PPM, and PWM. Principles of Noise Rando variables, White Noise, Shot, Theral and Flicker Noise, Noise in cascade aplifiers Pulse Code Modulation PCM and its derivatives, Quantising Noise, and Exaples Digital Counication Techniques ASK, FSK, PSK, QPSK, QAM, and M-ary QAM. Case Studies Spread Spectru Systes, Mobile radio concepts, GSM and Multiple Access Schees Mobile radio
Recoended Text Books An introduction to Analogue and Digital counication, Haykin (Wiley) Counication Systes, Carlson (McGraw & Hill) Inforation, Transission, Modulation and Noise, Schwartz (McGraw & Hill) Analogue and Digital Counication Systes, Raden (Prentice- Hall) Counication Systes, Haykin (Wiley) Electronic Counication Techniques, Young (Merril-Publ)
Introduction to Modulation and Deodulation The purpose of a counication syste is to transfer inforation fro a source to a destination. In practice, probles arise in baseband transissions, the ajor cases being: Noise in the syste 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 syste is not able to fully utilise the available bandwidth, for exaple telephone quality speech has a bandwidth 3kHz, a co-axial cable has a bandwidth of 100's of Mhz. Radio systes operating at baseband frequencies are very difficult. Not easy to network.
Multiplexing Multiplexing is a odulation ethod which iproves channel bandwidth utilisation. For exaple, a co-axial cable has a bandwidth of 100's of Mhz. Baseband speech is a only a few khz
1) Frequency Division Multiplexing FDM This allows several 'essages' to be translated fro baseband, where they are all in the sae frequency band, to adjacent but non overlapping parts of the spectru. An exaple of FDM is broadcast radio (long wave LW, ediu wave MW, etc.)
) Tie Division Multiplexing TDM TDM is another for of ultiplexing based on sapling which is a odulation technique. In TDM, saples of several analogue essage sybols, each one sapled in turn, are transitted in a sequence, i.e. the saples occupy adjacent tie slots.
Radio Transission Aerial diensions are of the sae order as the wavelength, λ, of the signal (e.g. quarter wave λ/4, λ/ dipoles). λ is related to frequency by For baseband speech, with a signal at 3kHz, (3x10 3 Hz) c f T λ = where c is the velocity of an electroagnetic wave, and c = 3x10 8 /sec in free space. 3x10 λ = 3x10 8 This iage 3 = 10 5 etres or 100k. Aerials of this size are ipractical although soe transissions at ery Low Frequency (LF) for specialist applications are ade. A odulation process described as 'up-conversion' (siilar 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 ake space counications possible. The ability to 'up convert' baseband signals has iplications on aerial diensions and design, long distance terrestrial counications, space counications and satellite counications. Background 'radio' noise is also an iportant factor to be considered. In a siilar content, optical (fibre optic) counications is ade possible by a odulation process in which an optical light source is odulated by an inforation source.
Networks A baseband syste which is essentially point-to-point could be operated in a network. Soe fors of access control (ultiplexing) would be desirable otherwise the perforance would be liited. Analogue counications networks have been in existence for a long tie, for exaple speech radio networks for abulance, fire brigade, police authorities etc. For exaple, 'digital speech' counications, in which the analogue speech signal is converted to a digital signal via an analogue-to-digital converter give a for ore convenient for transission and processing.
What is Modulation? In odulation, a essage signal, which contains the inforation is used to control the paraeters of a carrier signal, so as to ipress the inforation onto the carrier. The Messages The essage or odulating signal ay be either: analogue denoted by (t) digital denoted by d(t) i.e. sequences of 1's and 0's The essage signal could also be a ultilevel 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: v ( t) = cos( ω t + φ ) c c c If the essage signal (t) controls aplitude gives AMPLITUDE MODULATION AM If the essage signal (t) controls frequency gives FREQUENCY MODULATION FM If the essage signal (t) controls phase- gives PHASE MODULATION PM or φm c
Considering now a digital essage d(t): If the essage d(t) controls aplitude gives AMPLITUDE SHIFT KEYING ASK. As a special case it also gives a for of Phase Shift Keying (PSK) called PHASE REERSAL KEYING PRK. If the essage d(t) controls frequency gives FREQUENCY SHIFT KEYING FSK. If the essage d(t) controls phase gives PHASE SHIFT KEYING PSK. In this discussion, d(t) is a binary or level signal representing 1's and 0's The types of odulation produced, i.e. ASK, FSK and PSK are soeties described as binary or level, e.g. Binary FSK, BFSK, BPSK, etc. or level FSK, FSK, PSK etc. Thus there are 3 ain types of Digital Modulation: ASK, FSK, PSK.
Multi-Level Message Signals As has been noted, the essage signal need not be either analogue (continuous) or binary, level. A essage signal could be ulti-level or levels where each level would represent a discrete pattern of 'inforation' bits. For exaple, = 4 levels
In general n bits per codeword will give n = different patterns or levels. Such signals are often called -ary (copare with binary). Thus, with = 4 levels applied to: Aplitude gives 4ASK or -ary ASK Frequency gives 4FSK or -ary FSK Phase gives 4PSK or -ary PSK 4 level PSK is also called QPSK (Quadrature Phase Shift Keying).
Consider Now A Pulse Train Carrier where and p p p ( t) = E, 0 < t < τ This iage cannot currently ( t) = 0, τ < t < T Eτ Eτ nωω ( ) t = + sinc cos( nωω) T T n= 1 The 3 paraeters in the case are: Pulse Aplitude E Pulse width vt Pulse position T Hence: If (t) controls E gives PULSE AMPLITUDE MODULATION PAM If (t) controls t - gives PULSE WIDTH MODULATION PWM If (t) controls T - gives PULSE POSITION MODULATION PPM In principle, a digital essage d(t) could be applied but this will not be considered further.
What is Deodulation? Deodulation is the reverse process (to odulation) to recover the essage signal (t) or d(t) at the receiver.
Suary of Modulation Techniques 1
Suary of Modulation Techniques
Suary of Modulation Techniques with soe Derivatives and Failiar Applications
Suary of Modulation Techniques with soe Derivatives and Failiar Applications
Suary of Modulation Techniques with soe Derivatives and Failiar Applications
Modulation Types AM, FM, PAM
Modulation Types AM, FM, PAM
Modulation Types (Binary ASK, FSK, PSK)
Modulation Types (Binary ASK, FSK, PSK)
Modulation Types 4 Level ASK, FSK, PSK
Modulation Types 4 Level ASK, FSK, PSK
Analogue Modulation Aplitude Modulation Consider a 'sine wave' carrier. This iage cannot currently be displayed. v c (t) = c cos(ω c t), peak aplitude = c, carrier frequency ω c radians per second. Since ω c = πf c, frequency = f c Hz where f c = 1/T. Aplitude Modulation AM In AM, the odulating signal (the essage signal) (t) is 'ipressed' on to the aplitude of the carrier.
Message Signal (t) In general (t) will be a band of signals, for exaple speech or video signals. A notation or convention to show baseband signals for (t) is shown below
Message Signal (t) In general (t) will be band liited. Consider for exaple, speech via a icrophone. The envelope of the spectru would be like:
Message Signal (t) In order to ake the analysis and indeed the testing of AM systes easier, it is coon to ake (t) a test signal, i.e. a signal with a constant aplitude and frequency given by This t iage cannot currently cos t
Scheatic Diagra for Aplitude Modulation DC is a variable voltage, which can be set between 0 olts and + olts. This scheatic diagra is very useful;; fro this all the iportant properties of AM and various fors of AM ay be derived.
Equations for AM v ( t) = ( +( t) ) cos( ω t) Fro the diagra This iage cannot currently be s DC c where DC is the DC voltage that can be varied. The equation is in the for Ap cos ω c t and we ay 'see' that the aplitude is a function of (t) and DC. Expanding the equation we get: v ( This ) iage cannot ( currently ) be ( displayed. s t =DCcos ωct + t) cos( ωct)
Equations for AM Now let (t) = cos ω t, i.e. a 'test' signal, Using the trig identity we have v 1 cosacosb = = DCcos ωct + cos v ( This ) iage cannot ( currently ) be displayed. s t =DCcos ωct +cos( ωt) cos( ωct) [ cos( A+ B) + cos( A B) ] s ( t) ( ) ( ωc +ω ) ( t) + cos( ( ω ω ) t) Coponents: Carrier upper sideband USB lower sideband LSB Aplitude: DC / / c Frequency: ω c ω c + ω ω c ω f c f c + f f c + f This equation represents Double Aplitude Modulation DSBAM
Spectru and Wavefors The following diagras represent the spectru of the input signals, naely ( DC + (t)), with (t) = cos ω t, and the carrier cos ω c t and corresponding wavefors.
Spectru and Wavefors The above are input signals. The diagra below shows the spectru and corresponding wavefor of the output signal, given by v s t DC cos c t cos c t cos c t
Double Sideband AM, DSBAM The coponent at the output at the carrier frequency f c is shown as a broken line with aplitude DC to show that the aplitude depends on DC. The structure of the wavefor will now be considered in a little ore detail. Wavefors Consider again the diagra DC is a variable DC offset added to the essage;; (t) = cos ω t
Double Sideband AM, DSBAM This is ultiplied by a carrier, cos ω c t. We effectively ultiply ( DC + (t)) wavefor by +1, -1, +1, -1,... The product gives the output signal v s t DC t cos ct
Double Sideband AM, DSBAM
Modulation Depth Consider again the equation The ratio is T h DC v s v s ( t) = ( + cos ( ω t) ) cos( ω t) DC =DC 1+ cos ωt DC ( t) ( ) cos( ω t) c, which ay be written as defined as the odulation depth,, i.e. Modulation Depth Fro an oscilloscope display the odulation depth for Double Sideband AM ay be deterined as follows: c = This iage DC DC E ax E in
Modulation Depth E ax = axiu peak-to-peak of wavefor E in = iniu peak-to-peak of wavefor Modulation Depth This ay be shown to equal T h DC = E E This iage cannot currently ax be displayed. in E ax as follows: + E in EThis iage cannot currently be This iage cannot currently ax DC E in DC = DC DC DC + + + DC + 4 This ia T h ge i DC DC = = 4
Double Sideband Modulation 'Types' There are 3 ain types of DSB Double Sideband Aplitude Modulation, DSBAM with carrier Double Sideband Diinished (Pilot) Carrier, DSB Di C Double Sideband Suppressed Carrier, DSBSC The type of odulation is deterined by the odulation depth, which for a fixed (t) depends on the DC offset, DC. Note, when a odulator is set up, DC is fixed at a particular value. In the following illustrations we will have a fixed essage, cos ω t and vary DC to obtain different types of Double Sideband odulation.
Graphical Representation of Modulation Depth and Modulation Types.
Graphical Representation of Modulation Depth and Modulation Types.
Graphical Representation of Modulation Depth and Modulation Types 3 Note then that DC ay be set to give the odulation depth and odulation type. DSBAM DC >>, 1 DSB Di C 0 < DC <, > 1 (1 < < ) DSBSC DC = 0, = The spectru for the 3 ain types of aplitude odulation are suarised
Bandwidth Requireent for DSBAM In general, the essage signal (t) will not be a single 'sine' wave, but a band of frequencies extending up to B Hz as shown This iage cannot currently be displayed. Reeber the 'shape' is used for convenience to distinguish low frequencies fro high frequencies in the baseband signal.
Bandwidth Requireent for DSBAM Aplitude Modulation is a linear process, hence the principle of superposition applies. The output spectru ay be found by considering each coponent cosine wave in (t) separately and suing at the output. Note: Frequency inversion of the LSB the odulation process has effectively shifted or frequency translated the baseband (t) essage signal to USB and LSB signals centred on the carrier frequency f c the USB is a frequency shifted replica of (t) the LSB is a frequency inverted/shifted replica of (t) both sidebands each contain the sae essage inforation, hence either the LSB or USB could be reoved (because they both contain the sae inforation) the bandwidth of the DSB signal is B Hz, i.e. twice the highest frequency in the baseband signal, (t) The process of ultiplying (or ixing) to give frequency translation (or up-conversion) fors the basis of radio transitters and frequency division ultiplexing which will be discussed later.
Power Considerations in DSBAM Reebering that Noralised Average Power = ( RMS ) = we ay tabulate for AM coponents as follows: v This iage cannot currently be displayed. s ( t) =DCcos( ωct) + cos ( ωc +ω ) Coponent Carrier USB LSB This pk ia ( t) + cos( ( ω ω ) t) c Aplitude pk DC Power Power T DC hi T DC hi This iage cannot = DC This iage cannot 8 8 This iage cannot = This iage DC cannot 8 8 Total Power P T = Carrier Power P c + P USB + P LSB
Power Considerations in DSBAM Fro this we ay write two equivalent equations for the total power P T, in a DSBAM signal P T This iage cannot currently be displayed. DC DC = + 8 + 8 = + 4 and P T This iage cannot currently be displayed. DC DC DC = + 8 + 8 The carrier power P c This iage cannot DC = currently i.e. P T 4 This iage cannot currently be displayed. = Pc + Pc + Pc 4 or P T This iage cannot currently be displayed. = P 1 c + Either of these fors ay be useful. Since both USB and LSB contain the sae inforation a useful ratio which shows the proportion of 'useful' power to total power is P P Pc 4 Pc 1+ This iage cannot currently be displayed. USB T = = 4+
Power Considerations in DSBAM For DSBAM ( 1), allowing for (t) with a dynaic range, the average value of ay be assued to be = 0.3 Hence, ( ) ( 0.3) This iage cannot 0.3currently be displayed. = = 4+ 4+ 0.015 Hence, on average only about.15% of the total power transitted ay be regarded as 'useful' power. ( 95.7% of the total power is in the carrier!) Even for a axiu odulation depth of = 1 for DSBAM the ratio This iage cannot = 4+ 1 6 i.e. only 1/6th of the total power is 'useful' power (with /3 of the total power in the carrier).
Exaple Suppose you have a portable (for exaple you carry it in your ' back pack') DSBAM transitter which needs to transit an average power of 10 Watts in each sideband when odulation depth = 0.3. Assue that the transitter is powered by a 1 olt battery. The total power will be where P c Thi s 4 = 10 Watts, i.e. P 4 4( 10) 40 = 0.3 4 This iage cannot currently be displayed. T = Pc + Pc + Pc P c This iage cannot currently be displayed. = ( ) = 444.44 Watts Hence, total power P T = 444.44 + 10 + 10 = 464.44 Watts. Hence, battery current (assuing ideal transitter) = Power / olts = i.e. a large and heavy 1 olt battery. 464.44 This iag 1 aps! Suppose we could reove one sideband and the carrier, power transitted would be 10 Watts, i.e. 0.833 aps fro a 1 olt battery, which is ore reasonable for a portable radio transitter.
Single Sideband Aplitude Modulation One ethod to produce signal sideband (SSB) aplitude odulation 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 diagra below. The type of SSB ay be SSBAM (with a 'large' carrier coponent), SSBDiC or SSBSC depending on DC at the input. A sequence of spectral diagras are shown on the next page.
Single Sideband Aplitude Modulation
Single Sideband Aplitude 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 soe part of the rejected sideband (the LSB in this case) will be present in the SSB signal. A ethod which eases the proble is to produce SSBSC fro DSBSC and then add the carrier to the SSB signal.
Single Sideband Aplitude Modulation
Single Sideband Aplitude Modulation with (t) = cos ω t, we ay write: v s ( t) =DCcos( ωct) + cos ( ωc +ω ) The SSB filter reoves the LSB (say) and the output is Again, note that the output ay be SSBAM, DC large SSBDiC, DC sall SSBSC, DC = 0 v ( t) + cos( ( ω ω ) t) This iage cannot currently be displayed. s ( t) =DCcos( ωct) + cos ( ωc +ω ) ( t) c For SSBSC, output signal = v s ( t) (( ) ) This iage cannot currently be displayed. = cos ωc +ω t
Power in SSB Fro previous discussion, the total power in the DSB signal is P T This iage cannot = currently P be displayed. c 1+ This iage cannot currently be = PT = displayed. Pc + Pc + Pc for DSBAM. 4 4 Hence, if P c and are known, the carrier power and power in one sideband ay be deterined. Alternatively, since SSB signal = v s ( t) =DCcos( ωct) + cos ( ωc +ω ) ( t) then the power in SSB signal (Noralised Average Power) is P This iage cannot currently be displayed. DC DC SSB = + = + 8 Power in SSB signal = This iage DC cannot + 8
Deodulation of Aplitude Modulated Signals There are ain ethods of AM Deodulation: Envelope or non-coherent Detection/Deodulation. Synchronised or coherent Deodulation.
Envelope or Non-Coherent Detection An envelope detector for AM is shown below: This is obviously siple, low cost. But the AM input ust be DSBAM with << 1, i.e. it does not deodulate DSBDiC, DSBSC or SSBxx.
Large Signal Operation For large signal inputs, ( olts) the diode is switched i.e. forward biased ON, reverse biased OFF, and acts as a half wave rectifier. The 'RC' cobination acts as a 'soothing circuit' and the output is (t) plus 'distortion'. If the odulation depth is > 1, the distortion below occurs
Sall Signal Operation Square Law Detector For sall AM signals (~ illivolts) deodulation depends on the diode square law characteristic. The diode characteristic is of the for i(t) = av + bv + cv3 +..., where v = ( +( t) ) ( ω t) This iage cannot currently be DC cos c i.e. DSBAM signal.
Sall Signal Operation Square Law Detector i.e. = a a ( +( t ) cos( ω t) +b +( t) DC DC +a t cos ωct +b DC c ( ) cos( ω t ) +... DC ( ) cos ( ω t) +... ( ) ( ) + ( t) +( t) DC c c = = a a ( ) ( ω t) ( ) ( ) ( ) ( ) 1 DC +a t cos ωct + bdc + bdc t +b t + cos bdc DC +a( t) cos( ωct) + 'LPF' reoves coponents. b + DC ( ) b( t) t + 1 DC +b cos c ( ω t) +... c Signal out = a This iage cannot currently be bdc DC + +bdc displayed. ( t ) i.e. the output contains (t)
Synchronous or Coherent Deodulation A synchronous deodulator is shown below This is relatively ore coplex and ore expensive. The Local Oscillator (LO) ust be synchronised or coherent, i.e. at the sae frequency and in phase with the carrier in the AM input signal. This additional requireent adds to the coplexity and the cost. However, the AM input ay be any for of AM, i.e. DSBAM, DSBDiC, DSBSC or SSBAM, SSBDiC, SSBSC. (Note this is a 'universal' AM deodulator and the process is siilar to correlation the LPF is siilar to an integrator).
Synchronous or Coherent Deodulation If the AM input contains a sall or large coponent at the carrier frequency, the LO ay be derived fro the AM input as shown below.
Synchronous (Coherent) Local Oscillator If we assue zero path delay between the odulator and deodulator, then the ideal LO signal is cos(ω c t). Note in general the will be a path delay, say τ, and the LO would then be cos(ω c (t τ), i.e. the LO is synchronous with the carrier iplicit in the received signal. Hence for an ideal syste with zero path delay Analysing this for a DSBAM input = ( This iage ( cannot DC + t) ) cos( ωct)
Synchronous (Coherent) Local Oscillator X = AM input x LO = This iage cannot currently be ( + ( t) ) cos ( ω t) DC c = = ( This + iage ( cannot t) ) cos currently ( ω tbe ) displayed. cos( ω t) DC 1 1 This iage cannot currently be displayed. ( DC + ( t) ) + cos( ωct) c c ( ) ( t) This iage cannot currently be displayed. DC DC t x = + cos( ωct) + + cos ( ω t) c We will now exaine the signal spectra fro 'odulator to x'
Synchronous (Coherent) Local Oscillator (continued on next page)
Synchronous (Coherent) Local Oscillator and Note the AM input has been 'split into two' 'half' has oved or shifted up to ( ) This iage t cannot currently be displayed. fc cos( ωct) +DCcos( ωct) and half shifted down to baseband, DC T h and ( ) t T hi
Synchronous (Coherent) Local Oscillator The LPF with a cut-off frequency f c will pass only the baseband signal i.e. This iage cannot DC outcurrently = be + ( ) t In general the LO ay have a frequency offset, Δω, and/or a phase offset, Δφ, i.e. The AM input is essentially either: DSB SSB (DSBAM, DSBDiC, DSBSC) (SSBAM, SSBDiC, SSBSC)
1. Double Sideband (DSB) AM Inputs The equation for DSB is ( This iage ( cannot )) currently DC + t cos( ωct) diinished carrier or suppressed carrier to be set. Hence, x = AM Input x LO Since 1 cosacosb = = where DC allows full carrier (DSBAM), ( +( t) ) cos( ω t). cos( ( ω + Δω) t + Δφ) x DC c [ cos( A+ B) + cos( A B) ] ( +( t) ) [ (( + Δω) t + Δφ) + cos( ( ω + Δω) t + Δφ ω t) ] DC x = cos ωc +ωc x = t + ( ) DC cos ωc x = ( t) + cos This DC iage cannot currently be displayed. cos ωc + Δω t + Δφ [ (( + Δω) t + Δφ) + cos( Δωt + Δφ) ] DC (( ) ) + cos( Δωt+ Δφ) (( ω + Δω) t + Δφ) c ( t) + cos ( Δωt+ Δφ) c c c
1. Double Sideband (DSB) AM Inputs The LPF with a cut-off frequency f c Hz will reove the coponents at ω c (i.e. coponents above ω c ) and hence This iage cannot currently be displayed. ( t) out = DC cos( Δωt + Δφ) + cos ( Δωt + Δφ) This iage cannot Obviously, if Δω= 0 and Δφ This = 0 DC t we have, as previously outcurrently = be + Consider now if Δω is equivalent to a few Hz offset fro the ideal LO. We ay then say This iage DC cannot currently be displayed. ( ) ( t) out = cos Δωt + cos( Δωt) The output, if speech and processed by the huan brain ay be intelligible, but would include a low frequency 'buzz' at Δω, and the essage aplitude would fluctuate. The requireent Δω = 0 is necessary for DSBAM. ( )
1. Double Sideband (DSB) AM Inputs Consider now if Δω is equivalent to a few Hz offset fro the ideal LO. We ay then say This iage DC cannot currently be displayed. ( ) ( t) out = cos Δωt + cos( Δωt) The output, if speech and processed by the huan brain ay be intelligible, but would include a low frequency 'buzz' at Δω, and the essage aplitude would fluctuate. The requireent Δω = 0 is necessary for DSBAM. Consider now that Δω = 0 but Δφ 0, i.e. the frequency is correct at ω c but there is a phase offset. Now we have ( ) ( ) t This iage DC cannot currently be displayed. out = cos Δφ + cos ( Δφ) 'cos(δφ)' causes fading (i.e. aplitude reduction) of the output.
1. Double Sideband (DSB) AM Inputs The ' DC ' coponent is not iportant, but consider for (t), if if Δφ= π This iag This π Δφ= iage This π (90 0 ), cos iage = 0 i.e. (180 0 ), cos( π) = 1 i.e. ( ) t π = This iage cannot currently be = displayed. out cos ( ) t 0 ( ) ( t) This iage cannot currently be displayed. out = cos π = The phase inversion if Δφ = π ay not be a proble for speech or usic, but it ay be a proble if this type of odulator is used to deodulate PRK However, the ajor proble is that as Δφ increases towards π the signal strength output gets weaker (fades) and at π the output is zero
1. Double Sideband (DSB) AM Inputs If the phase offset varies with tie, then the signal fades in and out. The variation of aplitude of the output, with phase offset Δφ is illustrated below Thus the requireent for Δω = 0 and Δφ = 0 is a 'strong' requireent for DSB aplitude odulation.
. Single Sideband (SSB) AM Input The equation for SSB with a carrier depending on DC is i.e. assuing ( tthis ) = iage cos cannot ( ωt) ( ) ( t) DCcos ωct + cos ωc +ω Hence x = ( ω t) + cos( ω +ω ) t cos( ( ω + Δω) t + Δφ) DC cos c c c = + 4 DC (( ) + Δφ) + cos( Δωt+ Δφ) DC cos ωc + Δω t cos (( ω +ω + Δω) t + Δφ) + cos( ( ω Δω) t Δφ) c 4
. Single Sideband (SSB) AM Input The LPF reoves the ω c coponents and hence 4 ( Δωt+ Δφ) + cos( ( ω Δω) t Δφ) DC cos Note, if Δω = 0 and Δφ = 0, recovered. ( ) DC This iage cannot currently + be cos displayed. ωt 4,i.e. ( tthis ) = iage cos cannot ( ωt ) has been Consider first that Δω 0, e.g. an offset of say 50Hz. Then ( ) (( ω Δω) t) This iage DC cannot currently be displayed. out = cos Δωt + cos 4 If (t) is a signal at say 1kHz, the output contains a signal a 50Hz, depending on DC and the 1kHz signal is shifted to 1000Hz - 50Hz = 950Hz.
. Single Sideband (SSB) AM Input The spectru for out with Δω offset is shown Hence, the effect of the offset Δω is to shift the baseband output, up or down, by Δφ. For speech, this shift is not serious (for exaple if we receive a 'whistle' at 1kHz and the offset is 50Hz, you hear the whistle at 950Hz (Δω = +ve) which is not very noticeable. Hence, sall frequency offsets in SSB for speech ay be tolerated. Consider now that Δω = 0, Δφ = 0, then ( ) ( ω t Δφ) This iage DC cannot currently be displayed. out = cos Δφ + cos 4
. Single Sideband (SSB) AM Input This indicates a fading DC and a phase shift in the output. If the variation in Δφ with tie is relatively slow, thus phase shift variation of the output is not serious for speech. Hence, for SSB sall frequency and phase variations in the LO are tolerable. The requireent 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 ore siple than for DSB and power and bandwidth requireents are reduced.
Coents In ters of 'evolution', early radio schees and radio on long wave (LW) and ediu wave (MW) to this day use DSBAM with < 1. The reason for this was the reduced coplexity and cost of 'illions' of receivers copared to the extra cost and power requireents of a few large LW/MW transitters for broadcast radio, i.e. siple envelope detectors only are required. Nowadays, with odern integrated circuits, the cost and coplexity of synchronous deodulators is uch reduced especially copared to the additional features such as synthesised LO, display, FM etc. available in odern receivers. Aplitude Modulation fors the basis for: Digital Modulation Aplitude Shift Keying ASK Digital Modulation Phase Reversal Keying PRK Multiplexing Frequency Division Multiplexing FDM Up conversion Radio transitters Down conversion Radio receivers