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INTRODUCTION TO MODELLING WITH TIMS

1. Another name used interchangeably is a bandpass signal An important observation can be made about a narrowband signal that is it can contain no harmonics a baseband signal is one which extends from DC so f 0 to a finite frequency f It is thus a wideband signal Speech for communications is generally bandlimited to the range 300 to 3000 Hz It thus has a bandwidth in excess of 3 octaves This is considered to be a wideband signal After modulation to a higher part of the spectrum it becomes a narrowband signal but note that its absolute bandwidth remains unchanged This reduction from a wideband to a narrowband signal is a linear process it can be reversed In the context of communications engineering it involves modulation or frequency translation You will meet all of these signals and phenomena when working with TIMS measurement The bandwidth of a signal can be measured with a SPECTRUM ANALYSER Commercially available instruments typically cover a wide frequency range are very accurate and can perform a large number of complex measurements They are correspondingly expensive TIMS has no spectrum analyser as such but can model one with the TIMS320 DSP module or in the form of a simple WAVE ANALYSER with TIMS analog modules See the experiment entitled Spectrum analysis the WAVE ANALYSER within Volume A2 Further amp Advanced Analog Experiments Without a spectrum analyser it is still possible to d
2. INTRODUCTION TO MODELLING WITH TIMS Po PUN bulding sssri aaa i aes ek Soe Panne ated Saas Falah nets 2 why have patching diagrams ccccesesscessceseceeeeseceseeseessecseeeeeeseeenes 2 organization Of EXPEriIMents 3 sdsssccsdiseseassissesauteariierarehicses 3 who is running this experiment cccccessseceteceseesecceeeeeaeees 3 Carly CX PUNCH Sissy e lass E EAE EE A RAEE AAG 4 76 076 101 11 0 n Wee eee ee eee TE eee re 4 TICSSA SCS uiesistc seat sushaka sd ngnetde r o a dt obelic atasea Nastia lass 4 ANALOGS IMESSALES EE EE A gh EEG ca tives cczund deh E 4 digital ME SSA ES 4 serevssehcivs cee aaraa a Ea O Ea AE E aaa ara erana 5 bandwidths and spectra c0 baie ceca tina aeons 5 INE ASUPEMEN tivo e eren AA EE T ATE E A 6 graphical conventions ssssseeseeseesseessesesssressessrssressessessresseesee 6 representation Of spectra essssessseserseeseesessteressesrtsrsstesessteresseseseeseesesses 6 PULSES ago E T oe oe a 8 Other PUNCHIONS essiri ienie E aE E EEEE E RK R RE 9 IME ASUTIN SMS TUMICHI SS so ter on cares cohen casas u teva sees stssesrosstesresresseesee 9 the oscilloscope time domain ceccececeeeseesceeseeeeeeeeeeeeeeeeeeeeeeeeneeeereees 9 the rms voltmeter feiss ch Hace dene ctagdeh cpeetece eee etek oa aah dees 10 the spectrum analyser frequency domain cccecceesseeseeeeceteeeteeeseenees 10 oscilloscope triggering vacinvcavieensssic aes aes 10 what you see and wha
3. It is particularly important when the measurement involves noise Its bandwidth is adequate for all of the signals you will meet in the TIMS environment An experiment which introduces the WIDEBAND TRUE RMS METER is entitled Power measurements Although it appears at the end of this Volume it could well be attempted at almost any time the spectrum analyser frequency domain The identification of the spectral composition of a signal its components in the frequency domain plays an important part when learning about communications Unfortunately instruments for displaying spectra tend to be far more expensive than the general purpose oscilloscope It is possible to identify and measure the individual spectral components of a signal using TIMS modules Instruments which identify the spectral components on a component by component basis are generally called wave analysers A model of such an instrument is examined in the experiment entitled Spectrum analysis the WAVE ANALYSER in Volume A2 Further amp Advanced Analog Experiments Instruments which identify the spectral components of a signal and display the spectrum are generally called spectrum analysers These instruments tend to be more expensive than wave analysers Something more sophisticated is required for their modelling but this is still possible with TIMS using the digital signals processing DSP facilities the TIMS320 module can be programmed to provide spect
4. 1940 or easier Mr Tompkins in Paperback Cambridge University Press 1965 Introduction to modelling with TIMS Al 15 from a YELLOW socket and is a TTL signal with the DC component removed ie DC shifted SIN or COS Single frequency signals are generally referred to as sinusoids yet when manipulating them trigonometrically are often written as cosines How do we obtain coswt from a sinusoidal oscillator There is no difference in the shape of a sinusoid and a cosinusoid as observed with an oscilloscope A sinusoidal oscillator can just as easily be used to provide a cosinusoid What we call the signal sin or cos will depend upon the time reference chosen Remember that cosat sin t 71 2 Often the time reference is of little significance and so we choose sin or cos in any analysis as is convenient the ADDER Gandg 16 Al Refer to the TIMS User Manual for a description of the ADDER module Notice it has two input sockets labelled A and B In many experiments an ADDER is used to make a linear sum of two signals a t and b t of amplitudes A and B respectively connected to the inputs A and B respectively The proportions of these signals which appear at the ADDER output are controlled by the front panel gain controls G and g The amplitudes A and B of the two input signals are seldom measured nor the magnitudes G and g of the adjustable gains Instead it is the magnitudes GA and gB which ar
5. a factor of 100 and if the oscilloscope sensitivity is not changed they appear to be reduced to zero and in relative terms this is so If the sensitivity of the oscilloscope is increased by 100 however the screen will no longer be empty There will be the system noise and perhaps the signal of interest is still visible Engineering judgement must then be exercised to evaluate the significance of the signals remaining overload If wanted signal levels within a system fall too low in amplitude then the signal to noise ratio SNR will suffer since internal circuit noise is independent of signal level If signal levels within a system rise too high then the SNR will suffer since the circuitry will overload and generate extra unwanted distortion components these distortion components are signal level dependent In this case the noise is 5 TIMS claims a system signal to noise ratio of better than 40 dB Introduction to modelling with TIMS Al 1l derived from distortion of the signal and the degree of distortion is usually quoted as signal to distortion ratio SDR Thus analog circuit design includes the need to maintain signal levels at a pre defined working level being not to high and not too low to avoid these two extremes These factors are examined in the experiment entitled Amplifier overload within Volume A2 Further amp Advanced Analog Experiments The TIMS working signal level
6. is frequency translated to become an upper single sideband b and a lower single sideband c A three channel frequency division multiplexed FDM signal is also illustrated d Note that these spectral diagrams do not show any phase information Despite all the above be prepared to accept that these diagrams are used for purposes of illustration and different authors use their own variations For example some slope their triangles in the opposite sense to that suggested here filters In a block diagram there is a simple technique for representing filters The frequency spectrum is divided into three bands low middle and high each represented by part of a sinewave If a particular band is blocked then this is indicated by an oblique stroke through it The standard responses are represented as in the Figure below block diagrammatic representations of filter responses The filters are respectively lowpass bandpass highpass bandstop and allpass wo ls In the case of lowpass and highpass a wo responses the diagrams are often further simplified by the removal of one of the cancelled sinewaves the result being as in the figure opposite LPF HPF 8 Al Introduction to modelling with TIMS other functions eh Eh Uh ils amplify multiply amplitude integrate limit some analog functions measuring instruments the oscilloscope time domain The most frequently used measuring facility with TIMS
7. is the oscilloscope In fact the vast majority of experiments can be satisfactorily completed with no other instrument Any general purpose oscilloscope is ideal for all TIMS experiments It is intended for the display of signals in the time domain 4 It shows their waveforms their shapes and amplitudes From the display can be obtained information regarding waveform shape waveform frequency by calculation using time base information waveform amplitude directly from the display system linearity by observing waveform distortion an estimate of the bandwidth of a complex signal eg from the sharpness of the corners of a square wave When concerned with amplitude information it is customary to record either e the peak to peak amplitude e the peak amplitude of the waveform visible on the screen Unless the waveform is a simple sinewave it is always important to record the shape of the waveform also this can be 1 as a sketch with time scale and annotation to show clearly what amplitude has been measured 2 as an analytic expression in which case the parameter recorded must be clearly specified Introduction to modelling with TIMS 4 but with adaptive circuitry it can be modified to display frequency domain information Al 9 the rms voltmeter The TIMS WIDEBAND TRUE RMS METER module is essential for measurements concerning power except perhaps for the simple case when the signal is one or two sinewaves
8. or TIMS ANALOG REFERENCE LEVEL has been set at 4 volts peak to peak Modules will generally run into non linear operation when this level is exceeded by say a factor of two The background noise of the TIMS system is held below about 10 mV this is a fairly loose statement since this level is dependent upon the bandwidth over which the noise is measured and the model being examined at the time A general statement would be to say that TIMS endeavours to maintain a SNR of better than 40 dB for all models overload of a narrowband system Suppose a channel is narrowband This means it is deliberately bandlimited so that it passes signals in a narrow typically much less than an octave 6 frequency range only There are many such circuits in a communications system If this system overloads on a single tone input there will be unwanted harmonics generated But these will not pass to the output and so the overload may go unnoticed With a more complex input say two or more tones or a speech related signal there will be in addition unwanted intermodulation components generated Many of these will pass via the system thus revealing the existence of overload In fact the two tone test signal should always be used in a narrowband system to investigate overload the two tone test signal A two tone test signal consists of two sine waves added together As discussed in the previous section it is a very useful signal for testing systems es
9. special symmetries result in all or nearly all of the ODD or EVEN harmonics being absent With these observations and more it is generally easy to make an engineering estimate of the bandwidth of a periodic signal multipliers and modulators The modulation process requires multiplication But a pure MULTIPLIER is seldom found in communications equipment Instead a device called a MODULATOR is used In the TIMS system we generally use a MULTIPLIER rather than a MODULATOR when multiplication is called for so as not to become diverted by the side effects and restrictions imposed by the latter In commercial practice however the purpose designed MODULATOR is generally far superior to the unnecessarily versatile MULTIPLIER multipliers An ideal multiplier performs as a multiplier should That is if the two time domain functions x t and y t are multiplied together then we expect the result to be x t y t no more and no less and no matter what the nature of these two functions These devices are called four quadrant multipliers There are practical multipliers which approach this ideal with one or two engineering qualifications Firstly there is always a restriction on the bandwidth of the signals x t and y t There will inevitably be extra unwanted terms in the output noise and particularly distortion products due to practical imperfections Provided these unwanted terms can be considered insignificant
10. with the flip of a switch In addition channel identification is simplified if the habit is adopted of consistently locating the trace for CH1 above the trace for CH2 Colour coded patching leads can also speed trace identification what you see and what you dont Instructions such as adjust the phase until there is no output or remove the unwanted signal with a suitable filter will be met from time to time These instructions seldom result in the amplitude of the signal in question being reduced to zero Instead what is generally meant is reduce the amplitude of the signal until it is no longer of any significance Significance here is a relative term made with respect to the system signal to noise ratio SNR All systems have a background noise level noise threshold noise floor and signals wanted within these systems must over ride this noise unwanted TIMS is designed to have a working level the TIMS ANALOG REFERENCE LEVEL of about 4 volts peak to peak The system noise level is claimed to be at least 100 times below this 5 When using an oscilloscope as a measuring instrument with TIMS the vertical sensitivity is typically set to about 1 volt cm Signals at the reference level fit nicely on the screen If they are too small it is wise to increase them if possible and appropriate to over ride the system noise or if larger to reduce them to avoid system overload When they are attenuated by
11. assessment it is you who are running the experiment and you must make up your mind as to how you are going to do it You can do this best if you read about it beforehand If you do not understand a particular instruction consider what it is you have been trying to achieve up to that point and then do it your way Introduction to modelling with TIMS Al early experiments The first experiment assumes no prior knowledge of telecommunications it is designed to introduce you to TIMS and to illustrate the previous remarks about being systematic The techniques learned will be applied over and over again in later work The next few experiments are concerned with analog modulation and demodulation modulation One of the many purposes of modulation is to convert a message into a form more suitable for transmission over a particular medium The analog modulation methods to be studied will generally transform the analog message signal in the audio spectrum to a higher location in the frequency spectrum The digital modulation methods to be studied will generally transform a binary data stream the message at baseband frequencies to a different format and then may or may not translate the new form to a higher location in the frequency spectrum It is much easier to radiate a high frequency HF signal than it is a relatively low frequency LF audio signal In the TIMS environment the particular part of the spectrum chosen for HF s
12. e of more interest and these are measured directly at the ADDER output The measurement of GA is made when the patch lead for input B is removed and that of gB is measured when the patch lead for input A is removed When referring to the two inputs in this text it would be formally correct to name them as the input A and the input B This is seldom done Instead they are generally referred to as the input G and the input g respectively or sometimes just G and g This should never cause any misunderstanding If it does then it is up to you as the experimenter to make an intelligent interpretation Introduction to modelling with TIMS abbreviations This list is not exhaustive It includes only those abbreviations used in this Text abbreviation meaning BPSK binary phase shift keying dB decibel o DPSK DSB DSBSC DSSS device under test _ S O DUT i ext synch ext trig external trigger of an oscilloscope FM frequency modulation FSK FSD ISB ISI LSB B NBFM OOK PAM PCM PDM phase modulation S O M hase modulation P P P P PPM P P P Q Q lt a Q c Q E Q n n ry PRK PSK PWM SDR SNR SSB SSBSC SSR sideband suppression ratio TDM THD VCA WBFM wide band frequency modulation Introduction to modelling with TIMS Al 17 list of symbols The following symbols are used throughout the text and have the following meanings a t atime
13. er Accepting restrictions in some areas generally results in superior performance in others so that in practice it is the switching modulator rather than the idealized four quadrant multiplier which finds universal use in communications electronics Despite the above TIMS uses the four quadrant multiplier in most applications where a modulator might be used in practice This is made possible by the relatively low frequency of operation and modest linearity requirements 9 this is the basis of a voltage controlled amplifier VCA 14 A1 Introduction to modelling with TIMS envelopes Every narrowband signal has an envelope and you probably have an idea of what this means Envelopes will be examined first in the experiment entitled DSB generation in this Volume They will be defined and further investigated in the experiments entitled Envelopes within this Volume and Envelope recovery within Volume A2 Further amp Advanced Analog Experiments extremes Except for a possible frequency scaling effect most experiments with TIMS will involve realistic models of the systems they are emulating Thus message frequencies will be low and carrier frequencies high But these conditions need not be maintained TIMS is a very flexible environment It is always a rewarding intellectual exercise to imagine what would happen if one or more of the normal conditions was changed severely 1 It is then even more
14. ignals is centred at 100 kHz It is necessary of course that the reverse process demodulation can be carried out namely that the message may be recovered from the modulated signal upon receipt following transmission messages Many models will be concerned with the transmission or reception of a message or a signal carrying a message So TIMS needs suitable messages These will vary depending on the system analog messages The transmission of speech is often the objective in an analog system High fidelity speech covers a wide frequency range say 50 Hz to 15 kHz but for communications purposes it is sufficient to use only those components which lie in the audio frequency range 300 to 3000 Hz this is called band limited speech Note that frequency components have been removed from both the low and the high frequency end of the message spectrum This is bandpass filtering Intelligibility suffers if only the high frequencies are removed Speech is not a convenient message signal with which to make simple and precise measurements So initially a single tone sine wave is used This signal is more easily accommodated by both the analytical tools and the instrumentation and measuring facilities l defined later 4 Al Introduction to modelling with TIMS The frequency of this tone can be chosen to lie within the range expected in the speech and its peak amplitude to match that of the speech The simple tone can the
15. n be replaced by a two tone test signal in which case intermodulation tests can be carried out 2 When each modulation or demodulation system has been set up quantitatively using a single tone as a message or preferably with a two tone test signal a final qualitative check can be made by replacing the tone with a speech signal The peak amplitude of the speech should be adjusted to match that of the tone Both listening tests in the case of demodulation and visual examination of the waveforms can be very informative digital messages The transmission of binary sequences is often the objective of a digital communication system Of considerable interest is the degree of success with which this transmission is achieved An almost universal method of describing the quality of transmission is by quoting an error rate 3 If the sequence is one which can take one of two levels say 0 and 1 then an error is recorded if a 0 is received when a was sent or a 1 received when a 0 was sent The bit error rate is measured as the number of errors as a proportion of total bits sent To be able to make such a measurement it is necessary to know the exact nature of the original message For this purpose a known sequence needs to be transmitted a copy of which can be made available at the receiver for comparison purposes The known sequence needs to have known and useful statistical properties for example a random sequence Rather simple gene
16. nal DC component at one input will produce new components at the output Specifically each component at the other input will be multiplied by this DC component a constant and so a scaled version will appear at the output To overcome this problem there is an option for AC coupling in the MULTIPLIER module It is suggested that the DC mode be chosen only when the signals to be processed actually have DC components otherwise use AC coupling modulators In communications practice the circuitry used for the purpose of performing the multiplying function is not always ideal in the four quadrant multiplier sense such circuits are generally called modulators Modulators generate the wanted sum or difference products but in many cases the input signals will also be found in the output along with other unwanted components at significant levels Filters are used to remove these unwanted components from the output alternatively there are balanced modulators These have managed to eliminate either one or both of the original signals from the output These modulators are restricted in other senses as well It is allowed that one of the inputs can be complex ie two or more components but the other can only be a single frequency component or appear so to be as in the switching modulator This restriction is of no disadvantage since the vast majority of modulators are required to multiply a complex signal by a single component carri
17. on occasions be experimenting or just doodling not knowing what to expect But in most cases your goal will be quite clear and this is where a systematic approach is recommended If you follow the steps detailed in the first few experiments you will find that the models are adjusted in a systematic manner so that each desired result is obtained via a complete understanding of the purpose and aim of the intermediate steps leading up to it why have patching diagrams Many of the analog experiments and all of the digital experiments display patching diagrams These give all details of the interconnections between modules to implement a model of the system under investigation It is not expected that a glance at the patching diagram will reveal the nature of the system being modelled The patching diagram is presented as firm evidence that a model of the system can be created with TIMS The functional purpose of the system is revealed through the block diagram which precedes the patching diagram 2 Al Introduction to modelling with TIMS It is the block diagram which you should study to gain insight into the workings of the system If you fully understand the block diagram you should not need the patching diagram except perhaps to confirm which modules are required for particular operations and particular details of functionality These is available in the TIMS User Manual You may need an occasional glance a
18. pecially those which are of narrow bandwidth The properties of the signal depend upon the frequency ratio of the two tones the amplitude ratio of the two tones For testing narrowband communication systems the two tones are typically of near equal frequency and of identical amplitude A special property of this form of the signal is that its shape as seen in the time domain is very well defined and easily recognisable 7 After having completed the early experiments you will recognise this shape as that of the double sideband suppressed carrier DSBSC signal If the system through which this signal is transmitted has a non linear transmission characteristic then this will generate extra components The presence of even small amounts of these components is revealed by a change of shape of the test signal 12 Ai 6 defined above 7 the assumption being that the oscilloscope is set to sweep across the screen over a few periods of the difference frequency Introduction to modelling with TIMS Fourier series and bandwidth estimation Fourier series analysis of periodic signals reveals that e itis possible by studying the symmetry of a signal to predict the presence or absence of a DC component e ifa signal is other than sinusoidal it will contain more than one harmonic component of significance e ifa signal has sharp discontinuities it is likely to contain many harmonic components of significance some
19. rators can be implemented using shift registers and these provide sequences of adjustable lengths They are known as pseudo random binary sequence PRBS generators TIMS provides you with just such a SEQUENCE GENERATOR module You should refer to a suitable text book for more information on these bandwidths and spectra Most of the signals you will be examining in the experiments to follow have well defined bandwidths That is in most cases it is possible to state quite clearly that all of the energy of a signal lies between frequencies f and f Hz where f lt f the absolute bandwidth of such a signal is defined as f f1 Hz It is useful to define the number of octaves a signal occupies The octave measure for the above signal is defined as octaves log f f Note that the octave measure is a function of the ratio of two frequencies it says nothing about their absolute values a wideband signal is generally considered to be one which occupies one or more octaves 2 3 the corresponding measurement in an analog system would be the signal to noise ratio relatively easy to measure with instruments or if speech is the message the intelligibility not so easy to define let alone to measure the two tone test signal is introduced in the experiment entitled Amplifier overload Introduction to modelling with TIMS A1 5 a narrowband signal is one which occupies a small fraction of an octave
20. raw conclusions about the location of a spectrum by noticing the results when attempting to pass it through filters of different bandwidths There are several filters in the TIMS range of modules See Appendix A and also the TIMS User Manual graphical conventions 6 Al representation of spectra It is convenient to have a graphical method of depicting spectra In this work we do not get involved with the Fourier transform with its positive and negative frequencies and double sided spectra Elementary trigonometrical methods are used for analysis Such methods are more than adequate for our purposes When dealing with speech the mathematical analysis is dropped and descriptive methods used These are supported by graphical representations of the signals and their spectra In the context of modulation we are constantly dealing with sidebands generally derived from a baseband message of finite bandwidth Such finite bandwidth signals will be represented by triangles on the spectral diagrams The steepness of the slope of the triangle has no special significance although when two or more sidebands from different messages need to be distinguished each can be given a different slope Introduction to modelling with TIMS frequency gt a baseband signal eg a message Although speech does not have a DC component the triangle generally extends down to zero the origin of the frequency scale rather than being truncated j
21. rewarding to confirm our imaginings by actually modelling these unusual conditions TIMS is sufficiently flexible to enable this to be done in most cases For example it is frequently stated for such and such a requirement to be satisfied that it is necessary that x gt gt x Quite often x and x are frequencies say a carrier and a message frequency or they could be amplitudes You are strongly encouraged to expand your horizons by questioning the reasons for specifying the conditions or restrictions within a model and to consider and then examine the possibilities when they are ignored analog or digital What is the difference between a digital signal and an analog signal Sometimes this is not clear or obvious In TIMS digital signals are generally thought of as those being compatible with the TTL standards Thus their amplitudes lie in the range 0 to 5 volts They come from and are processed by modules having RED output and input sockets It is sometimes necessary however to use an analog filter to bandlimit these signals But their large DC offsets would overload most analog modules Some digital modules eg the SEQUENCE GENERATOR have anticipated this and provide an analog as well as a digital TTL output This analog output comes 10 for an entertaining and enlightening look at the effects of major changes to one or more of the physical constants see G Gamow Mr Tompkins in Wonderland published in
22. rum analysis facilities Alternatively the distributors of TIMS can recommend other affordable methods compatible with the TIMS environment oscilloscope triggering synchronization As is usually the case to achieve text book like displays it is important to choose an appropriate signal for oscilloscope triggering This trigger signal is almost never the signal being observed The recognition of this point is an important step in achieving stable displays This chosen triggering signal should be connected directly to the oscilloscope sweep synchronizing circuitry Access to this circuitry of the oscilloscope is available via an input socket other than the vertical deflection amplifier input s It is typically labelled ext trig external trigger ext synch external synchronization or similar sub multiple frequencies If two or more periodic waveforms are involved they will only remain stationary with respect to each other if the frequency of one is a sub multiple of the other 10 A1 Introduction to modelling with TIMS This is seldom the case in practice but can be made so in the laboratory Thus TIMS provides at the MASTER SIGNALS module a signal of 2 083 kHz which is 1 48 of the 100 kHz system clock and another at 8 333 kHz 1 12 of the system clock which channel Much time can be saved if a consistent use of the SCOPE SELECTOR is made This enables quick changes from one display to another
23. t the patching diagram for confirmation of a particular point Try to avoid patching up mechanically according to the patching diagram without thought to what you are trying to achieve organization of experiments Each of the experiments in this Text is divided into three parts 1 The first part is generally titled PREPARATION This part should be studied before the accompanying laboratory session 2 The second part describes the experiment proper Its title will vary You will find the experiment a much more satisfying experience if you arrive at the laboratory well prepared rather than having to waste time finding out what has to be done at the last moment Thus read this part before the laboratory session 3 The third part consists of TUTORIAL QUESTIONS Generally these questions will be answered after the experimental work is completed but it is a good idea to read them before the laboratory session in case there are special measurements to be made While performing an experiment you should always have access to the TIMS user manuals namely the TIMS User Manual fawn cover which contains information about the modules in the TIMS Basic Set of modules and the TIMS Advanced Modules and TIMS Special Applications Modules User Manual red cover who is running this experiment These experiments and their Tasks are merely suggestions as to how you might go about carrying out certain investigations In the final
24. t you don t cccceeseesseeeeceeeeeteeeeseeees 11 WV CEI OAs piste E acco ae Lace cas tect E ee Na odes one ae Taek 11 overload of a narrowband SySteI eccecceesceeceseeeesecseeeeeeseeeeeeeeeeeeeeeees 12 the two tone test Signal 0 0 ecceesceesceesceseceeeceseceseceeecseecaeeeseeeeeeneeeereneeens 12 Fourier series and bandwidth estimation ccccccceseeseeeeeees 13 multipliers and modulators eeeecceesseesteceeeeeeeeeeeeesseeeeeeeees 13 Multipliers rejoint e RE ee re ee 13 76 076 101 F100 gt Pee ee eee E E E 14 CTV LOPES caiseicntatin Wakes a wale eh A A a aes 15 RAY A E siete E EA Shee A AEA EEE 15 analog or digital issued catactyakdesoiavasecte sheladedatsty htelegaatdateeeutets 15 SINO COS orsa ra a e cae tate a aaas 16 the ADDER G and omeisindir coinn enn ina DiE 16 abbreviations arisen ii aE Aaa aad E AS 17 listof symbols inona raa E ii 18 Introduction to modelling with TIMS Vol Al ch 1 rev 1 0 1 INTRODUCTION TO MODELLING WITH TIMS model building With TIMS you will be building models These models will most often be hardware realizations of the block diagrams you see in a text book or have designed yourself They will also be representations of equations which themselves can be depicted in block diagram form What ever the origin of the model it can be patched up in a very short time The next step is to adjust the model to perform as expected It is perfectly true that you might
25. ust before it For the special case in which a baseband signal does have a DC component the triangle convention is sometimes modified slightly by adding a vertical line at the zero frequency end of the triangle freq a DSBSC The direction of the slope is important Its significance becomes obvious when we wish to draw a modulated signal The figure above shows a double sideband suppressed carrier DSBSC signal Note that there are TWO triangles representing the individual lower and upper sidebands They slope towards the same point this point indicates the location of the suppressed carrier frequency freq an inverted baseband signal The orientation is important If the same message was so modulated that it could be represented in the frequency spectrum as in the figure above then this means the signal is located in the baseband part of the spectrum e spectral components have been transposed or inverted frequency components which were originally above others are now below them since the signal is at baseband it would be audible if converted with an electric to acoustic transducer a pair of headphones for example but would be unintelligible You will be able to listen to this and other such signals in TIMS experiments to come It is common practice to use the terms erect and inverted to describe these bands Introduction to modelling with TIMS Al ae aes be ee ee In the Figure above a message a
26. varying amplitude a phase angles B deviation in context of PM and FM of a small frequency increment Ab peak phase deviation t a small time interval g t atime varying phase m inthe context of envelope modulation the depth of modulation u alow frequency rad s typically that of a message u lt lt a high frequency rad s typically that of a carrier gt gt u y t atime varying function 18 A1 Introduction to modelling with TIMS
27. with respect to the magnitude of the wanted terms then the multiplier is said to be ideal In the TIMS environment this means they are at least 40 dB below the TIMS ANALOG REFERENCE LEVEL 8 Such a multiplier is even said to be linear That is from an engineering point of view it is performing as expected 8 defined under what you see and what you don t Introduction to modelling with TIMS Al 13 In the mathematical sense it is not linear since the mathematical definition of a linear circuit includes the requirement that no new frequency components are generated when it performs its normal function But as will be seen multiplication always generates new frequency components DC off sets One of the problems associated with analog circuit design is minimization of unwanted DC off sets If the signals to be processed have no DC component such as in an audio system then stages can be AC coupled and the problem is overcome In the TIMS environment module bandwidths must extend to DC to cope with all possible conditions although more often than not signals have no intentional DC component In a complex model DC offsets can accumulate but in most cases they can be recognised as such and accounted for appropriately There is one situation however where they can cause much more serious problems by generating new components and that is when multiplication is involved With a MULTIPLIER the presence of an unintentio

INTRODUCTION TO MODELLING WITH TIMS

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