Design and Construction of an Arbitrary.docx

《Design and Construction of an Arbitrary.docx》由会员分享，可在线阅读，更多相关《Design and Construction of an Arbitrary.docx（6页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、398 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM -32, NO. 3, SEPTEMBER 1983 Design and Construction of an Arbitrary Waveform Generator DANIELE D. CAVIGLIA, MEMBER, IEEE, ALESSANDRO DE GLORIA, STUDENT MEMBER， 丨 EEE, GIULIANO DONZELLINI, GIANCARLO PARODI, AND DOMENICO PONTA Abstract 一

2、 The purpose of this paper is to describe the design and characteristics of an arbitrary waveform generator, built at the Biophysical and Electronic Engineering Division of the Electrical Engineering Department of the University of Genoa, which exhibits the following features: a) The signal waveform

3、 is any band-limited periodic signal, whose frequency content ranges from 0.125 mHz up to 30 MHz. The low- frequency limit has been chosen in order to meet the needs of bioengineering, mechanical, and chemical applications. The high-frequency limit covers, for instance, TV and image processing appli

4、cations. b) The noise level is at least 66 dB below the maximum signal level. c) Typical distortion is less than 66 dB. d) The generators performance can be easily improved, depending on the availability of up-to-date solid-state devices, without changing its design. I. INTRODUCTION T HE AVAILABILIT

5、Y of arbitrary waveform generators is a frequent need in several applications. Most available waveform generators are designed for special-purpose appli- cations, hence they can deliver a limited class of signals only. The main requirement of a truly general-purpose waveform generator is full progra

6、mmability of the waveform, without the need for any special expertise by the user. The easiest way to attain such a goal is to use a microcomputer programmed to control each instrument function and the operator dialogue. In our case, after the user has entered, through a TTY/CRT terminal, the signal

7、 function f ( t ) that must be generated, a software routine computes the signal samples f ( t i ) over the signal period at a suitable sampling rate (max 40 MHz). The signal samples are stored at adjacent locations of a high-speed memory, whose contents are cyclically addressed to drive a D/A conve

8、rter, which generates the output waveform. Accordingly, the system can be divided into four blocks: a microcomputer, which provides the computing facility and controls the whole operation of the generator; a high-speed memory; a memory addressing system, and a D/A converter and an output amplifier (

9、Fig. 1). Manuscript received April 27, 1982. The authors are with the Biophysical and Electronic Engineering Division of the Electrical Engineering Department, University of Genoa, Genoa, Italy. Fig. 1. General block diagram of the arbitrary waveform generator. II. SYSTEM DESIGN The two main error s

10、ources in the output signal u ( t ) , as compared with the input function/( , are due to quantization and sampling. The corresponding effects on u ( t ) are evaluated separately in order to obtain, from distortion and noise requirements, the characteristics of the signal synthesizer which allow us t

11、o meet them. We express, as usual, the quantized signal as the sum of the ideal signal /(/) plus a quantization error signal e ( ( ) . If the conditions described in 1, 2, are fulfilled (i.e., moderate correlation through successive samples; large number of output points close to the midpoint of the

12、 corresponding quantization intervals), it can be proven that e ( t ) is almost uncorrelated to /(/), and that its spectrum is quasi-white. The influence of this error on the output is measured by the signal-to-noise ratio due to quantization SNR = 0 o g a / ( j l ) (1) where aj is the variance of t

13、he input signal and a 2 e is the variance of the error signal, i.e., the output mean square distortion due to quantization. The signal characteristics are fully known, so that, at least 0018-9456/83/0900-0398S01.00 1983 IEEE CAV1GLIA el ai: DESIGN AND CONSTRUCTION OF A WAVEFORM GENERATOR 399 in prin

14、ciple, the evaluation of (1) is feasible for each/(/), but it is not practical. On the other hand,/( can be any arbitrary waveform so that we cannot give a general expression for (1) unless we limit the class of functions to be synthesized 1. Therefore we introduce a more practical approach letting

15、SNR, SNRP = 20 log (Ypp/A) (2) where Ypp is the peak-to-peak output signal amplitude and A is the quantizing interval, which is assumed to be constant over the whole dynamic range of the instrument. For an Ai-bit quantization it is A = Ym/2n, where Ym is the output full scale. The output amplitude i

16、s a fraction 1 /r = Ypp/Ym 1 of the full scale so that SNRp = 6Mn - 20 log r. (3) In order to show the usefulness of relationship (3) we compute SNR according to (1) for a sinusoidal waveform f(t)= 0. 5 Ym sin (oot). We can obtain the corresponding signal- to-noise ratio due to quantization from the

17、 corresponding input variance, which becomes Fm2/8, and from the output mean square distortion. For its evaluation we can consider the error noise as a uniformly distributed random variable over the interval -A/2 to +A/2; this leads to - A2/12 = Ym2/2 22n). Hence we obtain SNR, = 6.02n + 1.76 (4) sh

18、owing that the expression (2) is a very good approximation of (1). Of course, the minimum of (3) is reached for n constant and for r = 1. In any case, the dependence of SNR on n is linear 1. For the readers convenience, we have computed, in Table 1, the value of SNRp for some values of n and r of pr

19、actical interest. It becomes apparent that, in order to obtain, for instance, SNR 60 dB, it is necessary to employ at least 12 bits. The contribution of sampling to output noise can be estimated using again a sinuosoidal waveform f(t) = Ys sin cot + p). Sampling theory offers the theoretical backgro

20、und for the synthesis of any band-limited signal: the sampled signal with a zeroth-order holding 3 is given by KA(，） = (Ky/7) E m TABLE I. SIGNAL TO QUANTIZATION NOISE RATIO FOR VARIOUS BIT NUMBERS AND REDUCTION FACTORS r SA (dB) 8 10 12 1 48 60 72 2 42 54 66 5 34 46 58 TABLE II HARMONIC AMPLITUDES

21、OF A SAMPLED SIGNAL FOR VARIOUS SAMPLE NUMBERS N AND FOURIER INDEXES m m N-10 haem* | Am| N-100 harm* | Am| N-1000 harm. |Am| 0 fund* .9836 fund* .9998 fund* 99998 -1 9 1093 99 0101 999 00101 1 11 .0894 101 0099 1001 00099 -2 19 .0518 199 0050 1999 .00050 2 21 .0468 201 0050 2001 00050 When using 40

22、96 memory words, which require 12 bits for the address, the most important harmonic is the 4095th, with an amplitude coefficient A- = 2.4420 X 10-4. This is the main contribution to distortion, together with the 4097th harmonic (|+i | = 2.4408 X 10-4). The corresponding sig- nal-to-noise ratio is SN

23、R, = 20 log (lol/l.j |) = 72 dB. (7) With such an oversampling, the harmonic distortion is not larger than the quantization noise so far obtained. This result has been achieved by using as many bits for the memory words where the samples are stored as for their addresses. We conclude that the implem

24、entation of a system which satisfies the above SNR condition, requires that the waveform to be synthesized be defined in a “square lattice” of 2” X dimensions, where n is the number of bits needed for both the sample word and the address word. fTh sin (co + moos)(t - r) + ipdi) (5) where Ts = lir/oo

25、s is the sampling period and Th is the holding interval. In our case Th = Ts, so that + Yh(t) = Ys Y, rnAm sin (co + m(j)s)t ir/u)s) + (p (6) 一 oo where Am = 5m sin (Troo/ )s)Tr(m + co/co5) with dm = (l)w . On the other hand, the number of samples is = /co, so that the modulus of Am can be computed

26、as a function of m and N and of the harmonic order (Table II). III. IMPLEMENTATION AND RESULTS The generator has been implemented using TTL and NMOS logic circuits, on double Eurocard boards. The address system consists of a clock and a 12-bit programmable counter. The clock is the core element of t

27、he generator, since its performance directly affects the output signal waveform. It must ensure good frequency stability and cover the frequency range 0.5 Hz-40 MHz with a 4-digit accuracy and be easily programmable via the microcomputer. The clock is based on a Phase Locked Loop (PLL), which for th

28、is application can be simple, due to the modest settling time requirement for the clock frequency. 400 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-32, NO. 3, SEPTEMBER 1983 Frequency Fig. 2. Clock generator block schematics. stop counting word Fig. 3. Programmable counter block sch

29、ematics. Fig. 2 shows the crystal oscillator which gives the reference frequency, the PLL which controls the upper band (5-50 MHz), and the decade group which controls the other 7 bands (0.5 Hz-5 MHz). Both the frequency-programmable input and the clock output are TTL compatible. The clock output en

30、ters the 12-bit programmable counter, which generates the address word for the high-speed memory in the following operating modes： WRITE, CYCLIC READOUT, and SINGLE READOUT (Fig. 3). The counter is adequate for working at the maximum sampling frequency (40 MHz), and allows full programmability of bo

31、th the start and the end words. The counting block consists of three parallel 4-bit counters. The 12-bit input of this block forms the start word. The comparison for equality between the output word and the end word gives an output signal from the comparator which is used to feed a load input to the

32、 counters; thus they can repeat the counting procedure. Another set of comparators can be software programmed to obtain a synchronism signal from any one of the signal samples. The control logic circuit delivers the load and clock signals to the counters that are needed at each step; furthermore, it

33、 delivers the CKA signal that drives the D/A converter latch. The address generated by the programmable counter is the input of the high-speed memory which stores the signal samples. The scanning of the addresses sends the corresponding samples to Fig. 4. High-speed memory and D/A converter. the lat

34、ch. After a time interval corresponding to the memory access time, the latch freezes the last sample, which is D/A converted into the analog output voltage (Fig. 4). The control and programming functions of the signal generator are implemented on a microcomputer, coupled to an arithmetic processor,

35、a memory, and two I/O serial interfacesone for a TTY or CRT terminal, the other for a cassette unit (Fig. 5). Beside the control of the instrument, the standalone operating system allows an interactive definition of the signal waveform. The operating system controls and executes the following functi

36、ons: MONITOR COMPUTATION of the sample amplitudes of the signal waveform EDITOR FILE MANAGEMENT. The MONITOR program is devoted to the supervision of the instrument and executes the operators instructions， which are entered via TTY or CRT; namely, choice and visualization of the scan frequency of th

37、e sample memory; of the sample which gives the external synchronism signal; and of the time markers which identify the first and last signal samples; running and stopping waveform generation; single shot or periodic output; choice of internal and external clock; and running of other programs. The ty

38、pical format is CAVIGLIA et al. DESIGN AND CONSTRUCTION OF A WAVEFORM GENERATOR 401 Fig. 5. Microcomputer general block diagram. COMMAND ,ARGUMENT1,ARGUMENT2. Furthermore, the Monitor program controls all the I/O lines and the TTY/CRT interfaces, the system start-up and the diagnostic program. COMPU

39、TATION is performed in two steps. During the first step, the operator gives the Fortran-like expression of the desired waveform. A subroutine translates it into Reverse Polish Notation and checks for syntax errors. In the second step, the operator is asked to give the time interval in which the samp

40、les are to be computed and the sample number. These data permit the computation of the sample amplitude by means of the arithmetic processor in floating point (32 bits). The amplitude of each sample is normalized to 12 bits and stored in the high-speed memory, starting from the address chosen by the

41、 operator. Fig. 6(a) shows, on a CRT, the sequence of commands that lead from start-up to the synthesis of the waveform in Fig. 6(b). We can point out, for example, the commands that define the function (DF), generate the waveform after computing (RU), and change frequency (FR) (see Appendix). An al

42、ternative choice for the operator is to store directly in the high-speed memory the values of the signal samples. The program EDITOR allows the following options: visualization and modification of the sample amplitudes stored at any memory location or at any location subset; changing of the memory p

43、ointer of n steps backwards or forwards; choice of a subset of memory addresses where new sample amplitudes can be stored. The sample amplitudes can be given either in hexadecimal or in decimal forms. The FILE MANAGEMENT program controls the cassette unit, where the most important signal waveforms a

44、re stored. It allows us to save on the cassette any sample subset stored in the high-speed memory, or to reload the memory with any previously stored cassette content. Every file is identified by a Label and a Comment, both in alphanumeric characters. The operating system is written in Intel 8085 as

45、sembly language, and requires about 8K bytes of EPROM and at least IK bytes of RAM. All the instrument functions can be pro- (b) Fig. 6. Example of command dialogue (a) and correspondent waveform at the oscilloscope (b). Fig. 7. Spectrum analysis of a 10-sample “sine wave” at 2 kHz; at the top and b

46、ottom ends of the photos the signal amplitudes and frequencies of (a) the fundamental and, (b) of the 9th harmonic can be seen. grammed via TTY or CRT, without involving the front panel controls, thereby allowing remote entry and control of the signal generator. To evaluate the Arbitrary Waveform Ge

47、nerator performance we made use of a HP 3582A spectrum analyzer. First, we can control theory correctness. Fig. 7 shows the spectrum obtained by generating a “sine wave， with 10 samples: the 9th 402 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-32, NO. 3, SEPTEMBER 1983 Fig. 8. Monit

48、or image of a “grey ramp” after acquisition and sampling. Working frequency is 14 MHz. Fig. 9. Similar to Fig. 8 but with a more complex pattern. The original waveform is also shown on the screen. and 11th harmonics are of the same amplitude as already indicated, given in Table II for = 10 and m = 1

49、, l.A similar good agreement with theory can be obtained by any sample number and at every sampling frequency up to 40 MHz. IV. APPLICATIONS The signal generator of arbitrary waveforms described in this paper delivers any waveform programmed by the operator whose frequency content may range between 0.125 mHz and 40 MHz, and whose amplitude ranges between 4.5 and +4.5 V. Aside from obvious laboratory or industrial applications, we want to quote two special applicati