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COM.POTER BITS By STEVE PAYOR Digital wave£orm generation This month we will look at some of the finer points of digital signal generation, using the simple 8-bit D-A converter described last month. Armed with a good working knowledge of BASIC, you should have little trouble in getting your PC to generate useful signals up to several kHz. To begin, let's consider the question of software speed. The programming language which the author prefers to use is TURBO BASIC (formerly produced by Borland). This language is easily managed by anyone who is proficient with GWBASIC, and it will run 99% of GWBASIC programs without any changes. A program originally written in GWBASIC will run from 2 to 100 times faster under TURBO BASIC. The difference is that TURBO BASIC is a compiler, whereas GWBASIC is an interpreter. An interpreter processes each line of the program as it comes to it. For example, a line such as "GOTO 500" is scanned character by character until the word "GOTO" has been recognised as a reserved word, then the number "500" is put together by taking the '' 5' ', multiplying by 10, adding a "0", multiplying by 10, and adding the other "0". As if this isn't slow enough, in order to perform the actual GOTO, the interpreter now has to scan through all the line numbers in the program listing to find line 500, if it exists. The next time this statement is encountered, the interpreter has to go through the entire process again. A compiler will initially process a "GOTO 500" in the same way, but having deciphered it, all that will remain in the final machine code is a single JMP instruction, which only takes a few microseconds to execute. Traditionally, compilers have tended to be rather awkward in interactive situations. Before a program can be run, it first has to be compiled, and this used to take some time and lots of keystrokes, whereas an interpreter like GWBASIC only requires you to type RUN (or press the F2 key) and the program is off and running. TURBO BASIC is just as easy to use in this regard. You can go from editing to running a program with two keystrokes, and the only difference you will notice is a delay of around a second or so while the program is being compiled. Machine code This photo shows the completed D-A converter with the filter components added. The filter gives a response that is 13dB down at lOkHz. 80 SILICON CHIP An alternative, and very effective way of speeding up a GWBASIC program is to write the most critical part of the program in machine code. In our case, this is the loop which outputs the bytes to the D-A converter. The machine code for this part only requires simple integer arithmetic. The rest of the program, which contains tricky stuff like floating point SIN calculations, can be left in its original, slow UNFILTERED OUTPUT (1k) CENTRONICS PIN NUMBERS (9) 07 JUMPER 2.7k .01 10•1. 1.,. * 5.6k (8) 06 OUTPUT ADJUST VR1 2k 5.6k (7) 05 22k *470!J (6) 04 * MAY NEED ADJUSTMENT ALL RESISTORS 1% (4) 02 180k (3) 01 o--..JN,Ar--• (19) TO (30) GNO~ running form, because it is only used once during the waveform setup. Another way of getting a faster program is to use a more machineoriented language such as "C". The code produced by the TURBO C compiler is almost as short as handwritten machine code. (We hope to present some C routines in a future issue. At this stage the results appear to be about 2-3 times faster than TURBO BASIC). In summary, the options, in order of increasing speed, are: (1). GWBASIC interpreter (waveforms up to a few hundred Hertz). (2). TURBO BASIC or similar compiler (approx. 10kHz). (3). TURBO C compiler (approx. 20kHz). (4). Any language with a machine code subroutine (Z0kHz plus). (5). Hardware buffer memory for D-A converter (MHz). Turbo Basic Fig.1: the filter circuit consists of an inductor and two capacitors and is simply tacked onto the output of the D-A converter circuit described last month. It gives approximately .06dB ripple from 0-4.5kHz and 13dB of attenuation at lOkHz. For simplicity, we will stick with TURBO BASIC for now. As mentioned last month, we achieved a sample rate of 20k samples/sec on a 4.77MHz PC-XT. This was achieved using the tightest possible loop we could write. The fact that the loop execution time is almost precisely 50µ.s is just a coincidence, but it does make the figures come out nice and round. For example, the maximum waveform frequency we can construct is tokHz. Before we can start producing useful waveforms however, we need to add one more thing to our D-A converter hardware - namely, a low-pass filter. The need for a filter Fig.2: what better way to reveal the filter's frequency response than with a linear frequency sweep, from lkHz to beyond tokHz. Note the aliasing around the lOkHz point. The spectrum folds back on itself beyond this point - a direct consequence of the 20kHz sampling frequency. Sampling theory says that if we have a sampling frequency of 20kHz, then a low-pass 0-tokHz filter is required to reconstruct the desired waveform without distortion. Furthermore, this only applies for a filter with an ideal, infinitely sharp, rectangular cutoff. If you try generating a t0kHz signal, you may wonder why such a sharp cutoff is necessary. There will be exactly two samples per cycle, one up, one down, and the MARCH 1990 81 Fig.3: This is a logarithmic frequency sweep, from 400Hz to 4kHz (just r ight for testing a voice communications channel perhaps?) The sweep time is .05s. Fig.5: a rather short logarithmic frequency sweep, from lkHz to 2kHz in 5ms, ju'st to show how clean the waveform can be. Fig.4: exactly the same waveform as Fig.3, but with the filter out of circuit. What a mess! Fig.6: the same as Fig.5 but without the filter to "reconstruct" the waveform. resultant square wave is easily filtered to a pure sine wave by a filter with a cutoff anywhere below the third harmonic; ie. 30kHz. However, if you try to generate a 9.9kHz signal, the true nature of the problem becomes apparent. Because there are not quite exactly two samples per cycle, the sampling points on the waveform gradually shift until they pa ss through the zero crossings, and then the amplitude begins to rise again. The resulting waveform looks like a double sideband signal, which is exactly what it is. You have actually generated two frequencies, namely 9.9kHz and 10. lkHz. The 10. lkHz signal is an "alias", or beat frequency , caused by the beating of the 9.9kHz signal with the ZOkHz sampling frequency. Wanted: Your Circuit & Design Ideas Have you got a good circuit idea languishing in the ol' brain cells? If so, why not send it in to us and save us from circuit burnout? We'll pay up to $ 50 for a really good circuit . So transfer your circuit to paper and send it to SILICON CHIP, PO Box 139, Collaroy Beach, NSW 2097. 82 SILICON CHIP The only way to convert this heavily modulated signal to a pure sine wave at 9.9kHz is to have a filter which will pass the 9.9kHz component, and completely reject the 10. lkHz component. This is a rather tall order. Filter compromise We chose a simple 3rd order lowpass filter for our demonstration unit, mainly because it only requires one inductor to be wound and the results repres ent a reasonable compromise between performance and complexity. Referring to the circuit diagram, the filter is simply tacked onto the output of last month's D-A converter circuit. If you like, the ex- ' SILICON CHIP LOG/LINEAR FREQUENCY SWEEP GENERATOR DEFINT A-Z DIM WAVE(lOOOO) ' ' ' ' (TURBO BASIC 1.1) All variables are integers unless otherwise stated Array containing output data (sufficient for approx. 1/2 sec of stored waveform, given the sample time listed below) 'Program constants: PORT.A=&H378 ' Parallel port Note: Other possible addresses PORT.C=PORT.A+2 ' addresses for PORT.A are Hex 3BC or Hex 278 PI!=3.141593 SAMPLE.TIME!=50E-6 ' 50fsec (as determined by experiment for this computer, a '4.77 MHz PC-XT, running this program. This will need to ' be changed to accommodate faster or slower systems.) ' Variables defining frequency sweep: ' START.FREQ!=lOOO ' Hz END.FREQ!=lOOOO ' Hz DURATION!=.1 sec Change these three variables to produce the desired sweep range and time N=DURATION!/SAMPLE.TIME! ' Total no. of samples in sweep PHASE!=O 'This section of code fills the output waveform FOR I=O TON 'array with the required frequency sweep (this WAVE(I)=127.5+128*SIN(PHASE!) 'takes a few seconds) FREQ!=START.FREQ!*EXP(I/N*LOG(END.FREQ!/START.FREQ!))' Log sweep, or 'FREQ!=START.FREQ!+I/N*(END.FREQ!-START.FREQ!) 'Linear sweep PHASE!=PHASE!+2*PI!*FREQ!*SAMPLE.TIME! ' (Disable either of the NEXT I 'above statements by ' changing it to a remark) OUT &H21,INP(&H21) OR 1 ' Disable DOS real time clock interrupt WHILE NOT INSTAT OUT PORT.C,O 'Keep repeating the frequency sweep until a key is pressed ' Positive edge of CRO sync pulse '------------------------------------------------------------------------------ FOR I=O TON ' This FOR loop outputs the w~veform to the D-A converter. OUT PORT.A,WAVE(I) ' As you can see, it is about the tightest loop that can be NEXT I 'written in TURBO BASIC - It takes 50fsec. '-----------------------------------------------------------------------------' "Zero" the waveform OUT PORT.A,127 OUT PORT.C,1 WEND ' Negative edge of CRO sync pulse OUT &H21,INP(&H21) AND &HFE ' Restore clock interrupt END Fig.7: this listing is for a sweep generator with programmable sweep time & start & end frequencies isting .0047µF capacitor can be combined with the .OlµF capacitor, but we kept them separate for those occasions when we might want to use the D-A converter without a filter eg, when generating square pulses. The component values chosen give a Chebyshev response with approximately .06dB ripple from O to 4.5kHz, which is the usable frequency range for a flat, clean out- put. The response is 13dB down at lOkHz, which is not quite infinite, resulting in some noticeable aliasing in this region (see Fig.2). However, for a signal at say 4kHz, the nearest alias is at 16kHz, where the filter response is well down. So, for frequencies up to 4kHz at least, the signal quality is perfectly acceptable: as good as any function generator, and second only to a low distortion analog oscillator, such as a thermistor stabilised Wein bridge. Pick a waveform The big advantage that a software driven D-A converter has over other waveform generators is that it can produce any waveform you want. So what should we try our hand at first? The author's first thoughts were along the lines of a tone burst MARCH 1990 83 generator, to specification IHFA-202 1978 (see SILICON CHIP, July 1988}. However, you will have to wait for this one. This month's software solves a more immediate need. For our first demonstration program we present a frequency sweep generator, with programmable start and end frequencies, as well as sweep time. You also have a choice of logarithmic or linear frequency sweep. If you have access to a CRO, this is just the ticket for instant frequency response tests, and incredibly useful for filter alignment, which is why we chose .it first up: to align the D-A's own filter. Looking at the CRO photograph (Fig.3} you will see that the frequency response is quite flat up to 4kHz. (Each horizontal graticule ·division is lkHz, starting at lkHz). Twiddling the inductance adjuster, you will find that the response " droops" slightly if the inductance is too low, or " peaks" if the inductance is a shade too high. Adjusting this filter for a flat response How To Make The Inductor First of all, you will need a suitable ferrite core. We chose a a PCB-mounting RM10 core assembly, with an AL value of 400. Nearly all the ferrite core manufacturers can supply this type and it is very easy to assemble and mount. If you are using a different core type, you will need to know its AL value in order to calculate the number of turns required. The calculation is quite simple: ( 1 ) . Express the desired inductance in nH; eg, 37 .3mH = 37,300,000nH (2). Divide this by the AL value of the core; eg, 37,300,000 + 400 = 93,250 (3). Take the square root; eg, (93,250)½ = 305.4 = the required number of turns (305 and a couldn't be easier! One final note: In order to get a perfectly stable CRO display, we used bit O of PORT.C to output a ANTRIM TOROIDAL TRANSFORMERS QUALITY TOROIDAL POWER TRANSFORMERS, MANUFACTURED IN U.K. NOW AVAILABLE EX-STOCK AT REALISTIC PR ICES. half will be near enough). If the core has an adjuster, find out how much it can increase the inductance and subtract about half this amount before doing the above calculation. For example, the adjuster on our ferrite core had an adjustment range of +20%, so we calculated the number of turns for an inductance of 37 .3mH less 10% = 33.6mH, which came to 290 turns. We used 0.25mm enamelled copper wire, for which there is ample room within the core window. A complete RM10, AL 400 core assembly, including adjuster, coil former and mounting clips is available from Radiospares Components (stock no. 228-258) for $5. 7 4 plus sales tax. TTL level trigger pulse. This is a short, negative-going pulse, the positive edge of which signifies the start of the frequency sweep. ~ General Construction OUTER W INDING INNER WINDING CQ AE INSULA TION TAX PAID PRICES 15VA 30VA 50VA SOVA 120VA 160VA 225VA 300VA 500VA 625VA 10+ 1- 9 32 .80 31.70 36.00 35.00 38.50 37.20 41.75 40.35 44.95 43.50 55.70 52.20 62.00 58.20 72.80 68.25 100.00 93.75 112.00 105.00 Enquiries from resellers and OE Ms welcome. Quantity prices and data sheets available on request. Distributed in Australia by Harbuch Electronics Pty Ltd, 90 George St., HORNSBY, NSW, 2077 Phone (02)476-5854 Fax (02)476-3231 84 SILICON CHIP