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Fig.7. Supply wiring to reduce noise. S upply C ircuit 1 S ignal Fig.9. Triaxial connector used with triaxial cables for guarded connections. Guard C ircuit 2 S upply Ground loops When two circuits, sub-circuits, instruments, or other equipment are grounded at two separate points on a ‘ground bus’ we have a situation know as a ground loop (or earth loop) (see Fig.8). The ground bus may be a circuit board track, the chassis of the equipment, point-to-point wiring, or the mains earth connected at different outlets – many people have suffered unnecessary levels of hum in their Hi-Fi systems due to earth loops! The ground loop will pick up magnetic interference, probably mains hum and may also act like an antenna picking up radio frequency interference (RFI). Large loops will make the problem worse. Ground loops are a particular problem when two or more mains-powered systems (such as lab instruments and sensor circuits) are separately earthed and connected together. It is also possible for mains leakage currents to cause currents to flow in the earth (eg, shields) of connections linking equipment. Leakage currents can flow through parasitic capacitances and equipment ground, for example in transformers and EMI filters. The interference causes a current IL to flow in the ground loop, which in turn causes an additional voltage drop (ILRG) across the resistance (RG) of the ground connection between the equipment or subcircuits. The solution to ground loops is to avoid them by using a single grounding point (Fig.8). Use of differential signals, only connecting screens at one end, use of very low resistance ground connections between circuits (reducing RG), and signal isolation using transformers or opto-isolators also help minimise ground loop problems. Power isolation transformers may also help with mains wiring. Again, it is worth pointing out that some potential ‘solutions’ related to mains wiring, such as disconnecting earths, could be lethal. O uter shield/ chassis/ ground/ signal return T riax ial C ab le S ignal S ensor Ground Fig.10. Guarded signal connection. of shielding. The inner shield is connected to a signal of equal voltage to the signal provided by a unity-gain amplifier (see Fig.10). This means that there is a zero-voltage difference between the signal and inner shield, so the leakage currents (and capacitance effects) are minimised. The outer shield is usually grounded and provides interference protection for the guard signal. IM – IL C ircuit 1 IM RS A ) IM–IL RG C ircuit 2 VM IL Signal guarding Signal guarding is concerned with getting the most out of screened cable connections, particularly when connecting very low-level signals from high-impedance sources to high-precision circuits. In such cases, effects such as leakage currents in the cables and cable capacitance can cause significant errors. Signal guarding uses triaxial cables and connectors (see Fig.9), which have an inner conductor, carrying the signal of interest and two layers x1 Guard RS IM IM RC VM IL B ) IM S ignal Guard RS x1 IM VM IL Ground IM C ircuit 1 IM RC 1 C ircuit 2 0 v RS IM I L2 VM Guard RC 2 x1 VM I L2 Ground Fig.8. Ground loops: currents induced in ground loops cause voltage drops which introduce noise (upper schematic). Using a common ground point can eliminate the loop (lower schematic). 56 Fig.11. Guarded resistance measurement: a) non-guarded setup, b) non-guarded equivalent circuit, c) guarded setup, d) guarded equivalent circuit. Practical Electronics | January | 2021 As an example of how guarding works, consider the schematic in Fig.11a, for which an equivalent circuit is shown in Fig.11b. Here we are trying to measure the resistance of a sensor (RS) which has a very high resistance value and therefore leakage through the cable insulation resistance RC is significant. We apply VM and measure IM – this should give the value of RS as VM/IM, but if actually gives us this parallel combination of RS and RC due to the leakage current IL. Using a guard (Fig.11c and Fig.11d) means that the voltage across RC1 between the inner conductor and guard is zero and hence no leakage current flows. The buffer amplifier has no difficulty in supplying the guard-to-ground leakage current IL2 and this does not disrupt the measurement. ESR Electronic Components Ltd All of our stock is RoHS compliant and CE approved. Visit our well stocked shop for all of your requirements or order on-line. We can help and advise with your enquiry, from design to construction. Vibration and chemistry Systems processing low-level signals are also prone to a variety of forms of interference-based noise and errors other than electrically/magnetically coupled signals, including mechanical and electrochemical effects. Movement and vibration of cables can create electric current through the triboelectric effect – charges created due to friction between a conductor and an insulator. Low-noise cables are available for situations where this may be a particular problem. Making sure that cables are well supported and not subject to vibration or large temperature fluctuations helps reduce this effect for any cable. Movement can also generate unwanted signals through the piezoelectric effect, which occurs when mechanical stress is applied to insulators. Unwanted signals due to movement and mechanical stress are sometimes called microphonic effects, because if the signal is listened to, the movement of (for example) a cable will be audible. Batteries create electric current through electrochemical effects. Similar processes can occur if contaminants are present on PCBs and terminals. Variations in humidity can affect sensor systems with very high impedances. 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Our patented range of Plug-of-Nails™ spring-pin cables plug directly into a tiny footprint of pads and locating holes in your PCB, eliminating the need for a mating header. Save Cost & Space on Every PCB!! Solutions for: PIC . dsPIC . ARM . MSP430 . Atmel . Generic JTAG . Altera Xilinx . BDM . C2000 . SPY-BI-WIRE . SPI / IIC . Altium Mini-HDMI . & More www.PlugOfNails.com Tag-Connector footprints as small as 0.02 sq. inch (0.13 sq cm) Practical Electronics | January | 2021 Vi s i t o u r Sh o p , Ca l l o r B u y o n l i n e a t : w w w .c r i c k l e w o o d e l e c t r o n i c s .c o m 020 8452 0161 Vi s i t o u r s h o p a t : 40- 42 Cr i c k l e w o o d B r o a d w a y Lo n d o n NW2 3ET 57 Max’s Cool Beans By Max the Magnificent Flashing LEDs and drooling engineers – Part 11 G ood grief! I am bubbling over with excitement. I have so many things I want to talk about that I don’t have a clue where to begin. I know, I know... I need to sit down, take a deep breath, start at the beginning, work my way through the middle, and eventually stagger my way to the end. The problem is deciding what to talk about first. Ah, I can see in your eyes that you are desperate for me to commence with gamma correction. Well, if you insist... 0 ° P rim ary 330 ° T ertiary F F F F R ose 30 ° T ertiary 0 0 0 0 F lush O range 0 0 8 0 F F 30 0 ° S econdary F F 8 0 0 0 6 0 ° S econdary Magenta 0 0 F F 11 10 27 0 ° T ertiary Electric I ndigo Feeling off-colour R ed 9 0 Y ellow F F 1 2 F F 0 0 9 0 ° T ertiary C hartreuse 3 58 B rightness B rightness B rightness 8 0 F F 0 0 Way back in the mists of time when we started this mega-mini4 8 8 0 0 0 F F series (PE, March 2020), we introduced the concept of pulse7 5 6 width modulation (PWM). Since we can turn an LED on and 24 0 ° P rim ary 120 ° P rim ary off very quickly, the way we control its brightness is to vary B lue Green the proportion of on time to its off time. We refer to this as the 0 0 0 0 F F 0 0 F F 0 0 ‘duty cycle.’ A 20% duty cycle means the LED is on 20% of 210 ° T ertiary 150 ° T ertiary the time and off for the other 80%, while an 80% duty cycle A z ure 18 0 ° S econdary S pring Green means the LED is on 80% of the time and off the other 20%. 0 0 8 0 F F 0 0 F F 8 0 C yan 0 0 F F F F In the case of the microcontroller unit (MCU) we are working with – the Seeedunio XIAO – we can use values from 0 (0x00 Fig.1. The colour wheel we’ve been using in our experiments. in hexadecimal) being fully off (0% brightness) to 255 (0xFF in hexadecimal) being fully on (100% brightness). Using this I created a quick test sketch (program) to see how this would PWM technique, a value of 128 (0x80 in hexadecimal) means affect the colours on my 12×12 array (the full sketch is presented the LED will be on half of the time and off the other half, rein file CB-Jan21-01.txt – it and the other files associated with this sulting in 50% brightness. article, are available on the January 2021 page of the PE website). In a later column (PE, September 2020), we introduced the Since the folks at Adafruit were conscious that some of their users colour wheel (Fig.1) that we decided to use for our 12×12 pingwould be using low-end Arduinos with limited SRAM, they store pong array experiments (Fig.2). If you have built one of these their table in PROGMEM (the Flash program memory). By comarrays yourself, or if you are playing with tricolour LEDs in parison, my Seeedunio XIAO has so much memory that I can general, you may have noticed that some of the colours seem afford to flaunt it, so I dispatched the butler to fetch my flauntto be a tad ‘off’. For example, the rose may appear very close ing trousers and stored my table in SRAM (Fig.3.). to magenta, while the flush orange may appear more yellow Previously (PE, October 2020), we met the GetRed(), Getthat one might expect. Green(), and GetBlue() functions that extract and return the On the bright side (no pun intended), the red, green, and 8-bit red, green, and blue components from a 32-bit colour value. blue elements in our tricolour LEDs work as expected and Also, we introduced the BuildColor() function that accepts 8-bit provide a linear response such that a 50% duty cycle does red, green, and blue components and returns a 32-bit colour value. indeed result in 50% brightness (Fig.2a). The problem is that The thing is, we have to apply our gamma correction to each our eyes have evolved to accommodate a huge dynamic range, of the colour channels individually. Thus, in our new sketch, from moonlight to sunlight and – as part of this – they have a we’ve added a GetGammaCorrectedColor() function that sort of built-in non-linearity (Fig.2b). accepts a 32-bit colour value, splits it into its red, green and Although not immediately obvious from my diagram, the blue components, uses our GammaXref[] look-up-table to curve of this non-linearity is defined by a somewhat tricky apply gamma correction to each component, and then returns power-law function. In order to address this, we need to drive the gamma-corrected 32-bit result. the red, green, and blue LEDs using the inverse of this function, which results in our eyes per10 0 % ceiving what we were hoping for in the first W hat our eyes perceiv e T he LED place (Fig.2c). We call the process of applying W hat our work s as eyes perceiv e ex pected this inverse function, ‘gamma correction.’ 50 % There’s a great article on Adafruit’s website covering all of this in depth (https://bit.ly/31zaSLK). H ow the LED H ow the LED is driv en is driv en As part of this, they provide what they call ‘The H ow the LED is driv en Quick Fix’ in the form of a cross-reference lookP W M P W M P W M 0 % up table that we can use to remap the linear 0 x 0 0 0 x 8 0 0 x F F 0 x 0 0 0 x 8 0 0 x F F 0 x 0 0 0 x 8 0 0 x F F values we would like to use into their gamma( a) W hat we ex pect to see ( b ) W hat we actually see ( c) A pplying gam m a correction corrected counterparts that will provide us with the colours we want to see. Fig.2. Gamma correction. Practical Electronics | January | 2021 gammaCorrectedColor = BuildColor(tmpRed, tmpGreen, tmpBlue); The idea is that you have two programs fighting each other in a virtual machine known as the Memory Array Redcode Simulator (MARS). The objective is to be the last program standing. To that end, each program can try to sabotage the other one and/or try to defend itself by self-repairing. You can get a really good feel as to what this is all about by reading the Beginner’s Guide to the Redcode pseudo assembly language that is used to create the warrior programs (https://bit.ly/34m5YUo). As Ken said in his email, ‘I figure this can be made visually appealing by presenting the memory array on a screen (or ping-pong ball array) and colour-coding each cell either ‘Neutral,’ ‘Last written for or by Program A,’ or ‘Last written for or by Program B’ — using green, blue, and red respectively, for example — and running the programs at only a few steps per second so progress can be followed.’ Initially, I was a tad skeptical that a 144-element MARS would suffice but – having looked at the Redcode Beginner’s Guide – I’ve changed my mind. Now I’m thinking about creating a MARS simulator to run on the Seeeduino XIAO that I’m using to power my 12×12 array. I’m also thinking about creating a Redcode assembler utility that can generate the warrior programs to run on the simulator. But wait, there’s more! Do you remember me talking about the NeoPixel Simulator that you can use to test your own programs to run on my 12×12 array (PE, November 2020)? Well, if I manage to find the time to get a MARS simulator up and running, we could combine it with our NeoPixel Simulator, thereby allowing you to create and test your own Code War warrior programs and then send them to me to be run on the real array. return gammaCorrectedColor; Keep your balance const uint8_t GammaXref[] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 7, 7, 8, 8, 8, 9, 9, 9, 10, 5, 6, 6, 6, 6, 7, 7, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105, 107, 109, 110, 112, 114, 115, 117, 119, 120, 122, 124, 126, 127, 129, 131, 133, 135, 137, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 167, 169, 171, 173, 175, 177, 180, 182, 184, 186, 189, 191, 193, 196, 198, 200, 203, 205, 208, 210, 213, 215, 218, 220, 223, 225, 228, 231, 233, 236, 239, 241, 244, 247, 249, 252, 255 }; Fig.3. Gamma-correction cross-reference look-up table. uint32_t GetGammaCorrectedColor (uint32_t uncorrectedColor) { uint8_t tmpRed; uint8_t tmpGreen; uint8_t tmpBlue; uint32_t gammaCorrectedColor; tmpRed = GammaXref[ GetRed(uncorrectedColor) ]; tmpGreen = GammaXref[ GetGreen(uncorrectedColor) ]; tmpBlue = GammaXref[ GetBlue(uncorrectedColor) ]; } The rest of the sketch is used to load the left-hand side of the array with uncorrected colours directly from our colour wheel and the right-hand side with their gamma-corrected counterparts, starting with red at the bottom and ending with rose at the top (Fig.4). Although it’s not easy to see from this image, in the real world the gamma-corrected values do present what appears to be a richer colour palette. For example, the gamma-corrected orange (second row from the bottom) looks more orange and the gamma-corrected rose (top row) appears more vibrant. War, what is it good for? According to Edwin Starr in his 1970 hit single ‘War’ – and Frankie Goes to Hollywood more than a decade later – the answer is ‘Absolutely nothing.’ Of course, it may be that neither of these luminaries were familiar with the concept of ‘Code War’. Actually, if the truth be told, neither was I until my chum, Ken Wood, who has been following these columns, sent me an email telling me all about this idea. In 1984, Alexander Dewdney wrote a column in Scientific American magazine about a programming game called Core War that he had created with DG Jones. A scan of this original article, along with a lot of supporting material, can be found on the CoreWars.org website and Wikipedia. Fig.4. Uncorrected colours (left) vs. gamma-corrected colours (right). Fig.5. 9DOF BoB (Image source: Adafruit.com) Practical Electronics | January | 2021 When I was a kid, my parents bought me a wooden marble maze toy. I just found something quite similar on Amazon (https://amzn.to/2HwZg4M), although the one I owned had larger mazes and used smaller ball bearings. The reason I mention this here is that a reader emailed me to suggest I attach a sensor to my 12×12 array such that, if the array is held in a horizontal plane, I could control the ‘rolling’ of a lit pixel by detecting the tilt of the array. By some strange quirk of fate, I just happened to have one of Adafruit’s BNO055-based 9DOF (nine degrees of freedom) Fusion breakout boards (BOBs) in my treasure chest (junk box) of spare parts (Fig.5) (https://bit.ly/3dP8EwU). This little beauty is based on a BNO055 microelectromechanical system (MEMS) sensor from Bosch. In turn, the BNO055 contains a 3-axis accelerometer, a 3-axis gyroscope, and a 3-axis magnetometer (they also throw in a temperature sensor for good measure). The really cool thing about this device is that it also contains a 32-bit Arm Cortex M0+ processor, which performs all sorts of mindbogglingly complicated sensor algorithms for you and provides you with data in a form you can use without your brains leaking out of your ears. As usual, the folks at Adafruit provide a wealth of information on this sensor, including pinouts, wiring, and how to download the required libraries (https://bit.ly/35sVvpz). Also included is some sample Arduino Code, which I used to create my first test program. The purpose of this initial sketch was to make sure I could get my XAIO microcontroller to talk to the BNO055. All we do is loop around reading the x, y, and z orientation values from the BNO055 and display them as floating-point values on the Arduino’s Serial Monitor. Note that the XIAO communicates with the BNO055 via an I2C bus, which uses pins 5 and 6 on the XIAO, but we don’t declare these pins in our sketch because Adafruit’s libraries handle all of this for us (file CB-Jan21-02.txt). The next step involved some mental gymnastics to visualize how I was going to mount my breadboard in the 12×12 array case, and which (sensor) values corresponded to what (left-right and forward-backward) tilts. Eventually, I determined that the 59