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Get thousands of capacitance values with this . . . 6-Decade Capacitance Substitution BBox ox By NICHOLAS VINEN When breadboarding or prototyping, sometimes you need to experiment with a capacitor value. Substituting a range of different capacitors can be a bit tedious. What you need is a capacitance decade box, which makes it easy to find the right value for your circuit. O UR 6-DECADE RESISTANCE Substitution Box described in April 2012 lets you easily find the right value for a resistor in your circuit. Sometimes though, you also need to vary a capacitance. For example, you may have an RC oscillator where the resistor is integrated in an IC so you can’t change it. For whatever reason, when you need to tune the value of a capacitor, this 84  Silicon Chip new 6-Decade Capacitance Substitution Box is ideal. It gives you hundreds of thousands of different capacitance values to play with, from about 30pF to 6µF. It can be used to tune oscillators, filters, time delays, compensation networks, rise and fall times, AC-coupling stages, rail-splitters, feedback loops and so on. Even in situations where you can calculate the required value of a ca- pacitor, you may still need to tweak it to work in a real circuit. Design A capacitance substitution box is slightly trickier to design than a resistance substitution box. Because resistor values sum when connected in series, a rotary switch can be connected to a resistor string giving you a variable “tap” point. For example, with 10 x siliconchip.com.au 6 S1b 4 3 9 100nF 1 F 1 F 4 5 100nF 100nF 2 150nF 150nF 180nF 220nF 100nF 180nF 220nF 3 S2 x100nF 8 1 F 6 1 10 1 F 3 S1a 1 12 1 F 2 x1 F 2 11 1 F 1 5 270nF 330nF 100nF 270nF 330nF 330nF 470nF 4 220nF 680nF 5 7 11 6 10nF 12 1 10 9 10nF 2 15nF 15nF 18nF 22nF 10nF 18nF 22nF 3 S3 x10nF 8 10nF 27nF 33nF 10nF 27nF 1nF 2.7nF 3.3nF 33nF 33nF 47nF 4 22nF 68nF 5 7 11 6 1nF 12 1 10 9 1nF 2 1.5nF 1.5nF 1.8nF 2.2nF 1nF 1.8nF 2.2nF 3 S4 x1nF 8 1nF 2.7nF 3.3nF 3.3nF 4.7nF 4 2.2nF 6.8nF 5 7 11 6 100pF 12 1 10 9 2 150pF 150pF 180pF 220pF 3 S5 x100pF 8 100pF 100pF 100pF 180pF 220pF 270pF 330pF 100pF 270pF 330pF 330pF 470pF 4 220pF 680pF 5 7 11 6 10pF 12 1 10 9 10pF 15pF 15pF 18pF 3 S6 x10pF 8 2 10pF 4 22pF 2.7pF 47pF 27pF 33pF T2 2.2pF 68pF 33pF 47pF 22pF 68pF 5 7 6 T1 SC 2012 CAPACITANCE DECADE BOX Fig.1: the circuit for the Capacitance Decade Box consists of just six rotary switches, two binding posts and a bunch of different non-polarised capacitors. Sets of capacitors are paralleled to give the values required and switches S1-S6 select one set for each decade. The selected sets are connected in parallel, giving the required capacitance across binding posts T1 and T2. siliconchip.com.au July 2012  85 18nF 22nF 10nF 18nF 15nF 15nF 27nF 68pF 100pF 100pF 270pF 180pF 100pF 220pF 180pF S6 T2 10pF 10pF 10pF x10pF 15pF 15pF 2.7pF 47pF 2.2nF 68pF 330pF 22pF 33pF 2.2pF x100pF 1.5nF 33pF 270pF 150pF 47pF 100pF 220pF 1.8nF 100pF 330pF 1.5nF 2.2nF 1.8nF x1nF 1nF 1nF 3.3nF S5 470pF 1nF 2.7nF 1nF T1 10nF 33nF 22nF 100nF 150nF 680pF S4 3.3nF x10nF 220pF 1nF 2.7nF 10nF 27nF 100nF 220nF 180nF 100nF 330nF 1 F 10nF 10nF 27pF 6.8nF 1 F x100nF 270nF 2.2nF 3.3nF 1 F 4.7nF 1 F 1 F 180nF x1 F 330nF 220nF 1 F 270nF S3 33nF 33nF S2 100nF 47nF 150nF S1 Capacitance Decade Box © 2012 22nF 100nF 330nF 68nF 220nF 680nF 160140 1 204106121 470nF 18pF 22pF Fig.2: follow this parts layout diagram to build the 6-Decade Capacitance Box. Note that the switches must be installed with their anti-rotation spigots orientated as shown. The tops of these spigots must also be removed using side cutters. 100Ω resistors and an 11-position rotary switch, you can select a resistance in the range of 0-1000Ω in 100Ω steps. But connecting capacitors in series gives a different result: two 100pF capacitors in series gives 50pF, three gives 33pF, four 25pF and so on. The resulting values aren’t multiples of 10 and even if the values were convenient, there’s the additional problem that the more capacitors you put in series, the larger they need to be for the whole string to have even a modest capacitance. So we need to connect capacitors in parallel to make a substitution box. In practice, this means we need 10 sets of capacitors per decade, with values of (for example) 100pF, 200pF, 300pF, etc. Each switch selects one set for that decade and the decades are wired in parallel so that the capacitances combine. For example if you select 300pF with one switch and 2nF with anoth­ er, that will give you 300pF || 2nF = 2.3nF. Because capacitor values are assigned logarithmically, to get decimal values, we need one, two or three capacitors in parallel. For example, 300pF can be made using two 150pF capacitors while 400pF can be made with 220pF and 180pF capacitors. We have used values from the E6 series where possible as these are the most 86  Silicon Chip common ones. A few values from the E12 series have also been used, where necessary. The result of all this is that you can basically just “dial up” a value using the six switches. Circuit description Stray capacitance The full circuit is shown in Fig.1. There is one rotary switch per decade, labelled S1-S6. For the 10pF through to 100nF decades they are single-pole, 10-position switches (S2-S6) while S1 has two poles and six positions. All the capacitors in the circuit are connected together at one end and to binding post T1. Switches S1-S6 connect the other ends of the selected capacitors to T2 while the others remain unconnected and so don’t contribute to the total capacitance. The capacitors around S2, S3, S4 and S5 are arranged identically. The only difference is in their values. The lowest range (S6) is slightly different because we can use two fewer capacitors since we don’t worry about sub-picofarad errors. S1 controls the 1µF range and this is arranged a differently than the others, to reduce the number of large capacitors required. It works the same way as the other switches to select values up to 3µF. For 4µF, the capacitors used for the 1µF and 3µF positions are connected in parallel, using both switch poles. Similarly, for 5µF, the capacitor sets for 2µF and 3µF are connected in parallel. In an ideal world, the capacitance you get would be exactly what you have selected using S1-S6 but in reality, it will vary slightly, for a couple of reasons. The first is the stray capacitance of the PCB itself which is around 30pF. This adds to whatever capacitance you have selected using the rotary switches. It is irrelevant for large values but could be significant for values below a couple of nanofarads. The 10pF range is still useful, despite the fact that this stray capacitance is so large in comparison. It means that you can increase the capacitance in small steps (~10pF). You just need to remember to mentally add about 30pF when selecting very small values. Then there are the tolerances of the capacitors themselves. 1% resistors are commonly available and cheap but a typical MKT or ceramic capacitor is either ±10% or ±20%. For this project, stick with the 10% types if possible. Capacitor value variations are somewhat mitigated when paralleling similar values. Say we have two 1nF±10% capacitors connected in parallel and their errors are uncorrelated. Each siliconchip.com.au Parts List 1 PCB, code 04106121, 146 x 86mm 1 PCB, code 04106122, 157.5 x 95mm (front panel/lid) OR 1 front panel label 1 UB1 Jiffy box (Jaycar HB6011, Altronics H0201) 1 2-pole 6-position rotary switch (S1) 5 1-pole 12-position rotary switches (S2-S6) 6 16-20mm knobs to suit S1-S6 (Jaycar HK7762, Altronics H6042) 2 captive binding posts (Jaycar PT0454, Altronics P9254) capacitor will be between 0.9nF and 1.1nF, an error of ±0.1nF. While the worst case values for the combination are 1.8nF and 2.2nF, the average error of any two capacitors is √(0.1nF2 + 0.1nF2) = 0.141nF or 7.07%. If the capacitors are of the same value and from the same batch, we can’t assume the errors are uncorrelated. This effect is also less pronounced when the capacitor values paralleled vary significantly. But given the above, when we parallel multiple capacitors of similar values, we can generally expect slightly less variation in the resulting capacitance than the individual tolerances would suggest. Using 10% capacitors, the result will be accurate enough for most purposes but if you want better accuracy, use capacitors with a tighter tolerance (eg, 5%) or else buy several of each and pick those closest to their nominal values, using an accurate capacitance meter. To be really tricky, where multiple capacitors are paralleled, you can select them on the basis of the lowest total error for each set. Capacitor type We use non-polarised capacitors in this project to make it as versatile as possible. MKT (metallised polyester) types are used for values from 1nF up to 680nF as they have good perforsiliconchip.com.au mance, are commonly available and have a consistently small size. Ceramic capacitors are used for values below 1nF because they are more common at these values. Those with an NP0/C0G dielectric are better; these are common for values of 100pF and below. You can substitute different types if you prefer, provided they fit. The 1µF capacitors can be either MKT or monolithic multilayer ceramic (MMC). MKTs have better performance and tend to have tighter tolerances but cost more and some 1μF MKT capacitors may be too large (they need to have a 5mm or 0.2-inch pin spacing). Note that through-hole MKT and MMC capacitors generally have a voltage rating of at least 50V and this should generally be sufficient. Test leads The most convenient way to use the Capacitance Decade Box is to connect it to your circuit with a short pair of banana-plug-to-alligator-clip test leads. But keep in mind that the leads will have some capacitance which will be added to that from the box itself. Longer leads have more capacitance so keep them short. The leads also have some inductance (as does the PCB). In practice, this limits the use of the box to circuits operating at up to a few megahertz, MKT Capacitors 6 1µF MKT or monolithic ceramic (5mm lead spacing) 1 680nF 3 22nF 1 470nF 2 18nF 3 330nF 2 15nF 2 270nF 5 10nF 3 220nF 1 6.8nF 2 180nF 1 4.7nF 2 150nF 3 3.3nF 5 100nF 2 2.7nF 1 68nF 3 2.2nF 1 47nF 2 1.8nF 3 33nF 2 1.5nF 2 27nF 5 1nF Ceramic Capacitors* 1 680pF 2 47pF 1 470pF 2 33pF 3 330pF 1 27pF 2 270pF 2 22pF 3 220pF 1 18pF 2 180pF 2 15pF 2 150pF 3 10pF 5 100pF 1 2.7pF 2 68pF 1 2.2pF Note1*: C0G/NP0 ceramic capacitors preferred Note 2: the PCBs are available from the SILICON CHIP Partshop ie, it may not be suitable for use with some RF circuits, mainly because of stray capacitance. Construction The Capacitance Decade Box is built on a 146 x 86mm PCB coded 04106121 which fits into a UB1 jiffy box. Construction is easy; simply fit the capacitors where shown on the overlay diagram (Fig.2). Start with July 2012  87 CONTROL KNOB BINDING POST SWITCH MOUNTING NUT BOX LID STAR WASHER SWITCH SHORTEN PLASTIC SPIGOT BINDING POST MOUNTING NUT Fig.3: the PCB is secured to the back of the lid by resting it on the tops of the switches and doing up the switch nuts. The binding post spigots are then soldered to their pads. PCB the lowest profile MKTs, then mount the ceramic capacitors and the rest of the MKTs. Before fitting the switches, remove the small plastic spigots that protrude from the base using side-cutters (see Fig.3). Clean up with a file, if necessary, then cut the shafts of all six switches to a length of 10mm. This is easily done by clamping the shaft in a vice and cutting it with a hacksaw. File off any burrs. The switches can then be soldered to the PCBs. Make sure the 2-pole switch (S1) is fitted with the orientation shown in Fig.2. All the switches must be mounted flush with the PCB; check before soldering more than two pins. Housing You can either drill the box lid and attach a front panel label or else purchase a pre-drilled and screen printed PCB which replaces the plastic lid (157.5 x 95mm, coded 04106122). This PCB lid gives your Capacitance Decade Box a professional appearance (the front-panel PCB is available from the SILICON CHIP Partshop). Alternatively, you can download the front-panel label (in PDF format) from the SILICON CHIP website, print it out and use it as a drilling template to make the eight holes in the plastic lid. A second copy can then be printed out, laminated and attached to the lid using silicone adhesive. Next, loosely fit the two binding posts onto the lid, then remove the nuts and washers from the rotary switches. The lower washer has a locking pin and this is used to select the number of switch positions available. To do this, place the PCB flat on your workbench, turn all the switches fully anti-clockwise and insert the washers for S2-S6 so that each locking pin goes 88  Silicon Chip into the hole marked “10”. By contrast, for switch S1, insert the locking pin of the washer into the hole marked “6”, so that it only rotates through six positions. That done, slip the star-washers over the shafts, then push them through the lid while keeping the PCB horizontal, so you don’t knock the washers out of alignment. Guide the binding post shafts through the matching holes on the PCB and then do up the six nuts tight. You can then tighten up the binding post nuts using a small spanner and after checking that they are correctly aligned, solder them to the PCB pads. Fit the knobs and then drop the lid assembly into the box and attach it using the four provided self-tapping screws. If your box came with rubber plugs that cover the screw holes and you are not using the PCB lid, you can fit them now. Using it As stated earlier, the Capacitance Decade Box is most convenient in combination with short alligator clip leads but you can also connect bare wires into the binding posts, You can even use solid-core wire so that the other end can be plugged into a breadboard. Keep in mind that the rotary switches will have either “make before break” or “break before make” operation, depending on the type supplied. This means that if you change the capacitance while the unit is connected to a working circuit, the capacitance will briefly be either very low (~30pF) or higher than usual while switching. In most cases, this won’t upset the circuit but it depends on its exact configuration. Once you have found the optimal capacitance for your circuit using the Capacitor Codes Value 1µF 680nF 470nF 330nF 270nF 220nF 180nF 150nF 100nF 68nF 47nF 33nF 27nF 22nF 18nF 15nF 10nF 6.8nF 4.7nF 3.3nF 2.7nF 2.2nF 1.8nF 1.5nF 1nF 680pF 470pF 330pF 270pF 220pF 180pF 150pF 100pF 68pF 47pF 33pF 27pF 22pF 18pF 15pF 10pF 2.7pF 2.2pF µF Value 1µF 0.68µF 0.47µF 0.33µF 0.27µF 0.22µF 0.18µF 0.15µF 0.1µF .068µF .047µF .033µF .027µF .022µF .018µF .015µF .01µF .0068µF .0047µF .0033µF .0027µF .0022µF .0018µF .0015µF .001µF   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA IEC Code   1u0 680n 470n 330n 270n 220n 180n 150n 100n   68n   47n   33n   27n   22n   18n   15n   10n   6n8   4n7   3n3   2n7   2n2   1n8   1n5    1n 680p 470p 330p 270p 220p 180p 150p 100p   68p   47p   33p   27p   22p   18p   15p   10p   2p7   2p2 EIA Code 105 684 474 334 274 224 184 154 104 683 473 333 273 223 183 153 103 682 472 332 272 222 182 152 102 681 471 331 271 221 181 151 101   68   47   33   27   22   18   15   10   2.7   2.2 decade box, you can disconnect the it and measure the capacitance across the output terminals. Alternatively, you can just read out the position of the switches, which should be accurate to within a few percent of the true value SC for settings above 1nF. siliconchip.com.au