# Gas station without pumps

## 2014 July 6

### Battery connectors

Filed under: Uncategorized — gasstationwithoutpumps @ 02:32
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I spent a little time today working on my book, but I got side tracked into a different project for the day: designing a super-cheap coin-cell battery connector. I’ve used coin-cell battery holders before, like on the blinky EKG board, where I used a BH800S for 2 20mm CR2032 lithium cells. That battery holder is fairly large and costs over $1—even in 1000s it costs 70¢ a piece. So I was trying to come up with a way to make a dirt cheap coin-cell holder. The inspiration came from the little LED lights that “glovers” use inside their gloves. They are powered by two CR1620 batteries (that means a 16mm diameter and 2.0mm thickness for the battery). Because the lights have to be made very cheaply, they don’t use an expensive holder, but put the negative side of the batteries directly against a large copper pad on the PC board. The batteries are held in place by the positive contact, which is a piece of springy metal pressing the battery against the board—and each manufacturer seems to have a slightly different variant on how the clip is made. Unfortunately, I was unable to find any suppliers who sold the little clips—though I found several companies that make battery contacts, it seems that most are custom orders. My first thought was to bend a little clip out of some stainless steel wire I have sitting around (not the 1/8″ welding rod, but 18-gauge 1.02362mm wire). That’s about the same thickness as a paperclip (which is made out of either 18-gauge or 19-gauge wire), but the stainless steel is stiffer and less fatigue-prone than paperclips. I was a little worried about whether stainless steel was solderable, so I looked it up on Wikipedia, which has an article of solderability. Sure enough, stainless steel is very hard to solder (the chromium oxides have to be removed, and that takes some really nasty fluxes that you don’t want near your electronics). So scratch that idea. I spent some time looking around the web at what materials do get used for battery contacts—it seems there are three main ones: music wire, phosphor bronze, and beryllium copper, roughly in order of price. Music wire is steel wire, which gets nickel plated for making electrical connections. It is cheap, stiff, and easily formed, but its conductivity is not so great, though the nickel plating helps with that. The nickel oxides that form require a sliding contact to scrape off to make good electrical connection. Phosphor bronze is a better conductor, but may need plating to avoid galvanic corrosion with the nickel-plated battery surfaces. Most of the contacts I saw on the glover lights seemed to have been stamped out of phosphor bronze. Beryllium copper is a premium material (used in military and medical devices), as it has a really good ratio of yield strength to Young’s modulus, so it can be cycled many times without failing, but also has good conductivity. Since I don’t have metal stamping machinery in my house, but I do have pliers and vise-grips, I decided to see if I could design a clip out of wire. It is possible to order small quantities of nickel-plated music wire on the web. For example, pianoparts.com sells several different sizes, from 0.1524mm diameter to 0.6604mm diameter. I may even be able to get some locally at a music store. My first design was entirely seat-of-the-pants guessing: First clip design, using 19-gauge wire, with two 1mm holes in PC board to accept the wire. This design is intended for two CR1620 batteries. The idea was to have a large sliding contact that made it fairly easy to slide the batteries in, but then held them snugly. Having a rounded contact on the clip avoids scratching the batteries but can (I hope) provide a fair amount of normal force to hold the batteries in place. But how much force is needed? I had a very hard time finding specifications on how hard batteries should be held by their contacts. Eventually I found a data sheet for a coin battery holder that specified “Spring pressure: 50g min. initial contact force at positive and negative terminals”. Aside from referring to force as pressure and then using units of mass, this data sheet gave me a clear indication that I wanted at least 0.5N of force on my contacts. I found another battery holder manufacturer that gave a tiny graph in one of their advertising blurbs that showed a range of 100g–250g (again using units of mass). This suggests 1N-2.5N of contact force. Another way of getting at the force needed is to look at how much friction is needed to hold the batteries in place and what the coefficient of friction is for nickel-on-nickel sliding. The most violently I would shake something is how fast I can shake my fingertips with a loose wrist—about 4Hz with an peak-to-peak amplitude of 22cm, which would be a peak acceleration of about 70 m/s^2. Two CR1620 cells weigh about 2.5±0.1g (based on different estimates from the web), so the force they need to resist is only about 0.2N. Nickel-on-nickel friction can have a coefficient as low as 0.53 (from the Engineering Toolbox), so I’d want a normal force of at least 0.4N. That’s in the same ballpark as the information I got from the battery holder specs. So how stiff does the wire have to be? I specified a 0.2mm deflection, so I’d need at least 2N/mm as the spring constant for the contact, and I might want as high as 10N/mm for a really firm hold on the batteries. So how should I compute the stiffness of the contact? I’ve never done mechanical engineering, and never had a statics class, but I can Google formulas like any one else—I found a formula for the bending of a cantilever loaded at the end: $\frac{F}{d} = \frac{3 E I}{L^{3}}$, where F is force, d is deflection, E is Young’s modulus, I is “area moment of inertia”, and L is the length of the beam. More Googling got me the area moment of inertia of a circular beam of radius r as $\frac{\pi}{4} r^{4}$. So if I use the 0.912mm wire with an 8mm beam I have F/d = 200E-6 mm E. More Googling got me some typical values of Young’s modulus: material E [MPa = N/(mm)^2] phosphor bronze 120E3 beryllium copper 135E3 music wire 207E3 If I used 19-gauge phosphor bronze, I’d have about 24N/mm, which is way more than my highest desired value of 10N/mm. Working backwards from 2–10N/mm what wire gauge would I need? I get a diameter of 0.403mm to 0.603mm, which would be #6 (0.4064mm), #7 (0.4572mm), #8 (0.5080mm), #9 (0.5588mm), or #10 (0.6096mm), on the pianoparts.com site. I noticed that battery contact maker in Georgia claims to stock 0.5mm and 0.6mm music wire for making battery contacts, though they first give the sizes as 0.020″ and 0.024″, so I think that these are actually 0.5080mm and 0.6096mm (#8 and #10) music wire. It seems that using #8 (0.020″, 0.5080mm) nickel-plated music wire would be an appropriate material for making the contacts. Note that the loop design actually results in two cantilevers, each with a stiffness of about 4N/mm, resulting in a retention force of about 1.6N. The design could be tweaked to get different contact forces, by changing how much deflection is needed to accommodate the batteries. How much tweaking might be needed? I found the official specs for battery sizes (with tolerances) in IEC standard 60086 part 2: The thickness for a 1620 is 1.8mm–2mm, the diameter is 15.7mm–16mm, and the negative contact must be at least 5mm in diameter. The standard also calls for them to take an average of 675 hours to discharge down to 2v through a 30kΩ resistor (that’s about 56mAH, if the voltage drops linearly, 67mAH if the voltage drops suddenly at the end of the discharge time). If the batteries can legally be as thin as 1.8mm, then to get a displacement of 0.2mm, I’d need the zero-point for the contacts to be only 3.4mm from the PC board, not 3.8mm, and full thickness batteries would provide a displacement of 0.6mm, and a retention force of about 4.8N. If I were to do a clip for a single CR2032 battery, I’d need to have a zero-point 2.8mm from the board, to provide 0.2mm of displacement for the minimum 3.0mm battery thickness. So now all I need to do is get some music wire and see if I can bend it by hand precisely enough to make prototype clips. I’d probably change the spacing between the holes to be 0.3″ (7.62mm), so that I could test the clip on one of my existing PC boards. Update 2014 July 6: I need to put an insulator on the verticals (heat shrink tubing?), or the top battery will be shorted out, since the side of the lower battery is exposed. ## 2013 July 10 ### Some failed designs For the past couple of days I’ve been exploring variations on the Blinky EKG project, looking at alternative approaches. For example, I looked at the possibility of eliminating the most expensive part (the instrumentation amp), and decided that building my own instrumentation amp out of op amps and discrete resistors was unlikely to be reliable. I discovered (after doing calculations for 2-op-amp and 3-op-amp designs) that 1% tolerance on the resistors would produce poor common-mode rejection. In Common-mode noise in EKG, I reported measurements of the common-mode noise with a fairly short twisted-pair connection to the EKG electrodes (close to a best-case scenario). I concluded that the common-mode noise was way too large for using unmatched resistors to be a reasonable design, and using an integrated instrumentation amp is still a good choice. Yesterday, I tried turning the question around? Could I eliminate the op-amp chip? Currently, I’m using the op amp for two things: to provide a unity-gain buffer to make the reference voltage source between the power rails, and to do second-stage amplification after a high-pass filter removes the DC offset. To eliminate the op-amp chip, I need to replace both these functions. Replacing the unity-gain buffer seems fairly easy—I could use a low-drop-out linear regulator to generate the reference voltage instead of a voltage divider and unity-gain buffer, which would be somewhat smaller and cheaper (11¢ rather than 25¢ in 100s). I didn’t have an LDO linear regulator at home, so I tried using a TL431ILP voltage reference instead. Unfortunately, it provides very little current, and was unable to maintain the desired voltage when hooked up to the reference voltage input of the instrumentation amp. I believe that a part like the LM317L would work fine, though, and I may want to test that at some point. Removing the second-stage amplifier is more problematic. I can set the gain of the instrumentation amp up to 2000 or 2500 easily, but any DC component in the input differential signal results in saturating the amplifier (with a 6v output range, and a 1mV AC signal, we’d need the DC bias to be less than 1mV also to avoid hitting the power rails). I tried putting high-pass filters in front of the instrumentation amp, but with the long time constants needed to avoid filtering out the EKG signal, the filters never settled to within 1mV of each other, and the instrumentation amplifier always saturated. So I need to keep the first-stage gain small enough to avoid saturation, which means I need a second-stage amplifier. I could use a single op amp for the second stage and a low-drop-out regulator for the reference voltage, which would produce a cleaner output signal (since my voltage-divider-plus-unity-gain-buffer reference introduces noise from the power lines). The MCP6001 single op amp is only 18¢ in 100s (rather than 25¢ for the MCP6002 dual op-amp), but the MCP6001 is only available as a surface-mount component, which I think is inappropriate for a first soldering project. The MCP6001 + LM317L would cost about 4¢ more than the MCP6002. I considered redesigning the Blinky EKG to use the LM317L voltage regulator and the MCP6002, even though half the MCP6002 would be unused, but the LM317L needs a 1.5mA load to maintain regulation, and that seems like a lot for a battery operated device—more than the op amp or the instrumentation amp use (though less than the LED when it is lit). Even using a TL431ILPR voltage reference (10¢ in 100s) and the unity-gain buffer would only need 1mA, and would save one resistor. There are lower-current voltage references, like the LM385, but they cost a lot more (42¢ in 100s). The non-rechargeable CR2032 batteries I’ve been using for the Blinky EKG have about a 225 mAh capacity, and cost about 19¢ in 100s (but the design needs 2, so 39¢). I could probably get about a 100-hour life with the present Blinky EKG design—I need to measure the current and the duty cycle of the LED to get a better estimate. The Blinky EKG weighs about 20g (not counting the wires to the electrodes), which is a bit heavy for a pendant or brooch. Most of the weight is in the batteries, but a lighter battery would give up a lot of running time. The smaller batteries also cost a lot more, probably because Digikey only buys them in quantities around 10,000 rather than in the millions. (From other suppliers CR2032 batteries cost about 60¢ in 100s, not under 20¢). It has been good to fool around with the Blinky EKG design, as it has gotten me to think a bit about design issues other than the first can-I-get-it-to-work one. I rarely get my students past that point in their thinking, and I’m not sure how I would do so, as there is always so much time pressure to cover new stuff, that they get very little time to tinker with designs. ## 2013 July 8 ### Common-mode noise in EKG Filed under: Circuits course — gasstationwithoutpumps @ 18:00 Tags: , , , , , , , , In 2-op-amp instrumentation amp, I said I’ll have to make some measurements later this week to see how large the common-mode noise on the EKG signals really is. Of course, it is likely to be highly variable, depending on the electrodes and the wiring to them, but ball-park estimates would be useful. If the AC common-mode voltage is ±200mV and we have worst-case resistor values, then we would have a ±8mV common-mode output from the instrumentation amp. With the lowest differential amplification (6.6 at Rgain=∞), a 1mV EKG signal would be smaller than the common-mode noise. Such a large common-mode voltage would easily justify the expense of the instrumentation amp chip. (Note: large DC common-mode voltages don’t matter, as the DC-blocking capacitor I used after the instrumentation amp can eliminate them.) If the AC common-mode voltage is only ±1 mV, then the Blinky EKG could probably work even with very poor common-mode rejection in the instrumentation amp, and building it out of op amps and discrete resistors is feasible. So today I tried measuring the common-mode signal. As it turns out, I had built an EKG amplifier on the protoboard that had a split Rgain resistor (two 12kΩ resistors in series). The node between the 2 resistors should be at (Vp+Vm)/2, the common-mode voltage. That node was fed to a unity-gain buffer, so I tried measuring the AC common-mode voltage. I did this with two different tools: my Fluke 8060A multimeter (which measures RMS voltage) and my BitScope Pocket Analyzer, which can measure peak-to-peak voltage. With the multimeter, I saw about 20–35 mV RMS, and with the BitScope I saw 90–130 mV peak-to-peak (depending on where my arms were relative to the wires to the electrodes). Trace of common mode noise recorded by the BitScope Pocket Analyzer, at 20mV/division. The fundamental frequency of the noise is 60Hz. Sorry about the black background—the manufacturers are promising a white background as an option in some future release of the software. Maybe they’ll add some labels for the x and y tick marks at the same time! If I take the leads off the electrodes and clip them all together, then the common-mode noise drops below the level that the BitScope can measure (its noise floor is about 10mV). The multimeter also has trouble, reporting values from 0.05mV to 1.5mV. If I put a 3.3MΩ resistor between the two signal leads, and connect one of them to the Vref lead, then the multimeter reports about 13–20 mV RMS and the BitScope around 80–90 mV peak-to-peak. The common-mode problems are definitely coming from the wiring to the electrodes. With 130mV peak-to-peak common-mode voltage and a common-mode gain of 0.02 or 0.04, we’d have 2.6–5.2 mV of common-mode noise at the output of an instrumentation amp made with discrete resistors and op amps. If the gain of the amplifier were around 6.6, we’d have a peak-to-peak signal of about 6.6 mV for the EKG signal, and the details of that signal would be buried in common-mode noise. If we got lucky with the resistor values and they matched better than the specs claim (which is actually fairly likely), then the Blinky EKG would sort-of work with discrete op amps—as long as the 60Hz noise is no worse that what I saw. Many people are likely to be in electromagnetically noisier locations than my room, so the common-mode noise is likely to be much higher sometimes, and even with lucky matching of the resistors the common-mode signal is likely to swamp the real signal. Thus I have confirmed that an integrated instrumentation amp is needed for the Blinky EKG, and there is no point trying to design one using discrete resistors and op amps. ## 2013 July 7 ### 2-op-amp instrumentation amp Filed under: Circuits course — gasstationwithoutpumps @ 20:50 Tags: , , , , , , , , Last summer, I tried building an instrumentation amp using the MCP6002 op amps and external discrete resistors, and ended up with an amplifier that had terrible common-mode rejection, which is why I decided to use the INA126P instrumentation amp chip for the Blinky EKG boards and for the instrumentation amp protoboards. I think I’d like to revisit that idea though, to see if I can make a cheaper Blinky EKG. If I put together a Blinky EKG kit with the current design, the parts would cost about$9.30 (buying quantities of 100).  The mist expensive single part is the instrumentation amp at $2.44. If I could get the 2-op amp instrumentation amp to work using discrete components, I might be able to save most of that. Replacing them MCP6002 dual op amp with an MCP6004 quad op amp and 4 more resistors would cost about 22¢ rather than$2.44, bring the parts cost down to around $7.07. I could also reduce the price by using surface-mount devices (SMDs) instead of through-hole components. An instrumentation amp like the INA826 ($1.34 in 100s) would be a good choice if I went with SMDs. But if I used SMDs, the Blinky EKG would probably have to be a finished product rather than a kit, which would add substantial manufacturing costs, especially for things like a case, which could be omitted in a kit. The idea of a blinky board is to be an easy soldering project for beginners, so I’m not sure that a pre-assembled blinky EKG has much appeal for me (which is not to say there is no market for it, just that I’m not particularly interested in designing for that market).

I looked at my old post and realized that I had miscomputed the gain for the differential signal, and never computed the gain for the common-mode signal.  If the resistors are perfectly matched, the common-mode gain is 0, but without the laser trimming that makes the instrumentation amp chips so expensive, we’re not going to get perfect matching.  The classic approach of adding trimpots takes up too much space and ends up costing almost as much as using an instrumentation amp chip.

So the rest of this post is dedicated to better understanding the 2-op-amp instrumentation amp.  I drew a schematic of a possible design, in order to have names for the parts and signals.

Schematic drawn with SchemeIt and captured as a screenshot. The native exports into PNG and PDF formats were useless, because SchemeIt messed up the Unicode character Ω. I also had to do this as a 24-bit PNG, because WordPress.com seems to mess up 8-bit PNGs (they look fine when editing, but not in the Preview.)

To analyze the circuit assuming ideal op amps (so the voltage difference between the two inputs of the op amp is 0), we need to look at the current through each resistor:

$I_{1} = (V_{out} - V_{p}) /R_{1}$
$I_{2} = (V_{p} - V_{mid}) /R_{2}$
$I_{3} = (V_{mid} - V_{m}) /R_{3}$
$I_{4} = (V_{m} - V_{ref}) /R_{4}$
$I_{gain} = (V_{p} - V_{m}) /R_{gain}$

We also have that
$I_{1} = I_{2}+ I_{gain}$ and $I_{4} = I_{3} + I_{gain}$, by Kirchhoff’s current law.

We can add to get $I_{1} + I_{4} = I_{2} + I_{3} + 2 I_{gain}$, which can be expressed as
$(V_{out} - V_{p}) /R_{1} + (V_{m} - V_{ref}) /R_{4} =$
$(V_{p} - V_{mid}) /R_{2} + (V_{mid} - V_{m}) /R_{3} + 2 (V_{p} - V_{m}) /R_{gain}$

If $R_{1}=R_{4}$ and $R_{2}=R_{3}$, then we can multiply both sides by $R_{1}$ to get
$V_{out}-V_{ref} - (V_{p}-V_{m}) = R_{1} (V_{p}-V_{m}) (1/R_{2} +2 /R_{gain})$,
or
$\frac{V_{out}-V_{ref}}{V_{p}-V_{m}} = 1+ R_{1}/R_{2} + 2 R_{1}/R_{gain}$.

For the values in the schematic above the differential gain is 6.6 + 112kΩ/Rgain.

To look at common-mode gain, it is best to solve the pair of equations for the currents I1 and I4. Being lazy, I used maple to do the algebra:

solve( { (vout-vp)/r1= (vp-vmid)/r2 + (vp-vm)/rgain, (vm-vref)/r4=(vmid-vm)/r3+(vp-vm)/rgain, \
vor=vout-vref}, {vout,vor,vmid});
simplify(taylor(subs(vp=vcomm+vdiff/2+vref, vm=vcomm-vdiff/2+vref, rhs(%[3])),vdiff));


which produced

vcomm (-r2 r4 + r1 r3)
- ---------------------- +
r2 r4

2 r1 rgain r4 + r2 rgain r4 + 2 r1 r2 r4 + 2 r1 r4 r3 + r1 r3 rgain
------------------------------------------------------------------- vdiff
2 r2 rgain r4



that is,

$V_{out}-V_{ref} = V_{common} \left(1- \frac{R_{1} R_{3}}{R_{2}R_{4}}\right) + V_{diff} \frac{R_{1}}{R_{2}}\left(1 +\frac{R_{2}}{2 R_{1}} + \frac{R_{2}}{R_{gain}} + \frac{R_{3}}{R_{gain}} + \frac{R_{3}}{2 R_{4}}\right)$,
where $V_{diff} = V_{p}-V_{m}$, and $V_{common} = \frac{V_{p}+V_{m}}{2} - V_{ref}$

We can check for some copying errors by simplifying with $R_{1}=R_{4}$ and $R_{2}=R_{3}$, where we get a common-mode gain of 0, and differential gain of $\frac{R_{1}}{R_{2}} + 1 + \frac{2 R_{1}}{R_{gain}}$. Note that the common-mode gain is independent of the value of Rgain, and depends only on the matching of the other resistors.

If R1 and R3 are 1% low, and R2 and R4 are 1% high, then the common-mode gain is 0.039. If R1 and R3 are 1% high, and R2 and R4 are 1% low, then the common-mode gain is –0.041. If you prefer thinking in decibels, the common-mode rejection with 1% tolerance resistors could be as poor as 27.8dB (compared to 80dB to 90dB for an INA126P chip).

I’ll have to make some measurements later this week to see how large the common-mode noise on the EKG signals really is. Of course, it is likely to be highly variable, depending on the electrodes and the wiring to them, but ball-park estimates would be useful.

If the AC common-mode voltage is ±200mV and we have worst-case resistor values, then we would have a ±8mV common-mode output from the instrumentation amp. With the lowest differential amplification (6.6 at Rgain=∞), a 1mV EKG signal would be smaller than the common-mode noise. Such a large common-mode voltage would easily justify the expense of the instrumentation amp chip.  (Note: large DC common-mode voltages don’t matter, as the DC-blocking capacitor I used after the instrumentation amp can eliminate them.)

If the AC common-mode voltage is only ±1 mV, then the Blinky EKG could probably work even with very poor common-mode rejection in the instrumentation amp, and building it out of op amps and discrete resistors is feasible.

## 2013 July 4

Filed under: Circuits course — gasstationwithoutpumps @ 18:26
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