Choosing an Amplifier circuit

Searching the internet for reviews of the most commonly used ICs it seemed like the LM3886 is a good balance between price and performance in the power range that I was aiming for which is about 40W per channel to drive some decent speakers. The LM3886 has a good total harmonic distortion and noise characteristic (THD+N) which is important for clear and noise free sound output. A rough value that is accepted as being HiFi is a THD+N value below 0.5% but lower is better. The LM3886 has a typical THD+N value of 0.03% which is not ultra high end but since I want to use it in a non-studio environment i.e. my living room, this is more than good enough.

Reading the datasheet there is one thing that cought my attention: the power supply noise rejection ratio (PSRR) is quite poor at frequencies above 1kHz: it drops below 80dB. This means that the power supply must be a linear power supply instead of a switched mode supply so there is no switching noise. Also an power input filter to get rid of noise from the power grid is probably a good idea. I used a power socket with integrated fuses and filter, a Schurter 4304.4021 which I salvaged from the trash at work. There are similar ones available on Aliexpress.

There are many designs available based on this IC and since I did not want to do my own design I checked online and found that there are a few available for a good price on Aliexpress. Looking at component choices of the vendors as well as proper and decent layout of the PCB of the different versions available I found one that looks properly done and using good quality components. I ordered it as a kit to at least solder it myself.

To power the whole thing I ordered a matching transformer. Initially I wanted to use a switch-mode power supply but found that it is almost impossible to filter the switching noise to a level where it will not be audible. The best choice for audio amplifiers (or low noise amplifier circuits in general) is still to use a linear transformer. I got one from the same shop as the amplifier (Aliexpress – CIRMECH, see component list below). It has a total power output of 200W and in addition to the main 28V AC output for the power amplifiers (generates approximatel±38VDC) also features two isolated auxiliary outputs of 12V, one for the pre-amp which is a symmetrical 12V AC output i.e. 24V with a center tap and one 12V AC to power everything else like the VU meters and the LEDs. It is important that the auxiliary outputs are isolated as this helps to eliminate ground-loops between the amplifier and the pre-amp.

A toroidal transformer is a very good choice for an audio application as it runs silently (i.e. no mechanical hum) and has a very low magnetic stray field which can induce hum in groundloops. To shield the magnetic field even more I put a metal cage around the transformer (see mechanical design below).

Just as important: the pre-amplifier

The pre-amp takes care of attenuation and provides a high impedance input for the audio source. It also must be low distortion and low noise. The choice for decent opamps to be used is vast. A good an honest overview over the most commonly used OpAmps can be found here. I wanted my amplifier to have tone-adjustment capability as well as left-right volume adjustment. I found a well designed pre-amp board on Aliexpress that does just everything I need. You can always tell the quality of a board by checking the capacitor brands. Also MELF resistors are a good thing as they are lower noise.

The only thing that did not fit my design idea was the position of the volume knob. I wanted it to be larger and further apart from the balance knobs. I ordered a different 50k potentiometer and connected it using shielded wires. In fact I wired all audio signals with shielded, coaxial wires to minimize crosstalk and induced noise. The 12V AC power input to the board is directly coming from the transformer’s isolated symmetrical 12V auxiliary power output.

The volume potentiometer on the board is a 50k type. I replaced it with a better one (chinese ALPS type, probably not genuine) but keeping the 50k value to not mess with the original circuit. It turned out that the impedance of the potentiometer is too high for the power amp stage. In fact it did work well until I added the VU-meter amplifier. Without an additional amplifier there was some audible distortion as well as noise and crosstalk between the channels. So I added a simple voltage follower using an NE5532 powered directly from the ±12V DC of the pre-amp board. To minimize ground loops and induced noise to the pre-amp stage I wrapped it in Kapton tape and added a layer of copper tape which is connected to the GND of the preamp. Also I added copper tape to the volume potentiometer. It’s not pretty but it works very well.

Connecting it to the outside world

With the amplifier stages tested and working I set out to design the rest of the circuit. To be able to connect multiple sources to the amp there are relay-boards with rotary switches or push-buttons. Since I was aiming for a more vintage or industrial look I went for a rotary knob version. The input RCA sockets had to be gold plated, not only for the looks but also for the lower contact resistance over time.

The rotary switch that comes with the relay board kit is a DPST switch which means that there are two isolated switches that are activated at the same time. One switches the channel’s relay the other one can be used to change an indicator. I use 4 white panel-mount 12V compatible LEDs. The power for the LEDs is taken from the DC voltage rail of the VU-meter board: the +12V terminal is connected to the common tab of the rotary switch, the four switch positions connect to the anodes of the indicator leds, the kathodes are wired together and connect to GND of the VU-meter board (see schematic below).

The analog VU meters were already described in an earlier blog post.

To fit the retro design I wanted a beefy rocker switch for the 230V input power line. I found a nice one that comes with an on/off label plate for the front panel: the CR521B. It has two switches inside so I wired phase and neutral of the input AC line. A green power LED was not really required since the VU meters are illuminated when it is on but I put one in anyway. It is directly wired to the VU-meter 12V DC and is always on when the amp is powered.

Now the only thing missing are the output terminals. To easily plug and unplug the speakers I did not just want those standard cable-clamps. Instead I found banana sockets that are more high-end and of course gold plated. Not that it really matters on the really low impedance output of the power amp but it just looks nice.

How it is all connected

Two things are very important when wiring audio amplifiers: use shielded cables for the audio signals and avoid ground loops if possible or at least keep them small. I learned this the hard way, always getting hum on the outputs and then trying to figure out where it was coming from. There are two sources of for low frequency noise: magnetically coupled through ground loops and electrically coupled through insufficient shielding of the sensitive signals. A ground loop usually causes a 50Hz hum while an improper shielding results in 100Hz hum.

The enclosure also must be made of metal and connected to earth ground to eliminate noise from the environment. The wiring schematic below shows all components and how they are connected. The two areas with potential ground loops are also indicated. The whole circuit is completely isolated from the earthed case.

Before designing a custom case I built up the complete circuit to test it. The ‘prototype’ build was put in two standard aluminium boxes I had laying around. I tested different wiring configurations and earthing/grounding concepts to get rid of the hum which was quite strong in the beginning befor eliminating the ground loops.

Designing and building a custom case

The prototype was running for several weeks and it was time to put it in a nice box. It had to go well together with the Volumio player both in shape and material. The shape was determined by the tilted front design of the wooden Volumio box and the parts would fit in the same width so I kept that as well and the shape was more or less given at this point. The case has to be made of metal or at least have a metal shield on the inside. I wanted a vintage industrial look with at least parts of the housing rusted. I did some experimentation on how to get a nice rusty look on untreated steel plates from the DIY store. It turned out that it is quite easy to rust the surface with salt water but it takes quite a long time, like a few weeks.

Since I was happy with the rusty look of my experiments I went for untreaded steel as the material for the housing. Now with the material and the rough shape determined I put all components in to the CAD and started rearranging the components to make the design as compact as possible but always keeping in mind that it may need to be disassembled for repair. Finding a good way to split the parts so it is possible for me to bend the sheets myself on the manual bending press was not an easy task. I also wanted to weld the side plates to the main housing but was advised not to do that as it will not look nice and may distort parts and is hard to do anyways on these thin steel sheets. So I used aluminium profiles with adhesive. The removable parts are screwed to those aluminium profiles using M3 screws and threads cut directly into the aluminium profiles.

Here are a few screenshots from the CAD, the complete design can be found on my OnShape repo.

The last image above shows how the cooling concept of the amp: the air intake is at the bottom, the heat-sink fins heat up the air and it rises and leaves the housing through the slots at the top.

I put the flattened metal parts on github to download as a dxf, dwg and pdf. The parts are designed to be cut from 1.5mm steel and bent using a 2mm inner radius. I had the parts cut using the plasma cutter in a nearby workshop.

Plasma cutting is not as clean (or accurate) as laser cutting, water jet cutting or milling but it is fast and cheap and more than good enough for my purposes. After cutting, the edges need some sanding and I used a drill to re-cut all the holes as some turned out too small.

I marked the bending lines and bent the plates using an old manual bending machin in the shop at work. Since the plates are quite thin and soft steel it would also be possible to bend them using a fixture made from hard wood, which I was thinking about before learning I had access to a professional bending tool. To get the 60° angle at the front just right I used one of the side plates and slowly increasing the bend until it fit. I was surprised on how accurate the bending process turned out: after assembling the parts for the first time there were no gaps larger than a few tenths of a millimeter.

After making sure everything fits it was time to paint the parts – on the inside. I did not want the metal to rust so I aplied a layer of rust-protection varnish, the type that leaves a nice metallic pattern after painting. After the paint was dry I glued the cut aluminium profiles directly on the paint using silicone adhesive. Why silicone? I probably could have used epoxy as well but since the housing will get warm I thought that silicone can handle the thermal expansion better.

On some points I had to scratch off the paint again to make sure there is electrical contact between parts to form a complete electromagnetic shield. I used tape to fix the parts in place and then marked the screw hole positions on the aluminium profiles before drilling the holes and cutting the M3 threads.

After a first assembly test I sprayed vinegar mixed with a lot of salt on the outside of the housing, adding some more like every half hour over half a day. This resulted in some rusting but it was just taking too long. Here is what it looked like after 1 day of salt and vinegar treatment with all components mounted on the front panel:

I already really liked the look of it but it just was not rusty enough. What does work much faster than vinegar and salt is to use some stronger acid. I went to the pharmacy and bought 3% hydrogen peroxide. Anything stronger requires a license in Switzerland. It turns out that this works just fine. I sprayed the acid on and after just 15 minutes the rust really starts to form. I repeated the treatment until the rust was not perfectly uniform and darker in some places. It flakes off very easily though and after I was happy with the look I sprayed on some clear non-glossy varnish which prevents the rust from falling off when touching it.

Assembly and final touches

The assembly turned out to be tedious, especially connecting cables to the amp was hard to do as there was just no access to the screw terminals and mounting the amp to the ‘balcony’ part with all the cables already mounted was not easy.

I had to remove the amp more than once to adjust the cable length and after I finally had it mounted correctly the output relay driver failed and I had to disassemble it once more to replace the part.

Access to the parts mounted to the front is also limited which was a little frustrating as my hands barely fit to hold the parts in place but with patience I managed to assemble everything.

Testing the amp for some time I improved the wiring several times and tested different earthing-points. I found that for this configuration it is best to keep everything inside isolated from earth ground i.e. have no connection from earth to any of the inside potentials. The potentiometers knobs however are not isolated from the housing for safety reasons. The knobs seem to be isolated from the rest of the potentiometer circuit so this has no influence on hum or noise.

I tuned the amplification for the VU meter such that the zero level is reached with a 1.2V rms input voltage which according to Wikipedia is the norm. This signal level makes the amp run at about 10W and is already very loud. So I just decided to max out the amplification for the VU meters so they would at least have some needle movements at more reasonable sound levels. It still was not enough to make the needle move at the usual ‘background music level’.

Here is another foto of the amp after the final assembly.

Component List

• LM3886 Amplifier
• Power Transformer
• Fused AC input with EMI filter: Schurter 4304.4021 
• Preamplifier with tone control
• Volume Potentiometer (50k)
• 4-way input signal select
• Gold RCA Sockets
• Power Switch CR521B
• 12V Panel mount LEDs
• VU Meters (here is how I modified them)
• Speaker Terminals
• Speaker cable banana connector
• Volume knob
• Input select knob
• Tone adjust knobs (4x)

There are other small things required, like wires, screws, nuts, spacers, washers etc. which I got from the local hardware store or ordered online.

For my amp the front window has to be glass and I wanted the frame to be made of wood. Also the incandecent bulbs had to be replaced with LEDs without sacrificing the very warm light temperature.

Modifying the Light

First I disassembled the meter and took out the lamps. They are 12V rated which is the usual power rail voltage for auxiliary board in audio amplifier applications. So I need a LED light source fitted on a board not much bigger than the original lamp with a yellow-orange color running off of 12V. Taking a small warm-white LED was still not giving the right light so I added two amber colored LEDs on each side, all connected in series. With a series resistor the brightness was adjusted to match the original light bulb.

The perceived light color is a close match although it is not perfectly identical but good enough for my taste. The small cut-to-size perfboard with the LEDs matches the size of the original bulb and thus was quite easy to mount.

Comparing the original to the modified VU meter shows a small difference but it is only noticeable in direct comparison (original is on the right):

Preparing the glass

As a cover glass I ordered 31mm diameter flat watch cover glasses. Since I have no need for the zero-point adjustment screw after the initial calibration there is no need to drill a hole in the glass. I simply spray-painted the glass black on the back side to cover the bottom part of the meter.

The wooden cover

The original ugly plastic cover is just a snap-on part. Ba carefully measuring the diameter I was able to make a wooden ring that just fits without the need of any adhesive. This is an advantage if I ever need to repair it for some reason. The rings were CNC-milled from an 18mm oak board then sanded and oiled. The design is available in OnShape:

https://cad.onshape.com/documents/0b759c1b37256f58fd369f20/w/911e7cfc65ee9c2fbac2bf63/e/bfa623b9546c35a9c7a9f348

The glass was glued into the wooden ring at the correct orientation. As mentioned above, the ring just fits on the plastic part of the VU meter with a light press fit.

The final result looks like a quality VU meter:

After some research I decided to build it based on a Raspberry Pi running Volumio which does everything I wanted out of the box. I was in for some surprises though by not using a setup that was fully supported by the developers so some coding ensued. I also wanted to spin my own housing design to give it a unique look. Here is how it turned out:

Electrical design

The Raspberry Pi was already given. I wanted a knob-free design so I needed a touch screen and went for a 7″ Waveshare screen since it just looked much nicer with the higher resolution than the 5″ standard touchscreens. What else is needed? A DAC board to generate HiFi audio and some internal storage capacity would be nice. At least one USB port for external storage, Ethernet and a DC power jack. Oh and of course two RCA output sockets. Sounds simple enough… turned out a few more things were necessary but I got that all covered: A complete list of materials used is at the bottom.

The DAC board

The most important design factor for high quality music is the digital to analog converter (DAC). I wanted it to be high quality but for a reasonable price. Also I did not want to use a standard Raspi ‘hat’ so I would be able to play with it and learn something in the process. I quickly found that some of the best DACs even for professional equipment is made by ESS tech. They have one very cheap DAC which is named ES9018K2M and there is also cheap PCBs with this IC available on ebay and aliexpress. I ordered mine from a shop called ‘Derone Audio Parts’. The reason I chose this particular model is when looking at the photos you can see that not the bottom of the barrel components were used and the design looks properly done (although it could be improved). There are other ICs from ESS tech in every price range but comparing the specs they all seemed very similar. So similar in fact that the actual implementation of the DAC part in the chip is probably identical but the digital filtering stages may be different: IC manufacturers tend to copy working designs or parts of it, no need to reeinvent the wheel every year. Since this particular DAC is much newer than their professional grade DAC it is likely that it uses the same exact converter circuit. I have no alternative high end DACs to compare to currently but the sound quality appears solid to me.

 The output stage of the DAC board is made for headphones. I want to hook it up to a stereo amplifier so I wanted to reduce the voltage level. I quickly reverse-engineered the output stage circuit and put it into a LTspice simulation. Also I wanted to see what this circuit actually does to the sound. Here is the schematic:

I changed R1 and R2 (on both L & R channel) to 10k and the gain is reduced by 4.1dB which gives an output close to line-out level. Here is a comparison on the output stage frequency response before and after the modification:

The frequency response looks fine: it is flat (i.e. below 0.1dB attenuation) from 0.4Hz to 30kHz. The LTspice simulation file is in my github repo. Make sure to use minimelf quality resistors if available for best audio quality.

The opamp used in the circuit is a JRC5532 which is quite good and one of the best for it’s low price (low noise, high fidelity). I replaced it with a slightly higher grade NE5532A from Texas Instruments but did not hear any difference at all.

I did some other minor modifications to the board like adding additional ferrite filters and capacitors to improve the noise but it turned out this was not really helping: the noise was just coming from the Raspberry Pi through the I2S lines. I fixed that later, see below.

The two RCA outputs did not fit the design so I added nicer ones connected with shielded cables:

The DAC chip has some cool features but those are not accessible since it does not come with a proper linux driver. I took care of that by re-writing a python script that exists for a similar board with this DAC but uses UART commands. The driver checks the Volumio state and sets some parameters in the IC. Like this it is possible to also play 16bit files on the ES9018K2M without upsampling them to 24bit (which is not possible on Spotify plugins). Also it supports hardware volume control. Read on how to get it up and running in the Volumio forum.

On this particular board the I2C lines are pulled up to 3.3V which works perfect with a Raspberry Pi. The wires for the I2C control lines can be soldered directly to the pads of the resistors. On the ES9018 chip itself the I2C lines are on pin 3 (SCL) and pin 4 (SDA). The GND connection can be taken from the I2S connector or the marked area (scratch open the solder mask):

The four resistors with the marking ‘6k2’ in the photo above are the ones I replaced with 10k resistors as mentioned earlier to get the output voltage to a more reasonable level.

The wiring

To nicely fit the display without wasting a lot of space for the HDMI and micro-USB connector I wanted 90° bent connectors. I saw some elegant solutions for other displays

using a PCB mountet connector but was unable to find a shop that sells them. Searching up and down on Aliexpress I finally found a ribbon-cable HDMI connector that was exactly what I wanted.

For the USB I was not so lucky: all 90° connectors I found were quite bulky and did not fit so I made my own from a solderable usbe plug and some twisted pair USB cable and covered it in epoxy. I soldered the other side of that cable directly to one of the USB sockets of the Raspberry pi, see photo on the left.

Here is how the display looks after assembing the connectors:

The connections on the Raspberry Pi are quite simple BUT I found that if I do not galvanically isolate the I2S lines there is way too much noise on poisoning the ground of the DAC. The I2C lines on the other hand were fine and required no isolation which seemed a bit peculiar to me on why the direct GND connection would not result in any audible noise but it could be related to where the GND connection is soldered: I scratched open the GND-plane just next to the I2C line resistors.

The I2S lines on the Rpi GPIO header are Pin 12 (BCK, GPIO18), Pin 35 (LRCK, GPIO 19) and Pin 40 (DATA, GPIO21). As mentioned above these lines induce a lot of noise to the DAC when connected directly, even when using shielded cables. To get rid of the noise a low jitter Si8660BA digital isolater is used. The ES9018K2M uses some clock recovery magic to reduce jitter although I do not know how well this works or how such a jitter would affect the sound quality but from what I read it is a good thing to have the feature as the Raspberry Pi clock does not seem to be the best. On the breakout board I also added a 100nF decoupling capacitor on the two power supply pins (Pin1, Pin16). Primary supply voltage is taken from a 3.3V pin of the Rpi, secondary 3.3V supply is conveniently available on the I2S connector of the DAC board (see image above). The isolator IC cannot be used for the I2C lines as it is not bi-directional. On my test setup I had the problem that 16bit files would not play properly. When checking the wiring I found that it would play just fine as soon as I touch the cables of the I2S lines on the DAC side of the isolator. Such a behaviour usually means that there is a bad impedance mismatch between the IC’s output stage and the cable. The usual fix is to add a 22 Ohm resistor in series to increase the source impedance but since touching the cable already fixed this I added copper tape on the cable and grounded it to the GND of the IC (see image below) this increases the cable capacitance. And as the characteristic impedance of a transmission line is the square root of inductance over capacitance (Z = sqrt(L/C)) increasing the capacitance lowers the impedance. This did the trick and the signal now works perfectly. When there is a large mismatch in impedance on signals with fast clocks (or sharp clock edges in this case) the signal can get distorted due to signal reflections causing all sorts of problems.

The power supply

A clean voltage is highly important for analog circuits. For mixed-signal circuits like the DAC good decoupling and GND separation can help but if the power supply itself already is bad nothing will get you to clean sound.

The DAC board requires a power supply between 9V and 15V and the Raspberry Pi of course needs 5V. I decided to use a 12VDC power supply from MeanWell as these usually are of decent quality. To get the 5V for the Raspi a step-down converter with enough power output is used. I still got ‘low voltage’ warnings from time to time on the Raspbery so I added a 2200uF capacitor on the 5V input.  This converter causes additional noise so I added a filter between the 12V input jack and the DAC module. The filter design was done in LTspice. I wanted at least 50dB attenuation above 100kHz and good filtering up to 10MHz. For the high frequencies this is quite easy to achieve by adding ferrite beads with the proper current rating but for the frequencies below 1MHz an L-C filter must be used. The filter design looks like this:

The rated current of the beads and inductor is 3A so it can take plenty of power although I would not use this filter for more than half the current rating because ferrite beads only work well up to about half the rated current. With the filter in place the noise from the power supply, the buck converter and the Raspi vanished.

Only one problem left: when connecting the RCA output to the stereo amplifier the noise from the power supply is back! The ground-loop is formed through the whole signal and power chain and is closed at the AC power outlet. This means that this noise is coupled to the circuit as common-mode noise so in order to get rid of it I need a common mode choke. I first tried with a self-wound choke to check if it helps. It did but only to a certain extent.  So I ordered one from digikey that is properly specified and can filter the noise down to the audible level i.e. 1kHz. With the choke  in series to the  other filter the noise is not audible at reasonable sound levels but it is not completely gone.  I guess there is a good reason everybody uses linear transformers instead of switching types for audio applications…

Instead of using a the choke on the power lines it could also be added to the audio lines. There are special filters designed for that but they can be expensive and the cheap ones probably create some distortion on the sound so I decided to break the (common mode) loop on the other side.

The mechanical design

The design is based on 18mm thick wooden panels although it probably can be adjusted for thinner panels down to 6mm. I went for oak because of its durability and looks. As a manufacturing method I chose to put the milling machine at FabLabWinti to a test but before that I made a ‘proof of concept’ out of laser-cut PMMA (acrylic) to check if the angled front with the display works at all as a design. It does.

The basic design idea was to have just a wooden box with the front in an angle presenting the display. All connections are hidden on the back-side and no knobs or anything on the front. Also I wanted to have as little ‘frame’ as possible around the display (hence the angled connectors). Also I did not want the display to be too far set back from the front but still wanted to wood to cover the edge of the glass so the wood has to be milled down to about 1mm thickness from the back.

The thick wood allowed me to use normal wooden screws for the assembly: I marked the drill positions with the mill but drilled the holes by hand.

The parts can be milled with a 6mm diameter piece although corner reliefs are required. Where sharp angled corners are required (i.e. on the USB and Ethernet cutouts) I used a file and sandpaper. The pdf and dxf drawings are available on github, so is the step file.

Since the 6mm mill piece was way too big to dill holes for the screwholes to fix the electronics I just used it to mark the positions by drilling 1mm deep holes. I then drilled the center of these markings manually to a size where the M3 screws would just fit (I think I made 2.5mm holes).

The angles on the front, top and bottom parts would take forever to mill so I roughly cut those with a band-saw and used a disc-sander at the correct angle.

The assembly

After finishing the parts I glued the sides, the top and the front. The bottom and the back are screwed on.

The most critical part is to get the display to fit nicely. I had to file a few edges after milling to make it fit. I aligned the display and fixed it with hot melt glue allowing me to adjust the position to perfectly align and center it. To permanently fix it I used two component epoxy on the four corners. The wood is too thin there to use screws.

The electronic boards were all mounted on the bottom plate by adding M3 screw spacers.

The final touch was to use linseed oil to give the wood a nice finish.

Stay tuned for the matching stereo amplifier

Part list

• Raspberry Pi 3B+
• Waveshare 7″ Display
• ES9018K2M DAC board
• Gold plated RCA Sockets
• Shielded cable
• 90° HDMI ribbon cable (10cm)
• 1m twisted pair USB cable
• Si8660BA digital isolator
• SOP16 breakout board
• 12V Power Supply (Mean Well GST25B12-P1J)
• DC/DC Buck converter
• 2200uF capacitor
• 1206 SMD Ferrite beads
• 22µH Inductor
• Common mode choke

There are several methods to do capacitive sensing with a microcontroller. The easiest and most common way in the Arduino world is to charge the capacitive probe through a high value reseistor and measuring the time it takes to charge it. While this is indeed a simple method it is highly susceptable to interferance and noise as the wire acts as an antenna due to the high impedance. Also it is not very sensitive compared to other methods but good enough for a simple button.

Here is a video comparing the resistor method to the two methods discussed in this blog post:

https://youtu.be/61M58UF3VVc

The Arduino code I wrote for this demo can be found at the bottom. Here is a close-up shot of the wiring: I soldered the 5MΩ resistor for the ‘resistor method’ directly between pins 8 and 9. The other two sensors are on separate prototyping boards and are connected with wires.

Charge transfer method

What is most commonly used in capacitive sensing ICs is the charge transfer method: the capacitor that is to be measured is charged repeatedly through a larger ‘sample’ or ‘reference’ capacitor that accumulates charge. Counting the number of cycles is a measure for the capacitance of the probe. This method can be implemented with two digital pins of a microcontroller and is way more sensitive and very stable. The method is described in detail here. Basically this is how it goes:

Both pins are set low to start with, the sample capacitor is discharged.

Step 1: GPIO2 is set as an input, GPIO1 is set to high, charging the the capacitive probe through the 10nF sampling capacitor. Since there is no connection to GND only a tiny amount of electrons flow into the capacitor. How many depends on the capacitance of the probe.

Step 2: GPIO1 is set as an input and GPIO2 is set to GND. This discharges the probe but does not discharging the sampling capacitor as GPIO1 is now floating and no current can flow.

Now repeat the two steps (set GPIO2 floating, set GPIO1 high, etc.) and with each cycle some more charge builds up on the sample capacitor. The voltage on GPIO1 is checked at the end of each cycle until eventually it reaches the ‘high’ trigger level. Counting the number of cycles gives an idea of the capacitance of the probe, it is by no means a good method to measure the exact capacitance as there are ‘stray’ capacitances all over the place influencing an exact measurement but for relative capacitance changes like in a proximity sensor or a capacitive slider switch this works very well.

The sample capacitor should be chosen somewhere between 1nF and 100nF depending on the size of the probe. Choosing a too large capacitor makes the measurement very slow and a too small capacitor will not give a good enough resolution.

The filter overflow method

I invented this method a few years ago when looking at a design for a capacitive probe. When researching and looking at the schematics of some other methods I had the idea for this circuit:

In addition to the sample capacitor it requires a resistor/potentiometer and a diode with a low capacitance like the very common 1N4148. The input and the output are connected to digital GPIOs of the Arduino, I used D3 as the clock and D4 as the sensing input in the code below. The way it works is quite the opposite way of the charge transfer method. That is also why in the video the two signals go the opposite way. Here is how it works:

Step 1: apply a positive voltage to ‘CLOCK_IN’. The probe is charged quickly through the resistor (the initial sensitivity is adjustable if potentiometer is used) and as soon as it is charged enough the diode will switch on and the current will ‘overflow’ to the bigger capacitor.

Step 2: set the input low and check the output voltage. If the foltage at the output is not yet ‘high’ then repeat.

For a large capacitance on the probe it takes more cycles than for a small one: the probe acts like a low-pass filter on the signal. The trick is to make the clock fast: the faster it is the more sensitive the probe can be made. If the clock is chosen too fast for a large probe then the diode will stop switching on after a few cycles and the output may never reach ‘high’. At that point the on-time should be increased. This is done in the code by switching to a longer on-time after counting a few hundred (or thousand) clock cycles so there is no infinite loop. In the code below I use the assembler command ‘nop’ which waits exactly one clock cycle or 62.5ns at 16MHz. More ‘nop’ operations can be added to decrease the clock speed.

The ability to choose the sensitivity of the circuit just by changing the on-time is another advantage over the charge transfer method which is fixed in sensitivity without changing the sample capacitor.

If the resistor/capacitor/clock combination is tuned just right the probe can be made very sensitive: I was able to sense my hand as far as 30cm away from the elctrode by using a 51k resistor, a 1nF sampling capacitor and five ‘nop’ in the code with a 30cm long cable as the probe. The noise picked up at this sensitivity is horrible though.

If you want to use multiple probes on a single clock here is how you would wire this up:

In the code both outputs have to be checked after the clock line is set low of course. This cascading can be continued with more probes. If the circuit is done with SMD components it can still be made very small on a prototyping board.

Comparing the waveforms

The stuff above explains how these methods work in theory but let’s look at what the voltages actually look like. It may help to understand what is going on in the world of electrons. The photo shows a ‘behind the scenes’ shot of the setup used in the demo video: the copper clads used to be taped to a wooden surface, hence the dirty look on the bottom side. This setup was also used to take the shots below.

First off the resistor method. The blue signal shows the voltage being set to high, then the capacitive probe starts charging through the resistor. Once the pin is charged up, the software takes the time and sets both pins low. The video shows this in action: when I touch the glass plate with my finger the charging time increases as the capacitance of the probe gets bigger but also there is a lot of jitter picked up as my body acts as an antenna bringing the noise close to the circuit. So why is only this circuit so susceptible to this noise? Because of the high resistor value it takes very little AC-currents to cause large voltages on the circuit. The other circuits do not use such large resistors so they can just ‘eat up’ that current without causing much noise.

The charge transfer method has a completely different approach: it uses a clocked circuit and is more ‘digital’ and hence also very stable. The screenshot shows the charging up of the capacitor. Channel1 (yellow) shows the voltage pattern on the GPIO1 pin: the lower end  increases with every cycle until the Arduino pin triggers as ‘high’. Channel2 (blue) on the other hand shows the voltage at the probe which is zero when set to low and shows the difference between 5V and the sample capacitor voltage when left floating, so it looks like a mirror image of channel1. Each time channel 1 is set to high the current flows through the sample capacitor into the probe, charging the sample capacitor up by a little bit.

Again, the video shows how it behaves when I touch the glass plate: as the capacitance of the copper plate increases the number of cycles it takes to charge up the sample capacitor decreases.

The third method is probably a bit more complicated to understand. The yellow line shows the clock input. The current through the resistor (or potentiometer) charges up the capacitive probe very quickly: you can barely see the blue curve rising more slowly than the yellow line. Once it reaches a voltage higher than the sampling capacitors voltage (channel 3 in purple) the diode starts conducting and charging the sampling capacitor up some more. See how the blue and purple lines start rising in parallel. When the clock is set low the probe is discharged. Also note how the sampling capacitor loses just a tiny bit of charge as well. This is due to leakage currents. If the clock is too fast for the size of the capacitive probe you can imagine that this game can reach an equilibrium state before the sampling capacitor is charged enough to trigger the ‘high’ level at about 2.5V.

In contrast to the ‘charge transfer method’ you can see that the number of clocks it takes when coming close to the glass plate increases. So this method could be viewed as a combination of the resistor method and the charge transfer method as it takes the best from both circuits: it uses only one pin per additional channel (like the resistor method) but has the stability and sensitivity of the charge transfer method.

Arduino Code

I put the example I used to create the video at the top up on git: Arduino Code

I hope you enjoyed this little (or rather lengthy?) lesson about capacitive sensing. If you have any suggestions or questions please leave a comment.

The motor is not intended to drive anything, how could it at such low power… just to put this into perspective: if you put a drop of cold water in your hand and let it warm up, the energy transferred to the water could run the motor for hours. I hooked mine up to an amorphous silicon solar cell salvaged from a solar toy and with a super capacitor as an energy storage it runs 24/7 just from ambient light in a room, no direct sunlight necessary.
It can also run from various other low power sources like a peltier element (TEG) or any home-brew battery like potato battery or even an aluminium-saltwater battery: I had one of the motors running for three months on just aluminium foil and salt water before the battery shorted out due to corrosion.

Design Process

This all started when I saw an interesting video on youtube by lasersaber. Since he came to the design of the pulse motor by experimentation I thought I may be able to improve it even more by taking the engineering approach and doing a simulation of the magnetic field to find the best ratio of magnet to coil size. I simulated the magnetic field of a cylindrical magnet with femm a free FEA simulation tool and overlayed the ideal position of the coils in power point (final result shown below). It turned out that he had it not quite right in his initial deisgns (coils too thick) but then came to the same conclusion in later designs as can be seen on his blog it just took him a few months to figure this out while the simulation approach only took me like 20 minutes. Engineering skills for the win!

Just a little motor theory on how a pulse motor works (and how the simulation shows this is a ‘good’ design):
unlike other motors a pulse motor does not have a continuous torque nor a continuous current and is therefore useless for higher power applications but it is a great demonstration of the physics at play and very easy to build. The trick is to apply a voltage to the coils only for a brief moment when the magnet is at the ideal position to generate the maximum amount of force. This moment is shown in the image above:the magnet is exactly between two coils. The current in the coils flow in opposite directions.  The image also shows that the field drops quickly when going away from the magnet which means any current flowing close to the magnet produces way more force than the current at the back of the coil which is why a thinner coil is more efficient than a long coil as it generates more force per current. The part of the coil where the current returns (most left and most right purple squres) will generate a force in the opposite direction except if the magnetic field also flows in the opposite direction i.e. is on its returning loop. You can see from the field lines that this is exactly the case in the chosen geometry of the coils: in this case the returning current meets the returning magnetic field and generates even more force even if it is way less then the two central parts of the coils. Say the current in the windings closer to the magnet flows into the screen and the magnetic north pole faces the coil then the Lorentz force produced points to the left, tangential to the rotor making it spin counter clockwise.
Adding more than two coils increases the force but in theory should not increase the efficiency but in reality a more symmetrical design runs more smoothly because the parasitic foces generated from imperfections are balanced out making the rotor run more smootly.

The geometry can be scaled to any size. The first motor I built has six 12mm magnets and 12 coils but since winding these coils is a very tedious process I improved the design and made it smaller with only four coils. Compared to the design done by lasersaber mine is much easier to print and assemble.

How it works in practice

The theory sound solid but how do you produce a current pulse just at the right moment? Normal motors use sensors (or back EMF) to sense the rotor position and with some advanced switching electronics apply the right current at the right time. This could be done for this motor as well but the electronics would use way more power than is required to run the motor itself.
The trick here is to use a reed switch which closes when a magnet is close to it and opens if the magnetic field is too weak so it acts both as a sensor and a switch at the same time. The rotor has the magnets and if the reed switch is poisitioned just right a current pulse is applied in the right moment. It can be tricky to get it just right and the use of an oscilloscope can be very helpful but it can be done without one. The schematic diagram of the circuit looks like this:

Build instructions

If you want to build your own little pulse motor here is what you need:

• 3D printed parts (download from thingiverse)
• Neodymium magnets
  • 12mm diameter, 3mm thick for large design
  • 6mm diameter, 2-3mm thick for small design
  • 3mm diameter for holding pin
• Reed switch, the smaller the better (aliexpress has some)
• Thin enameled copper wire (I used 0.05mm wire)
• Sowing Needle for rotor shaft (get a set)
• Sapphire/Corondum bearing or flat Sapphire glass (aliexpress)

Optional:

• Amorphous silicon solar cell (the reddish brown ones)
• Supercapacitor to match solar cell voltage, 1F-2F capacitance

After you collected all the items and printed all the parts and made sure everything fits together start off by winding the coils. The bobbins are made out of two parts. Put them together to form a bobbin and use a solderin iron set to 200°C to melt the pin and weld it at the back of the coil. You can also use superglue.

The tool to wind the coils is also provided in the 3D files. I used a brushless motor clamped in a vice to wind the large coils as this is much faster but an electric drill works just as well. Leave a length of about 10cm of wire at the beginning and the end of the coil and secure them with tape. A drop of superglue on the coil before winding the last few rounds helps to keep it from unwinding.

Try to wind it as nicely packed as possible but do not put too much strain on the wire. I found that a good way to do it is to hold a paper towel in your hand and run the wire through it, applying slight pressure on the towel and guide the wire to where it needs to go. Wind a few extra coils as spares in case one is bad or the wires break during the assembly. The winding direction is not important but it has tho be the same for all coils!

Now mount the coils into the base with both wires of each bobbin coming out the top. To connect the wires twist them together and solder them by passing them through a liquid ball of solder on the tip of the soldering iron. It helps to set the temperature to 400°C or even higher and use fresh solder on the tip for each wire. To get the enameled copper wire to take the solder can be frustrating at times, believe me. In order to get the current to flow clockwise in one coil and counterclockwise in the next (as explained above) connect the end of the wire of the first coil with the end of the second one, then the beginning of the second one with the beginning of the third one and so on generating an alternating pattern but do not connect the beginning of the first coil to the beginning of the last: that is where the reed switch and the supply voltage comes in. Trim the soldered wires and tuck away the solder joint somewhere it will not come in contact of the rotor.

To test if the polarity of all coils is correct there is a simple trick: connect a AA battery or any power supply of choice to the open circuit. Tin the end of the wires first and maybe check the resistance with a multimeter (depending on the wire used it is a few hundred ohms to a few kilo ohms). With the batter connected and the current flowing each coil acts as an electro-magnet. Holding a small magnet in front of each coil the magnet will indicate the field direction which has to be alternating north-south-north-south-… when going around the motor. This rule applies for both motor designs even though the small one only has four coils.

Next prepare the rotor. Put the magnets in and seure them with some glue. The orientation of the magnets has to be the same for all of them! To check this take a stack of magnets and check if each magnet is facing the same way.
Stick a needle into the hole in the center, use a small drill if it does not go through but make sure you do not drill in an angle! Now try to spin the rotor on a tabletop and see if it runs smoothly without too much wobbling. Depending on how well calibrated your 3D printer is it may wobble quite a bit. You can try to bend the needle a little to make it wobble less but if it is just too much you may need to align and calibrate your printer first.
Before securing the needle with some more glue it needs to be adjusted to the correct height. To be able to do that the bearing needs to be placed into the base. If you got a ruby bearing (or made one as described in my last post) mount it in the center using hot melt glue or plasticine (or print yourself something). If you want to use a sapphire glass (a piece of normal glass like a microscope slide works at first but wears out very quickly, like within a few weeks and then grinds down the needle so really not recommended) you need to put a small magnet under it, like a 4-6mm diameter, 2-3mm thick magnet to  always keep the needle at the center. That is what the center hole was designed for. Secure the magnet with some glue then put the glass in.
Now mount the rotor on top of the bearing and adjust the needle height so the magnets  align well with the coils (center height should be the same).

You can test how well the rotor spins by holding it in place with a magnet mounted just above the top of the needle. I used an adjustable arm for that as shown in the picture.

To mount the arc with the adjustable holding-pin the needle has to be trimmed. Cut it to length using some strong side-cutter becauase needles are made of hardened steel. The length should be such that there is a few millimeters of space between the top of the needle and the arc.
Mount the small magnet to the adjustable pin and glue it. Put the pin in and adjust it until the rotor stands straight but the needle does not touch the magnet of the pin: there should be a gap of about 1-2mm. Now the rotor spins very easily and it can be spun up by blowing on it. If you own an oscilloscope, hook it up to the two wires and see how it generates an AC voltage. You can also hook up a AA battery (or several in series if your coils are in the kilo ohms) and try to apply short pulses by hand to see if you can get it to spin.

To make it work is now just a few steps away. Take the reed switch and shorten the leads a little. Actually to trim them down to 1mm is key to run the motor at very low speeds but with such short leads it becomes very difficult to solder the wires. Wrap one of the copper wires from the motor around one of the leads a few times then solder it (you may want to tin the copper wire first). Take another piece of copper wire like 10cm long and solder it to the other lead of the reed switch.
Solder the two wires that are now left to some thicker wire to make it easier to experiment then hook them up to a battery. For the small motor made with 0.05mm wire a voltage of 1-2V is plenty, for the large motor with the same wire 4-10V is more adequate. To check if all is workin you can use a small magnet and hold it close to the reed switch and the rotor will twitch.
To find a good position for the reed switch slowly move it towards the rotor and a soon as you see a reaction try to move it left and right to find a spot where the motor starts to spin up. To find this position is quite easy but finding the spot where it runs at minimal power is a lot harder. I use scotch tape to fix the switch in a position and only glue it after I am sure it is a good spot. The fotos show where this sweetspot was on my motors, both the small and the large one. You may notice I used a tiny reed switch on the small motor, I do not know what type it is nor where to get it, I got it from a leftover pile of an experiment at work. You may also notice the capacitor ant the diode on the reed switch of the large motor: this is a so called snubber circuit I use to reduce voltage spikes that made this switch get stuck from time to time.

Once you get the hang of it it becomes easier to adjust the position. But not only the position but also the orientation of the switch is important: it must be positioned so it catches just enough of the magnets field to switch on but only very briefly. To tune this without the help of an oscilloscope can be difficult but not impossible and just takes a lot longer. First you have to find approximately the right distance, then the best position and orientation and finally tune the distance at that position and mabe fine tune some more. The right distance and approximately the right position is where the motor spins up on its own. Once you found that stop the rotor and adjust the position of the reed switch such that that the magnets get a push when moved exactly between two coils but not if just slightly (more than 2mm) off from that position. Once you get that to happen you are already very close to the sweet spot and if you do not want to go record-breaking low power then it is good enough. However if you want to go as low as it can go you need to reduce the voltage of the power supply and tune further until it spins very very slowly without stopping. I got it as slow as one rotation taking over 10 seconds. Measuring the actual power also helps, see below on how to do this correctly.

Fine Tuning and measuring power

To measure the point where the reed switch is turned on it is easiest to measure the voltage over the switch with an oscilloscope. Since the oscilloscope probes are magnetic an additional wire has to be soldered to the switch so the probe can be placed further away from the motor. The ideal point for the switch to turn on is when the voltage generated from the rotor is at the lowest point. The voltage is shaped like an ‘m’ as shown in the screenshot below. The part where the voltage is zero is where the switch is on. The measurement was taken on the small version of the motor but it looks similar on the large one. Notice how the voltage drops almost to zero just before the switch is turned on showing the voltage generated by the magnets is almost the same as the voltage applied to the motor. It can also be seen that there is some asymmetrical behaviour coming from a not perfectly symmetrical rotor: not all magnets may be the same strength or exactly at the same distance from the switch making it turn on or off at different times. When the switching behaviour is as shown the position of the switch is very good, if it is wrong the ‘zero voltage’ spike is off center from the ‘m’ shaped waveform resulting in additional current draw. The most important thing is to have the switch turn on at exactly the lowest point, not too soon, not too late and not too long. To optimize the power consumption even more the switch would need to be moved further away so the on-state is as short as possible. It is also ok if the switch does not turn on for each magnet but only for two or even just once per rotation, that is when I got the best results for low power but if you want the motor to run reliably for a long time that is not ideal as it can stop running if the rotor moves just a tiny bit away from the switch over time.

To measure the power consumption two multimeters are required: one to measure the voltage and one to measure the current. At low speeds the current spikes for a short time and is then zero for a long time. In the measurement abofe with the motor running at 1.3 revolutions per second (1.3Hz) the on time for each pulse is less than 50ms which a multimeter does not handle well. The current has to be averaged with a capacitor and a resistor so it is constant. I use a 1000µF capacitor and feed the current to the capacitor through a 1k resistor resulting in a 10s time constant meaning the pulses are averaged over about 50 seconds (five times the time constant). The voltage is fed to the motor from the capacitor so its voltage is the input voltage to the motor (not the voltage of the power supply connected to the resistor). It takes a few minutes until the everything is stable: the rotation speed, the voltage and the current and that is when the power can be measured.

The limits of low power

I was curious about the efficiency of the motor and what the minimum power would be if the motor was just tuned right. First I just played around with the alignment of the reed switch and then lowering the supply voltage as low as possible without the motor stopping. I got it as low as 60nW at one point. The second small motor I built was not able to run at a power below 500nW so I must have either tuned the first one better or hit some kind of a sweet spot.
But is this the lowest it can go? What power is actually lost in the friction of the bearing and air friction of the rotor? Lasersaber claimed in one of his videos that he got it running at just 4nW which is more than ten times less than my best effort and I simply could not believe this was even possible so I had to know if my design was just more inefficient or if he cheated.

The power lost in the rotor are from air friction and friction in the bearing. The friction of the needle bearing I approximated as a tiny cylinder rotating on a flat surface because the needle point will not only touch on one atom. The reality is somewhat different but assuming there are two solid surfaces touching there will be rigid body friction which generates a constant drag at low speeds. A constant drag means that the loss is linear to speed since power is force*speed so if the needle bearing dominates the friction the rotor losses should be linear. Now the air friction losses on the other hand are not linear to speed but squared with the speed (for low speeds) and even cubed with the speed at higher speeds. Since the rotor spins at low speeds a laminar air flow can be assumed but let’s not only assume, let’s measure.
In order to get the losses by friction (both air and bearing) the energy lost in the rotor can be measured. To do this we can calculate (approximately) the moment of inertia of the rotor which is it’s ‘rotational mass’. I measured the weight of the rotor and the magnets and calculated the corresponding moments of inertia:

magnets (4.1g) rotating at a radius of 14mm: J =  8e-7 kgm^2
bare rotor (2.3g without magnets) of a radius of 15mm: J =  3e-7 kgm^2

The experiment was to speed up the rotor by blowing on it and then measure the speed at certain intervals. The speed was measured by measuring the voltage over the reed switch with an oscilloscope (like shown in the above screenshot) which gives very accurate readings. I put this all into calculation sheet, calculated deceleration from the speed and with the deceleration known and the moment of inertia known the power loss at each measurement point is also known. It shows very nicely a square function of power loss. What can also be checked if the drag coefficient is constant or proportional to speed. The graph shows that for speeds above about 1Hz it is almost constant and then increases meaning the drag force no longer depends on rotation speed and the bearing friction dominates. With the drag coefficient being constant for speeds above 1Hz it means that the assumption of laminar flow is correct.

Ok with the theory and assumptions veryfied what does this mean now. It means that at speeds larger than 1Hz the air friction is the dominating factor of losses and below 0.5Hz the needle bearing starts take over and losses become very small.
But what’s important is that the minimum power required to keep it rotating at about 0.5Hz which is quite slow already is still 150-200nW. Now with the drag being dominated by the friction of the bearing the power decreases now linearly with the speed so at 0.1Hz or one rotation every 10 seconds the power required is 30-40nW.
At 6Hz the measurement is more accurate though and at this speed the losses are about 13µW. The power required to run the motor at this speed I measured to be 24µW so the efficiency of the motor is just above 50%. Not really great but for the simple design it is not too bad. I honestly would have expected it to be below 30%.

The bottom line is that no matter what a power consumption below 10nW is simply not possible to achieve with this design. To make it possible much more precise parts would be needed, a heavier rotor that can store more energy and therefore go to even lower speeds and maybe a harder rotor material like a very pointy ceramic tip. The light weight rotor is at one point locked to the earth magnetic field and cannot escape it if it is too slow so higher speed or a heavier rotor would be needed.

Here are a few measurement results just to show what some tuning of the reed switch can do. Three measurements were taken at the same speed after tweaking the power almost dropped to half.

6.2hz, 16uA 1.5V = 24uW
492mHz, 4uA, 160mV = 0.64uW
492mHz, 3.7uA, 151mV = 0.55uW
492mHz, 3.2uA, 117mV = 0.37uW
320mHz, 3.0uA, 90mV = 0.2uW
85mHz, 1.7uA, 35mV = 60nW

]]> https://bashtelorofscience.wordpress.com/2018/09/02/nanowatt-pulse-motor/feed/ 4 bashtelorofscience DSC02691 magnetsimulation circuit DSC02133 DSC02137 DSC02684 DSC02681 rotor_losses drag_coeff https://bashtelorofscience.wordpress.com/2018/06/23/grinding-ruby-needle-bearings/ https://bashtelorofscience.wordpress.com/2018/06/23/grinding-ruby-needle-bearings/#comments Sat, 23 Jun 2018 12:11:18 +0000 http://bashtelorofscience.wordpress.com/?p=892 Continue reading "Grinding Ruby bearings"]]> Ruby (or Corundum) bearings are used as small low friction bearings in watches or high quality measurement equipment. I wanted to have some bearings for my nanowatt power motors but I was unable to find any for a reasonable price which is somewhat ironic as there are plenty of watch manufacturers here in Switzerland. I asked around and nobody was able to tell me where I could buy a few. These things are also available cheaply from China but there are minimum order quantities of a hundred pieces or so for a doller per piece.

What I was able to find on aliexpress though was 3mm Corundum crystals used for jewelery. You can get them in small quantities for less than ten bucks. I learned quickly that they are useless for needle bearings because the needle jumps off the small flat surface all the time: it must have a dent in the center.

Since Corundum is a very hard material it is not easy to shape, it can only be done with diamond tools. After several failed attempts using a vice or pliers to hold the crystals I found a method that works well. Here is how I do it:

Mount the crystal in a 3mm collet for the Dremel tool. I used a flat piece of glass to push it in so the flat face of the jewel is well aligned. Mount the collet into the Dremel tool.

Using a round head diamond grinding tool grind a dent into the flat face. Slowly rotate and tilt the tool to avoid deep grooves and also try to get it not to vibrate too much or the center part will not be ground into a nice dent. This step takes less than a minute.

I did try the bearings at this stage but the rough surface did not give me the results I hoped for. There is still some friction and the needle eventually gets worn down, similarly to what ordinary glass does over time. The surface has to be as smooth as possible to make a good bearing so I had to find a way to polish it.

I first tried Zirconium Oxide which is an abrasive used to polish glass. Of course it did not work on the hard surface of the Corondum so I ordered diamond polishing paste. I did the polishing in three steps going from 800 to 1500 to 10000 grit paste (green, blue, gray). To apply the polish I had ordered small felt polisher tools but they were not very effective, toothpicks on the other hand worked very well.

I polished the surface for about one minute in each step checking in between with a magnifying glass until the surface has a very smooth and shiny finish. Here is what the crystals look like before and after grinding:

To mount the bearing I use hot melt glue or plasticine if I want to be able to make adjustments. As shown in the photos a magnet held by an adjustable arm works great to hold the needle in place. The actual rotor was removed in the photo to show the needle standing in the bearing.

Finally the motor runs very silent and smoothly and the rotor does not touch the sides even if the motor is slightly tilted. You can find a video of an earlier version running at 270 nanowatts with a Sapphire glass as a bearing.

It would be a lot easier if there was some kind of jig to build it and get the ground reflectors to the correct angle and all the rods at the right length. That is what I set out to do. The design is for a 868MHz antenna but in theory it can just be scaled for other frequencies. Update: there is now also a 915MHz version of the jig available on thingiverse. I did not build and measure that one though.

Design and verification

First I thought I’d just do some simulations and ‘get it right the first time’. Let me just say that with having no previous experience with neither antennas nor high frequency designs I did fail in that. After some searching I found a neat and free software called MMANA that lets you design and optimize antennas. I am not sure what I did wrong but the optimization process led to an antenna length of 80mm where a 1/4 lambda at 868MHz is actually 86mm. Not really knowing what I am doing I went on and built the first antenna with an 80mm rod just as found by simulation. The images show the radiation pattern the simulation software MMANA calculates for this antenna. As expected it has the typical donut shape and has a 1.92dBi gain in the horizontal axis.

Hooking it up to the spectrum analyser at work revealed that my build was actually better suited for 900MHz so I increased the length and tuned it until it was very close to 868MHz and surprise surprise the ideal length is 86mm. In the following images the marker is set to 868.9MHz and the SWR is just under 1.1 for a bandwidth of about 50MHz which is close to perfect.

The design itself is very simple: just five 2mm diameter brass tubes cut to the right length and soldered directly to a female SMA connecter. I saw this design somewhere in a forum but I was unable to find the link again.

How to build it

The difficult part is to get the tubes cut to the right length and solder them in the correct angle. In order to make this a whole lot easier I designed a jig that can be 3D-printed. It has features at the base to measure the length of the tubes and a replaceable top piece that can be printed again fast in case it melts in the soldering process.

Here is what you need:

• 3D-printed stencil (get it on thingiverse)
• 2mm brass tube, at least 40cm long
• Female SMA connecter (Aliexpress)
• Adapter cable (to u.FL for example)

Take the 2mm diameter brass pipe and use the jig to mark the cutting length. You need four shorter pieces that are 71mm in length for the ground reflector and one 86mm piece for the radiating antenna part. The images above show how to use the jig to measure the length. I used a side cutter to cut the tubes and then used pliers to push the now flat ends back into shape but there may be a better way.

Prepare the SMA connecter by cutting the four legs (but not the center part!) and sanding or filing the cornders to an appriximate 45° angle similar to what I did in the foto shown below.

Mount the connecter into the top-piece and place it in the jig. Make sure the four dimples in the top piece are aligned with the four corners of the connecter. Place one of the four ground rods into the jig and solder it to the connecter using plenty of solder and enough heat. The plastic part in the center of the connecter is usually made from teflon and will not melt. Repeat until done with all four pieces. Now make sure the antenna part fits nicely on the center tap and that it can move all the way down to the plastic part. Pull it back until it just touches the top of the center part and add plenty of solder so it flows over the pin as well as the tube and then push the tube all the way down to the plastic while the solder is still liquid. If done right you get a very good solder joint with the tube soldered also on the inside forming a strong joint. Thats all there is to it.

Results

To test the antennas performance I hooked it up to my LoRa node (ESP32 from Heltec). The original antenna that came with the node is one of those little 40mm long monopole antennas. I did get a connection to the TTN gateway that currently sits in the FabLab Winti which is in the basement of a building about 300m away behind some other buildings and the signal was quite poor. With my own antenna the connection is not great either but it is a lot better. I expected an increase of about 2dB in the signal to noise ratio (SNR) thanks to some directionality of the antenna (see simulation results above). To my surprise the SNR actually improved by about 4dB compared to the monopole antenna which means the signal strength more than doubled!

Monopole antenna signal:

DIY ground dipole antenna:

As usual I did the design in OnShape and you can find it here.

I did take a different approach than using a shunt resistor. Since the maximum current I usually have to measure when working with small microcontrollers or Arduinos is below 50mA I chose to use a transimpedance amplifier architecture rather than a voltage amplifier. This circuit has the advantage of having zero burden voltage but bears other disadvantages which I soon discovered but in theory it sounded like a good solution.

The input current to the circuit to measure is fed to the negative input and the output current is taken from GND. The circuit has to be floating against the power source to work. Also positive and negative rail voltages are needed with respect to GND. With proper amplification a transimpedance amplifier is able to measure tiny currents down to picoamps. The opamps output actually feeds the circuit through feedback resistor so there is virtually zero burden voltage on this ‘active shunt’, apart from the input offset voltage of the opamp.

There are three main problems: the circuit is so sensitive that it picks up any noise in the environment (the switching cap inverter I use does also not help the purpose), the output voltage swing of low input bias current amplifiers is horrible under higher currents (by higher I mean over 10mA) and there is the stability problem of transimpedance amplifiers with low impedance feedback resistors.

I started out using an LMC662 as the input stage amplifier as it is easily available, cheap and has a very low input bias current. Turns out it gets unstable at loads below 500Ω so there is lots of ringing or even just oscillation. Using a larger resistor than the chosen 33Ω was not an option as I wanted to have at least ±40mA output current at ±3V including the opamps internal resistrance (i.e. the output swing). I next tried a TS912. That is where I learned what output swing limitations really mean. This opamp is just the worst possible choice in that regard: it has a voltage drop of 3V at 30mA. Paying more attention when selecting another opamp I found the OPA2350 which is fast, has a low input bias current and a high drive capability. As a bonus it also has a very low input offset voltage of just 0.15mV. The disadvantig is that it only works up to ±3V. I did try it anyway. Running it at ±4.5V works fine even though this is way beyond its absolute maximum voltage rating of ±3.5V. I guess it will brake down pretty fast but I do not intend on using it that often an so far it worked already for a few hours. If I ever find a more suitable opamp I will replace it.

There now was still the problem of stability. A good article from Maxim Integrated about the stability of transimpedance amplifiers suggests to use a capacitor in the feedback loop to increase stability. I did that previously but only tried up to 100pF. Piling up ever increasing values of capacitors and testing the output ringing I found that by putting a 100nF (!) capacitor in the feedback loop gets things more stable. This comes at the cost of reduced bandwidth which is now 50kHz. Still fast enough though.

The last problem of induced noise could be solved by a more careful layout, adding filters and LDOs or not using a switch cap inverter to get the negative voltage supply. Also putting everything in a shielded box and using shielded cables would greatly improve noise. For the intended purpose the circuit works fine and I can live with the noise of about ±25mV on a 500mV output signal.

Demo Measurements

Here is a measurements I did on a Lambda Node showing one measurement and sendout cycle:

The setting was 10x on the preamp using a 33Ω resistor (actually resulting in a 33x amplification from current to voltage) with the setting of post amplification also on 10x (actually -3.3x) totalling in a 100x current to voltage amplification. The measurement shows nicely how the firmware goes through different power saving modes, acitvating and deactivating peripherals and finally sending out the payload with peak currents of about 13mA which corresponds nicely to the NRF24L01 datasheet for sending/receiving current. The blue line is the math channel set to integral mode. The integrated voltage shows a final value of 19mU. On the Rigol DS1054Z I found that one ‘unit’ in integral mode corresponds to 1Vs, independent of the current channel setting. So 19mU is actually 19mVs which with 1mV = 10µA comes to 190µAs. With a load supply voltage of 3.0V the required energy is just 570µWs or 570µJ. This value can be used to accurately calculate battery lifetime.

Another example showing an Arduino with sleep mode activated firmware (not sure what exact code I ran):

Circuit Features

• Selectable pre- and post amplification.
• Single supply input (onboard switching cap inverter)
• Integrator circuit to integrate the current (could not get it to work without huge drifts)
• On/Off switch to use with a battery as a supply
• Ground pad on the corner for oscilloscope probe grounding
• Guard traces around sensitive inputs

Source Files

The eagle design files, Gerbers and the schematic are available on GitHub.

The painter library makes it a lot easier to program animations on digital LED strips with individually adressable LEDs like the WS2812. It works on a buffer called ‘canvas’ that in additon to HSV color values for each LED also contains some properties to control fading effects. To paint on the canvas the library contains a class called the ‘brush’ that contains a HSV color which it will transfer to the pixel at its current position as well as movement properties that can be initialized to create the animations. The library supports the creation of multiple brushes and even multiple canvases to create color-mixing effects.

After creating the buffers and initilizing the brush(es) the update functions can just be called in a loop. The position of the brush is actually at a sub-pixel resolution so that the brush can move slowly and does not have to be painting a pixel on each iteration.

The whole library was written with low-ram microcontrollers like the Arduino in mind and I tried to use as little ram as possible by using individual bits as flags instead of whole bytes i.e. bools.

The library is available on my GitHub repository as well as in the library manager of the Arduino IDE.

Comparing the library to my original NeoPixelPainter library I noticed that the animations run indeed faster with the FastLED library but at the expense of using a little more ram. Eyeballing it I’d say it runs 30-50% faster. Compiling the ‘simple demo’ for the Arduino Uno:

• NeopixelPainter library – Flash: 6278b  Ram: 231b
• FastLEDPainter library – Flash: 7648b  Ram: 478b

The two magnets are mounted on a steel washer and the magnetic circuit is closed at the bottom of the inductors with some more ferrite parts from small inductors. While this design kind of worked it did by no means produce the outcome I had hoped. The voltage from this circuit was barely enough to light up a white LED and the brightness was nowhere near useful. Why? There’s a couple of reasons for that. First off the number of turns on the inductors are not enough, even though I used the highest indutance values I could find on DigiKey that were still in a small form factor. Then the ferrite core probably saturates and therefor is not able to carry the full flux the magnets would be able to push through, an iron core would perform better. And the main reason is a poor design: I did not do any calculations or simulations on the magnetic circuit or I could have seen this before I actually built it. But all in all it was a fun experiment.

The more elegant solution

I almost gave up on building my own bicycle light when a few weeks later it hit me: what cheap part has a coil with lots of windings and a magnetic circuit already built in? Of course: a relay! It just so happened that I had a few cheap chinese 5VDC relays laying around so I cut one open, removed the switching part and was left with a now open magnetic circuit.

Again the voltage output was not too great but moving a magnet really close and fast brought the voltage spike up to almost 10V if I remember correctly. The white LED was still not lighting up as brightly as necessary for a safety light but there are higher voltage relays around. So I ordered a bunch of 12V relays (with more windings on the relay coil) and when I tested those the result was just what I had hoped for. I later also tried the 24V version of the relay but there was no significant improvement over the 12V relay when the LEDs are connected.

The DC resistance of the 12V coil is around 400Ω and the 24V coil has 1.5kΩ. The calculated peak current from the above measured voltages assuming a 3.6V forward voltage is roughly 9mA for both relays so there really seems to be no benefit in using the higher voltage relay except maybe that it produces a higher voltage at slower magnet movement and thus has a lower speed threshold to reach the forward voltage of the LED.

Beware of the reverse voltage

The voltage peaks are of course in both directions and a diode rectifier would be in order to protect the reverse voltage sensitive LED from being destroyed: most LEDs have an absolute maximum rating for the reverse voltage of just 5V. Adding a higher voltage diode in series wold be one option but probably the worst possible choice since it eats up energy in forward direction and does not use the reverse voltage peak. A bridge rectifier is a little over the top. The most elegant (and obvious) solution is to just connect another LED in reverse so the voltage is clamped to the forward voltage in both directions.

Building the circuit

With the experimental phase coming to a close it was time to build a circuit. By pure chance I had a few very cheap keychain lights laying around which I actually ordered to salvage the solar cell as well as the rechargeable LIR battery for another project.

Sidenote: I just have to say that these key chain lights just take the cake when it comes to (fraudulent) chinese product development ingenuity. To my disappointment there were no LIR batteries inside but two non-rechargeable CR2016. The solar cell is not even connected to the circuit! But why then use an expensive solar cell (it does work) instead of just a fake glass? Well the solar cells all have a marking on the back which is normally used to mark bad units in a batch. So these cells did not pass the quality check at the factory and instead of ending up in a dumpster they are used as a deceiving decorative cover in a key-chain light.

The pitch of the relay coil pins just happen to fit the input pads on LED lamp circuit! All there is left to do is to remove the button and short out the pads as well as flipping one of the LEDs and we have a very simple induction light. Now it has to be mounted close to the spokes of the bicycle where the magnet(s) will be placed.

Designing the housing

It took a couple of hours and two or three design iterations before I came up with the final version. It had to be 3D printable of course and easily pottable to protect it from rain and dirt. While the first design worked just fine it was not possible to adjust the angle at which the LEDs are mounted due to limitiations of 3D printing technology. You can find the OnShape designfiles here.

Build your own

You can read the detailed instructions on how to build your own version of the “VeloBlinky” on my instructable.