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authorjaseg <git@jaseg.net>2018-05-19 14:43:28 +0200
committerjaseg <git@jaseg.net>2018-05-19 14:43:47 +0200
commit7bc656ca2a026d91a845dd4d8bfeb812021cdf4d (patch)
tree4f1896fe65afc9079e766602184cf0126d29913a /content/posts/multichannel-led-driver
parent24ad9ee7a0a8095d56c330a39321f40dee020dcb (diff)
downloadblog-7bc656ca2a026d91a845dd4d8bfeb812021cdf4d.tar.gz
blog-7bc656ca2a026d91a845dd4d8bfeb812021cdf4d.tar.bz2
blog-7bc656ca2a026d91a845dd4d8bfeb812021cdf4d.zip
Add multichannel LED driver post
Diffstat (limited to 'content/posts/multichannel-led-driver')
-rw-r--r--content/posts/multichannel-led-driver/images/asymmetric_iled.svg2222
-rw-r--r--content/posts/multichannel-led-driver/images/asymmetric_vgate.svg1933
-rw-r--r--content/posts/multichannel-led-driver/images/bcm_schema.jpgbin0 -> 1626022 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/corrected_brightness_sim.svg765
-rw-r--r--content/posts/multichannel-led-driver/images/driver_linearity_raw.svg937
-rw-r--r--content/posts/multichannel-led-driver/images/driver_output_ltspice_schematic.jpgbin0 -> 876019 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/driver_pcb_built.jpgbin0 -> 1229840 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/driver_ringing_strong.jpgbin0 -> 285952 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/driver_ringing_weak.jpgbin0 -> 292100 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/led_strip_alight.jpgbin0 -> 1752106 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/linearization_setup.jpgbin0 -> 2038436 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/olsndot_output_schematic.jpgbin0 -> 1410898 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/olsndot_pcb.pngbin0 -> 137479 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/olsndot_schematic.pngbin0 -> 362216 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/overshoot_sim_r0.svg1885
-rw-r--r--content/posts/multichannel-led-driver/images/overshoot_sim_r100.svg1788
-rw-r--r--content/posts/multichannel-led-driver/images/pwm_schema.jpgbin0 -> 840134 bytes
-rw-r--r--content/posts/multichannel-led-driver/images/uncorrected_brightness_sim.svg727
-rw-r--r--content/posts/multichannel-led-driver/index.rst454
-rw-r--r--content/posts/multichannel-led-driver/olsndot_v02_schematics_and_pcb.pdfbin0 -> 1036117 bytes
20 files changed, 10710 insertions, 1 deletions
diff --git a/content/posts/multichannel-led-driver/images/asymmetric_iled.svg b/content/posts/multichannel-led-driver/images/asymmetric_iled.svg
new file mode 100644
index 0000000..c18d5de
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diff --git a/content/posts/multichannel-led-driver/index.rst b/content/posts/multichannel-led-driver/index.rst
index ff8930e..8d5ad42 100644
--- a/content/posts/multichannel-led-driver/index.rst
+++ b/content/posts/multichannel-led-driver/index.rst
@@ -1,5 +1,457 @@
---
-title: "Multichannel Led Driver"
+title: "32-Channel LED tape driver"
date: 2018-05-02T11:31:14+02:00
+draft: true
---
+Theoretical basics
+==================
+
+Together, a friend and I outfitted the small staircase at Berlin's Chaos Computer Club with nice, shiny RGB-WW LED tape
+for ambient lighting. This tape is like regular RGB tape but with an additional warm white channel, which makes for much
+more natural pastels and whites. There are several variants of RGBW tape. Cheap ones have separate RGB and white LEDs,
+which is fine for indirect lighting but does not work for direct lighting. Since we wanted to mount our tape in channels
+at the front of the steps, we had to use the slightly more expensive variant with integrated RGBW LEDs. These are LEDs
+in the 5050 (5.0mm by 5.0mm) form factor common with RGB LEDs that have a small section divided off for the white
+channel. The red, green and blue LED chips sit together in the larger section covered with clear epoxy and the white
+channel is made up from the usual blue LED inside a yellow phosphor in the smaller section.
+
+Since we wanted to light up all of 15 steps, and for greatest visual effect we would have liked to be able to control
+each step individually we had to find a way to control 60 channels of LED tape with a reasonable amount of hardware.
+
+LED tape has integrated series resistors and runs off a fixed 12V or 24V constant-voltage supply. This means you don't
+need a complex constant-current driver as you'd need with high-power LEDs. You can just hook up a section of LED tape
+to a beefy MOSFET to control it. Traditionally, you would do *Pulse Width Modulation* (PWM) on the MOSFET's input to
+control the LED tape's brightness.
+
+Pulse Width Modulation
+----------------------
+
+`Pulse Width Modulation`_ is a technique of controlling the brightness of a load such as an LED with a digital signal.
+The basic idea is that if you turn the LED on and off much too fast for anyone to notice, you can control its power by
+changing how long you turn it on versus how long you leave it off.
+
+PWM divides each second into a large number of periods. At the beginning of each period, you turn the LED on. After
+that, you wait a certain time until you turn it off. Then, you wait for the next period to begin. The periods are always
+the same length but you can set when you turn off the LED. If you turn it off right away, it's off almost all the time
+and it looks like it's off to your eye. If you turn it off right at the end, it's on almost all the time and it looks
+super bright to your eye. Now, if you turn it off halfway into the cycle, it's on half the time and it will look to your
+eye as half as bright as before. This means that you can control the LED's brightness with only a digital signal and
+good timing.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/pwm_schema.jpg" alt="A visualization of PWM at different duty cycles.">
+ <figcaption>Waveforms of two PWM cycles at different duty cycles.</figcaption>
+ </figure>
+
+PWM works great if you have a dedicated PWM output on your microcontroller. It's extremely simple in both hardware and
+software. Unfortunately for us, controlling 32 channels with PWM is not that easy. Cheap microcontrollers only have `a
+handful of hardware PWM outputs`_, so we'd either have to do everything in software, bit-banging our LED modulation, or
+we'd have to use a dedicated chip.
+
+Doing PWM in software is both error-prone and slow. Since the maximum dynamic range of a PWM signal is limited by the
+shortest duty cycle it can do, software PWM being slow means it has poor PWM resolution at maybe 8 bits at most. Poor
+color resolution is not a problem if all you're doing is to fade around the `HSV rainbow`_, but for ambient lighting
+where you *really* want to control the brightness down to a faint shimmer you need all the color resolution you can get.
+
+If you rule out software PWM, what remains are dedicated `hardware PWM controllers`_. Most of these have either of three
+issues:
+
+* They're expensive
+* They don't have generous PWM resolution either (12 bits if you're lucky)
+* They're meant to drive small LEDs such as a 7-segment display directly and you can't just hook up a MOSFET to their
+ output
+
+This means we're stuck in a dilemma between two poor solutions if we'd want to do PWM. Luckily for us, PWM is not the
+only modulation in town.
+
+.. _`Pulse Width Modulation`: https://en.wikipedia.org/wiki/Pulse-width_modulation
+.. _`a handful of hardware PWM outputs`: https://www.nxp.com/parametricSearch#/&c=c731_c380_c173_c161_c163&page=1
+.. _`HSV rainbow`: https://en.wikipedia.org/wiki/HSL_and_HSV
+.. _`hardware PWM controllers`: http://www.ti.com/lit/ds/symlink/tlc5940.pdf
+
+Binary Code Modulation
+----------------------
+
+PWM is the bread-and-butter of the maker crowd. Everyone and their cat is doing it and it works really well most of the
+time. Unbeknownst to most of the maker crowd, there is however another popular modulation method that's mostly used in
+professional LED systems: Enter `*Binary Code Modulation* (BCM) <http://www.batsocks.co.uk/readme/art_bcm_1.htm>`_.
+
+BCM is to PWM sort of what barcodes are to handwriting. While PWM is easy to understand and simple to implement if all
+you have is a counter and an IO pin, BCM is more complicated. On the other hand, computers can do complicated and BCM
+really shines in multi-channel applications.
+
+Similar to PWM, BCM works by turning on and off the LED in short periods fast enough to make your eye perceive it as
+partially on all the time. In PWM the channel's brightness is linearly dependent on its duty cycle, i.e. the percentage
+it is turned on. In PWM the duty cycle D is the total period T divided by the on period T_on. The issue with doing PWM
+on many channels at once is that you have to turn off each channel at the exact time to match its duty cycle.
+Controlling many IO pins at once with precise timing is really hard to do in software.
+
+BCM avoids this by further dividing each period into smaller periods which we'll call *bit periods* and splitting each
+channel's duty cycle into chunks the size of these bit periods. The amazingly elegant thing in BCM now is that as you
+can guess from the name these bit periods are weighted in powers of two. Say the shortest bit period lasts 1
+microsecond. Then the second-shortest bit period is 2 microseconds and the third is 4, the fifth 8, the sixth 16 and so
+on.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/bcm_schema.jpg" alt="A visualization of BCM at different duty cycles.">
+ <figcaption>Waveforms of a single 4-bit BCM cycle at different duty cycles. This BCM can produce 16 different
+ levels.</figcaption>
+ </figure>
+
+Staggered like this, you turn on the LED for integer value of microseconds by turning it on in the bit periods
+corresponding to the binary bits of that value. If I want my LED to light for 19 microseconds every period, I turn it on
+in the 16 microsecond bit period, the 2 microsecond bit period and the 1 microsecond bit period and leave it off for the
+4 and 8 mircosecond bit periods.
+
+Now, how this is better instead of just more complicated than plain old PWM might not be clear yet. But consider this:
+Turning on and off a large number of channels, each at its own arbitrary time is hard because doing the timing in
+software is hard. We can't use hardware timers since we only have two or three of those, and we have 32 channels.
+However, we can use one hardware timer to trigger a really cheap external latch to turn on or off the 32 channels all at
+once. With this setup, we can only controll all channels at once, but we can do so with very precise timing.
+
+All we need to do is to set our timer to the durations of the BCM bit periods, and we can get the same result as we'd
+get with PWM with only one hardware timer and a bit of code that is not timing-critical anymore.
+
+Applications of Binary Code Modulation
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+BCM is a truly wondrous technique, and outside of hobbyist circles it is in fact very widely known. Though we're using
+it to control just 32 channels here, you can do much more channels without any problems. The most common application
+where BCM is invariably used is *any* kind of LED screen. Controlling the thousands and thousands of LEDs in an LED
+screen with PWM with a dedicated timer for each LED would not be feasible. With BCM, all you need to dedicate to a
+single LED is a flipflop (or part of one if you're multiplexing). In fact, there is a whole range of `ICs with no other
+purpose than to enable BCM on large LED matrices <http://www.vabolis.lt/stuff/MBI5026.pdf>`_. Basically, these are a
+high-speed shift register with latched outputs much like the venerable 74HC595_, only their outputs are constant-current
+sinks made so that you can directly connect an LED to them.
+
+.. _74HC595: http://www.ti.com/lit/ds/symlink/sn74hc595.pdf
+
+Running BCM on LED tape
+~~~~~~~~~~~~~~~~~~~~~~~
+
+In our case, we don't need any special driver chips to control our LED tape. We just connect the outputs of a 74HC595_
+shift register to one MOSFET_ each, and then we directly connect the LED tape to these MOSFETs. The MOSFETs allow us to
+drive a couple of amps into the LED tape from the weak outputs of the shift register.
+
+The BCM timing is done by hooking up two timer channels of our microcontroller to the shift registers *strobe* and
+*reset* inputs. We set the timer to PWM mode so we can generate pulses with precise timing. At the beginning of each
+bit period, a pulse will strobe the data for this bit period that we shifted in previously. At the end of the bit
+period, one pulse will reset the shift register and one will strobe the freshly-reset zeros into the outputs.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/olsndot_output_schematic.jpg" alt="From left to right, we see the STM32, one of the shift
+ registers, and the LEDs and MOSFETs. The LED tape is driven to ground by the MOSFETs, which are in turn directly
+ driven from the shift register outputs. The shift register is wired up to the STM32 with its clock and data
+ inputs on SCK and MOSI and its RESET and STROBE inputs on channel 2 and 3 of timer 1.">
+ <figcaption>
+ The schematic of a single output of this LED driver. Multiple shift register stages can be cascaded.
+ </figcaption>
+ </figure>
+
+
+Our implementation of this system runs on an STM32F030F4P6_, the smallest, cheapest ARM microcontroller you can get from
+ST. This microcontroller has only 16kB of flash and 1kB of RAM, but that's plenty for our use. We use its SPI controller
+to feed the modulation data to the shift registers really fast, and we use two timer channels to control the shift
+registers' reset and strobe.
+
+We can easily cascade shift registers without any ill side-effects, and even hundreds of channels should be no problem
+for this setup. The only reason we chose to stick to a 32-channel board is the mechanics of it. We thought it would be
+easier to have several small boards instead of having one huge board with loads of connectors and cables coming off it.
+
+The BOM cost per channel for our system is 3ct for a reasonable MOSFET, about 1ct for one eighth of a shift register
+plus less than a cent for one resistor between shift register and MOSFET. In the end, the connectors are more expensive
+than the driving circuitry.
+
+.. _MOSFET: https://en.wikipedia.org/wiki/MOSFET
+.. _STM32F030F4P6: http://www.st.com/resource/en/datasheet/stm32f030f4.pdf
+
+Hardware design
+===============
+
+From this starting point, we made a very prototype-y hardware design for a 32-channel 12V LED tape driver. The design is
+based on the STM32F030F4P6_ driving the shift registers as explained above. The system is controlled through an RS485_
+bus that is connected up to the microcontroller's UART using an MAX485_-compatible RS485 transceiver. The LED tape is
+connected using 9-pin SUB-D_ connectors since they are cheap and good enough for the small current of our short segments
+of LED tape. The MOSFETs we use are small SOT-23_ logic-level MOSFETs. In various prototypes we used both International
+Rectifier's IRLML6244_ as well as Alpha & Omega Semiconductor's AO3400_. Both are good up to about 30V/5A. Since we're
+only driving about 2m of LED tape per channel we're not going above about 0.5A and the MOSFETs don't even get warm.
+
+.. _RS485: https://en.wikipedia.org/wiki/RS-485
+.. _MAX485: https://datasheets.maximintegrated.com/en/ds/MAX1487-MAX491.pdf
+.. _IRLML6244: https://www.infineon.com/dgdl/?fileId=5546d462533600a4015356686fed261f
+.. _AO3400: http://aosmd.com/pdfs/datasheet/AO3400.pdf
+.. _SUB-D: https://en.wikipedia.org/wiki/D-subminiature
+.. _SOT-23: http://www.nxp.com/documents/outline_drawing/SOT23.pdf
+
+Switching nonlinearities
+------------------------
+During testing of our initial prototype, we noticed that the brightness seemed to jump around when fading to very low
+values. It turned out that our extremely simple LED driving circuit consisting of only the shift register directly
+driving a MOSFET, which in turn directly drives the LED tape was maybe a little bit too simple. After some measurements
+it turned out that we were looking at about 6Vpp of ringing on the driver's output voltage. The picture below is the
+voltrage we saw on our oscilloscope on the LED tape.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/driver_ringing_strong.jpg" alt="Strong ringing on the LED voltage waveform edge at about
+ 100% overshoot during about 70% of the cycle time.">
+ <figcaption>Bad ringing on the LED output voltage caused by wiring inductance. Note that the effect on the
+ actual LED current is less bad than this looks since the LED's V/I curve is nonlinear.</figcaption>
+ </figure>
+
+
+Dynamic switching behavior: Cause and Effect
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+A bit of LTSpice_ action later we found that the inductance of the few metres of cable leading to the LED tape is the
+likely culprit. The figure below is the schematic used for the simulations.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/driver_output_ltspice_schematic.jpg" alt="The LTSpice schematic of one output of the driver,
+ taking into account the shift register's output ESR and the wiring ESL.">
+ <figcaption>The schematic of the simulation in LTSpice</figcaption>
+ </figure>
+
+As tested, the driver does not include any per-output smoothing so the ~.5A transient on each BCM cycle hits the cable
+in full. Combined with the cable inductance, this works out to a considerable lag of the rising edge of the LED
+current, and bad ringing on its falling edge. Below is the voltage on the LED output from an LTSpice simulation of our
+driver.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/overshoot_sim_r0.svg" alt="The result of the LTSpice simulation of our driver output. The LED
+ current shows similar ringing to what we measured using the oscilloscope. Interestingly, the gate voltage shows
+ strong ringing, too.">
+ <figcaption>The result of our LTSpice simulation. This simulation assumes 1µH of wiring inductance and 50Ω of
+ output impedance on the part of the shift register. The ringing at the gate visible in the gate voltage graph is
+ due to feed-through of the ringing at the output through the MOSFET's parasitic Cgd.</figcaption>
+ </figure>
+
+We were able to reduce the rining and limit the effect somewhat by
+putting a 220Ω series resistor in between the shift register output and the MOSFET gate. This resistor forms an RC
+circuit with the MOSFET's nanofarad or two of gate capacitance. The result of this is that the LED current passing the
+wire's ESL rises slightly more slowly and thus the series inductance gets excited slightly less, and the overshoot
+decreases. Below is a picture of the waveform with the dampening resistor in place and a picture of our measurement for
+comparison. The resistor values don't agree perfectly since the estimated ESL and stray capacitance of the wiring is
+probably way off.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/driver_ringing_weak.jpg" alt="Weak ringing on the LED voltage waveform edge at about 30%
+ overshoot during about 20% of the cycle time.">
+ <figcaption>Adding a resistor in front of the MOSFET gate to slow the transition dampened the ringing somewhat,
+ but ultimately it cannot be eliminated entirely. Note how you can actually see the miller plateau on the
+ trailing edge of this signal.
+ </figcaption>
+ </figure>
+
+.. raw:: html
+
+ <figure>
+ <img src="images/overshoot_sim_r100.svg" alt="The result of the LTSpice simulation of our driver output with an
+ extra 100 Ohms between shift register output and MOSFET gate. Similar to the oscilloscope measurement the
+ ringing is much reduced in its amplitude.">
+ <figcaption>The LTSpice simulation result with the same parameters as above but with an extra 100Ω between the
+ shfit register's output and the MOSFET's gate.</figcaption>
+ </figure>
+
+A side effect of this fix is that now the effective on-time of the LED tape is much longer than the duty cycle at the
+shift register's output at very small duty cycles (1µs or less). This is caused by the MOSFET's `miller
+plateau`_. For illustration, below is a graph of both the excitation waveform (the boxy line) and the resulting LED
+current (the other ones) both without dampening (top) and with 220Ω dampening (bottom). As you can see the effective
+duty cycle of the LED current is not at all equal to the 50% duty cycle of the excitation square wave.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/asymmetric_iled.svg" alt="The result of an LTSpice simulation of the LED duty cycle without and
+ with dampening. Dampening widens the LED current waveform from 50% duty cycle with sharp edges to about 80% duty
+ cycle with soft edges.">
+ <figcaption>Simulated LED duty cycle with and without dampening. The dampening resistance used in this
+ simulation was 220Ω.</figcaption>
+ </figure>
+
+.. raw:: html
+
+ <figure>
+ <img src="images/asymmetric_vgate.svg" alt="The gate voltages in the spice simulation above. The undampened
+ response shows sharp edges with the miller plateau being a barely noticeable step, but with strong ringing on
+ the trailing edge. The dampened response shows RC-like slow-edges, but has wide miller plateaus on both edges
+ adding up to about 50% of the pulse width.">
+ <figcaption>The MOSFET gate voltage from the simulation in the figure above. You can clearly see how the miller
+ plateau (the horizontal part of the trace at about 1V) is getting much wider with added dampening, and how the
+ resulting gate charge/discharge curve is not at all that of a capacitor anymore.</figcaption>
+ </figure>
+
+
+
+In conclusion, we have three major causes for our calculated LED brightness not matching reality:
+
+* Ringing of the equivalent series inductance of the wiring leading up to the LED tape
+* Miller plateau lag
+* The dampening resistor and the MOSFET gate forming an RC filter that helps with wire ESL ringing but worsens the
+ miller plateau issue and deforms the LED current edges.
+
+Added up, these three effects yield a picture that agrees well with our simulations and measurements. The overall effect
+is neglegible at long period durations (>10µs), but gets really bad at short period durations (<1µs). The effect is
+non-linear, so correcting for it is not as simple as adding an offset.
+
+.. _LTSpice: http://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
+.. _`miller plateau`: https://www.vishay.com/docs/68214/turnonprocess.pdf
+
+Measuring LED tape brightness
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+In order to correct for the nonlinearities mentioned above, we decided to implement a lookup table mapping BCM period to
+actual timer setting. That is, each row of the table contains the actual period length we need to set the
+microcontroller's timer to in order to get our intended brightness steps.
+
+To calibrate our driver, we needed a setup for reproducible measurement of the relative brightness of our LED tape at
+different settings. Absolute brightness is not of interest to us as the eye can't perceive it. To perform the
+calibration, the LED driver is set to enable each single BCM period in turn, i.e. brightness values 1, 2, 4, 8, 16 etc.
+
+The setup we used to measure the LED tape's brightness consists of a bunch of LED tape stuck into a tin can for
+shielding against both stray light and electromagnetic interference and a photodiode looking at the LED tape. We used
+the venerable BPW34_ photodiode in our setup as I had a bunch leftover from another project and because they are quite
+sensitive owing to their physically large die area.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/linearization_setup.jpg" alt="The led measurement setup consists of several PCBs and a
+ breadboard linked with a bunch of wires and a big tin can to shield the LEDs and the photodiode. A large sub-D
+ connector is put into the top of the tin can as a feed-through for the LED tape's control signals and the
+ photodiode signal. In the background the control laptop is visible.">
+ <figcaption>The LED brighness measurement setup. The big tin can contains a bunch of LED tape and the
+ photodiode. The breadboard on the right is used for the photodiode preamplifier and for jumpering around the LED
+ tape's channels. The red board next to it is the buspirate used as ADC. The board on the bottom left is a
+ TTL-to-RS485 converter and the board in the middle is the unit under test.</figcaption>
+ </figure>
+
+The photodiode's photocurrent is converted into a voltage using a very simple transimpedance amplifier based around a
+MCP6002_ opamp that was dampened into oblivion with a couple nanofarads of capacitance in its feedback loop. The
+MCP6002_ is a fine choice here since I had a bunch and because it is a CMOS opamp, meaning it has low bias current that
+would mess up our measurements. For many applications, opamp bias current is not a big issue but when using the opamp to
+directly measure very small currents at its input it quickly swamps out the signal for most BJT-input types.
+
+The transimpedance amplifier's output is read from the computer using the ADC input of a buspirate USB thinggamajob. In
+general I would not recommend the buspirate as a tool for this job since it's ADC is not particularly good and it's
+programming interface is positively atrocious, but it was what I had and it beat first wiring up one of the dedicated
+ADC chips I had in my parts bin.
+
+The computer runs a small python script cycling the LED tape through all its BCM period settings and taking a brightness
+measurement at each step. Later on, these measurements can be plotted to visualize the resulting slope's linearity, and
+we can even do a simulation of the resulting brightness for all possible control values by just adding the measured
+photocurrents for a certain BCM setpoint just as our retinas would do.
+
+.. raw:: html
+
+ <figure>
+ <img src="images/driver_linearity_raw.svg" alt="">
+ <figcaption>
+ A plot of the measured brightness of our LED tape for each BCM period. The brightness values are normalized
+ to the value measured at the LSB setpoint (brightness=1/65535). Ideally, this plot would show a straight
+ line with slope 1. Obviously, it doesn't. The bend in the curve is caused by the above-mentioned duty cycle
+ offset adding an offset to all brightness values. Shown is both the raw data (light), which has essentially zero
+ measurement error and a linear fit (dark).
+
+ The plot is in log-log to approximate how the human eye would perceive brightness, i.e. highly sensitive at
+ low values but not very sensitive at all at large values.
+ </figcaption>
+ </figure>
+
+While it would be possible to fully automate the optimization of BCM driver lookup tables, we needed only one and in the
+end I just sat down and manually tweaked the ideal values we initially calculated until I liked the result. You can see
+the resulting brightness curve below.
+
+.. raw:: html
+
+ <figure>
+ <figure class="side-by-side">
+ <img src="images/uncorrected_brightness_sim.svg" alt="">
+ <figcaption>
+ Calculated brightness curve for the uncorrected BCM setup. As you can see, at low setpoints the result
+ is about as smooth as sandpaper, which is well in line with our observations. At high setpoints the
+ offset gets swamped out and the nonlinearity in the low bits is not visible anymore.
+ </figcaption>
+ </figure><figure class="side-by-side">
+ <img src="images/corrected_brightness_sim.svg" alt="">
+ <figcaption>
+ Brightness curve for the corrected BCM setup extrapolated using actual measurements. Looks as buttery
+ smooth in real life as it does in this plot.
+ </figcaption>
+ </figcaption>
+ </figure>
+ </figure>
+
+.. _BPW34: http://www.vishay.com/docs/81521/bpw34.pdf
+.. _MCP6002: http://ww1.microchip.com/downloads/en/DeviceDoc/21733j.pdf
+
+Controlling the driver
+----------------------
+
+Now that our driver was behaving linear enough that you couldn't see it actually wasn't we needed a nice way to control
+it from a computer of our choice. In the ultimate application (our staircase) we'll use a raspberry pi for this. Since
+we already settled on an RS485_ bus for its robustness and simplicity, we had to device a protocol to control the driver
+over this bus. Here, we settled on a simple, COBS_-based protocol for the reasons I wrote about in `How to talk to your
+microcontroller over serial <serial-protocols>`_.
+
+To address our driver nodes, we modified the Makefile to build a random 32-bit MAC into each firmware image. The
+protocol has only five message types:
+
+1. A 0-byte *ping* packet, to which each node would reply with its own address in the
+ first 100ms after boot. This can be used to initially discover the addresses of all nodes connected to the bus. You'd
+ spam the bus with *ping* packets, and then hit reset on each node in turn. The control computer would then receive
+ each device's MAC address as you hit reset.
+2. A 4-byte *address* packet that says which device that the following packet is for. This way of us using the packet
+ length instead of a packet type field is not particularly elegant, but our system is simple enough and it was easy to
+ implement.
+3. A 64-byte *frame buffer* packet that contains 16 bits of left-aligned brightness data for every channel
+4. A one-byte *get status* packet that tells the device to respond with...
+5. ...a 27-byte status packet containing a brief description of the firmware (version number, channel count, bit depth
+ etc.) as well as the device's current life stats (VCC, temperature, uptime, UART frame errors etc.).
+
+Wrapped up in a nice python interface we can now easily enumerate any drivers we connect to a bus, query their status
+and control their outputs.
+
+.. _COBS: https://en.wikipedia.org/wiki/Consistent_Overhead_Byte_Stuffing
+
+Conclusion
+----------
+
+.. raw:: html
+
+ <figure>
+ <figure class="side-by-side">
+ <a href="images/olsndot_schematic.png">
+ <img src="images/olsndot_schematic.png" alt="A picture of the LED driver schematic">
+ </a>
+ <figcaption>The LED driver <a href="images/olsndot_schematic.png">schematic</a></figcaption>
+ </figure><figure class="side-by-side">
+ <a href="images/olsndot_pcb.png">
+ <img src="images/olsndot_pcb.png" alt="A picture of the LED driver PCB layout">
+ </a>
+ <figcaption>The LED driver <a href="images/olsndot_pcb.png">PCB layout</a></figcaption>
+ </figure>
+ </figure>
+
+Putting some thought into the control circuitry and software, you can easily control large numbers of channels of LEDs
+using extremely inexpensive driving hardware without any compromises on dynamic range. The design we settled on can
+drive 32 channels of LED tape with a dynamic range of 14bit at a BOM cost of below 10€. All it really takes is a couple
+of shift registers and a mildly bored STM32 microcontroller.
+
+Get a PDF file of the schematic and PCB layout `here <olsndot_v02_schematics_and_pcb.pdf>`_ or download the CAD files
+and the firmware sources `from github <https://github.com/jaseg/led_drv>`_.
+
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