Add multichannel LED driver post

109 files changed, 11608 insertions, 12101 deletions

diff --git a/config.toml b/config.toml
index 3145c44..10ba64a 100644
--- a/config.toml
+++ b/config.toml
@@ -1,5 +1,4 @@
-baseURL = "https://jaseg.net/"
+baseURL = "https://jaseg.github.io/_testrepo/"
 languageCode = "en-us"
 title = "jaseg.net"
 theme = "hugo-classic"
-publishDir = "docs"
diff --git a/content/posts/led-characterization/images/photodiode_sensitivity.svg b/content/posts/led-characterization/images/photodiode_sensitivity.svg
new file mode 100644
index 0000000..e845444
--- /dev/null
+++ b/content/posts/led-characterization/images/photodiode_sensitivity.svg
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diff --git a/content/posts/led-characterization/index.rst b/content/posts/led-characterization/index.rst
index 0f6e32b..ebcc16c 100644
--- a/content/posts/led-characterization/index.rst
+++ b/content/posts/led-characterization/index.rst
@@ -103,14 +103,13 @@ over the problem, there are several sources for imperfections:
         <figure class="side-by-side">
             <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>The shift register logic output of the multichannel LED driver directly driving a small mosfet's
-            gate through an inch or so of PCB trace caused extremely bad ringing at high driving
-            frequencies.</figcaption>
+            <figcaption>The LED strip being at the end of a couple meters of wire caused extremely bad ringing at high
+            driving frequencies.</figcaption>
         </figure><figure class="side-by-side">
             <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 dampened the ringing somewhat, but ultimately it cannot be eliminated
-            entirely.</figcaption>
+            <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.</figcaption>
         </figure>
     </figure>
 
@@ -371,6 +370,17 @@ The photodiode's response is strongly wavelength-dependent. In particular in the
 gets very poor down to about 20% at the edge to ultraviolet. This effect is strong enough to move the apparent location
 of the blue peak towards red.
 
+.. raw:: html
+    
+    <figure>
+        <img src="images/photodiode_sensitivity.svg" alt="A plot of photodiode sensitivity against wavelength relative
+        to peak sensitivity at 820nm.  The sensitivity rises from 20% at 380nm approximately linearly to 80% at 620nm,
+        then the rise rolls off.">
+        <figcaption>A plot of the photodiode's relative sensitivity in the visible spectrum. The sensitivity is
+        normalized against its peak at 820nm.
+        </figcaption>
+    </figure>
+
 The problem is that in order to remove this non-linearity, we would already have to know the wavelength of the measured
 light. Since I don't, I settled for a two-step process. First, a coarse wavelength calibration is done relative to the
 red peak and the short-wavelength edge of the blue peak. The photodiode measurements are then sensitivity-corrected
@@ -390,7 +400,6 @@ wavelength in nanometers.
         </figcaption>
     </figure>
 
-
 .. FIXME re-do these measurements, avoiding clipping
 .. FIXME re-do calibration using CCFL
 .. FIXME calibration for brightness imbalance due to wedge-shaped projection of spectrum
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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>`_.
+
diff --git a/content/posts/multichannel-led-driver/olsndot_v02_schematics_and_pcb.pdf b/content/posts/multichannel-led-driver/olsndot_v02_schematics_and_pcb.pdf
new file mode 100644
index 0000000..2a4e037
--- /dev/null
+++ b/content/posts/multichannel-led-driver/olsndot_v02_schematics_and_pcb.pdf
diff --git a/content/posts/serial-protocols/index.rst b/content/posts/serial-protocols/index.rst
new file mode 100644
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--- /dev/null
+++ b/content/posts/serial-protocols/index.rst
@@ -0,0 +1,8 @@
+---
+title: "How to talk to your microcontroller over serial"
+date: 2018-05-19T08:09:46+02:00
+draft: true
+---
+
+
+
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-<div class="article-meta">
-<h1><span class="title">Led Characterization</span></h1>
-
-<h2 class="date">2018/05/02</h2>
-<p class="terms">
-  
-  
-  
-  
-  
-</p>
-</div>
-
-
-
-<main>
-<div class="document">
-
-
-<div class="section" id="preface">
-<h2>Preface</h2>
-<p>Recently, I have been working on a <a class="reference external" href="https://jaseg.net/posts/wifi-led-driver/">small driver</a> for ambient lighting using 12V LED strips like you can get
-inexpensively from China. I wanted to be able to just throw one of these somewhere, stick down some LED tape, hook it up
-to a small transformer and be able to control it through Wifi. When I was writing the firmware, I noticed that when
-fading between different colors, the colors look <em>all wrong</em>! This observation led me down a rabbit hole of color
-perception and LED peculiarities.</p>
-<p>The idea of the LED driver was that it can be used either with up to eight single-color LED tapes or, much more
-interesting, with up to two RGB or RGBW (red-green-blue-white) LED tapes. For ambient lighting high color resolution was
-really important so you could dim it down a lot without flickering. I ended up using the same driver stage I used in the
-<a class="reference external" href="https://jaseg.net/posts/multichannel-led-driver/">multichannel LED driver</a> project for its great color resolution and low hardware requirements.</p>
-<figure>
-    <img src="/images/rgb_cube.svg" alt="An illustration of the RGB color cube.">
-    <figcaption>An illustration of the RGB color cube.
-        <a href="https://commons.wikimedia.org/wiki/File:RGB_color_cube.svg">Picture</a> by
-        <a href="https://commons.wikimedia.org/wiki/User:Maklaan">Maklaan from Wikimedia Commons</a>,
-        <a href="https://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA 3.0</a>
-    </figcaption>
-</figure><p>To make setting colors over Wifi more intuitive I implemented support for HSV colors. RGB is fine for communication
-between computers, but I think HSV is easier to work with when manually inputting colors from the command line. RGB  is
-close to how most monitors, cameras and the human visual apparatus work on a very low level but doesn't match
-higher-level human color perception very well. When we describe a color we tend to think in terms of &quot;hue&quot; or
-&quot;brightness&quot;, and computing a measure of those from RGB values is not easy.</p>
-</div>
-<div class="section" id="colors-and-color-spaces">
-<h2>Colors and Color Spaces</h2>
-<p><a class="reference external" href="https://en.wikipedia.org/wiki/Color_space">Color spaces</a> are a mathematical abstraction of the concept of color. When we say &quot;RGB&quot;, most of the time we actually
-mean <a class="reference external" href="https://en.wikipedia.org/wiki/SRGB">sRGB</a>, a standardized notion of how to map three numbers labelled &quot;red&quot;, &quot;green&quot; and &quot;blue&quot; onto a perceived
-color. <a class="reference external" href="https://en.wikipedia.org/wiki/HSL_and_HSV">HSV</a> is an early attempt to more closely align these numbers with our perception. After HSV, a number of other
-<em>perceptual</em> color spaces such as <a class="reference external" href="https://en.wikipedia.org/wiki/CIE_1931_color_space">XYZ (CIE 1931)</a> and <a class="reference external" href="https://en.wikipedia.org/wiki/Lab_color_space">CIE Lab/LCh</a> were born, further improving this alignment.  In
-this mathematical model, mapping a color from one color space into another color space is just a coordinate
-transformation.</p>
-<figure>
-    <img src="/images/hsv_cylinder.png" alt="An illustration of the HSV color space as a cylinder.">
-    <figcaption>An illustration of the HSV color space as a cylinder.
-        <a href="https://commons.wikimedia.org/wiki/File:HSV_color_solid_cylinder.png">Picture</a> by
-        <a href="https://commons.wikimedia.org/wiki/User:SharkD">SharkD from Wikimedia Commons</a>,
-        <a href="https://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA 3.0</a>
-    </figcaption>
-</figure><p>CIE 1931 XYZ is much larger than any other color space, which is why it is a good basis to express other color spaces
-in. In XYZ there are many coordinates that are outside of what the human eye can perceive. Below is an illustration of
-the sRGB space within XYZ. The wireframe cube is (0,0,0) to (1,1,1) in XYZ.  The colorful object in the middle is what
-of sRGB fits inside XYZ, and the lines extending out from it indicate the space that can be expressed in sRGB but not in
-XYZ. The fat white curve is a projection of the <em>monochromatic spectral locus</em>, that is the curve of points you get in
-XYZ for pure visible wavelengths.</p>
-<p>As you can see, sRGB is <em>much</em> smaller than XYZ or even the part within the monochromatic locus that we can perceive. In
-particular in the blues and greens we loose <em>a lot</em> of colors to sRGB.</p>
-<figure>
-    <video controls loop>
-        <source src="/video/sRGB.mkv" type="video/h264">
-        <source src="/video/sRGB.webm" type="video/webm">
-        Your browser does not support the HTML5 video tag.
-    </video>
-    <figcaption>Illustration of the measured sRGB color space within XYZ. The thick, white line is the spectral
-        locus.
-
-        <a href="/video/sRGB.mkv">mkv/h264 download</a> /
-        <a href="/video/sRGB.webm">webm download</a>
-    </figcaption>
-</figure><p>The wrong colors I got when fading between colors were caused by this coordinate transformation being askew. Thinking
-over the problem, there are several sources for imperfections:</p>
-<ul class="simple">
-<li>The LED driver may not be entirely linear. For most modulations such as PWM the brightness will be linear starting
-from a certain value, but there is probably an offset caused by imperfect edges of the LED current. This offset can be
-compensated with software calibration. I built a calibration setup for driver linearity in the <a class="reference external" href="https://jaseg.net/posts/multichannel-led-driver/">multichannel LED
-driver</a> project. Below are pictures of ringing on the edges of an LED driver's waveform.</li>
-<li>The red, green and blue channels of the LEDs used on the LED tape are not matched.  This skews the RGB color space.
-In practice, the blue channel of my RGB tape to me <em>looks</em> much brighter than the red channel.</li>
-<li>The precise colors of the red, green and blue channels of the LEDs are unknown. Though the red channel <em>looks</em> red, it
-may be of a slightly different hue compared to the reference red used in <a class="reference external" href="https://en.wikipedia.org/wiki/SRGB">sRGB</a> which would also skew the RGB color
-space.</li>
-</ul>
-<figure>
-    <figure class="side-by-side">
-        <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>The shift register logic output of the multichannel LED driver directly driving a small mosfet's
-        gate through an inch or so of PCB trace caused extremely bad ringing at high driving
-        frequencies.</figcaption>
-    </figure><figure class="side-by-side">
-        <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 dampened the ringing somewhat, but ultimately it cannot be eliminated
-        entirely.</figcaption>
-    </figure>
-</figure><p>These last two errors are tricky to compensate. What I needed for that was basically a model of the <em>perceived</em> colors
-of the LED tape's color channels. A way of doing his is to record the spectra of all color channels and then evaluate
-their respective XYZ coordinates. If all three channels are measured in one go with the same setup the relative
-magnitudes of the channels in XYZ will be accurate.</p>
-<p>To map any color to the LEDs, the color's XYZ coordinates simply have to be mapped onto the linear coordinate system
-produced by these three points within XYZ. LEDs are mostly linear in their luminous flux vs. current characteristic so
-this model will be adequate. The spectral integrals mapping the channels' measured responses to XYZ need only be
-calculated once and their results can be used as scaling factors thereafter.</p>
-</div>
-<div class="section" id="measuring-the-spectrum">
-<h2>Measuring the spectrum</h2>
-<p>In order to compensate for the cheap LED tape's non-ideal performance I had to measure the LED's red, green and blue
-channels' spectra. The obvious thing would be to go out and buy a <a class="reference external" href="https://en.wikipedia.org/wiki/Ultraviolet%E2%80%93visible_spectroscopy">spectrograph</a>, or ask someone to borrow theirs. The
-former is kind of expensive, and I did not want to wait two weeks for the thing to arrive. The latter I could probably
-not do every time I got new LED tape. Thus the only choice was to build my own.</p>
-<p>Luckily, building your own spectrometer is really easy. The first thing you need is something that splits incident light
-into its constituent wavelengths. In professional devices this is called the <em>`monochromator`_</em>, since it allows extraction
-of small color bands from the spectrum. The second thing is some sort of optics that project the incident light onto a
-screen behind the monochromator. In professional devices lenses or curved mirrors are used. In a simple homebrew job a
-pinhole as you would use in a <a class="reference external" href="https://en.wikipedia.org/wiki/Pinhole_camera">camera obscura</a> does a remarkably nice job.</p>
-<p>For the monochromator component several things could be used. A prism would work, but I did not have any. The
-alternative is a <a class="reference external" href="https://en.wikipedia.org/wiki/Diffraction_grating">diffraction grating</a>. Professional gratings are quite specialized pieces of equipment and thus
-rather expensive. Luckily, there is a common household item that works almost as well: A regular CD or DVD. The
-microscopic grooves that are used to record data in a CD or DVD work the same as the grooves in a professional
-diffraction grating.</p>
-</div>
-<div class="section" id="household-spectra">
-<h2>Household spectra</h2>
-<p>From this starting point, a few seconds on my favorite search engine yielded an <a class="reference external" href="http://www.candac.ca/candacweb/sites/default/files/BuildaSpectroscope.pdf">article by two researchers from the
-National Science Museum in Tokyo</a> providing a nice blueprint for a simple cardboard-and-DVD construction for use in
-classrooms. I replicated their device using a DVD and it worked beautifully. Daylight and several types of small LEDs I
-had around did show the expected spectra. Small red, yellow, green, and blue LEDs showed narrow spectra, daylight one
-continuous broad one, and white LEDs a continuous broad one with a distinct bright spot in the blue part. The
-single-color LED spectra are quite narrow since they are determined by the LED's semiconductor's band gap, which is
-specific to the semiconductor used and is quite precise. White LEDs are in fact a blue LED chip covered with a so-called
-<em>phosphor</em>. This phosphor is not elementary phosphorus but an anorganic compound that absorbs the LED chip's blue light
-and re-emits a broader spectrum of more yellow-ish wavelengths instead. The final LED spectrum is a superposition of
-both spectra, with some of the original blue light leaking through the phosphor mixing with the broadband yellow
-spectrum of the phosphor.</p>
-<figure>
-    <figure class="side-by-side">
-        <img src="/images/spectrograph_step1_parts.jpg">
-        <figcaption>The ingredients. The cup of coffee and Madoka Magica DVD set are essential to the eventual
-        function of the appartus.</figcaption>
-    </figure><figure class="side-by-side">
-        <img src="/images/spectrograph_step2.jpg">
-        <figcaption>Step 1: Cut to size and mark down all holes as described in <a
-        href="http://www.candac.ca/candacweb/sites/default/files/BuildaSpectroscope.pdf">the manual</a></figcaption>
-    </figure>
-    <figure class="side-by-side">
-        <img src="/images/spectrograph_step3.jpg">
-        <figcaption>Step 2: Cut out all holes</figcaption>
-    </figure><figure class="side-by-side">
-        <img src="/images/spectrograph_step4_complete.jpg">
-        <figcaption>The finished result with the back side showing. The viewing window is on the bottom of the other
-        side.</figcaption>
-    </figure>
-</figure><p>Now that I had a spectrograph, I needed a somewhat predictable way of measuring the spectrum it gave me.</p>
-</div>
-<div class="section" id="measuring-a-spectrum">
-<h2>Measuring a spectrum</h2>
-<p>Pointing a camera at the spectrograph would be the obvious thing to do. This produces pretty images but has one critical
-flaw: I wanted to acquire quantitative measurements of brightness across the spectrum. Since I don't have a precise
-technical datasheet specifying the spectral response of any of my cameras I can't compare the absolute brightness of
-different colors on their pictures. Some other sensor was needed.</p>
-<figure>
-    <img src="/images/daylight_spectrum_dvd.jpg">
-    <figcaption>The daylight spectrum as seen using a DVD as a grating.
-        <a href="https://commons.wikimedia.org/wiki/File:SpectresSolaires-DVD.jpg">Picture</a> by
-        <a href="https://commons.wikimedia.org/wiki/User:Xofc">Xofc from Wikimedia Commons</a>,
-        <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC-BY-SA 4.0</a>
-    </figcaption>
-</figure><div class="section" id="measuring-light-intensity">
-<h3>Measuring light intensity</h3>
-<p>Looking around my lab, I found a bag of <a class="reference external" href="https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf">SFH2701</a> visible-light photodiodes. Their
-datasheet includes their spectral response so I can compensate for that, allowing precise-ish absolute intensity
-measurements. Just like LEDs, photodiodes are extremely linear across several orders of magnitude. The datasheet of the
-classic <a class="reference external" href="http://www.vishay.com/docs/81521/bpw34.pdf">BPW34</a> photodiode shows that this photodiode's light current is exactly proportional to illuminance over at
-least three orders of magnitude. The <a class="reference external" href="https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf">SFH2701</a> datasheet does not include a similar graph but its performance will be
-similar. The <a class="reference external" href="https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf">SFH2701</a> photodiodes I had at hand were perfect for the job compared to the vintage <a class="reference external" href="http://www.vishay.com/docs/81521/bpw34.pdf">BPW34</a> since their
-active sensing area is really small (0.6mm by 0.6mm) compared to the BPW34 (a whopping 3mm by 3mm). If I were to use a
-<a class="reference external" href="http://www.vishay.com/docs/81521/bpw34.pdf">BPW34</a> I would have to insert some small apterture in front of it so it does not catch too broad a part of the
-spectrum at once. The <a class="reference external" href="https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf">SFH2701</a> is small enough that if I just point it at the projected spectrum directly I will
-already get only a small part of the spectrum inside its 0.6mm active area.</p>
-<p>To convert the photodiode's tiny photocurrent into a measurable voltage I built another copy of the <a class="reference external" href="https://en.wikipedia.org/wiki/Transimpedance_amplifier">transimpedance
-amplifier</a> circuit I already used in the <a class="reference external" href="https://jaseg.net/posts/multichannel-led-driver/">multichannel LED driver</a>. A <a class="reference external" href="https://en.wikipedia.org/wiki/Transimpedance_amplifier">transimpedance amplifier</a> is an
-amplifiert that produces a large voltage from a small current. The weird name comes from the fact that it works kind of
-like an amplified resistor (which can be generalized as an <em>impedance</em> electrically). Apply a current to a resistor and
-you get a voltage. A transimpedance amplifiert does the same with the difference that its input always stays at 0V,
-making it look like an ideal current sink to the connected current source.</p>
-<p>Transimpedance amplifiers are common in optoelectronics to convert small photocurrents to voltages. In this instance I
-built a very simple circuit with a dampened transimpedance amplifier stage followed by a simple RC filter for noise
-rejection and a regular non-inverting amplifier using another op-amp from the same chip to further boost the filtered
-transimpedance amplifier output. I put all the passives setting amplifier response (the gain-setting resistors and the
-filter resistor and capacitors) on a small removable adapter so I could easily change them if necessary. I put a small
-trimpot on the virtual ground both amplifers use as a reference so I could trim that if necessary.</p>
-<figure>
-    <img src="/images/preamp_schematic.jpg" alt="A drawing of the photodiode preamplifier's schematic">
-    <figcaption>The photodiode preamplifier schematic. Schematic drawn with an unlicensed copy of
-    DaveCAD.</figcaption>
-</figure><p>Following are pictures of the preamplifier board. The connectors on the top-left side are two copies of the analog
-signal for the ADC and a small panel meter. The SMA connector is used as the photodiode input since coax cables are
-generally low-leakage and have built-in shielding. The circuit is powered via the micro-USB connector and the analog
-ground bias voltage can be adjusted using the trimpot.</p>
-<p>For easy replacement, all passives setting gain and frequency response are on a small, pluggable carrier PCB made from a
-SMD-to-DIP adapter.</p>
-<p>Flying-wire construction is just fine for this low-frequency circuit. In a high-speed photodiode preamp, the
-transimpedance amplifier circuit would be highly sensitive to stray capacitance, but we're not aiming at high speed
-here.</p>
-<figure>
-    <figure class="side-by-side">
-        <img src="/images/preamp_front.jpg">
-        <figcaption>The front side of the preamplifier board.</figcaption>
-    </figure><figure class="side-by-side">
-        <img src="/images/preamp_back.jpg">
-        <figcaption>The wiring of the photodiode preamp.</figcaption>
-    </figure>
-</figure><p>Given a way to measure intensity what remains missing is a way to scan a single photodiode across the spectrum.</p>
-</div>
-<div class="section" id="scanning-the-projection">
-<h3>Scanning the projection</h3>
-<p>A cheap linear stage can be found in any old CD or DVD drive. These drives use a small linear stage based on a
-stepper-driven screw to move the laser unit radially. Removing the laser unit and connecting a leftover stepper driver
-module I was left with a small linear stage with about 45 steps per cm without microstepping enabled. The driver I used
-was an <a class="reference external" href="https://www.pololu.com/file/0J450/A4988.pdf">A4988</a> module that required at least 8V motor drive voltage. I used a small micro USB-input boost converter
-module to generate a stable 10V supply for the motor driver, with the USB's 5V rail used as a logic supply for the motor
-driver.</p>
-<p>The <a class="reference external" href="https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf">SFH2701</a> can easily be mounted to the linear stage using a small SMD breakout board glued in place with thin wires
-connecting it to the transimpedance amplifier. The DVD drive linear stage is not very strong so it is important that
-this wire does not put too much strain on it.</p>
-<p>Above the photodiode, I mounted a small piece of paper on the linear stage to be used as a projection screen to align
-the linear stage in front of the spectrometer viewing window. A line on the screen paper points to the photodiode die in
-parallel to the linear stage allowing precise alignment.</p>
-<p>The whole unit with photodiode preamplifier, linear stage, photodiode and stepper motor driver finally looks like this:</p>
-<figure>
-    <img src="/images/electronics_whole.jpg" alt="The complete electronics setup of the spectrograph. In the back
-    there is the DVD drive stepper stage. In front of it, mounted on a piece of wood are a small USB-to-12V
-    switching-regulator module to power the stepper motor in the top left, below on the bottom left is the
-    photodiode preamp and on the right is a breadboard with the stepper driver module and lots of jumper wires
-    interconnecting everything. On the right of the breadboard, a buspirate is attached to interface everything to a
-    computer. On the bottom edge of the piece of wood, two LED panel meters are mounted for readout of the preamp
-    output and the stepper supply voltages.">
-    <figcaption>The complete electronics setup. The buspirate on the right interfaces to a computer and controls the
-    stepper driver and ADC'es the preamp output. The two panel meters show the preamp output and stepper voltage for
-    setup.</figcaption>
-</figure><p>The projection of the spectrum can be adjusted by moving the light source relative to the entry slot and by moving
-around the grating DVD.</p>
-</div>
-<div class="section" id="the-capture-process">
-<h3>The capture process</h3>
-<p>To capture a spectrum, first the light source has to be mounted near the spectrograph's entry slot. The LED tape I
-tested I just taped face-down directly into it. Next, the grating DVD has to be adjusted to make sure the spectrum
-covers a sensible part of the photodiode's path. Mostly, this boils down to adjusting the photodiode distance and height
-to match the vertical extent and wiggling the grating DVD to adjust the projection's horizontal position.</p>
-<p>After the optics are set-up, the photodiode preamplifier has to be adjusted. In my experiments, most LED tape at 5GΩ
-required a high-ish amplification. The goal in this step is to maximize the peak response of the preamp  to be just
-shy of its VCC rail to make best use of its dynamic range. To adjust the pre-amp, I took several very coarsely-spaced
-measurements to give me an estimate of the peak while I did not yet know its precise location.</p>
-<p>Since stray daylight totally swamped out the weak projection of the LED's spectrum I shielded the entire setup with a
-small box made of black cardboard and two black t-shirts on top. This shielding proved adequate for all my measurements
-but I had to be careful not to accidentially move the DVD that was stuck into the spectrograph with the shielding
-t-shirts.</p>
-<p>For capturing a single spectrum I wrote a small python script that will automatically move the stepper in adjustable
-intervals and take two measurements at each point, one with the LED tape off that can be used for offset calibration and
-one with the LED tape on. All measurements are stored in a sqlite database that can then be accesssed from other
-scripts.</p>
-<p>I built a small script that shows the progress of the current run and an jupyter notebook for data analysis. The jupyter
-notebook is capable of live-updating a graph with the in-progress spectrum's data. This was quite useful as a sanity
-check for when I made some mistake easy to spot in the resulting data.</p>
-<p>After one color channel is captured, the LED tape has to be manually set to the next color and the next measurement can
-begin.</p>
-<figure>
-    <img src="/images/raw_plot_cheap_rgb.svg" alt="A plot with three wide peaks, two large peaks on both sides and
-    one smaller one in the middle. The middle one overlaps the two on the sides. The large ones are about 2.5V in
-    amplitude. Overall, the plot is about 300 stepper steps wide with each peak being around 130 steps wide.">
-    <figcaption>A plot of the raw preamp output voltage versus stepper position. From left to right, the three peaks
-    are blue, green and red. Step 0 corresponds to the bottommost stepper position and the shortest wavelength.
-    </figcaption>
-</figure></div>
-<div class="section" id="data-analysis">
-<h3>Data analysis</h3>
-<p>Data analysis consists of three major steps: Offset- and stray light removal, wavelength and amplitude calibration and
-color space mapping.</p>
-<div class="section" id="offset-removal">
-<h4>Offset removal</h4>
-<p>The first task is to remove the offset caused by dark current as well as stray light of the LED's bright primary
-reflection on the DVD. The LED is very bright and only a small part of its light gets reflected by the grating towards
-the photodiode screen. The remaining part of the light is reflected onto the table in front of the DVD spectrograph.
-Though I covered all of this with black cardboard, some of that light ultimately gets reflected onto the photodiode.
-This causes a large offset, in particular in the blue part of the spectrum since in this part the photodiode is closest
-to the spectrograph's opening.</p>
-<p>The composite offset can be approximated with a second-order polynomial that is fitted to all the data outside of the
-main peak's area. Since at this point the wavelength of each data point is still unknown this is done with a rough first
-estimate of the three colors' peaks' locations and widths.</p>
-</div>
-<div class="section" id="wavelength-and-amplitude-calibration">
-<h4>Wavelength- and amplitude calibration</h4>
-<p>The photodiode's response is strongly wavelength-dependent. In particular in the blue band, the photodiode's sensitivity
-gets very poor down to about 20% at the edge to ultraviolet. This effect is strong enough to move the apparent location
-of the blue peak towards red.</p>
-<p>The problem is that in order to remove this non-linearity, we would already have to know the wavelength of the measured
-light. Since I don't, I settled for a two-step process. First, a coarse wavelength calibration is done relative to the
-red peak and the short-wavelength edge of the blue peak. The photodiode measurements are then sensitivity-corrected
-using this coarse measurement. Then all three channel peaks are measured in the resulting data and a fine wavelength
-estimate is produced by a least-squares fit of a linear function. This fine estimate is then used for a second
-sensitivity correction of all original measurements and the scale is changed from stepper motor step count to
-wavelength in nanometers.</p>
-<figure>
-    <img src="/images/processed_plot_cheap_rgb.svg" alt="A plot with three wide peaks, all three of different
-    heights. The leftmost peak is highest at 6nA, the middle peak lowest at 1.6nA and the rightmost peak in between
-    at 4nA.  The middle one overlaps the two on the sides.  Overall, the plot spans about 300nm on its x axis with
-    each peak being around 100nm wide.">
-    <figcaption>A plot of the processed measurements. From left to right, the three peaks are blue, green and red.
-    </figcaption>
-</figure><!-- FIXME re-do these measurements, avoiding clipping -->
-<!-- FIXME re-do calibration using CCFL -->
-<!-- FIXME calibration for brightness imbalance due to wedge-shaped projection of spectrum -->
-</div>
-<div class="section" id="color-space-mapping">
-<h4>Color space mapping</h4>
-<p>Finally, to achieve the objective of measuring the LED tape's channels' precise color coordinates the measured spetra
-have to be matched against the color spaces' <em>color matching functions</em>. The color matching functions describe how
-strong the color space's idealized <em>standard observer</em> would react to light at a particular wavelength. Going from a
-measured spectrum to color coordinates XYZ works by integrating over the product of the measurement and each color
-coordinate's color matching function.</p>
-<p>The result are three color coordinates X, Y and Z for each channel R, G and B yielding nine coordinates in total. When
-written as a matrix conversion between XYZ color space and LED-RGB color space is as simple as multiplying that matrix
-(or its inverse) and a vector from one of the color spaces.</p>
-<p>In XYZ space, the set of colors that can be produced with this LED tape is described by the <a class="reference external" href="https://en.wikipedia.org/wiki/Parallelepiped">parallelepiped</a> spanned by
-the three channel's XYZ vectors. In the following figures, you can see a three-dimensional model of the RGB LED's color
-space (colorful) as well as sRGB (white) for comparison plotted within CIE 1931 XYZ. There is no natural map to scale
-both so for this illustration the LED color space has been scaled to fit. These figures were made with blender and a few
-lines of python.  The blender project file including all settings and the python script to generate the color space
-models can be found in the <a class="reference external" href="https://github.com/jaseg/led_drv">project repo</a>.</p>
-<figure>
-    <video controls loop>
-        <source src="/video/led_within_srgb_scale=1.0.mkv" type="video/h264">
-        <source src="/video/led_within_srgb_scale=1.0.webm" type="video/webm">
-        Your browser does not support the HTML5 video tag.
-    </video>
-    <figcaption>Illustration of the measured LED color space scaled to fit within XYZ with sRGB (light gray) for
-        comparison. The thick, white line is the spectral locus.
-
-        <a href="/video/led_within_srgb_scale=1.0.mkv">mkv/h264 download</a> /
-        <a href="/video/led_within_srgb_scale=1.0.webm">webm download</a>
-    </figcaption>
-</figure><p>As you can see, the result is pretty disappointing. The LED's color space parallepiped is very narrow, which is because
-the blue channel is much brighter than the other two channels. An easy fix for this is to scale-up the RGB space and
-drop any values outside XYZ. The scaling factor is a trade-off between color space coverage and brightness. You can
-produce the most colors when you clip all channels to brightness of the weakest channel (green in this case), but that
-will make the result very dim. Scaling brightness like that stretches the RGB parallelepiped along its major axis. Up to
-a point the number of possible colors (the gamut) increases at expense of maximum brightness. When the parallelepiped is
-stretched far enought for all three channel vectors to be outside the 1,1,1 XYZ-cube, maximum brightness continues to
-decrease but the gamut stays constant. I don't know a simple scientific way to solve this problem, so I just played
-around with a couple of factors and settled on 2.5 as a reasonable compromise. Below is an illustration.</p>
-<figure>
-    <video controls loop>
-        <source src="/video/led_within_srgb_fancy_camera_path_scale=2.5.mkv" type="video/h264">
-        <source src="/video/led_within_srgb_fancy_camera_path_scale=2.5.webm" type="video/webm">
-        Your browser does not support the HTML5 video tag.
-    </video>
-    <figcaption>Illustration of the measured LED color space at scale factor 2.5 within XYZ with sRGB (light gray)
-        for comparison. The thick, white line is the spectral locus.
-
-        <a href="/video/led_within_srgb_fancy_camera_path_scale=2.5.mkv">mkv/h264 download</a> /
-        <a href="/video/led_within_srgb_fancy_camera_path_scale=2.5.webm">webm download</a>
-    </figcaption>
-</figure></div>
-</div>
-</div>
-<div class="section" id="firmware-implementation">
-<h2>Firmware implementation</h2>
-<p>In the end, the above measurements yield two matrices: One for mapping XYZ to RGB, and one for mapping RGB to XYZ. Of
-the several versions of CIE XYZ I chose the CIE 1931 XYZ color space as a basis for the firmware because it is most
-popular. Mapping a color coordinate in one color space to the other is as simple as performing nine floating-point
-multiplications and six additions. Mapping Lab or Lch to RGB is done by first mapping Lab/Lch to XYZ, then XYZ to RGB.
-Lab to XYZ is somewhat complex since it requires a floating-point power for gamma correction, but any self-respecting
-libc will have one of those so this is still no problem. Lch also requires floating-point sine and cosine functions, but
-these should still be no problem on most hardware.</p>
-<p>My implementation of these conversions in the ESP8266 firmware of my <a class="reference external" href="https://jaseg.net/posts/wifi-led-driver/">Wifi LED driver</a> can be found <a class="reference external" href="https://github.com/jaseg/esp_led_drv/blob/master/user/led_controller.c">on Github</a>.</p>
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-<!DOCTYPE html>
-<html lang="en-us">
-  <head>
-    <meta charset="utf-8">
-    <meta name="viewport" content="width=device-width, initial-scale=1">
-    <title>Zeus Hammer | jaseg.net</title>
-    <link rel="stylesheet" href="/css/style.css" />
-    <link rel="stylesheet" href="/css/fonts.css" />
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-<h1><span class="title">Zeus Hammer</span></h1>
-
-<h2 class="date">2018/05/03</h2>
-<p class="terms">
-  
-  
-  
-  
-  
-</p>
-</div>
-
-
-
-<main>
-<div class="document">
-
-
-<p>In case you were having an inferiority complex because your friends' IBM Model M keyboards are so much louder than the
-shitty rubber dome freebie you got with your pc... Here's the solution: Zeus Hammer, a simple typing cadence enhancer
-for <a class="reference external" href="https://en.wikipedia.org/wiki/PS/2_port">PS/2</a> keyboards.</p>
-<!-- FIXME: add demo video -->
-<p>The connects to the keyboard's PS/2 clock line and briefly actuates a large solenoid on each key press. An interesting
-fact about PS/2 is that the clock line is only active as long as either the host computer or the input device actually
-want to send data. In case of a keyboard that's the case when a key is pressed or when the host changes the keyboard's
-LED state, otherwise the clock line is silent. We ignore the LED activity for now as it's generally coupled to key
-presses. By just triggering an NE555 configured as astable flipflop we can stretch each train of clock pulses to a
-pulse a few tens of milliseconds long that is enough to actuate the solenoid.</p>
-<img alt="/images/zeus_hammer_schematic.jpg" src="/images/zeus_hammer_schematic.jpg" />
-<p>Since PS/2 sends each key press and key release separately this circuit will pulse twice per keystroke. It would be
-possible to ignore one of them but I figure the added noise just adds to the experience.</p>
-<p>Built on a breadboard, the circuit looks like this.</p>
-<img alt="/images/zeus_hammer_breadboard.jpg" src="/images/zeus_hammer_breadboard.jpg" />
-<p>The completed system looks like this.</p>
-<!-- FIXME: add image of completed system -->
-<p>Since my solenoid did not have a tensioning spring I used a rubber band and some vinyl tape to make an adjustable
-tensioner. The small orange USB hub serves as an end-stop because I had nothing else of the right shape. The sound and
-resonance of the thing can be adjusted to taste by moving the end stop, adjusting the tensioning rubber and tuning the
-excitation duration using the potentiometer. My particular solenoid was a bit slow so I added some pieces of circuit
-board as shims between the plunger and the case to limit the plunger's travel inside the solenoid core. Here is another
-video of the thing in action in which I tune and de-tune the mechanical resonance using the potentiometer.</p>
-<!-- FIXME: add video w/ tune/detune -->
-</div>
-</main>
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-    <loc>https://jaseg.net/posts/multichannel-led-driver/</loc>
-    <lastmod>2018-05-02T11:31:14+02:00</lastmod>
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-    <lastmod>2018-05-02T11:31:03+02:00</lastmod>
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