Schematic explanation

README.md

@@ -9,8 +9,75 @@ The method I use to sense key depression is rather simple. In tests that I
 have done it works well provided some calibration is performed in the firmware
 to normalise the readings.
 
+The matrix crossing points of a Topre keyboard are essentially variable
+capacitors which connect a "strobe" line to a "read" line. The strobe and the
+read lines form the electrodes directly on the PCB, and the conical spring
+under the dome couples them together, creating a variable capacitor with the
+range 0 ~ 6 pF (roughly). The strobe lines are just digital signals from a
+digital out pin of the microcontroller. The read lines are dealt with in the
+following schematic:
+
 ![Schematic](schematic.png "Basic schematic")
 
+Each read line is pulled to ground with an individual 22k resistor, and fed
+into an analog multiplexer. Any unused inputs of the multiplexer should be
+grounded to prevent additional sources of noise: this goes for any unused op
+amp pins too. After selecting a read line on the multiplexer, the
+microcontroller strobes a column and a small voltage pulse can be seen on the
+selected read line, larger pulses correspond to greater key depression.
+
+The selected read line is connected to the capacitor C1, which causes the read
+line to behave like a simple RC decay circuit. The value can be chosen given
+the following formula:
+
+```
+                                       Capacitance of key we are sensing
+Peak output voltage = Input voltage * -----------------------------------
+                                             Total row capacitance
+```
+
+Here the input voltage is `Vdd`. The total row capacitance (to ground) consists
+of C1 plus the capacitance of all the keys in the row. As such it is clear that
+choosing a large value for C1 (compared to key capacitance) is important so
+that our reading is not significantly altered due to other keys on the row
+being depressed. We can't just make C1 enormous though, because it drops the
+peak output voltage which ultimately contributes to a higher noise level. I
+found 1 nF to be a good value.
+
+Ignoring the "drain pin" for now, the read line passes through a current
+limiting resistor into a non inverting amplifier. The purpose of this is to
+provide a clean signal boost back into the range of 0 - 3.3V. The gain is given
+by `1 + R2 / R4` which in this case is around 200. It also serves to protect
+the microcontroller from negative voltages which can happen when the strobe
+line returns to ground. I found it important to use a very fast amplifier here,
+opting for the OPA350A. Cheaper options proved to be too slow, turning the
+voltage spike into more of a voltage mound. The output of the amplifier should
+connect to an ADC pin of the microcontroller.
+
+### Drain pin
+
+With the selected read line forming an RC circuit we can see that the time for
+it to relax to ground is simply governed by `5 * RC time constant`. The time
+constant is just `R * C`, which in our case gives a total relax time of
+`5 * 22k Ohm * 1 nF ~ 100 us`. Bearing in mind that we must wait for the matrix
+to relax to ground before reading the next key, this translates to taking 100
+us per key of the keyboard - giving us a polling rate less than 1000 Hz for
+keyboards with more than 10 keys. In order to fix this, we just connect the
+read line to the pin of the microcontroller through a current limiting 1k
+resistor R1. This pin should be floating during the strobe and read process,
+but after we have captured the reading in the ADC (takes around 5 us)
+it can be grounded, reducing the resistance R according to the parallel
+resistor formula:
+
+```
+  1     1       1
+ --- = ---- + -----
+  R     R1     22k
+```
+
+which gives `R ~ 950 Ohms` for our chosen values. Recalculating the relax time
+now gives `5 * 950 Ohms * 1 nF ~ 5 us` - much faster.
+
 
 ## Hardware (case/plate)