Charlieplexing (also known as tristate multiplexing, reduced pin-count LED multiplexing, complementary LED drive and crossplexing) is a technique for accessing a large number of LEDs, switches, micro-capacitors or other I/O entities, using relatively few tri-state logic wires from a microcontroller. These I/O entities can be wired as discrete components, x/y arrays, or woven in a diagonally intersecting pattern to form diagonal arrays.
Etymology Although the technique was introduced in 2001 by Maxim Integrated, the name "Charlieplexing", however, first occurred in a 2003 application note. It was named after Charles "Charlie" M. Allen, an applications engineer of MAX232 fame, who had proposed this method internally.
Origin The Charlieplexing technique was introduced by Maxim Integrated in 2001 as a reduced pin-count LED multiplexing scheme in their MAX6951 LED display driver.
Also in 2001, when the name "Charlieplexing" became common, Don Lancaster illustrated the method as part of his musings about the "N-connectedness" problem, referring to Microchip Technology, who had already discussed it as "complementary LED drive technique" in a 1998 application note and would later include it in a tips & tricks booklet.
While Microchip did not mention the origin of the idea, they might have picked it up in the PICLIST, a mailing list on Microchip PIC microcontrollers, where, also in 1998, Graham Daniel proposed it to the community as a method to drive rows and columns of bidirectional LEDs. Daniel at the time had created simple circuits with PIC 12C508 chips driving 12 LEDs off 5 pins with a mini command set to set various lighting displays in motion.
The method, however, was known and utilized by various parties much earlier in the 1980s, and has been described in detail as early as in 1979 in a patent by Christopher W. Malinowski, Heinz Rinderle and Martin Siegle of the Department of Research and Development, AEG-Telefunken, Heilbronn, Germany for what they called a "three-state signaling system".
Reportedly, similar techniques were already in use as early as 1972 for track signaling applications in model railroading.
Display multiplexing is very different from multiplexing used in data transmission, although it has the same basic principles. In display multiplexing, the data lines of the displays are connected in parallel to a common databus on the microcontroller. Then, the displays are turned on and addressed individually. This allows the use of fewer I/O pins than it would normally take to drive the same number of displays directly. Here, each "display" could, for instance, be one calculator digit, not the complete array of digits.
With traditional multiplexing I/O pins can drive a maximum of LEDs, or listen to that many input switches. Charlieplexing can drive LEDs, or listen to buttons even if directionality is not enforced by a diode.
Tri-state multiplexing (Charlieplexing)
The Charlieplexing configuration may be viewed as a directed graph, where the drive pins are vertices and the LEDs are directed edges; there is an outward-pointing edge connected from each vertex to each other vertex, hence with n drive pins there are (n)(n-1) total edges (a pronic number). This equates to n pins being able to drive n2 − n segments or LEDs.
Pins LEDs 2 2 3 6 4 12 5 20 6 30 7 42 8 56 9 72 10 90 11 110 12 132 13 156 14 182 15 210 16 240 20 380 24 552 32 992 40 1,560 48 2,256 56 3,080 64 4,032 n n2 − n
If the number of LEDs (L) is known, then the number of pins (n) can be found from the equation: , the result being rounded to the nearest whole number.
Example: If L = 57, then √L = 7.549, and 1 + √L = 8.549; the nearest whole number to this is 9, so 9 pins are needed to drive 57 LEDs (9 pins could drive up to 72 LEDs, but 8 pins could drive only 56 LEDs at most).
If L = 56, then √L = 7.483, and 1 + √L = 8.483; the nearest whole number to this is 8, so 8 pins are needed to drive 56 LEDs.
Origin of the (n2 − n) equation in Charlieplexing
Unlike in a traditional x/y multiplexed array, where a sub-set of conductive elements crosses a different sub-set of conductive elements, in a "fully Charlieplexed" multiplexed array, each conductive element crosses every other conductive element.
Six (n) conductive elements in a standard x/y multiplexed array forms a maximum of nine ((n / 2)2) unique intersections (see figure on far left).
The other diagrams also show six (n) conductive elements, but here all six elements cross over themselves, forming a multiplexed array of 36 (n2) intersections. LEDs are shown placed at every intersection. However, each conductor also crosses itself at the diagonal. Horizontal conductor 1 crosses vertical conductor 1, horizontal conductor 2 crosses vertical conductor 2, etc. This means that six of these LEDs are short-circuited (e.g. D1 and D5 are short-circuited). The six (n) diagonal LEDs will, therefore, never light up, because no voltage can ever develop across them, so (n) has to be subtracted from the total. There is no point in installing these LEDs (they are simply included here for illustrative purposes).
This leaves 30 LEDs (n2 − n) that can be uniquely addressed and lit up independently.
Conductor "a" crossing conductor "b" is distinguishable from conductor "b" crossing conductor "a" because LED polarity is reversed. For example, when conductor 3 is positive and conductor 2 is negative, current flows through, and lights up LED D8, but when conductor 3 is negative and conductor 2 is positive, current flows through, and lights up LED D9.
These reverse polarity LED pairs are called complementary pairs. This diagram has 15 complementary pairs, allowing 30 LEDs to be lit independently.
The 6 unusable diagonal LEDs can be conveniently replaced by actual bidirectional shortcuts (so that there's no longer need to set up the interconnection lines grouped on the left and bottom of the diagrams, to drive the bottom input of vertical connectors from the matching left input of horizontal connectors).
By adjusting diagonally the form of horizontal and vertical connectors along the short-circuited main diagonal of the original matrix, this can be easily transformed into an array of 5 × 6 or 6 × 5 LEDs arranged on a regular grid.
A similar pattern could be used for a 10 × 11 matrix that could be used to drive up to 110 keys (including a few indicator LEDs) on a modern PC keyboard, where each key switch includes a small serial diode or LED, so that only 11 pins would be needed to individually control all of them (these individual diodes or LEDs inside each key switch would also avoid all common and undesirable "ghosting" effects, that are hard to eliminate completely when an arbitrary number of keys at any position are pressed at the same time).
Charlieplexing can also be used to significantly reduce the number of controlling pins for much larger matrixes, such as modern digital displays with high resolution. E.g. for a 4K RGB display at 3840 × 2160, this requires more than 8 millions individually addressable pixels, each featuring at least 3 colored LEDs or LCD cells, for a total of nearly 25 millions LEDs or LCD cells. Using a conventional x/y multiplexing would require at least (3840 + 2160 × 3) = 10320 controlling pins and many selection chips for controlling rows and columns all around the panel of LEDs or LCD cells. But with Charlieplexing, this can be reduced to only 63 controlling pins for the selection gate of display columns, plus 46 × 3 controlling pins for the selection and power-activation of RGB display rows, by a single transistor for each row or column (possibly with an extra common shielding ground to limit their mutual coupling); these controlling pins can easily fit around the output pins of one or two controller chips, even if we add the few additional pins needed on the controller for power, ground, clocks and I/O buses, surface-mounted with a high density and low cost on a single-layer PCB, and no need of complex routing and interconnection holes between layers; a dual layer is needed only for the basic Charlieplexing matrix mounted on borders of the panel itself.
Positions in the Charlieplexed matrix are not reduced to be just LEDs or diodes, they can be filled as well by two pins of a transistor (including its gate pin) so that its third pin is used as output to further control other devices, such as the horizontal and vertical selection lines of a large flat display panel (in that case, the two Charlieplexed matrices of transistors controlling and activating the rows or columns of the panel will be smartly arranged all along a border of that panel).
Complementary drive Charlieplexing in its simplest form works by using a diode matrix of complementary pairs of LEDs. The simplest possible Charlieplexed matrix would look like this:
By applying a positive voltage to pin X1 and grounding pin X2, LED 1 will light. Since current cannot flow through LEDs in reverse direction at this low voltage, LED2 will remain unlit. If the voltages on pin X1 and pin X2 are reversed, LED 2 will light and LED1 will be unlit.
The Charlieplexing technique does not actually make a larger matrix possible when only using two pins, because two LEDs can be driven by two pins without any matrix connections, and without even using tri-state mode. In this two-LED example, Charlieplexing would save one ground wire, which would be needed in a common 2-pin driver situation.
However, the 2-pin circuit serves as a simple example to show the basic concepts before moving on to larger circuits where Charlieplexing actually shows an advantage.
Expanding: tri-state logic If the circuit above were to be expanded to accommodate three pins and six LEDs, it would look like this:
This presents a problem, however: In order for this circuit to act like the previous one, one of the pins must be disconnected before applying charge to the remaining two. If, for example, LED 5 was intended to be lit, X1 must be charged and X3 must be grounded. However, if X2 is also charged, LED 3 would illuminate as well. If X2 was instead grounded, LED1 would illuminate, meaning that LED 5 cannot be lit by itself. This can be solved by utilizing the tri-state logic properties of microcontroller pins.
Microcontroller pins generally have several possible states: "output": the pin "drives". It can drive "high" (often 5 V) or "low" (usually 0 V). "input": the pin does not intentionally drive at all, but instead senses what some other device (or pin) is driving. It may draw current while doing so. "high-Z": the pin is in a high-impedance state. Essentially, it is disconnected from the circuit; it will neither drive nor draw any current.
This allows the circuit to see any number of pins connected at any time, simply by changing the state of the pins. In order to drive the six-LED matrix above, the two pins corresponding to the LED to be lit are connected to 5 V (I/O pin "high" = binary number 1) and 0 V (I/O pin "low" = binary 0), while the third pin is set in its high-impedance state.
In doing so, current leakage out of the third pin is prevented, ensuring that the LED which should be lit is the only one lit.
Because the a diode (such as a LED) reduces the voltage available in series, current will not flow across alternate paths (an alternate 2-LED path exists for every pair of pins in the 3-pin diagram, for example), so long as the voltage drop in the desired LED path is less than the total voltage drop across each string of alternative LEDs. However, in the variant with individual resistors this voltage-regulating effect does not affect the alternative paths so all LEDs used will not have to be lit with half the supply voltage applied because this variant does not benefit from the voltage-regulating effect of the desired path LED.