Electronic – How is the current limited through the LEDs in this LED matrix design

As the number of shift registers grows, it will become necessary to shift data through them faster in order to achieve a particular frame rate. This will in turn increase the amount of current required by each shift register.

It would probably be a good idea to use a partially-parallel arrangement. If the CPU can clock out eight or sixteen bits in parallel, that will reduce by a factor of eight or sixteen the number of bits that have to go through each shifter. It may also be useful to design a circuit which will take every eight or sixteen bits shifted in and send one to each of eight or sixteen shifters. Applying such circuits even one or two deep will greatly minimize the number of rapidly-switching signals required.

My inclination would probably be to use boards of e.g. 64x8 LEDs, multiplexed 64x8. Boards could be chained to a certain depth, but I probably wouldn't recommend chaining all 64 boards together. If the goal is a 128x64 grid, it might be reasonable to have eight pairs of 64x8 boards chained together, and output one bit to each pair simultaneously (so 128x8 bits for each 1/8 frame). I would suggest that the mutliplex timing be controlled by a master device, but each 8x64 panel should include its own row drivers along with some circuitry to limit each row's duty cycle to a maximum of 16% or so (when all is working properly, the duty cycle should be 1/8).

There are a number of options, most of them discussed in this post. Since the communication is one way you can use:

• Voltage dividers: cheap and easey: 2 resistors. Cannot provide stiff voltage sources unless you lose a lot of power through them
• A diode with a resistor circuit. Same as previous
• Level shifter (something like a 74LVC245)

There are shift registers that do run on 3.3V: depending on how many lines you need, an easier solution might be to shift the Arduino output to 3.3V, and feed that to a 3.3V shift register. This will likely (again, depending on your setup) in fewer lines to be level-shifted.

EDIT: Yes, you will need current-limiting resistors for your LEDs, however, voltage divider != a single resistor. Voltage divider looks like this:

^{simulate this circuit – Schematic created using CircuitLab}

EDIT2: Usually not. You should read the datasheet for the shift register you are planning to use about its various maximum voltages. P.S. When you say "serial pins" you don't mean the Serial TX and Serial RX, right? Usually, one drives shift registers using general purpuse digital IO pins. You can use serial pins for two of those, but usually you need a more pins to drive a shift register (usually at least three in the case of 74HC595). The point is 74HC595 is driven via SPI protocol, not RS-232