[Difficult] Simplified T flip-flop

[pgboswell]

Can you design a simple spintronic T flip-flop using only 3 transistors? T flip-flops are a type of flip-flop that toggle the output every time there is a rising edge on the input pin.

They’re used, for example, in quartz oscillator watches. If you string a series of them together, you can bring the 32,768 Hz frequency of the crystal down to a 1 Hz frequency to run the second hand. The first T flip-flop brings it down by half, to 16,384 Hz. The second T flip-flop brings it down to 8,192 Hz. The third T flip-flop brings it down to 4,096 Hz, and so on, until you get to 1 Hz. There’s a cool video on this particular use of T flip-flops here.

This is pretty tricky. I tried it myself, using a direct implementation of this logic diagram:

(image from T Flip Flop in Digital Electronics - Javatpoint)

It’s not even close to the most efficient way to build it. Here’s what it ended up looking like:

And here’s a link to the simulated circuit. It has pretty poor performance as well. It takes a looong time to switch back and forth. There’s GOT to be a simpler, better way to build it, and I think it can probably be done with only 3 transistors (possibly even two). Here’s a link to a circuit diagram that uses three.

Note that you won’t be able to directly translate that circuit to spintronics. Spintronic transistors behave differently than the “bipolar junction” type transistors (BJTs) in the circuit diagram. They’re more like “field effect” transistors (FETs).

Can you build a circuit that behaves like a T flip-flop using only 3 transistors?

[numbers]

EDIT: I realize that this isn’t a true flip-flop—the requirement for re-closing the input switch after a bit disqualifies it—but I am working on a circuit that replaces the switch with a transistor and takes the correct sort of input. I still think it can be done in two, however.

Here’s a two-transistor pseudo flip-flop.
There are a few caveats: It outputs in current rather than voltage (it actually can’t take much load before the interaction collapses), and it needs reset from a cold start. I also don’t have a physical set so I wouldn’t know if it could actually, physically work or is just because of quirks in the simulation; I only found out about Spintronics from Steve Mould’s video a couple days ago!

Before you can do anything with it, you need to open the upper (reset) switch, turn it so either capacitor holds charge, and then close the switch again. After that, you can toggle the bottom (input) switch freely. The sweet spot for how long the input should be open is somewhere between ½ and ⅓ seconds, unless your browser lags a bit.