What I'm doing this summer - part 3

So far I've talked about reconfigurable hardware in general and then the specific set-up of the FPAA. Now I'll start talking about what's actually inside the CABs (computaional analog blocks).

First there are simple transistors. There's both nMOS and pMOS varieties and you have access to their gate, source and drain - fairly straightforward. There are capacitors where you have access to both leads. There are some current mirrors which make it simple to replicate a current without having to go through the process of mirroring the current yourself at the transistor level. Then there are a couple of more complex parts. These are the Gilbert multipliers and the OTAs.

Gilbert multipliers are probably the first use of the translinear principle (TLP). In short, this concept allows you to multiply and divide currents by using logarithms and then addition and subtraction and then exponentiating the result again. I'd explain it further, but I actually made a wiki page for my OSS (Olin Self-Study) that I really like. There's actually a two-quadrant multiplier at the end that should give you a good idea of how these things could work. If some parts of the wiki seem difficult to understand due to the writer, please let me know and I can hopefully fix it up. Or feel free to fix it up yourself if you're familiar with TLP. Gilbert multipliers are great because they allow you to directly multiply two signals at substantially faster-than-digital speeds with much less power usage and with orders of magnitude fewer transistors. The catch you ask? Well you can only really trust about 6 bits of a signal and then multipliers love to overflow. So your input signals can only be about 3 bits if you want to guarantee that you don't get overflow... There are workarounds to maintain precision and speed, but they involve adding parts and complexity. This of course makes you use more power, but you still get orders of magnitude more efficiency than a digital multiplier.

This leaves just one part. The OTA (operational transconductance multiplier). These are actually fairly simple and extremely powerful. They have a differential voltage input and output a current that's proportional to the difference in the input voltages. As a simple example, let's do a voltage follower. Put your signal on the positive input. Now tie the negative input to the output. The output will now source or sink current until the output equals the input. This is somewhat similar to an op-amp, but different because the output is a current instead of a voltage.

OTAs are actually quite powerful and provide a fairly straight-forward way to go from a transfer function or differential equation to a circuit. I'll show you that in my next post...