A central problem — perhaps the central problem — in the advancement of neuronics is the lack of a technology that stores analog quantities indefinitely. Sample and hold circuits will not quite do it, not indefinitely. While it is possible to make one-bit hysteretic switches out of comparators or store a couple of bits of charge in a MOSFET gate, large-scale analog storage has yet to be devised. The following idea might not achieve this goal either, but maybe it can be a stepping-stone for someone’s bright idea that does.
In the 1980s, Barrie Gilbert was exploring multiple differential pairs of BJTs by combining their outputs while offsetting their input voltages from each other. This resulted in what he called multitanh technology: circuits with multiple hyperbolic tangent functions. The tanh function describes the familiar large-scale transmittance of diff-pairs, and (amazingly) nobody had yet explored it, though the BJT had been around for decades by the time Barrie did his research. An example of a multitanh circuit is shown below, extracted from one of his patents (US4476538). The constant current sources, I , and resistors, R , create the offset voltages at the input bases of the diff-pairs.
Multitanh circuits extend the linear input voltage range of the single diff-pair. Beyond this, the basis for the patent was the discovery that at the output, there is a slight ripple in the resulting function that, upon closer examination, is a sinusoid, shown below as the next figure in the same patent.
The sine function repeats through more than one cycle, and with some modification can be extended for multiple cycles. So what we have at this point is a function that is cyclically nonmonotonic in that for a given y value there are multiple x values.
Next, this function is inverted by swapping its axes (by flipping it over and rotating it 90°). This can be performed electronically by placing the function in the feedback path of an op-amp. A simpler example of op-amp function inversion is to connect the inputs of a multiplier together so that it becomes a squaring function, then place it in the feedback path of an op-amp, as shown below.
The multiplier has the transmittance (not transfer function, because this is not a linear circuit),
and the feedback path transmittance is
The input voltage, vI , is not attenuated because of the multiplier current-source output, and the error voltage at the inverting input of the op-amp is
The forward path through the op-amp has a gain of
Then the closed-loop transmittance is
Solving for vo /vi (by removing vo from the right side),
The squaring function, y = x2 in H results in a closed-loop function that is the inverse, x = y½ , y ≥ 0 . The op-amp inversion circuit works because the square-root function is monotonic, as is its inverse. The multitanh function is not.
In the next part of this blog, we will look at a different inverse-function technique with regard to the multitanh circuit.
- Large-Scale Integration: Neuronics, Part 1
- Large-Scale Integration: Neuronics, Part 2
- Neuronics Creates Highly Efficient Memory, Part 1
- Neuronics Creates Highly Efficient Memory, Part 2
- Getting From Scopes to Semiconductor Innovations
- Between Discrete & Integrated Circuits
- ASICs vs. Semi-Discrete Design