Following up on JL's suggestion coming out of the midst of a diss-fest in another thread:
Abstraction levels are important even in analogue hardware design.
Back in 2017, during my deposition in the Waymo v. Uber case (*), Waymo's attorney pressed me pretty hard about a recharging circuit for a pulsed diode laser for a vehicular time-of-flight (TOF) lidar for autonomous vehicles, which Waymo alleged infringed their patent under the doctrine of equivalents.
The circuits were roughly like this:
Waymo's patent:
Schottky
+24 0-----LLLL-->S---*------* | | CCC \|/ Laser few CCC V nF | === 0402 | | GND | *--| GaN |---- Trig *--| | GNDUber:
+48 0---BEAD---RRRR--*------* | | CCC \|/ Laser few CCC V nF | === 0402 | | GND | *--| GaN |---- Trig *--| | GND(These are both appnote circuits except for the parts choices and one bead that doesn't do anything, so no IP is being compromised here.)
The presence of the bead lent some superficial plausibility to the equivalence argument, since it behaves like a small inductance at the frequencies of interest, so that the circuits might plausibly look the same if you swap the resistor for a diode.
The operation of the two circuits is of course quite different--when the trigger pulse goes away, Uber's circuit charges up like a decaying exponential, with a maximum voltage equal to the supply, whereas Waymo's charges up like a half-cycle of a sine wave, with a peak near twice the supply, and then the diode holds it there. (After that the inductor rings at its free resonance, as in any other DCM switcher.)
Of course I had great fun with this. After all, if a resistor is equivalent to a diode, then a diode is equivalent to a resistor, right? I therefore I desoldered the resistor on one channel of Uber's diode laser driver board and replaced it with a very nice Schottky rectifier. (There was a fairly large ceramic reservoir cap on the supply side of the bead.) Then I set up a video camera and turned the circuit on, so that it flashed several otherwise identical lasers on the same board.
The hacked laser sure was brighter than the others, while it lasted--the FET melted about 5 seconds into the video, just about perfect for dramatic effect. Made a very entertaining expert report, for sure. (For some undisclosed reason, Waymo dropped the patent infringement side of the case very shortly thereafter.) ;)
The abstraction part was that during the depo, Waymo's attorney (a very smart guy whom I've worked with subsequently) tried very hard to get me to screw up by mixing levels of abstraction.
Even a small physical circuit probably has 10**22 atoms in it, each with its own time dependence over a very wide bandwidth (10**16 Hz maybe). Fortunately its behaviour can be conveniently approximated much more simply: resistors obey Ohm's law, capacitors look like capacitors, radiation and self-capacitance are negligible, and so on. That's why we can draw schematics and reason meaningfully about them.
At the highest abstraction level we usually use for circuit design, diodes conduct in one direction only, GaN FETs are perfect switches, op amps have no input current or offset voltage, and so forth. Diode drops may come in at this level, depending on the case.
At the next level down, it gets a bit more complicated: FETs, lasers, and traces have inductance and resistance, which limits the pulse width. (Uber's guys did a brilliant job--their discharge loop had a total inductance of less than 400 pH.)
At the next level, we worry about things like the leakage of diodes and FETs.
"But wait," says the attorney, "the supposed distinction between diodes and resistors is that resistors conduct in both directions, whereas diodes don't; but the diode's datasheet says right there in black and white that it conducts in both directions. Isn't that so?"
"No, counselor, not at the level of abstraction used in the patent specification." (Leading to a long back-and-forth discussion of the issues above, including many reiterations of the same sorts of questions.)
So abstraction levels are important in the process of designing hardware too.
Cheers
Phil Hobbs
(*) The total ask in the case was a cool $2.3B, of which about 10% was on the alleged patent infringement side where I was working. The rest was alleged misappropriation of trade secrets--the case settled during trial.