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Comment by klodolph | Hacker News Reader

It's not really linear anywhere, except in the sense that it's got a smooth VI graph, so you can pick a point on the curve and draw a tangent line if you want. That's not really linear, unless you have small enough signals or bad enough oscilloscopes.

It's much closer to exponential, which is Shockley diode equation / "diode law" which is the simplest model you would use besides the "diode is a one-way switch with a voltage threshold" model.

The diode law is I = Is[ exp(VD/nVT) - 1 ].

There are more sophisticated models of the diode that use multiple exponentials. Remember that these are all just approximations of reality based on some simplifying assumptions, the only real question is "how much do you want to simplify", and linear models are very rarely useful for modeling diodes.

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This is one thing that's always annoyed me about reading EE books - just tell me the equation and I'll approximate it (thank you), don't tell me a million approximations before the actual behaviour.

You're asking for "the equation", but "the equation" does not exist. There are always multiple approximations, and the only ground truth is experiments (with messy data that does not exactly fit the equations) and the underlying quantum mechanics (which is difficult to simulate).

If you want something super accurate you can end up running a solid state physics simulation.

If you want to model a circuit in SPICE, you get to pick from like a dozen different models for transistors, depending on what you care about--including execution time for your simulation!

If you're designing a circuit, it might be easier to think of a transistor as an infinite gain transconductance amplifier, or something equally absurd--and yet useful. If you're designing for RF, then you have to abandon the lumped component model--there is no longer any such thing as a "wire", everything is instead connected by miniature antennas. Trying to teach this to freshmen EE students is insanity.

The problem here is that actual insight into how something works is not something that you should conflate with accuracy. The model you choose is something that mediates your understanding of reality. By choosing the right simplifying assumptions, you get something that provides you with the right balance of insight and accuracy. Over the years, people have come up with many models at different points on that tradeoff between insight and accuracy, which allow you to understand circuits and components in different ways. It would be wise to "stand on these shoulders of giants", so to speak, and use these high-value models that balance insight with accuracy, unless you are really interested in studying solid-state-physics in which case, by all means, go as far into the deep end as you want.

We still teach freshmen physics students that momentum is mass times velocity, or something like that, for the same reason. It doesn't make sense to explode someone's head with quantum physics and general relativity and then try to introduce Newtonian mechanics as a limiting case. Precious few students would survive.

We do not however teach general relativity linearization-first and only then the full equations.

My point is that for the purposes of the book the equation does "exist", it's just introduced in an extremely meandering-y way. Giving different approximate circuits is fine afterwards but I've spent years and years honing my skills in other quantitative disciplines so I'd prefer to just be given detail in a practical way rather than have detail broken down into practical chunks that loses the essence of the model.

More subtly the idea of a limiting case doesn't always make any obvious sense in electronics unless you speak in unbelievably broad terms that only a physicist would care about (i.e. intuitively you can handwave about some quantity in a circuit relative to the speed of light but you ain't gonna be able to write down an equation and literally take a limit), abstractions/rules-of-thumbs in electronics are often very clever because of that.

I had a lot of fun playing around with RF going through metallic clothes (fencing lames) since basically no amount of theory would really help you so you just have to really stare at the VNA output.

> [...] I'd prefer to just be given detail in a practical way rather than have detail broken down into practical chunks that loses the essence of the model.

I am not trying to come across overly critical here, but I think this is a flawed approach to learning.

My professional experience with EE is from working on circuit simulators. As in, I was a software engineer working on a SPICE simulator tool (it was actually mixed-signal, and some other stuff, SPICE was just part of it). There are a lot of transistor models out there. There's not some ideal model out there which is the best model and the other models are just simplifications of it. I think you may be underestimating how rich the field of modeling is, underestimating how complicated the more accurate models are, and overestimating how much insight you would get by playing around with the more sophisticated / accurate equations.

One problem with these more complicated models is that you have so many parameters and the parameters have effects that typically vary by orders of magnitude depending on the regime you are interested in. Another problem is that the complicated models may require the use of mathematical techniques that I simply don't have the time to deal with. Whereas if I look at the humble Shockley diode equation, I can instantly understand a couple good approximations about diodes:

- The current always flows,

- Every diode is a temperature sensor.

These insights are (for me) easy to figure out from the Shockley diode equation, and that makes the Shockley diode equation extremely valuable.

However, if I'm trying to understand the frequency response of a particular diode, this model doesn't have it, and I might switch from ODEs to PDEs. The diode has an electrical field which varies from one end of the diode to the other, and it has two different charge carriers, which are generated and recombine at different rates at different positions in the diode, have various drift currents, different amounts of momentum, etc. This provides the additional accuracy. Given this more accurate model,

- I'm not sure that I would be able to derive the Shockley equation at all, certainly not in a reasonable time frame, except for the fact that I already know the Shockley equation and could "work in both directions".

- I'm not sure I could get the simpler insights out of this more complicated model, at least in a reasonable time frame.

I'm the kind of student who never memorized formulas and always derived things from first principles on tests. It took me a bit longer, but I was happy to do it this way. It works well enough in some fields--very well in mathematics and statistics, somewhat well in physics, less well in electrical engineering. That's why I think it's a flawed approach to learning--it's an approach which I've personally relied too much upon, and met its limitations.

In order to get any work done at all when designing circuits or doing practical EE work, I must have multiple models in my toolbox, with varying levels of complexity.

That's the difference between science and engineering. Engineering only needs to be good enough to achieve the desired results. If a simplified model gets you there then something more accurate isn't worth the bother.

That's something that mechanics books do a lot better than EE books, as far as I've seen.

Also, this is why you (can) use diodes in log amps and ring multipliers/mixers.

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