Decap picture of a Terabeam CD3109 APD/TIA module, taken with a lens glued to a cell
This odd circuit is an on-chip temperature balancer that uses thermal runaway to force N transistor arrays to all run at the same temperature. BJT dissipation goes up at low temperature, with very high gain. Here's its step response.
Sine wave generation is a perennial problem.
Direct-digital synthesis (DDS) uses a bunch of counters, lookup tables, and DACs,
but that's a relatively heavyweight solution that doesn't fit all problems.
BJT differential pairs naturally have a hyperbolic tangent (tanh) characteristic, which can be used to round off a triangle wave into a very passable sine. I'm not old enough to have invented this technique, but here are a couple of illustrations of how it works: TANH Sine Wave Shaper (PDF) and TANH Sine Wave Shaper (Mathcad).
Solid tantalum capacitors have a lot of advantages: very low inductance in surface mount packages, ESR low but not so low that your LDO regulators start oscillating; and good capacitance per unit volume. Unfortunately they're also prone to burn up when mistreated, which makes many engineers wary of them. This war story, entitled What a Cap-astrophe! talks about how to treat them properly, and how a bit of TLC after soldering can restore their full performance.
For RF folks, one of the perennial quests is for better frequency mixers: lower distortion,
lower power, better spurious performance. FETs can help. Nowadays CMOS muxes are the devices of choice for HF mixers, but to get the best performance, you still have to know how they work. Ed Oxner was a long-time Siliconix apps guy, and his paper on High dynamic range FET RF mixers is still right up there with the best:
(From a Siliconix databook, 1985.) The FET mux approach is often credited to Dan Tayloe, but since they work just the same, the "Tayloe mixer" should really be called the "Oxner mixer".