Since semiconductors aren't passive components, can I realistically derive analytic solutions for a circuit with BJTs? I know this may seem like a very naive question, but am I on the right track with this sort of analysis, or do I need more powerful numerical modelling even for basic circuits? e.g., the responses for single transistor amplifiers, etc.
I'm trying to teach myself more about circuit analysis – but after the 'RLC' passives, I don't want to end up on the wrong track. I understand this is bordering on opinions, but I really want to start on the right track.
I should mention, I've used 'rule-of-thumb' stuff for constant current, biasing etc. But I'm not entirely satisfied with this approach.
Thanks for the current (ha ha) feedback. Using some of the 'hobbyist' rules of thumb, I've found it easy to achieve switching (saturation) modes, and biasing giving consistent results with different small-signal transistors – which seemed counter intuitive and really surprised me! I really need something like a first-principles primer that doesn't gloss over the complexity, or the range of uses. My multimeter isn't teaching me much…
Best Answer
Transistors are fundamentally nonlinear devices, so no, a strictly linear analysis is not possible.
This is why circuit simulators like SPICE were developed. They take two approaches to make the problem tractable:
For small-signal analysis, you linearize the nonlinear equations around the operating point. This works as long as the deviations of the signal from the operating point cause negligible errors relative to the nonlinear equations.
For large-signal transient analysis, you linearize the equations around the current state, and pick a time step that is small enough that the deviations from the nonlinear equations are negligible. If you find that currents or voltages are changing "too fast" (a settable parameter), you reduce the size of the time step.