# Analysis of BJT transistor - is a linear analysis possible?

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...

• Are you comfortable with Taylor Series modeling of the Emitter-base junction? That lets you define Intercept Points (input) for all orders of distortion. I recall about 10dB difference between 2nd and 3rd order, with both being near -10dBv. The 2nd order products will drop dB-per-dB, thus inputs near -50dBv would cause input-referred 2nd order products of -40dBc. And 3rd order products will drop 2_dB-per-dB, thus inputs near -50dBv would cause input-referred products of -80dBc. All this from memory. – analogsystemsrf Sep 5 '18 at 11:45
• @analogsystemsrf - I get the feeling that if I'm to further my understanding, I'm going to have to make a serious investment in a (digital) oscilloscope if I'm to learn by doing. Because while I roughly grasp the dB concept, your comment was totally beyond me. – Brett Hale Sep 7 '18 at 7:27
• Try read this ittc.ku.edu/~jstiles/412/handouts/… – G36 Sep 7 '18 at 15:19

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.

• Thanks. I suspected as much, but it puts me on the right track - since I'm not formally educated in this field - and helps me see the bigger picture! – Brett Hale Sep 5 '18 at 11:08
• You might want to hold off a day or two before accepting this answer, in order to see whether anyone else wants to weigh in with additional information. – Dave Tweed Sep 5 '18 at 11:15
• Hold on here. After biasing it’s perfectly reasonable to use small signals model to perform linear analysis with BJT, considering you guarantee the BJT will work in the active region. – PDuarte Sep 5 '18 at 13:05
• @PDuarte: Isn't that what I said? What would you say differently? – Dave Tweed Sep 5 '18 at 13:20
• I don’t agree that strictly linear analysis is not possible. In applications that you use BJT for amplification, linear analysis is not only possible but recommended. Also SPICE don’t use linear models like you said, it generally use Gummel-Poon model which is much complex and handles non-linear characteristics. – PDuarte Sep 5 '18 at 13:26