Hi! I'm tinkering with a circuit for an amplifier and have a question about entities. What's is the difference between β (h_{FE}) and β_{max}?
Even if you just have full bucket of transistors of the same type (2N2222). Each of them will have a slightly different beta. So the BJT vendors in data sheet tell as that in our bucket we will find transistors with beta value between Hfe_min and Hfe_max. But most of our transistors will have a typical value of beta also given in the datasheet. And when we design the amplifier circuit we always pick Hfe_min form datasheet.
Do you understand what Beta IS? Min and max are just the highest and lowest expected values for a given type of transistor. If you don't know what the beta of a transistor is, then look it up.
I don't understand your question? Transistor beta (Hfe) is not constant and datasheet for every transistor part number gives a range for Hfe, also every transistor has its own unique Hfe value. The Hfe is a range of numbers because they cannot make transistors accurately. Also the Hfe changes when the collector current is changed and the hfe changes when the temperature changes.
is it true you can only use h-parameters for dc analysis? I know ebers-mole is their but I don't know calculus.
Here is a good place to learn Transistor Operation without needing calculus; just a little algebra instead. also So you see, β gives you a ball-park current gain which can be helpful to obtain ball-part circuit design results.
No, you cannot use a small signal h-parameters for DC analysis. You can use h-parameter only for small-signal analysis. For DC analysis all we need is to use both of Kirchhoff's law and Ohm's law.
You should always only use ball-park values to design transistor circuits. Any design that depends on an accurate value of any specific transistor parameter is a bad design.