beta = Ic/Ib
Vth - RthIb - Vbe - IeRe = 0
swap Ib for Ic/beta
Vth - Vbe - Ie(Rth/(beta+1) + Re) = 0, solve for Ie -> Ie = (Vth - Vbe)/(Rth/(beta+1) + Re)

biasing BJTs
changes in vcc (regulated power supply)
changes in beta
changes due to temp
Ic = Is * e^(Vbe/Vtherm)
Vbe = Vtherm * ln(Ic/Is)
best choice for accounting for Vbe is setting voltage divider properly (>> Vbe)
another option:
two DC source voltages, one + and one - with emitter and collector resistors, this allows the signal to swing below 0 like a normal signal, heart of diff amps/opamps

another option: single bias resistor (BAD OPTION)
Ie = (beta+1)(Vcc + Vbe)/Rb
does a great job for temp, but not great for changing beta

generally accepted BJT bias rule of thumb for determining goodness of design
	Given: Re >> Rth/(beta+1), Vth >> Vbe
	for bias stable circuit: Rth ~~ 0.1(1+beta)Re

may have to move the qpoint and iterate the design to get the gain, input/ouput resistance you want

ideal amp: infinite gain, inf input resistance, 0 output resistance

what do we mean by small signal?
applicastions where current and voltage variations are small enough that the device's characteristics are approximately independent of signal size, this allows the device to be represented by a simplified linear equivalent circuit model
small sig circuit params
these equations apply only at the dc qpoint selected, gm is called transconductance, rpi is input resistance between base and emitter looking into the base, re is emitter resistance, ro is output resistance
gm = Ic/Vtherm
rpi = Vtherm/Ib
re = 
ro = 
popular equivalent incorporating the early effect: thevinin on input, norton on output
T model is slightly different

separate amplifier from dc sources with caps to prevent bias from being changed accidentally
at mid-band varying signal, all caps should act as shorts
add DC response and AC response to get final answer, superposition ftw
common base is similar, current gain low, voltage gain high, low input resistance, high output resistance, medium power gain
common emitter: medium input and output resistance, medium current and voltage gain, very high power gain
common collector: high input resistance, low output resistance, medium current gain, low voltage gain, very low power gain