where we left off... Io/Iref = area of EBJ Q1/area of EBJ Q2 = 1/(1+2/beta), want beta large if beta very high, Io~~Iref ex: beta = 100 -> Io/Iref = 1/1.02 = .9803 beta = 300 -> Io/Iref = 1/1.007 = .993 Io/Iref = m != 1 Iref = Ic1 + Ib1 + Ib2 = Ic1(1 + (1+m)/beta) Io = m*Iref/(1+(1+m)/beta) -> Io/Iref = m/(1+(1+m)/beta) Ro2 = delVa/delIo = Va2/Io try to derive correction term exercise 6.6: recall Iref = 2Ic1/beta + Ic1 = Ic1(1+2/beta) -> Ic1 = Iref/(1+2/beta) = 9.80392e-4 beta = 100 Iref = 1mA Note: Vbe - Vce1 = 0 -> Vce1 = Vbe, ditto for Vce2, so Vce1 = Vce2 Vbe = Vtln(Ic1/1e-15) = .026ln(98) = 0.7199V Ic1 = Is1 e^(Vbe/Vthresh) = 1e-15*98e10 = 98e-5 = 0.98mA Ro = Ro2 = Va2/Io = 100/1e-3 ~~ 100Kohms Io = Iref*m/(1+(1+m)/beta) * (1+(Vo-Vbe)/Va2) = .001*1/(1+2/beta) * (1+ (5-.7179)/100) = 1.02mA frequency response for amplifiers: parasitic capacitances: gate/drain, gate/source, gate/body, etc good range for audio is 20Hz to 20KHz open circuit time constant metnod (OCTC) 2 port amplifier w/ Vin and Vout not easy: 1. derive the input/ouput voltage transfer ratio using node or mesh eqs: Vo/Vin = 2. set s = jw 3. mag(Vo(jw)/Vin(jw)) = M 4. set M = 1/sqrt(2) 5. solve for w, then f = w/2pi easy: methodology: example 3 pole transfer function T(s) = Vo(s)/Vi(s) = a0/((tau1s+1)(tau2s+1)(tau3s+1)) multiply out denominator b3 = tau1tau2tau3 b2 = tau1tau2 + tau1tau3 + tau2tau3 b1 = tau1 + tau2 + tau3 b0 = 1 T(s) = a0/(b3sss + b2ss + b1s + b0) assertion: near the 3db point, the 1st order term typically dominates all other terms T(s) ~~ a0/(b1s + 1) = a0/(sum(taui*s + 1)) OCTC method 1. compute the thevenin resistance facing each capacitor with all other capacitors killed (open) 2. form the product tauj = RjCj 3. sum all time constants (b1) 4. wv(estimated) = 1/(sum(RjCj)) look at example 6.6, we'll work it thursday