Widlar 2

Figure 4

4. What is the output current, Io, in the circuit shown in figure 4?

Vbe1 = Vbe2 + IoR
Vt*ln[Iref/2Is] = Vt*ln[Io/Is] = IoR
Vt*ln[Iref/2Io] = IoR
Iref = 930uA
Io = 150uA
IoRe = 30 mV
Vt*ln[Iref/2Io] = .0258*ln[930/300] = 29.1 mV close enough

What is the output impedance?

Rout = r_o[1 + Re*gm] = r_o[1 + ReIc/Vt]
VAF = 325V
Ic = 150x10^-6
where r_o = VAF/Ic = 325/150x10^-6 = 2.17 MEG
IcRe = 30 mV
Rout = r_o(1+IcRe/Vt) = 2.17(1+30/25) = 4.8 MEG
Recall ReIc / Vt is the number of thermal voltages across Re. One plus this number is the multiplier of r_o.