Now let's start discussing the circuit.

Let's concentrate on Q3, Q2, Q1, R1 and R2.

Q3 is split collector type transistor and is actually a current mirror, meaning the reference current which is also the emitter current going to Q2 is 'mirrored' (maybe equal or multiple/fraction) as collector current of Q1. Let's term this as Iref.

Now looking at Q2, the 10 actually refers to the number of emitters. It is as if there are 10 parallel transistors comprising Q2.

Now the Iref will be divided equally by 10 as collector current of each of 10 parallel transistor of Q2, so Ic2 = Iref/10.

Now Q3 as we say is current mirror and is 1:1 mirror so Ic3=Iref.

Now we calculate the Vbe of Q2 and Q1 as

Vbe2 = Vt*ln(Ic2/Is) = Vt*ln((Iref/10)/Is)

Vbe1 = Vt*ln(Ic1/Is) = Vt*ln(Iref/Is)

I forgot to mention that Is is the saturation current and is the same for both type of monolithic transistor on the same process.

Let's KVL on the bases of Q2, Q1 and R1:

Vbe2 + Vr1 = Vbe1

Vbe1 - Vbe2 = Vr1 : the delta of Vbe is across R1

Vt*ln(Iref/Is) - Vt*ln((Iref/10)/Is) = Vr1

Remembering logarithmic properties that ln(a/b) = ln(a) - ln(b)

Vr1 = Vt*ln (10)

How do we calculate K:

Ir1 = Vr1 / R1 is actually the same current on Ic1 because of the current mirror Q3

Ir2 = Ir1 + Ic1 = Ir1 + Ir1 = 2Ir1 = 2Vt*ln(10)/R1

Now how do we get Vref:

Vref = Vbe1 + KVt

Vref = Vbe1 + Ir2*R2 = Vbe1 + R2*2Vt*ln(10)/R1

Vref = Vbe1 + (2R2/R1*ln(10))*Vt

so K = 2R2/R1*ln(10)

So we now have bandgap reference voltage.

Q4 is for current boost. How about R3,Q5,Q6 and Q7? What is the purpose of these?

Next time we'll discuss about it.

Hope you like it