hi, I need explanation of the equations 1 to 8 starting from page 7/42 in the attached document.
I work slowly. Let me try to explain the first: the equation number 1:
First the assumptions. You need to take a print out of the block diagram on page 1 and follow during this. The author says:
"At the equilibrium, if we neglect the base currents, the current mirror brought by Q 8 and Q 9 duplicates I 1
which also circulates in Q 7 and Q 6 . Because of the current mirror arrangement between Q 1 and Q 4 , the same
current but scaled up by a ratio of 1 to 3 flows in Q 4 as well"
Is it clear that Q6, Q7 and Q8 has some current (say) I1- we ignore the base current and in the steady state (ignore capacitors), the collector and emitter currents are equal.
Now see Q8 and Q9. Do you think both will have the same collector current? (why and how)- Therefore Q9 also carries the same current I1. Same current must go via Q1 and hence this symmetry.
Is it clear that Q4 and Q5 currents will not be equal (but 3:1) - see the resistors R2 and R3, they are in the same ratio. If Q5 current is x, Q4 current will be 3x. I hope it is clearer.
Now look at Q5 and Q1. How do we know they have the same current?
Now you can understand the equation 1. It uses several important concepts in electronic circuits- but I guess you these better than me!!
I shall be going home and see the next equation later.