[sdiy] Re: current mirrors

[Magnus Danielson]

From: jhaible at t-online.de
Subject: current mirrors (was: AW: [sdiy] discrete SSM2018?)
Date: Wed, 07 Nov 2001 16:22:34 +0100 (MET)

> 
> > Well, the current transfer ratio of a mirror depends basically
> > on current gain. 
> 
> Is this true ?

Yes. If we assume the only property we have to consider is Ic = B * Ib
then, if I1 is the input current and I2 is the output current we have

I  = I   + I   + I
 1    C1    B1    B2

I  = I
 2    C2

I   = B  * I
 C1    1    B1

I   = B  * I
 C2    2    B2

if we assume matched transistors, we can assume

I   = I
 B1    B2

using this property we can now see that

I  = I   + 2 * I   = B  * I   + 2 * I   = (B  + 2) * I
 1    C1        B1    1    B1        B1     1         B1

from this we derive

               1
I   = I   = ------ * I
 B1    B2   B1 + 2    1

inserting this gives

                        B2
I  = I   = B2 * I   = ------ * I
 2    C2         B2   B1 + 2    1

Thus, the I2/I1 relation gets

I
 2     B2
-- = ------
I    B1 + 2
 1

In effect, you would want a pair of high-beta matched transistors for
this task for best I2/I1 mirroring.

If you add one transistor which has its base to I1, its collector to a
power line and its emitter feeds the bases of Q1 and Q1 instead of
having those to I1, then the ratio becomes much better:

I
 2       B2
-- = -----------
I           2
 1   B1 + ------
          1 + B3

Those, giving B3 high enougth, the error term of 2 nearly
distinguishes and you have a the B2/B1 relation.

You can then vary this theme further. All this was naturally done with
a very simple model, but it is sufficient to show the general behaivour.

Cheers,
Magnus