# [Microelectronic Circuits 6th Ed.] P2.27 (Regular Ed.) / P2.23 (International Ed.)

#### Starhowl

Joined Dec 3, 2013
25
Can someone please explain to me what I did wrong in trying to solve this task? Or maybe I did everything right and there's an error in both the international and regular edition?

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#### Starhowl

Joined Dec 3, 2013
25
As far as I understand my A is in truth $$A_{2}$$, which instead should be $$A_1$$ - I still don't get it. There seems to be no way to get to that form; when looking at the solution under
http://www.***********/doc/19231397/Microelectronic-Circuits-5thEd-Solution-Manual
2.27 the author of the solution suggests, that $$\Delta|G|$$ seems to linearly dependent on $$\Delta A$$, which in fact is not true, so the solution invalid?

#### studiot

Joined Nov 9, 2007
4,998
I haven't worked through your algebra, but algebra involving moduli is more tricky than ordinary algebra.

One equation becomes two or three as you have to consider three situations separately

Say you have to do some algebra with a modulus such as |x| then you must consider

x>0 then |x| = x
x<0 then |x| = -x
x=0 then |x| = 0

and put these separately into your equation and work it through three times.

Here is an example that actually a full professor of maths got wrong on another website!

post#6 there is correct.

#### shteii01

Joined Feb 19, 2010
4,644
Say you have to do some algebra with a modulus such as |x| then you must consider

x>0 then |x| = x
x<0 then |x| = -x
x=0 then |x| = 0
That does not seem right.

x>0, then |x|=x
x<0, then |-x|=x
x=0, then |0|=0

#### studiot

Joined Nov 9, 2007
4,998
That does not seem right.
Why not?

x<0, then |-x|=x

This is clearly wrong. if x = -15 what is |x|?

Did you read the worked example?

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#### t_n_k

Joined Mar 6, 2009
5,455
Some of the links don't open for me. In any event I make the minimum open loop gain to be Aol=20,098. Does that tally?

Note:
The value was based on the assumption that the ratio R2/R1 was selected to produce a gain of exactly -100 at the aforementioned amplifier open loop gain of 20,098. The gain falls to -99.5 when the amplifier open loop gain falls to 10,049. If the ratio of R2/R1 is preset to a nominal value of 100 then the answer would be different & easier to deduce.

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#### shteii01

Joined Feb 19, 2010
4,644
Why not?

x<0, then |-x|=x

This is clearly wrong. if x = -15 what is |x|?

Did you read the worked example?
Absolute value of negative fifteen is fifteen. In equation form I would write it the following way:
|-15|=15

#### studiot

Joined Nov 9, 2007
4,998
Well yes, if the x is -15 then the modulus is +15.

So how can the modulus equal x, which is -15.