# Op Amp dc error analysis

Discussion in 'Homework Help' started by chitofan, Oct 12, 2012.

1. ### chitofan Thread Starter New Member

Sep 30, 2012
15
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I am having difficulty understanding my lecture notes as the workings are extremely convoluted.
How was the Vout equation derived? Using nodal analysis, we can get (Vout - V-)/R2 = (V- - Vground)/R1 but the equation in the 3rd picture doesn't correspond to anything i know or can understand.
Also, at the node between R1 and R2, shouldn't the voltage should be (Ios/2-Ib)(Rx+1k)?
There shouldn't be any mistakes because the lecturer did an alternative analysis using superposition theorem to get the same result, but i would like to understand how she derived the workings as well (i would ask her, but i already have appointments scheduled and i don't want to fall behind in my studies)

P.S. if anybody knows a good reference for analyzing op amp choices while factoring just Vos and Ib, i would love to know it. I've hunted high and low for such materials and came up short.

Oct 8, 2012
59
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3. ### chitofan Thread Starter New Member

Sep 30, 2012
15
0
Can you upload it via mediafire or send it to my email <SNIP>? I am unable to access the file through your link..

Last edited by a moderator: Oct 12, 2012

Sep 30, 2012
15
0
CircuitZord,

5. ### CircuitZord Member

Oct 8, 2012
59
2
I sent you a few more stuff I have specifically on Op-Amps, including some tutorial questions and solutions, the rest of the lecture notes are on BJT's, MOSFET's, frequency response, etc.

chitofan likes this.
6. ### chitofan Thread Starter New Member

Sep 30, 2012
15
0
These were very helpful, thanks alot

Having read these, let me summarize what i THINK i understand thus far:

1) To calculate output offset voltage, Vos, consider the effect of input bias current, Ib, input offset current, Ios and input offset voltage, Vio. Other errors would be gain error which depends on the resistor tolerance values.

2) For easier analysis, add DC sources to an ideal op amp to model errors and analyze each error independently using superposition theorem then add up to get the total Vos.

3) To calculate the effect of Vio, place a voltage source Vio outside the inverting or non-inverting terminal and ignore the input voltage, Vin since we are looking at the impact of Vio on the output. Also, ignore the polarity since we are interested in the magnitude only. It is preferable to place Vio on the non-inverting terminal to simplify calculations : Vin = Vos x gain

4) Then to calculate the effect of Ib and Ios together, here is where i am having trouble.

Looking at the equations, i am making the guess that for RTO, voltage error is voltage drop due to Ib+ multiplied by gain, plus voltage drop due to Ib- multiplied by R2 (why the negative sign? i thought polarity shouldn't matter?)

while for RTI, the voltage drop for everything is inverted - voltage drop due to Ib- is now Ib- multiplied by gain and likewise for voltage drop due to Ib+.

Can anybody explain why is this so, and give me a hint how to start with getting a formal proof for these equations?

7. ### CircuitZord Member

Oct 8, 2012
59
2
OK, I am heaps sleepy so maybe my explanation will be a bit suspect, but essentially you know now for these kinds of questions you will have to apply superposition, AND, you will have to remember the Op-Amp golden rules; consider the ideal situation where current does NOT enter the Op-Amp, and the virtual ground principle where applicable.

So if current cannot enter the op-amp it must therefore flow through the resistors in the feedback path.

So let's consider the offset due to the Vos alone first.

Which means V+ is grounded and the voltage at that black dot (node) near R1 is Vos.

So now we can consider how a current will flow:

(0 - Vos)/R1 + (Vout - Vos)/R2 = 0

This is the current that flows from B to Vos and Vout to Vos, it's just KCL. Where B is presumably grounded.

Now you just rearrange the equation and solve for Vout, you will get Vout = Vos(1 + R1/R2)

Do the same thing for Ib+. I just did it for both and it worked out fine.

I hope it makes sense, that's kind of what I've done for op-amp questions in the past and it seems to have worked thus far. I'm sure someone will let you know if I've been talking nonsense.

8. ### chitofan Thread Starter New Member

Sep 30, 2012
15
0
Ok, now that i've tried a few attempts at solving for Ios and Ib, i still have a few more questions:

1) Direction of the input offset current, Ios: comparing

which is the correct model?

2) Another method seems to be solving for effect of Vos and Ib first, then substituting Ib1 = Ios - Ib2/2 and Ib2 = Ib - Ios/2

Last edited: Oct 14, 2012