http://www.maxim-ic.com/appnotes.cfm/appnote_number/3390

the first formula: V0/VIN=........(1+E1)-1.

What is the meaning of E1? How to get the following E1 expression?

I have checked some op-amp books but found nothing about the error term. Can anyone tell me what is the detailed meaning of error term E1 and how to calculate it?

Many Thanks.

 

The paper gives the calculation of E1 as:

- which looks fairly detailed. It also appears as if this is a calculation specific to the application, so a generalized definition of E1 may not be forthcoming. This applies to termination losses driving coax.

 

The error term is a function of the op-amps beta (feedback attenuation), and the open-loop gain. Check out my derivation of a simple op-amp using KCL.
The one in the Maxim app note uses the same concept, but is very, very involved.

http://nothingbutnode.freehostia.com/pdf/inampnonidealkcl.pdf

 

Check out my derivation of a simple op-amp using KCL.
The one in the Maxim app note uses the same concept, but is very, very involved.

http://nothingbutnode.freehostia.com/pdf/inampnonidealkcl.pdf

I see one error in your derivation. The value you have for B (near the very bottom) is B = (Rf+Rg)/Rg, but it should be B = Rg/(Rf+Rg)

 

Look on page 3. There is an expression for the gain if the opamp were ideal. Now compare that to the non-ideal gain expression on page 2 that has as its last term the parenthetical (1 + E1)^-1. The gain expression for a non-ideal opamp is very complicated. E1 is just what it takes so that if you multiply the ideal gain expression by (1 + E1)^-1 you will get the full, complicated, expression for the gain of a non-ideal opamp.

The E1 expression is clearly incorrect, because if the opamp gain, Aop-amp, becomes zero, the E1 expression becomes infinite, and then the infinite term (1 + E1)^-1 divides the Vo/Vin expression, causing it to go to zero. But, plainly, if the opamp gain is zero, the input signal will find its way to the output through R1 and R2 and Rtheta in series (if Rool is not zero).

 

I see one error in your derivation. The value you have for B (near the very bottom) is B = (Rf+Rg)/Rg, but it should be B = Rg/(Rf+Rg)

DOH! Good catch. I will have to update that soon.