Calculation of Gain In Multi-stage Op-Amp Circuit

[FloydCouncil]

Quote:

a multi-stage opamp system (such as a voltage gain stage followed by a current buffer - see the section on output stages for more information), if the input stage opamp has a bipolar input stage and narrow open-loop bandwidth, it may exhibit nonlinearities when fed high level, high frequency signals. The system in figure 5d has an input stage opamp, which has had its open-loop bandwidth effectively extended under local feedback. The overall gain of the system is 5, but the local gain of the input stage is about 100 for an effective open-loop bandwidth of 100kHz. The bandwidth extension should go well beyond the audio range.

Hello all,

I was studying the above schematic (from headwize) a while ago and trying to figure out its gain. From its description, I know its G = (1K/250 + 1) -- which is exactly the same as for a single op-amp in non-inverting configuration (i.e R2/R1 +1).

What I'm confused about is how did we come to this result? I can figure it out for a single op-amp using a simple voltage divider and making use of the ideal op-amp model, but am stuck when it comes to the above circuit.

The local gain of the first stage should be 1+[221K/(2.5K + 0.25)] or just 1+(221K/2.5K)?

Any help analyzing this would be greatly appreciated.

 

[rds]

Hope that helps.

 

[cobaltmute]

Electronics Calculators and the calculator for knowing the gain given the resistor values may help.

 

[FloydCouncil]

G = [(R6 + R5)(R4 + R3)] / [R5(R3+R4) + R3R6]

This is the value for G that i've gotten using the above Resistor symbols. However, tangent posts the result as:

Plugging in values for the resistors, for instance:

R3 = 250, R4 = 1K, R5 = 2.5K and R6 = 221K, using my formula I get G = 4.7858, however using the formula on tangent, I get G = 4.7697.

I derived my formula using

(Vout - Vin) / R6 = (Vin - Vx) / R5

Where Vx is the junction voltage between R4, R3 and R5. I replace Vx in terms of Vout using a simple voltage divider Vx = Vout (R3 / [R3 + R4]) and plug it in the above equation and solve for Vout/Vin (i.e Gain).

Am I doing something wrong? Why is my answer slightly off?

 

[FloydCouncil]

bump

Please help

 

[rds]

EDIT
nevermind... I thought I saw a very simple solution, but no you have to do some work. Still it's pretty basic. If you're applying the theory correctly just accept your answer and move on.

 

[NelsonVandal]

Focus on R3/R4. Local feedback has very little to do with the overall gain.

 

[FloydCouncil]

Yeah, but I only realized that after analyzing that circuit and coming up with an equation.

I'm really doing this for educational purposes. I'm studying to be an electronic engineer and so usually spend my free time trying to improve myself as I really hope I can be a good one.