OpAmp Circuit Analysis: Finding the Differential Equation for Vo

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Discussion Overview

The discussion revolves around finding the differential equation for the output voltage (Vo) in an operational amplifier (OpAmp) circuit. Participants are analyzing the circuit using nodal analysis and attempting to derive relationships between various voltages and currents in the circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a series of equations derived from nodal analysis at various nodes in the circuit, including equations for V1, Vp, Vn, V2, and Vo.
  • Some participants question the validity of an equation at node Vo, suggesting it should be omitted and that the other equations should be solved instead.
  • There is a discussion about the application of nodal analysis and whether certain currents at node Vo have been accounted for correctly.
  • One participant suggests that the problem involves a second-order system, implying that the final result will include first and second derivatives of Vo and Vin.
  • Another participant notes that the instructions specify not to use Laplace transforms, leading to a discussion about how to approach the problem using algebra instead.
  • Some participants inquire about the use of mathematical software for assistance, while others emphasize the need to solve everything by hand.
  • There is mention of Gaussian elimination and operational calculus as potential methods for solving the system of equations.
  • A participant expresses uncertainty about how to eliminate certain variables from the equations to isolate Vo.

Areas of Agreement / Disagreement

Participants express differing opinions on the validity of certain equations and the application of nodal analysis. There is no consensus on the best approach to eliminate variables or on the necessity of certain equations, indicating ongoing debate and uncertainty in the discussion.

Contextual Notes

Participants note that there are more unknowns than equations, which complicates the solution process. The discussion highlights the challenge of deriving a differential equation while adhering to the constraints of the homework assignment.

Who May Find This Useful

Students studying operational amplifier circuits, those interested in circuit analysis techniques, and individuals looking for collaborative problem-solving approaches in electrical engineering contexts may find this discussion useful.

  • #31
NascentOxygen said:
If you combine your first and fourth equations, the derivatives can disappear and you will be left with V2 in terms of things you know.
##\frac{V_1-V_{in}}{R_1}+\frac{V_1-V_p}{R_2}+\frac{V_2}{R_6}+\frac{V_2-V_o}{R_5}=0##

becomes

##\frac{\frac{R_3V_O}{R_3+R_4}+R_2C_1(\frac{R_3\dot{V_O}}{R_3+R_4})-V_{in}}{R_1}+\frac{R_2C_1(\frac{R_3\dot{V_O}}{R_3+R_4})}{R_2}+\frac{V_2}{R_6}+\frac{V_2-V_o}{R_5}=0##
How would I get rid of V2?
 
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  • #32
Isolate V2. Determine ##\dot V_2##.

Now you can substitute for all necessary terms so as to leave you with an equation relating Vo to Vin.
 
  • #33
NascentOxygen said:
Isolate V2. Determine ##\dot V_2##.

Now you can substitute for all necessary terms so as to leave you with an equation relating Vo to Vin.
I'm not really following. There is no other equation with V2.
 
  • #35
The Electrician said:
If you use the D operator technique, I think you will improve your ability to solve the system:

http://www.codecogs.com/library/maths/calculus/differential/linear-simultaneous-equations.php

http://www.solitaryroad.com/c658.html
Even with d operators, how would I get rid of V2? There is only one equation with V2
If I combine NodeV2 and NodeV1, I get rid of the derivatives.
If I derive the combined equation and then solve NodeV1 for V_2' and plug into get rid of V_2', would that work?
 
  • #36
eehelp150 said:
If I derive the combined equation and then solve NodeV1 for V_2' and plug into get rid of V_2', would that work?
That's what I've been anticipating.
 
  • #37
You seem to want to 'get rid of derivatives'. You can't. In fact the problem asks for the differential equation for Vo. That will include time derivatives of Vo and/or Vin.

Had you been asked to find Vo itself that would mean solving the diff. eq. But you weren't given an expression for Vin so you can't solve for Vo.
 

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