Finding the constraint equation of a circuit with a dependent voltage

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Discussion Overview

The discussion revolves around finding the constraint equation for a circuit involving a dependent voltage source. Participants explore various approaches to apply Kirchhoff's Current Law (KCL) and voltage node methods to derive the necessary equations for solving the circuit. The conversation includes technical details about the circuit components and the relationships between voltages and currents.

Discussion Character

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

Main Points Raised

  • One participant expresses difficulty in finding the constraint equation for current through a voltage source, noting that they cannot apply Ohm's law directly.
  • Another participant suggests writing out KCL equations for different nodes, proposing a specific form for the KCL at the bottom node.
  • Multiple participants provide KCL equations for nodes V0, V1, and V2, with some uncertainty about the correct formulation and the number of equations relative to unknowns.
  • A participant realizes that they are dealing with a dependent voltage source rather than a current source, which prompts a reevaluation of their equations.
  • There is discussion about the use of different circuit simulation software, with participants sharing experiences and preferences for tools like Qucs and LTSpice.
  • One participant mentions the need to set a specific node as ground to simplify the analysis, indicating a potential strategy for finding the constraint equation.
  • Another participant reflects on the learning curve associated with using circuit simulation software and the challenges of understanding different types of sources and their configurations.

Areas of Agreement / Disagreement

Participants express various viewpoints on the correct application of KCL and the formulation of equations. There is no clear consensus on the best approach to derive the constraint equation, and multiple competing views remain regarding the methods and interpretations of the circuit elements.

Contextual Notes

Participants note that they are using different methods (voltage node vs. current node) and that there may be dependencies on definitions and assumptions about the circuit components. Some equations presented may not be independent, leading to confusion about the number of unknowns.

  • #31
Baluncore said:
I question the polarity of the current controlled voltage source.
It is shown inverted in the original diagram.
Exactly what are you getting at when you say "I question the polarity of the current controlled voltage source."? That source is indeed shown inverted in the diagram as you assert, so what is your point?
 
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  • #32
It is OK. The 10 V source is sinking conventional current, so Id is negative.
Multiply by 20 and invert the CCVS to get +64 V, which sources the current to be sunk by the 10 V.
 
  • #33
Baluncore said:
I question the polarity of the current controlled voltage source.
It is shown inverted in the original diagram.
Only means a negative answer instead of a positive
 
  • #34
BvU said:
Only means a negative answer instead of a positive
Not quite.
I think if you reverse the CCVS polarity it produces 6.80851 V, and Vo becomes +7.65957 V.
The 10.0 V becomes a positive current source, so the CCVS is also positive.
 
  • #35
My turn to be confused: if ##V_2=+64## V, the CCVS delivers ##-##64 V and pumps 3.8 A towards point V2. The ##-##64 is 20 times the ##-##3.2 A ##i_\Delta##.

If the CCVS sets ##V_2=+ 6.80851 ## V, the dial must read ##-6.80851 ## V which is minus 20 times the then ##-##0.34 A ##i_\Delta##.
 
  • #36
BvU said:
My turn to be confused: if ##V_2=+64## V, the CCVS delivers ##-##64 V and pumps 3.8 A towards point V2. The ##-##64 is 20 times the ##-##3.2 A ##i_\Delta##.

If the CCVS sets ##V_2=+ 6.80851 ## V, the dial must read ##-6.80851 ## V which is minus 20 times the then ##-##0.34 A ##i_\Delta##.
Your first short paragraph above describes the situation as shown in the schematic of post #1.

The second short paragraph describes what would happen if the CCVS control law were changed from 20 IΔ to -20 IΔ, or if the orientation of the CCVS were flipped upside down with no change to the control law.

That's what Baluncore is referring to when he says "reverse the CCVS polarity".
 
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