RLC-circuits where phasor diagrams don't work

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Discussion Overview

The discussion revolves around the application of phasor diagrams in RLC circuits, specifically addressing scenarios where these diagrams may not be applicable or effective. Participants explore theoretical and practical aspects of RLC circuits, including linearity, frequency considerations, and the complexity of circuit responses.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant recalls a specific RLC circuit where phasor diagrams could not be applied, seeking clarification from others.
  • Another participant explains that phasor diagrams are typically used for AC problems and may not apply to situations like capacitor discharge.
  • It is noted that while phasor diagrams can represent the relative magnitude and phase of voltages and currents, their application may not transfer to more complex scenarios.
  • Examples of RLC circuits where phasor diagrams work are provided, but uncertainty remains about more complicated circuits where they may fail.
  • One participant asserts that phasor analysis is valid for any linear and passive RLC circuit, but acknowledges that non-linear components and transient responses complicate the use of phasors.
  • Another participant emphasizes that phasor diagrams are useful only when the applied signal is a single frequency and the circuit is linear.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of phasor diagrams in various RLC circuit scenarios. Some argue that phasors can be used universally for linear circuits, while others highlight specific conditions under which they may not be effective. The discussion remains unresolved regarding the exact circumstances where phasor diagrams fail.

Contextual Notes

There are limitations regarding the assumptions made about linearity and frequency, as well as the complexity of circuit responses that may affect the applicability of phasor diagrams. Some participants mention idealized circuits that present singularities, which complicate analysis.

Lars278
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TL;DR
When I studied Electronics I remember that there was some type of RLC-circuit where phasor diagrams could not be applied in order to find I, U and phi_u_i (φ_u_i). I've been searching the web to find that example. But I can't find it. Can anyone of you help me refresh my memory?
When I studied Electronics I remember that there was some type of RLC-circuit where phasor diagrams could not be applied in order to find I, U and phi_u_i (φ_u_i). I've been searching the web to find that example. But I can't find it. Can anyone of you help me refresh my memory?
 
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The relative magnitude and phase of voltages and currents in AC systems can be represented by vectors, or phasors on a phasor diagram.
The combined impedance of RLC elements can be represented as a complex number, Z=(R+jX), which can be seen as a vector.

The simplified examples used in education may conflate those two concepts.
Some technique used in a simple case with special conditions may not transfer to the general case.

It might be better if you could present an example that works, then we might extend that case to the situation where the assumptions do not hold and technique fails.

https://en.wikipedia.org/wiki/Electrical_impedance#Phasors
 
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As @Baluncore says, phasor diagrams are for AC problems. So if we want to describe a situation in which the current through the RLC circuit is not AC, eg. capacitor discharge, then the phasor technique will not work (or at least it will be so cumbersome that it is pointless).
 
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Here are two examples of RLC-circuits where phasor diagrams work, one serial and one parallel YouTube RLC tutorial. I was thinking the one where it didn't work might be a more complicated circuit, which was first serial then parallel, but I'm not sure.
 
For anyone frequency, series and parallel RLC circuits can always be resolved into a complex impedance.

The phasor diagram gets more complex when the excitation is not a pure sinewave. That is because R,L & C can be measured and marked with frequency independent values, but the reactance of that component in the circuit is a frequency dependent function; XL=wL; XC=–1/wC.

Where the driving signal has two or more frequencies, or a signal with several harmonics is present, you will need multiple diagrams, or multiple colours to separate the increasing confusion.

Any non-linear component such as a PN diode will generate signals with harmonic frequencies.
 
Lars278 said:
Summary:: When I studied Electronics I remember that there was some type of RLC-circuit where phasor diagrams could not be applied in order to find I, U and phi_u_i (φ_u_i). I've been searching the web to find that example. But I can't find it. Can anyone of you help me refresh my memory?

When I studied Electronics I remember that there was some type of RLC-circuit where phasor diagrams could not be applied in order to find I, U and phi_u_i (φ_u_i). I've been searching the web to find that example. But I can't find it. Can anyone of you help me refresh my memory?
I think you mis-remembered. Analysis with phasors is equally valid for ANY RLC circuit (linear and passive, by definition) regardless of complexity. There are other circuits (eg. non-linear) and some problems (eg. transient responses) where phasors aren't helpful. There are also idealized RLC circuits that have singularities and can't be solved, for example an LC tank (with Q=∞) driven at resonance.
 
DaveE said:
I think you mis-remembered. Analysis with phasors is equally valid for ANY RLC circuit (linear and passive, by definition) regardless of complexity.
Yes - with the proviso that the applied signal needs to be a single frequency ( and the circuit really needs to be linear - of course - it RLC). That's the only way that the phasor diagram can be 'frozen' as it rotates at the frequency of the input. The response to any other frequency or additional signal with different frequency will not 'stand still' so you would have to draw circles (or other closed loops) around the phasors at the frequency specified by the diagram. Phasors have a particular (and extremely useful) application but won't help in other contexts.
 

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