RLC-circuits where phasor diagrams don't work

[Lars278]

TL;DR 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?

 

[Baluncore]

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

 

[atyy]

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).

 

[Lars278]

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.

 

[Baluncore]

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; X_L=wL; X_C=–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.

 

[DaveE]

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.

 

[sophiecentaur]

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.