What is the Thevinin's equivalent resistance in a series RLC circuit?

[tete9000]

hey guys, i was just wondering, in a series RLC circuit, is "R" the Thevinin's equivalent resistance at the "Capacitor and Inductor" terminals?, if not please correct me. Thanks.

 

[berkeman]

hey guys, i was just wondering, in a series RLC circuit, is "R" the Thevinin's equivalent resistance at the "Capacitor and Inductor" terminals?, if not please correct me. Thanks.

Usually a series RLC circuit has all three components -- an R, an L and a C. In intro classes, these ae usually assumed to be ideal, so the C has no parasitic L or R, etc.

 

[tete9000]

Hi berkeman, sorry if my question isn't well-clarified, what i meant is "When solving for V(t) or I(t) of an RLC circuit (series or parallel), the resistance in the circuit is taken to be the Thevenin's equivalent resistance at the terminals of both "the Capacitor and Inductor"?I'm not sure if this is right...so I'm asking you guys?is this right?if not please correct me.

 

[berkeman]

Hi berkeman, sorry if my question isn't well-clarified, what i meant is "When solving for V(t) or I(t) of an RLC circuit (series or parallel), the resistance in the circuit is taken to be the Thevenin's equivalent resistance at the terminals of both "the Capacitor and Inductor"?I'm not sure if this is right...so I'm asking you guys?is this right?if not please correct me.

Sorry that I'm not understanding the question. An ideal capacitor has infinite resistance, and an ideal inductor has zero resistance. Are you asking about the full complex impedance of the series combination of the R, L and C?

 

[tete9000]

Sorry that I'm not understanding the question. An ideal capacitor has infinite resistance, and an ideal inductor has zero resistance. Are you asking about the full complex impedance of the series combination of the R, L and C?

exactly...i meant the series combination of a Resistor, Capacitor, and Inductor.
http://upload.wikimedia.org/wikipedia/commons/4/4e/RLC_series_circuit.png

 

[berkeman]

exactly...i meant the series combination of a Resistor, Capacitor, and Inductor.
http://upload.wikimedia.org/wikipedia/commons/4/4e/RLC_series_circuit.png

In that case, you just add the complex impedances of the 3 components in series. Can you write the equation for that?

(complex) Zin = ?

 

[Fish4Fun]

tete9000,

I think what you are asking is: "Does the R include R + ESR + RL? And then solve for Z = Rtotal + ZC + ZL" The simple answer to that is: "Not generally". In physics and Electronics 101, the reactive components are generally assumed to be "IDEAL", unless otherwise noted. In engineering the real-world properties of each component are evaluated and the circuit is designed to work within tolerances for each component; in general no component's properties are intentionally rated in combination with another component's, though the circuit design certainly takes these properties into account.

For instance here:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html

The components R & C & L are assumed to be "ideal", and the impedance is given by:

Z = ((R^2 + (ZL - ZC)^2)^1/2

The phase angle is given by:

Pa = arctan((ZL - Zc)/R)

In the real world, all resistors have some inductance, all inductors have some resistance, all capacitors have some inductance, etc, etc. In many cases the parasitic inductance/resistance/capacitance of the various components can be ignored, but in many other cases ignoring them can lead to a failed design.

Even in fairly simply circuits keeping track of the phase and impedance can get tricky and very time consuming, so modeling circuits in a software environment is now a very routine part of the design process. Typical enterprise level schematic capture software include parameters for numerous parasitic elements in the PCB itself, frequently defined by the engineering team on a per-trace basis.

I hope this helps.

Fish

 

[saim_]

Thevenin equivalent resistance, across the capacitor or inductor, is used to find the time constant in first-order circuits when using the step-by-step approach, though, it maybe found without it as well I think. In second-order circuits I don't think Thevenin equivalent resistance is necessarily required to find anything.

 

[tete9000]

Well, i didn't mean "Impedance and Phase". As a matter of fact, these are the subject of the next chapter in my course of "Circuit Theory".

saim,

Maybe you don't need to find "R" when using the General Way of finding responses, that is, by obtaining the differential equation from scratch, but here I'm talking about the particular cases of Series and Parallel of RLC Circuits.

When solving for the V(t), or I(t) in RLC circuits, you need to find the damping factor (alpha) which is (R/2L) for a series RLC, and (1/2RC) for a parallel RLC, my question is: this "R" that's required for alpha, Is it the Thevenin's equivalent resistance at the "Capacitor and Inductor terminals"?

 

[rbj]

Hi berkeman, sorry if my question isn't well-clarified, what i meant is "When solving for V(t) or I(t) of an RLC circuit (series or parallel), the resistance in the circuit is taken to be the Thevenin's equivalent resistance at the terminals of both "the Capacitor and Inductor"?

if you're want to model a source as having a real thevenin impedance, sure, you can team up the series R with the V or the parallel G (or 1/R) with the I. fine. but you are deciding which of those components to team up with the source.

it is the case that you can team up the thevenin resistance (the real part) with the series R or the real part of the norton conductance with the parallel G.

 

[saim_]

@tete9000: We never learned any separate methods for series and parallel RLCs; we just figure out the diff.eq for the circuit and solve. However, in an sample problem I have before me, which solves parallel RLC, the damping factor is found to be 0.5RC, as you said and in case of series RLC its is R/(2L). In general, for the case of parallel circuit I guess we can always find out the sum of the resistors and that would be the R that would be used for the damping factor. In case of series RLC, well, if all the resistors are in a single series we would add them and use them in this formula but if there do not form a single series I don't know what would be the general R for damping ratio; maybe Thevenin equivalent, maybe not. I'm sure you can write an equation and solve it to find out the general R for this case as well.