Talk:Circuit Idea/Connecting a Voltage Source in Series

Revealing the truth about electrical resonance phenomenon
I have copied the text below from Wikipedia Talk:Electrical resonance article. Circuit-fantasist (discuss • contribs) 08:55, 16 September 2011 (UTC)

Bless my soul! I know it looks strange and incredibly, and probably you will not believe me... but I have finally revealed the secret of the ubiquitous electrical resonance phenomenon! It is interesting that the negative impedance phenomenon has helped me to find out credible intuitive explanations about the impedances of series and parallel LC circuits. I would like first to share my insights with you here; then to compress these lengthy explanations into a few sentences and to place them in the main article...

Realizing the LC arrangement
The fault of the classic formal approach when explaining the zero and infinite impedance of series and parallel AC-supplied LC circuits is that it implies two dual impedances (inductive and capacitive) that cancel each other thus giving total zero or infinite LC impedance. But this widespread assertion is misleading...

It is hard for people to imagine how two humble impedances can cancel each other as "impedance" gives an impression of something passive. Two passive "things" shouldn't cancel each other; one of them should be active (a source). So, we have to consider an LC circuit as a combination of two elements: a source (active element) driving a load (passive element). Depending on the situation, the either element (the inductor or capacitor) can act as a source; meantime, the other element will act as a load. Strictly speaking, both they are sources containing energy (magnetic or electric); but figuratively speaking, the load is a source that is "forced" to act as a load (like a charging accumulator). They can be distinguished by the signs of the current through and the voltage across them - in the source they are different while in the load they are equal.

Why the impedance of a series LC circuit is zero


We have an arrangement consisting of four elements connected in series: an AC input voltage source, a load (a resistor), an inductor and a capacitor. Or, we may combine the input voltage source and the resistor into a real voltage source (with internal resistance).

The main article says: "Inductive reactance magnitudeXL increases as frequency increases while capacitive reactance magnitude XC decreases with the increase in frequency. At a particular frequency these two reactances are equal in magnitude but opposite in sign; so XL and XC cancel each other out. The only opposition to a current is coil resistance. Hence in series resonance the current is maximum at resonant frequency". Let's now try to comprehend this magic...

According to the considerations about LC arrangement above, we can think of the series LC circuit as of an AC source and impedance connected in series. At the resonant frequency, this "source" has the same polarity as the input source; the two AC voltages are in phase with each other so they add together. Let's for concreteness consider the voltage polarities travelling along the loop at both the half waves.

Positive input half wave (travelling clockwise): -VIN+ (source), +VLOAD- (impedance), -VL+ (source), +VC- (impedance). The charged inductor acts as a source that "helps" the input source. Note the voltage across the inductor (the source) is equal to the voltage drop across the capacitor (the impedance) so the total voltage across the series LC circuit is zero. Its total impedance is zero and it does not impede the current. Very interesting... as though the inductor acts like a negative capacitor or like the output part of the op-amp in an inverting integrator that neutralize the capacitor impedance! Well, there is still a subtle difference:) The true negative capacitor and the op-amp use additional external energy (a power supply) for this purpose while this "negative capacitor" draws energy from the input source.

Negative input half wave (travelling counterclockwise): -VIN+ (source), -VC+ (source), +VL- (impedance), +VLOAD- (impedance). Now the charged capacitor acts as a source "helping" the input source. The voltage across the capacitor (the source) is equal to the voltage drop across the inductor (the impedance) so the total voltage across the series LC circuit is zero again; its total impedance is zero and it does not impede the current again. Now as though the capacitor acts as a negative inductor that neutralizes the inductor impedance!

We can generalize the two cases by one conclusion: An AC supplied series LC circuit consists of two elements connected in series and having equal voltages across them; one of the elements acts as a voltage source while the other acts as impedance.

It is interesting fact that from this negative impedance viewpoint, both the reactive elements can have negative impedance in this sense. They change alternatively their roles: once the inductor acts as a negative impedance element, then the capacitor does the same and so on, and so forth...

Why the impedance of a parallel LC circuit is infinite
Now we have a simpler arrangement consisting of two elements: an AC input voltage source driving an LC tank.

The main article says: "Let R be the internal resistance of the coil. When XL equals XC, the reactive branch currents are equal and opposite. Hence they cancel out each other to give minimum current in the main line. Since total current is minimum, in this state the total impedance is maximum."

To comprehend this assertion as above, we can now think of the parallel LC circuit as of an AC "helping" source and impedance connected in parallel. At the resonant frequency, the "source" provides all the current needed for charging the impedance to the input voltage; so there is no need the input source to do this donkey work:) The helping "source" as though acts as a load canceller (i.e., as a negative impedance again)! Actually, this arrangement is similar to the exotic bootstrapping technique: a voltage "source" (i.e., the LC tank) is connected in opposite direction to the input voltage source; as a result, the current is almost zero and the impedance is infinite. Of course, there is a subtle difference again:)

Circuit dreamer (talk, contribs, email) 22:12, 21 July 2011 (UTC)