The answer is to do with what current actually is. Current isn't a thing in itself, it's the label for a process. When we say "current is flowing" we really mean charge is moving.
More precisely, in a capacitor, the current flowing in amps is the rate-of-change of the charge in coulombs it happens to be holding. So if the frequency increases, the charge moves faster, and we see the current increase. When I try the experiment again with several capacitors of different value, I find that the bigger the capacitor, the bigger the current.
So the voltage-to-current ratio for a capacitor is inversely proportional to both frequency and capacitance. It is very handy to be able to define a component in terms of the ratio of its voltage to its current. But we clearly ought not to speak of the "resistance" of a capacitor. Resistance implies that voltage and current are in phase, and that power is dissipated. A different word is needed to express the idea of the voltage-to-current ratio in a more general way, one which does not carry the implication that the two have to be in phase.
This word, of course, is impedance , written Z , and measured in ohms. But what is it? Like resistance, impedance limits current.
The capacitor is somehow limiting the current, just as a resistor would. How does it do that? Look back at the voltage and current waveforms for the capacitor. Well, no. For one thing, the current keeps passing through zero, and dividing anything by zero gives 'infinity' as the answer.
The voltage regularly passes through zero too, so all we can conclude is that their ratio is jumping rapidly between zero and infinity.
That isn't much help. So impedance is apparently not something that can be defined at a particular instant, as voltage can. It must be a property of the component that only makes sense when it's averaged over some sensible period of time, such as a full cycle of the applied voltage sinewave. This is believable, because the current flowing in or out of the capacitor at any instant depends not only on the applied voltage but also on how much charge the capacitor happens to have stored at that instant.
This charge movement averages out over a complete sinewave cycle. And the impedance of a capacitor depends very much on the frequency at which it is measured. If I could get hold of a few ideal inductors ha! Inductance is measured in Henrys and capacitance in fractions of a Farad, though if Faraday's name had to be abbreviated in that insulting fashion, why didn't they go all the way and call the unit a Far?
Or why not measure inductance in Hens? The definitions of the units won't allow it. Irritating, but life is like that. Since the impedance of capacitors and inductors or, for purists, the reactance of ideal capacitors and inductors depends on frequency, it follows that the impedance of a network containing these components also depends on frequency. It is meaningless to talk about the impedance of a network built from resistors and capacitors that is, an RC network without at the same time specifying the frequency.
Actually, that's the point of RC networks. If we wanted an impedance that was independent of frequency, a resistor would do. Suppose that we happen to have, lying around, an ideal nF capacitor and an ideal 54 mH inductor.
We're in the realms of fantasy now, you understand, where the theorists' little feet are floating some inches above the ground we lesser mortals walk on. We or anyway, they could find the impedance of each component at 1 kHz by putting each one in turn across the generator terminals and measuring the voltages and currents. The experiment is complicated by the phase shifts each component introduces, so to keep it simple let's measure the voltages and currents in RMS terms.
It involves integration, and it's in the textbooks if you really want to know, but for now it's enough to accept that it's what you would read off an AC voltmeter or ammeter in the circuit.
This means that at 1 kHz each has an impedance of. A capacitor is a very different type of component from an inductor, yet nF and 54mH both have the same impedance at 1 kHz. Something is obviously missing in the definition of impedance if it does not allow us to see at once that the two are different animals, and the missing information must be to do with phase shift.
In fact, it must show that v is at degrees to i. The j terms simply indicate that there is a phase shift, and whether it is positive or negative. But what is j? What does it mean? If we multiply the two j terms together, the j s vanish:. No j there, so no phase shift. And an inverting amplifier has a gain of So the? Negative numbers can't have square roots, can they? It seems to be a weird Zen concept, like the sound of one hand clapping.
But it is immensely useful, because j can be manipulated in the equations like any other variable. Frequency is always associated with phase shift, so it's helpful to write them together, like this:. The simplest possible RC networks are those containing just one resistor and one capacitor. The components must be either in series or in parallel. We know the impedance of each component, so we can quickly find the impedance of the combination.
For the series case,. The equations are saying that these two components, C and R, define between them a single unique frequency that depends on their values and on nothing else. These equations look pretty simple.
In other words, R and C in combination behave like a resistor whose value varies with frequency. Well, of course they do. How do you add the square root of -1 to something? And if you did, what would it look like? The key to understanding the next bit is to remember that j was only invented so that we could tell the difference between a positive phase shift and a negative one. Thiat would be adding apples to oranges.
But we can use geometry to see what the combination might mean. I'm kinda intrigued by the Powersoft modules myself, mostly since they are a big player in the pro market.
Armaegis , Sep 21, Hrodulf , Sep 21, I recently built a pair of DIY speakers from these kits. Last edited: Sep 21, I saw your post on reddit where you mentioned this.. All my comparison are made of course with amps SPL matched.
Discrete SS is only "slightly" better and actually worse in other way. My sony in the bass seem to have a sub attached to my speakers the sony seem to go much deeper. Class D is Not as holographic as tube amps and some ambience information is lacking. I will try to get my hand on the new Rega Brio to compare with those low powered amps. Im also interested to try in my system Hypex ncore and see how they compare to low powered class d. Last edited: Oct 3, Last edited: Oct 7, Class D is good for sub woofers, full stop.
Class D can also work if you really really need a lot of watts but don;t have that much cash. If you want a refined midrange and treble look elsewhere. The rules of Class D. Rule 1. In one sense, you can consider the effects of phase angle being built into the frequency response which represents voltage sensitivity over the full bandwidth : whether the phase angle is 0 degrees or 60 degrees, the voltage demanded from the amplifier remains the same.
Fortunately, 45 degrees is the worst case scenario for a real world loudspeaker; both above and below this point, the amount of power an amplifier is required to dissipate falls off.
Phase; Courtesy of Sound. Remember, the voltage waveform is no longer in phase with the current, so peak current is no longer being sourced from an amplifier at the same time as peak voltage. To handle a real world loudspeaker, a good quality amplifier must be built with the challenges of a less than benign phase angle in mind.
Naturally, that takes a lot of heat sinking or active cooling and a robust output stage. It is my hope that after reading and properly digesting this article, you the reader have a better understanding of the electrical characteristics of a loudspeaker, and how they matter when selecting an amplifier.
Happy listening! Confused about what AV Gear to buy or how to set it up? Read the Complete Thread. Steve81 posts on February 19,
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