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Old 03-30-2014, 12:23 AM
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Default Power measurements from audio amplifiers

Here's a Simple tutorial on the facts and equations of AC Power measurement and some misc important power facts.

Quick Notes:

- AC Voltage and current calculations MUST be figured in True RMS Values. You have peak, peak to peak, and RMS figures. The only usefull Figure is RMS. RMS = .707 * peak Measuremnt which means it is about 70% of the peak value. Cheap meters average AC voltage which only works with perfect sine waves which ain't realistic or reliable. True RMS metersuse digital to take a lot of samples of any possible input waveform be it distorted, square wave, music etc...and it THEN averages those points.

- True RMS current also exist, most meters measure this. True RMS current can be derived from RMS voltage over the resistance/impedance.

- Apparent Power(VA) is exactly what you are calculating as soon as you multiply RMS voltage and RMS current...note that RMS has nothing to do with apparent power however you must ALWAYS use RMS values because using peak values will give you peak a Measurement which are more "useless" then apparent power. Useless? You may see apparent power as useless once you learn what it is and some people refer to it as such. Apparent power is abbreviated VA, you may see KVA on power transformers for Instance, the k is kilo btw.

- Real and Reactive Power are the two components that makeup apparent power. Apparent Power is a raw VA calculation. Why do they call it VA? V and A next to each other means V * A, why not call it wattage? Since wattage is V * A. They call it VA because it is not dissipated power, more like posing power. AC power does not have a simple calculation like DC does. They actually have what's called an AC ohms law(for power and impedance).

Real power is important because it tells us exactly how much real power we are putting to work. Real power gets used and transferred to heat like a consumable. Power is never destroyed but transferred into the form of heat in this case.

Reactive power is the part which makes power Measurement complex. With no portion of reactive power there is no apparent power and we could then simply perform V*A to achieve a real wattage value just like with DC.

- raw simple resistance values dissipate true power.
- what creates reactance in a circuit are either inductors(coil windings etc), capacitance or both.
- A motor is Inductive obviously so it has a reactive component.

Disecting power with a motor:

- Only an AC motor will have a reactive power because you are feeding it with AC electricity. A DC motor will not have reactance only because it is not beeing fed an AC source and reactance only happens with AC, in fact part of the reactive equation uses frequency for determining reactance because it is heavily Frequency dependent.

Just as there are two components of Power, there is most definetly two components of impedance.
When I wrote about reactance a few lines up I wasn't clear but it is impedance I am describing not reactive power.
- The Term reactance when used alone refers to reactive impedance
- The term reactive power obviously refers to reactive power
So remember when I use the term reactance that it is reactive impedance.
Impedance can be used to include the lump of both resistance and reactance so when I use impedance alone it usually refers to either or both.

The term Impedance is commonly used loosely as either resistance, reactance, or both. It in fact is never normal resistance alone, however subwoofers state the Nominal resistance of their coils as an impedance, which could be for a few different reasons. The real resistance of a speaker is lower then the actual nominal value. The nominal value is actually where the resistance tends to rest(higher with a lot of power) with power from an amp due to heat. The rise from the raw coil resistance to nominal rating is not actually a reactive phenomena but a heat rise phenomena.

The two components of real(resistance) and reactive impedance are actually the cause of real and reactive power. Obviously, we already know that voltage applied to a raw resistance gives us a real power dissipation. But now we need to explore reactive impedance, where it comes from and it's calculation, etc.

Simply put, inductance creates the reactive impedance in the case of a motor. A simple calculation for reactance from inductance:


So 2*pi is 6.283
6.283* say...60hz for an AC mains motor is 376.98
Say..3mH* 376.98 is .754 Ohms which is relatively small lets just say 10mH

With 10mH we have 3.77Ohms at 60hz So you can think of inductors like reactive resistors. Resistors impede current flow (V/R), inductors also impede current flow....but as I stated before, you cannot simply go V/R or V/XL(XL simply represents Inductive reactance, x is reactance, L is inductance) in a reactive circuit you must know the phase angle of the Voltage to current, or the impedance phase angle(real to reactive phase angle).

- In a reactive circuit, voltage and current are out of phase. The voltage will be first and the current will have a lag which means they would look superimposed.

This is what happens and is the main reason/symptom of reactance:
- A voltage is applied to a motor, the motor's windings have a resistance, and also when the motor runs, heat is generated from work being done. This resistance is real raw resistance and even though resistive heat can vary due to motor temp, length of operation, etc...it is not part of the reactive component.

- As to the reactive component, when inductors are in a circuit and voltage is applied they produce a magnetic flux field as current runs through them. At first there is very little current flow, the inductor slowly allows current through in time(fractions of a second you get the point) the inductor allows a lot of current through and the Inductor stores energy in the form of a magnetic field. This is why it is hard for current to flow at first because it is first building the field. Once the field is created, the inductor will try to keep current flowing through it the same. The field does not like to change especially the higher the inductance is. Also it should be noticed that inductors do not like AC, they like current to stay the same and AC is always changing direction specifically at 60 cycles per second with AC mains(residential). Inductors don't like it because the field must collapse and rebuild in order to switch polarity like AC does at 60hz mains. So, the AC is forcing the inductor to collapse/rebuild it's field and switch polarity at 60hz and the inductor simply dosn't have the time to buildup to its max current flow/flux field in time so a smaller then max current is drawn through the inductor at a given frequency which is why reactance varys with frequency and also inductance(more inductance means more opposition to changing current). And yes this inductive opposition is the reactance created by the inductor since it impedes current flow. So we use an eqivalent resistance value to represent the opposition an inductor has.

Last edited by Novicaine; 03-30-2014 at 05:40 AM.
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Old 03-30-2014, 12:27 AM
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Okay almost done now were getting to the good stuff

Why exactly do we have a phase angle between voltage and current? Because the inductance stores the energy in its magnetic field and has a lag between supplying current in one direction and the other. When the AC source is flowing one way, the inductor is allowing no current flow at first while it building it's field and it starts to pickup and flow through but meanwhile the AC polarity changes and the inductor hates it so it shoots its stored energy in the form of a generated current against the change to try and keep its current flow the same this is why there is a lag between current and voltage because they are out of phase but it isn't 180 out of phase like it sounds like, the frequency is so high that the inductor discharges quickly and begins to fallow the voltage polarity then the voltage turns on it again, over and over. The phase angle is never very high but significant to make a big difference.

How do we calculate reactance(reactive impedance) alone:

First we find the cosine of the phase angle between V and I. Figuring out the phase angle goes into polar variables which you need a little triganometry tutorial to figure out you simply use x and y coordinates on a graph, you draw a line from one component on the x plane to the component on the y plane and use something to measure the angle. The impedance is also the same angle.

Anyway, If we have the phase angle already then we can use a calculator to find the cosine of that angle so lets say we have a 30 degree angle between voltage and current the cosine of 30 = .1542 Now, this value is actually the power factor

True Power/Power Factor = Reactive power

I should have explained power factor earlier but it's pretty simple. Power factor is an arbitrary number that describes the ratio of the Apparent power to the real power. One being perfect which would be a DC circuit or could be an AC circuit with no reactive parts such as an Inductor or capacitor. Since inductors and caps are opposite each other you can use one to basically cancel out the phase lag however in the real world you can only change it so much. With subs we don't apply caps to the output for a few reasons, one it would change the Q parameter(tsps) and would make the sub have no bass what so ever. Something similar to removing reactive impedance back in the day was tried but had no low end. We rely on Q parameters for sound response. The Reactance and Tsps are linked.

The second big reason is because speakers actually aren't just Inductive. The coils that attach to the amp are sure, however the moving parts are what generate a physical lag, but Inductive and capacitive, analogously. So you may need either an inductor or a cap depending on what side the resonance your frequency of choice is at(only for spl since sound quality isn't important for burping).

So, power factor below 1 is where it gets poor and the more inaccurate V*A will be. Also the main thing with Apparent power is this:

The Component of Reactive power is not true power which is why we call apparent power VA and not wattage. It APPEARS as power because we are multiplying V and A. The reason it is not real is because the current in the circuit is inflated but only in time. Power is the product of voltage and current together because they do work and turn to heat. The current the inductor controls, none of that current is consumed and turned to heat. The resistance of the motor is but the inductor stores energy in it magnetic field from current flow and it causes the absence of current at first, and it then shoots current out to compensate the voltage polarity change in time.

Sounds confusing but what it means is that impedance measured by say a meter...it is not a real dissipate resistance it actually stores energy in the inductor and it shoots it back to the source which even means you aren't getting charged by the power company for that small portion of apparent power since it gets equally returned. It is just a lag of power(current specifically) that is "hidden" at time but then returned back. You can say it is barrowed but given back in time meanwhile the motor demands its OWN desperate power draw to satisfy the motors needs. So we measure more current then there actually is with VA. And also there is more current flowing then needed for the same amount of work to be done so you will still need larger wires with a poor PF value and you may actually have some resistive losses from more current draw. less current is sometimes needed for more efficiency and less losses. Also since reactive and real current draw are not in phase the real resistive current draw will need to work harder just to go against the opposition to supply itself.

They make true power meters(not to be confused with true RMS). They are on the highish side for pricing but not a whole lot for the model I purchased.

Finally, the audio section...Sorry for the boredom.

In this section I will start off by letting you know that power factor correction(opposing reactive device like a cap to cancel out) is not going to happen in normal musical setups however it may work for burp setups.

I will also go over typical misconceptions...

One misconception is that one can wire their subwoofers low to compensate for what we call impedance rise. A few things we must know before delving:

- there is a difference between Resistive and Reactive impedance a as we read earlier, just like for motors.

A subwoofer is a motor however it's physical parts like the spider, coil mass, and cone mass(total mass and spring) literally make the soft parts reactive devices themselves. The spider is a capacitor and the mass represents an inductor, analogously. In fact a speaker is literally a transformer, an electric to physical one. It is NO different then a typical electic electric one. The soft parts create reactance and they actually do oppose each other in reactance at resonance as can be viewed with a woofer tester plot.

If you look at the phase angle plot for resistance to reactance, at resonance for instance, a sealed box FB of a subwoofer system will show you that the reactive impedance and the resistance are in phase at resonance while it shows the phase increasing as you look before and after the impedance peak. This is because the impeadence is cancelled out between the inductive and capacitive reactance opposing each other equally.
So yes designing your box building it a given size actually directly decides where your reactance will be nulled out or where your peak resonance lies. So even though you would think the coil is the only thing to create reactance via induction, it actually really is upto the soft parts and this is proven by the fact that box size directly changes where reactances cancel out(where your peak lies). The inductive aspect of the mass lies on the right side of the peak where the higher frequencies are at and the capacitive reactance is on the left side, or the low-end. Why? Because on higher frequencies the mass of parts impedes quick speed like high frequencies require, and the spider is a spring so if the sub is moving back and forth slow, the spring of the spider gets in the way it has to go against the spring. The reason why higher frequencies don't have a problem with the spider is because those frequencies don't require far movement at all and the spiders are designed to not have any real spring resistance with shallow movement.

So, if the resonance in the middle is the canceling out of the two sides of impedances then why the hell is the impedance Always highest at resonance(sealed box)!? It is because a speaker is a transformer like I said earlier. A physical to electric one. Transformers basically flip current and voltage relative to the ratio on electric transformers, 200v primary, 100v secondary due to a 2:1 ratio for example. So the voltage halfs but the secondary side draws 2:1 current that the primary does. So say you have 10a on sec, well then the pri has 5a. So as you can see transformers can flip values from one side to another as long as power is the same.

With speakers, the impedance is highest at resonance but to the amp it is very easy to drive because the amp does not have to supply much current. Remember, V/R = I. So high impedance means the amp is not even producing much power however at that frequency the sub is easiest to move, it is most efficient because there is 0 degrees of phase shift between the parts, they get along with no impedance, physically thus, there is no reactance keeping the sub from moving easily. A flat system will be designed to where the peak resonance still produces the same db at resonance as other frequencies do. This part is all in the box and depends on box size or other parameters.

Last edited by Novicaine; 03-30-2014 at 03:42 PM.
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Old 03-30-2014, 12:29 AM
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Now that we got that out of our system, lets go over rise.

Two components of rise are:


We discussed these however, we should really go over the real world of what happens.

In the real world subwoofers warm up, in my experience I have found this to reeealy depend on the application. Spl subs, or daily subs seeing a whole lot of power especially now adays seeing all these giant beefy subs and cheap priced amplifiers will have a lot of what's called:

- Thermal compression

With thermal compression there is degrees of it. You can have an extreme of all out thermal compression where say you are feeding a poor sub 4kw RMS, if you feed it any more even if it can handle it without dying it does not increase in output because the resistance conversely increases as it gets hotter from more power added. A coil can only handle so much current after all. God for forbid it dosnt die first. So at this point you would be wasting money if you wanted a larger amp. In fact I should not even say that you are increasing power after thermal compression what you are doing is increasing voltage drive from the amp which ideally is supposed to increases power draw, but the power is not increasing.

Vdrive * current from sub = power output(well Apparent power anyway but this is irrelevant to the point)

Increasing Vdrive * propotionaly less current via impedance increase for trying to drive more juice to the sub(heat) = canceling out of increased voltage effect to cause more current draw.

This is how you increase power:

V*I=P So, if you increase V and keep I static then you get an increase, if you increase current flow but keep voltage static you get an increase of power aswell, if you increase both then you still obviously increase power. Now, if you increase one but propotionanly decrease the other by the same ratio then you gain nothing at all as far as power goes.

In audio, the amplifier is a constant voltage source meaning it is static it means if any of the other two values change the voltage will still remain the same. Ohms law tells us there is 3 components, V I R. It shows that if just one changes then only one other has to change. Power also changes with any variation in change. So anyway, we have the ability to change the voltage amplitude of the amplifier output. We do this by moving the volume knob at the Head Unit. This tells the amp to increase the output(literally, amplification). When we do this, the voltage applied to the speaker by the wires creates a current draw depending exactly on the impedance of the speaker/sub. Vdrive/Imp=I.

So with fully blown thermal compression, V increases,
But R also increases proportionally, not necessarily at the same ratio at all in fact there are plenty of degrees of thermal compression it can be very little depending on power and sub model or be full fledged where no more power is drawn.

Thermal compression is always around it just may be so negligible at little power levels however it realllly also depends on speaker model because different sized subs, perhaps built with tank-like parts may withstand and put to use a lot of power. This is all relative. A small 3" 10w speaker may compress at say 20w for instance. In SPL we see the very little gain by going from already great power, to more.

A lot of SPL guys always say: oh wire real low wire real low an here's the thing:

Reactance is all over the place and dynamic to the music. The q and Ts parameters are linked to the reactive impedance profile which is why the box size both dictates the q(resonance) of the system and the impedance profile.

Misconception, or misuse of term

Alot of competitors refer to their rise as a reactive load. This is wrong because we cannot really effect the reactive impedance in the first place it is the resistance which we have most trouble with and you will also notice that you cannot beat that either by wiring low. Also if you have a musical system it is much more impossible to try and lower reactance as you are effecting your sound quality, or response profile. Low-end bass, linearity across the line(flat) is linked with whatever reactive impedance you will see. Changing it directly changes the Q outcome, FB etc of the box design and in fact the only common and real way to change it is to change box size, go figure...We should all know beter, musical quality and overall response is linked to reactance. In spl burping you have a better posibilty of messing with reactance for a better outcome such as a smaller box but IME, since it's related to efficiency aswell you may be reducing efficiency while increasing power and you know by now how opposites cancel out, efficiency gives you more then more power will anyway because of more possible heat losses and changing reactance gains you very little if you take notes on a change. In other words the smaller box used may reduce the efficiency enough to where the reduction in impedance is not helpful. You may notice something at a higher frequency since upper end efficiency may increase but this is not due to reactance decrease anyway.

Resistive, thermal rise

We know how there are the two components, well, now were looking at compensation misconception for thermal rise aswell, at least to a point, and it is much more possible then messing with reactance.

As I wrote about power compression, this term thermal rise is caused by it, so most of it is already explained but a misconception is that wiring low helps. Well it can help however people who are already in the compression zone are wanting to do it the most it seems. If you are already thermally compressing because you already have like 5kw to one sub think about it: if thermal compression is the cause of heat from a lot of current flow and its basically saturated with current to where you cannot draw no more through the subwoofer's coil, wiring lower will simply cause an even lower threshold for compression. Say it compresses at 5k and you wire it lower so now let's say it's already i the zone at 4k now and with more power added you are def spinning your wheels on this one. I'd say its better to to choose one or the other, wiring low or more power not both if you are already up there in limits.

If you are on much less power and have some thermal rise already but not too much then you can wire a little lower. If you have no thermal rise at all practically and you wire too low you are going to be destroying your amp, straining it, protection etc. so on the flip side, thermal compression actually allows you to wire maybe one step lower due to a safely idle impedance(higher then normal due to thermal rise) well not long idles only short idling as it can cool off, but this really depends I mean idling as in between music notes, etc...

On to the quest of True power:

Ideally, RMS Voltage / Nominal impedance rating is actually a very simple way to get the True power . This is because resistance creates no reactance. Nominal is a resistive value and not reactive.

The reason why we cannot simply say hey this sub is going to be wired at 1 ohm nominal so with 100V measured from the Amp output we don't even have to measure anything else, 100v/1=100A so well have 10,000 watts. The thing is, with the resistive rise, the speaker will rest up at a higher resistance. So a test or something to determine the actual total resistance will be required.

Also, as I have told people before just because the power appears to be less doesn't mean it isn't "hiding". With speakers, they store energy it is a conversion from one form of energy to another, electrical to mechanical. So you cannot see it with a meter.

There are other calculations for true power and reactive however the easiest and most ideal method is to invest in a true power meter...should be more reliable then an invention We all have seen, the "amp dyno" since you can measure with a true subwoofer load hooked up and it will see the true power after thermal rise from an actual sub. The reactance figure from a sub may not be the true power but the subwoofer has it's own thermal rise profile depending on power going to it. A True watt meter will see the full resistance because the sub is connected and you can play the amp. Something like the amp dyno uses a predefined resistance and not an actual subwoofer for a thermal profile.

Last edited by Novicaine; 03-30-2014 at 04:17 PM.
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Old 03-30-2014, 12:35 AM
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my brain hurts now
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Old 03-30-2014, 12:45 AM
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Uhhh... wut?
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Old 03-30-2014, 01:03 AM
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Give us the Cliffs Notes version
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Old 03-30-2014, 01:14 AM
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I'm sure you put a lot of effort into that.. but I'm not going to read all of that most likely. ^^ cliff's notes would be awesome.

EDIT: or at least add headings for each section that are bolded to split it up.
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Old 03-30-2014, 01:21 AM
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Originally Posted by hotshot27 View Post
my brain hurts now
A lot of information at once. You should have read half now and half later.
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Old 03-30-2014, 01:53 AM
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cliff notes please.
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Old 03-30-2014, 03:17 AM
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It took me like 4 hours....I didn't format it good. Spelling errors...I hate using the iPhone lol I used it to write. Anyway there may be a lot but its quick to read IMO. Maybe it's just me...Ill write cliffs tomarow.

I ordered a true watt meter I can't wait to get it.
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