# Speaker Ohmage

September 13, 2005 2:02 AM Subscribe

What is the significance of the ohm value given on speakers? (ie. "400w at 4 ohm or 200w at 8 ohm")

An amplifier doesn't exist in isolation, there must also be a load. Typically this is a speaker, and it is assumed that the load of a speaker can be approximated by the DC series resistance across the speaker's terminals. However, along with a the power rating, a real amplifier has a maximum voltage and a maximum current. So, depending on the speaker's resistance, it may not be possible to drive full power into a given speaker.

In this case the amplifier is specified at 400W into 4 ohm to indicate that it can drive at least 10A at 40V, which implies a total delivered power of 400W (P=VI). Adding the "200W at 8 ohm" shows that the amplifier simply can't develop enough voltage to drive full power into an 8 ohm load. It is basically indicating that the maximum voltage for the amplifier is 40V (V^2/R=P --> 40V^2/8ohm=200W). Finally, by not specifying a power into 2 ohm they imply that the maximum current is 10A.

In practice speakers are not properly modeled by their DC series resistance. However, the DC resistance can be a moderately useful guide to the relative current requirement - a 4 ohm speaker will require about twice as much current as an 8 ohm speaker.

Of course peak sound output of audio amplifiers isn't really well specified by these numbers anyway. These numbers assume that the signal is constant, like a 120Hz sine wave, but music is anything but constant.

posted by Chuckles at 3:29 AM on September 13, 2005

In this case the amplifier is specified at 400W into 4 ohm to indicate that it can drive at least 10A at 40V, which implies a total delivered power of 400W (P=VI). Adding the "200W at 8 ohm" shows that the amplifier simply can't develop enough voltage to drive full power into an 8 ohm load. It is basically indicating that the maximum voltage for the amplifier is 40V (V^2/R=P --> 40V^2/8ohm=200W). Finally, by not specifying a power into 2 ohm they imply that the maximum current is 10A.

In practice speakers are not properly modeled by their DC series resistance. However, the DC resistance can be a moderately useful guide to the relative current requirement - a 4 ohm speaker will require about twice as much current as an 8 ohm speaker.

Of course peak sound output of audio amplifiers isn't really well specified by these numbers anyway. These numbers assume that the signal is constant, like a 120Hz sine wave, but music is anything but constant.

posted by Chuckles at 3:29 AM on September 13, 2005

Why did I assume you were talking about an amplifier... Anyway, the numbers on the speakers are simplying saying what the maximum rating of the connected amplifier should be, in order to protect the speakers from overheating.

posted by Chuckles at 3:36 AM on September 13, 2005

posted by Chuckles at 3:36 AM on September 13, 2005

An amplifier has an output resistance Rout. That means that it outputs a voltage, but the speaker is not the only thing connected to that voltage source, there is also a resistance in series with the speaker.

When you attach a speaker with resistance R, you have a voltage across the series coupling of Rout and R. The power that is dissipated in a resistance is equal to the voltage across it times the current that flows through it. You want as much power as possible dissipated in the speaker - that's the power that you hear as "OMPH!". To get a clue about why the two resistances must be matched somehow, look at two extreme cases:

1) If you connect a speaker with very high resistance, all the output voltage falls between the speaker terminals, but almost no current can flow, so very little power is dissipated.

2) If instead you insert a speaker with very low resistance, lots of current flows, but the voltage will not fall across the speaker, but across the much higher amplifier resistance, Rout. That's where all the power is dissipated, istead of in the speaker and in the amp is not protected, you risk burning it up.

There must be a middle ground somewhere, and if you do the maths, it turns out that the maximum power is dissipated in the speaker when it has the same resistance as the amplifier.

That's why you have ratings like the one given in the question: The amplifier is most effective with a 4 ohms speaker, because that's what it's internal resistance is.

posted by springload at 3:55 AM on September 13, 2005

When you attach a speaker with resistance R, you have a voltage across the series coupling of Rout and R. The power that is dissipated in a resistance is equal to the voltage across it times the current that flows through it. You want as much power as possible dissipated in the speaker - that's the power that you hear as "OMPH!". To get a clue about why the two resistances must be matched somehow, look at two extreme cases:

1) If you connect a speaker with very high resistance, all the output voltage falls between the speaker terminals, but almost no current can flow, so very little power is dissipated.

2) If instead you insert a speaker with very low resistance, lots of current flows, but the voltage will not fall across the speaker, but across the much higher amplifier resistance, Rout. That's where all the power is dissipated, istead of in the speaker and in the amp is not protected, you risk burning it up.

There must be a middle ground somewhere, and if you do the maths, it turns out that the maximum power is dissipated in the speaker when it has the same resistance as the amplifier.

That's why you have ratings like the one given in the question: The amplifier is most effective with a 4 ohms speaker, because that's what it's internal resistance is.

posted by springload at 3:55 AM on September 13, 2005

Where everyone has written

(Pet peeve,

posted by mendel at 7:22 AM on September 13, 2005

**resistance**above, substitute impedance, since audio signals are AC.(Pet peeve,

*moi*?)posted by mendel at 7:22 AM on September 13, 2005

Springload got it.. Impedance matching achieves maximum power transfer.

Mendel, it's not always wrong.. Maybe the circuit has no reactance :)

posted by rajbot at 9:27 AM on September 13, 2005

Mendel, it's not always wrong.. Maybe the circuit has no reactance :)

posted by rajbot at 9:27 AM on September 13, 2005

Audiofiles are nuts, and rarely know what they are talking about.

The speakers are listed as being 4 ohm or 8 ohm. This indicates that the speaker is a purely resistive load (which is an approximation, I'm sure).

If they said the speaker's load was (4+j0.1) ohms, then you would have to say impedance, not resistance.

Fore a purely resistive load, impedance and resistance are the same thing, even in an AC circuit.

posted by rajbot at 10:55 AM on September 13, 2005

The speakers are listed as being 4 ohm or 8 ohm. This indicates that the speaker is a purely resistive load (which is an approximation, I'm sure).

If they said the speaker's load was (4+j0.1) ohms, then you would have to say impedance, not resistance.

Fore a purely resistive load, impedance and resistance are the same thing, even in an AC circuit.

posted by rajbot at 10:55 AM on September 13, 2005

Pet peeve people: Introducing impedance adds more confusion than clarity. To return the nitpicking, power is not dissipated in a reactance. Resistance can be defined as the dissipating part of impedance, including power lost in the form of sound. The actual reactance is a stray value which is absent from the ideal speaker. Hence the speaker is, or is well approximated by, a resistance. Please don't change anything in my previous post.

posted by springload at 11:26 AM on September 13, 2005

posted by springload at 11:26 AM on September 13, 2005

...and of course, as rajbot points out, a single, real impedance value given without reference to a particular frequency is a resistance.

posted by springload at 11:31 AM on September 13, 2005

posted by springload at 11:31 AM on September 13, 2005

The speakers may be specified in terms of their DC resistance, but they sure as hell aren't simple resistive loads in reality. They are huge coils for christ's sake.

So you might be correct saying that "a speaker is specified as a 4 ohm load for simplicity" but to say that "a speaker is a purely resistive load" is 100% bs.

posted by Rhomboid at 12:20 PM on September 13, 2005

So you might be correct saying that "a speaker is specified as a 4 ohm load for simplicity" but to say that "a speaker is a purely resistive load" is 100% bs.

posted by Rhomboid at 12:20 PM on September 13, 2005

Guys, there is no impedance matching going on between amplifier and speaker. Maximum power transfer is a real idea - it occurs when the load resistance (impedance if you want pedants) is equal to the source resistance.

If the source and load are equal, the power dissipated in each will be equal. That means that you have to supply two watts for every watt that gets to the load - not too effective. Power supplies and amplifiers have very low source impedance in order to maximize efficiency, minimize the internal supply voltage and because it is easy to build them with really low source impedance, what with the very low on resistance of FETs and all that...

Now in audiophile circles they will talk about matching speakers with amplifiers, but this is a frequency response issue more than a load matching issue. It can also be do to the high inductance of certain speakers. Some amplifiers deal with the high inductance better than other amplifiers (is that really an also, or is it the same as frequency response... whatever).

posted by Chuckles at 12:52 PM on September 13, 2005

If the source and load are equal, the power dissipated in each will be equal. That means that you have to supply two watts for every watt that gets to the load - not too effective. Power supplies and amplifiers have very low source impedance in order to maximize efficiency, minimize the internal supply voltage and because it is easy to build them with really low source impedance, what with the very low on resistance of FETs and all that...

Now in audiophile circles they will talk about matching speakers with amplifiers, but this is a frequency response issue more than a load matching issue. It can also be do to the high inductance of certain speakers. Some amplifiers deal with the high inductance better than other amplifiers (is that really an also, or is it the same as frequency response... whatever).

posted by Chuckles at 12:52 PM on September 13, 2005

*Resistance can be defined as the dissipating part of impedance,*

**including power lost in the form of sound**.i'm sorry, but this is absolutely misleading information and the part in bold is totally and completely flat-out wrong.

impedance is a complex value; it has a real part and an imaginary part. the real part DOES reflect the dissipative losses - that is, the coil heating due to current flow.

the imaginary part represents the reactance, which has both capacitive and inductive components. in a speaker, the capacitance is negligible, and the inductance dominates.

any time you pass current through a loop (such as in the coil of a speaker) a magnetic field is induced along the coil's axis. a high inductance means that much of the kinetic energy of an alternating-current signal near the resonant frequency of the circuit is stored in the magnetic field.

if you introduce a permanent magnet near the coil, there will be an attractive or repulsive force between the coil and the magnet, depending on the orientation of the coil and magnet. if the coil is attached to a paper cone, this will drive a pressure wave in air, which carries away some of the energy stored in the coil's magnetic field.

that energy comes from magnetic coupling through the coil to the current source. to the circuit this looks like an entirely inductive load. yes, the energy is ultimately dissipated and entropy increases, but that happens away from the circuit.

rajbot's right. i'm all for being helpful, but if you don't know what you're talking about, don't spread confusion by acting like you do. resistance CAN also be defined as cowshit on the moon, or betty grable's dentures, or two guys with fezzes, but unless you use the same definitions as everyone else, you'll make an ass out of yourself when you open your mouth.

posted by sergeant sandwich at 1:36 PM on September 13, 2005

*Guys, there is no impedance matching going on between amplifier and speaker.*

WTF?

The maximum power transfer from an active device like an amplifier to an external device like a speaker occurs when the impedance of the external device matches that of the source. That optimum power is 50% of the total power when the impedance of the amplifier is matched to that of the speaker.

posted by rajbot at 3:03 PM on September 13, 2005

sergeant sandwich is completely correct. The effective output resistance of the amp is milliohms, because of negative feedback. The amplifer is close to an ideal voltage source.

The part about matching impedance is relevent to RF.

posted by Rhomboid at 3:25 PM on September 13, 2005

The part about matching impedance is relevent to RF.

posted by Rhomboid at 3:25 PM on September 13, 2005

sergeant sandwich and Rhomboid:

Reactance is the "opposition to current flow without the dissipation of energy”, per definition. I shouldn't say resistance "can be defined" but "is defined" as the power dissipating part of impedance. How and where the energy eventually turns into heat is irrelevant, the key is that the resistance is what causes losses to the system. May I ask, what is your definition of resistance?

Like you say, the movement of the paper cone carries away some of the energy from the magnetic field. To say that it happens “away from the circuit” is just stupid. The impedance of the speaker is highly dependent on the mechanics – try muting one and measuring the impedance over a frequency band. The result will be entirely different from when the cone is free to move.

It is by returning previously stored energy to the circuit that an inductor may alter the phase of a signal. For sure, not all the energy is converted to sound, which means there is stray inductance, but that is a nonideality. If speakers could be built so that all the magnetic energy produced in the coil was converted to sound, it would be completely resistive from a circuit point of view.

Now, if you want to discuss this further, keep it civil. I know what I’m talking about and you seem to be ranting without thinking the physics through.

posted by springload at 3:34 PM on September 13, 2005

Reactance is the "opposition to current flow without the dissipation of energy”, per definition. I shouldn't say resistance "can be defined" but "is defined" as the power dissipating part of impedance. How and where the energy eventually turns into heat is irrelevant, the key is that the resistance is what causes losses to the system. May I ask, what is your definition of resistance?

Like you say, the movement of the paper cone carries away some of the energy from the magnetic field. To say that it happens “away from the circuit” is just stupid. The impedance of the speaker is highly dependent on the mechanics – try muting one and measuring the impedance over a frequency band. The result will be entirely different from when the cone is free to move.

It is by returning previously stored energy to the circuit that an inductor may alter the phase of a signal. For sure, not all the energy is converted to sound, which means there is stray inductance, but that is a nonideality. If speakers could be built so that all the magnetic energy produced in the coil was converted to sound, it would be completely resistive from a circuit point of view.

Now, if you want to discuss this further, keep it civil. I know what I’m talking about and you seem to be ranting without thinking the physics through.

posted by springload at 3:34 PM on September 13, 2005

*The effective output resistance of the amp is milliohms, because of negative feedback.*

Sigh.

I'm outta here.

posted by rajbot at 3:47 PM on September 13, 2005

*in a speaker, the capacitance is negligible, and the inductance dominates.*

This isn't quite right; look at the impedance plot of an average two-way speaker and you'll see capacitance in the octave or two above system resonance (impedance decreases as frequency rises). Above that, it usually flattens out for a bit and then the woofer's voice coil inductance starts to influence things.

In any case, the resistive component almost always dominates; impedance phase angles exceeding 45 degrees are rare (and very bad news for amplifiers).

*If the source and load are equal, the power dissipated in each will be equal. That means that you have to supply two watts for every watt that gets to the load - not too effective. Power supplies and amplifiers have very low source impedance in order to maximize efficiency, minimize the internal supply voltage and because it is easy to build them with really low source impedance, what with the very low on resistance of FETs and all that...*

This is correct. Check the ouput impedance on a standard solid-state power amp- they may not be milliohms but a fraction of an ohm is commonplace. The exception to this is low-power tube amplifiers with output transformers.

posted by the duck by the oboe at 4:56 PM on September 13, 2005

rajbot, I am an electrical engineer. Do you want me to quote my textbook from undergrad that supports what I just said?

posted by Rhomboid at 12:13 AM on September 14, 2005

posted by Rhomboid at 12:13 AM on September 14, 2005

To address the original question again: I stand corrected about speaker impedance matching. That appears to be a thing of the past.

posted by springload at 1:23 PM on September 14, 2005

posted by springload at 1:23 PM on September 14, 2005

This thread is closed to new comments.

posted by gaby at 2:39 AM on September 13, 2005