Speaker Impedance

The Impedance rating of a speaker attempts to simplify something that isn't.

The important thing is to use a speaker that matches the capabilities of the amplifier.  Too little impedance and the amp may be working to hard.  To high of an impedance and the amp will not be able to adquately drive the speaker.

More information.

Lemme take a stab at

Lemme take a stab at explaining speaker impedence interaction with amplifiers.

First, the equation for power (in watts) is  P (watts) = V (volts) x I (amps)

So, if you have 10volts and 0.5 amps you've got 5 watts.  5 watts where?  If we connect a resistor of 20 ohms (ohms are the unit that specifies how much an electronic/electric item resists letting electricity flow through it) across that 10V power supply we can use another formula, Ohm's law (named for the guy who figured this out who's name happened to be Ohm)    I (amps) = V (volts) / R (resistance in ohms).

In other words, if you double the voltage the current flow will double. If you double the resistance the current flow will be cut in half. Now back to that 20 ohm resistor across our 10 volt power supply.

   I (amps) = 10 volts / 20 ohms = 0.5 amps

We're assuming for the sake of computational ease that the wiring involved has negligible resistance. Now back to the power equation. It's that 20 ohm resistor that has having 5 watts disapated across it. That is, those 5 watts are released as heat in the resistor and if the resistor isn't rated at least 5 watts (which is physically a pretty large resistor btw) it's going to get exceedingly hot, possibly to the point of glowing red (briefly) and then burn out.

What does this have to do with speakers and amplifiers? How much power can an amplifier with a maximum voltage of 12V (a constraint of our DCC powered amplifiers) deliver into an 8 ohm speaker?  How about into a 4 ohm speaker? We'll treat the speaker as though it were a resistor connected across a voltage source (of course the amplifier is delivering a rather uneven AC (alternating current) waveform rather than DC)

Let's do a little high school algebra.  Since the power equation is

P = V x I

lets substitute ohms law

I = V / R

into the power equation

P = V x V / R = V² / R

From this you can see that an amplifier (under ideal conditions) can deliver TWICE the power into a 4 ohm speaker versus an 8 ohm speaker.

So why don't we use 1 ohm speakers and *really* get the power delivery up there?

Well, it's not so simple. ALL voltage sources have what's called an internal resistance. As the current being delivered from that voltage source rises so does the voltage being dropped over that internal resistance.

This internal voltage drop has two obvious effects

1) The amplifier starts getting hot because it's dumping a larger and larger portion of its power into itself.

2) As the voltage drop inside the amplifier rises, the voltage available externally to drive things like reisistors or speakers goes down.

Remember the revised power equation?

P = V² / R

The power available from an amplifier will drop as the square of the reduced output voltage. If the speaker impedence goes too low the extenal voltage available becomes what we might call 'feeble'. AND much of the power produced by the amplifier is used to heat itself up instead move a speaker around.

The amplifier manufacturers therefor specify a range of impedence for which the amplifier is best suited in terms of impedence matching.

But wait! There's another reason not to drop the speaker impedence too much.  A parameter of audio amplifiers that isn't much talked about is "damping factor". Lemme try to explain this.

Remember that speakers are electromagnetic devices (at least their voice coils are). When current flows through the voice coil in the speaker it generates a magnetic field which contends with the magnetic field of the fixed magnet in the speaker causing the voice cone to move which produces sounds.

One thing about electromagnetic devices, when they're not acting as a motor (electriciy in creates physical movement out), they can act as a generator (physical movement in causes electricity out).

Remember inertia? It's one of Newton's basic laws of motion. Simply put, an object at rest tends to stay at rest (not moving) and an object that is in motion will tend to remain in motion at the same velocity and in the same direction. This assumes no outside forces acting on the object.

How about our speaker's voice coil and cone/diaphram?  Once the amplifier generates voltage/current the voice coil will start to throw. Then the audio waveform being amplified changes perhaps going negative instead of positive. But the speaker, being made of materials with some mass will want to keep moving in its original direction. Here's where the damping factor comes in.

Once the speakers inertia/momentum has the voice coil over throwing that speaker becomes a generator and is creating electricity.

Remember now, that the amplifier has internal impedence (resistance)?  The speaker will be driving that internal resistance. If the amplifiers internal resistance is very low (a good design goal for amplifiers btw) the speaker will have it's inertia/momentum bled off by doing work to heat up the internal resistance of the amplifier.

The higher the speakers impedence in relation to the amplifiers internal impedence the more the "damping" factor on extracurricular speaker movement. So for this purpose a 16ohm speaker is better than an 8 or a 4 ohm speaker.

How much does damping factor matter? With hi-fi speakers attached to powerful amplifiers in your dolby-surround stereo system it does matter. In the lower frequencey ranges where the moving parts of the speakers have significan mass it matters a lot. But for the dinky little speakers in HO (and dinkier speakers in N) scale equipment I'm not sure the difference is audible.

Ok, this got pretty long (again) and I'm sure you physics majors out there will point out a bunch of places where I used the word "inertia" improperly, etc. The reference Blue posted is also quite correct in that a speaker has different impedences at different frequencies. But for our purposes we don't really need to worry about this.

But I think this helps explain why the manufactureres of amplifiers provide a range of speaker impedences to which their amps are best suited. Going lower than that reduces power delivered to the speakers and causes the amplifier internals to heat up more. Going above that range reduces power because the amplifier doesn't have the voltage needed to drive the higher impedence speaker to max output (think of trying to start a car in 3rd gear).

Hope this was helpful instead of confusing Jeff.

Charlie

So....

So, since the guys at Loksound said that the Select would work with both 8 and 4 ohm speakers, the 8 ohm is a better idea for the dampening factor although the 4 ohm will take less power to make the noise?

Information overload!

Some of us might want to stick to the oversimplified water pipe vs water pressure analogy...I know I do. )

In Jeff's case either the 4 Ohm or 8 Ohm speaker will work fine.  Based on Charlies thesis, I might pick the 8 Ohm speaker over the 4 ohm, but given the application, I can't see that it matters in the least.

Good refresher on speaker impedance as it applies to high fidelity audio!  Could you explain root mean square now?

If I'm understanding correctly

What Lok-sound is saying is that their amplifier requires a minimum of 4 ohms impedence and a max of 8 ohms.  Is that right?

The lower the Ohms the more power

I did work for Infinity Systems back in the early 80's in the research and development dept and at that time they had 18 inch 2-Ohm speakers that could cause your heart to stop if you were in the sound room while we tested them because of the ultra Low Impedance.

Dan

Hi or Low and small speakers

Well, I for one would be very interested to "hear" the difference between the 4 Ohm and the 8 Ohm HO sized speaker.  If the 4 Ohm speaker is going to provide much lower frequency response then that would be the one to choose for a locomotive.

Because we are talking about such tiny speakers though, I have doubts as to whether the difference will be audible, let alone noticeable.

How about a sound comparison?

I don't have any 4 Ohm

I don't have any 4 Ohm speakers to make the comparison. Let me give you a small comparison if you look at Scarpia's Blog Converting an Atlas S2 to DCC sound. in his case were talking about reflect responce or the Changing of the sound by simply putting the speaker into an Enclosure designed for it. Before The speaker was in the enclosure it was dull and not real loud but once in the little box that little speaker got alot louder and deeper in sound. Now the system Jeff is using has the ability to use either a 4-Ohm or 8-Ohm speaker in it. The difference will not make it sound like a 18 inch woofer but using a 4-Ohm speaker will make enough of a difference that it will be noticed by the human ear and from what I've seen of sound in Model Railroading every little bit helps. The only way your going to hear the difference is if Jeff buy's an 8-Ohm & a 4-Ohm speaker and swaps them out and makes a video set like Scarpia did showing the comparison.

I would use the 4-Ohm if I were Jeff just for the difference of the deeper sound the lower Impedance will produce and the fact the system can use the 4-Ohm speaker is a major factor.

Now it's up the Jeff to chose

Dan

Speaker sound

Dan,

In the case of Scarpia adding an enclosure to the speaker, of course this made a vast difference to the low end frequency response and clarity.  I don't have to explain the effects of the waves from the rear of the cone canceling sounds coming from the front, to a guy who worked for infinity!

I wasn't suggesting you do the test.  I was hoping Jeff might feel inclined to try both and see what the sound difference between the two really is.

I still question how much actual sound difference the 4 ohm over the 8 ohm speaker will make under these circumstances but there is only one way to tell, try them both.

Buying more speakers

Since I'll have two locomotives to play with, I just might equip one with 4 ohm and one with 8 ohm speakers. I suspect I may have to watch the interview I did with Loksound to see exactly what they were/are recommending.

But I stil don't know how big those speakers are...