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There is an enclosure in our product line that we have been making for twenty years called, the FH-1 low frequency enclosure. We use a four ohm loudspeaker in this enclosure; however, as long as the enclosure is operated above its cut-off frequency of 60 Hz, the actual load impedance that the power amplifier sees is nominally eight ohms. Likewise, we use a four ohm loudspeaker in the Mid bass horn of HDH-4 and HDH-1 speaker enclosures. As long as these horns are operated above their cut-off frequency of 300 Hz, the midbass of the enclosure will exhibit an eight ohm load to the amplifier.

The mechanical loading of the loudspeaker by the horn makes an impedance transformation so the amplifier sees a load impedance of 8 ohms within the horns operating bandpass. I mention the horn's operating bandpass because if you operate any horn below its cut-off (-3 dB down point on the low frequency portion of its response curve), the driver reverts back to its original lower impedance. As long as you send horn loaded enclosure frequencies that are above the cut-off, the system will offer a higher load impedance to the power amplifier.

The DC resistance of the loudspeakers discussed above is 3.2 to 3.8 ohms. Mounting the loudspeaker on a horn doesn't change the DC resistance, but a power amplifier driving that horn will see a load impedance that is more than twice that of the nominal four ohm impedance of the individual speaker. Hopefully some of us now understand how a four ohm loudspeaker can become an 8 ohm loudspeaker system when mounted on a properly designed horn.

I had mentioned earlier a situation I discovered in Africa where a technician had a basic understanding of impedance, but he didn't understand how horn loading can change the impedance of a loudspeaker. We used to have a low frequency enclosure called the FH-2. This enclosure had two four ohm loudspeakers wired in parallel within a folded horn. Since each of the loudspeakers was loaded by the horn, the individual loudspeakers were mechanically raised to eight ohms. Therefore, in parallel the two equivalent eight ohm speakers offered a four ohm load to the amplifier when operated in its designated bandpass 60 Hz - 400 Hz.

The technician thought he was correct and that perhaps the manufacturer had goofed. So he wired what he thought were two four ohm loudspeakers in series, thinking that he then had an eight ohm load for the power amplifier. However, since these were horn-loaded speakers, he actually changed a four ohm enclosure into a sixteen ohm enclosure. He changed them from two horn-loaded eight ohm speakers that were mixed in parallel to two eight ohm loudspeakers wired in series that now offered a sixteen ohm load for his CS-800 amplifier. So instead of the CS-800 producing 400 watts into 4 ohms (200 to each speaker), it produced only 100 Watts (50 watts to each speaker). Now not only did he have a 6 dB loss in SPL, he totally destroyed the damping or control capability of the power amplifier by reducing his potential damping factor from a rating of 200 to that of 0.5. More on Damping Factor later.

Perhaps now that you have further insight into complex impedance, you may also agree that when misinformed people try to "out think" the manufacturer of a loudspeaker system, they more often than not have their own foot crushed by the wheel that they are trying to reinvent.

I mentioned that loudspeakers should not be wired in series for sound reinforcement applications. And it was all right to wire them in parallel, but that they should each have their own pair of speaker cable leads and be wired in parallel at the output terminals of the power amplifier. This is the professional way of wiring loudspeakers in parallel. All loudspeakers generate a back voltage due to the motion of the voice coil within the magnetic field of the voice coil gap. This is referred to as a Back-EMF or backward-electro-motive-force.

Sir Issac Newton said that for every action there is an equal and opposite reaction. If you would take a fifteen inch Black Widow loudspeaker and hook its terminal up to the input of an oscilloscope and slap the cone abruptly with the palm of your hand, you could cause a voltage to be displayed on the scope greater that 80 volts peak to peak, 40 volts peak, or about 28 volts RMS.

If two loudspeakers are wired in parallel within an enclosure at a distance from the power amplifier, each speaker creates a back-EMF that causes low frequency cancellation as these voltages are out of phase with the incoming signal. When the two loudspeakers are wired in parallel at the output terminals of the power amplifier, the very low internal output impedance (source impedance) of the amplifier (typically 0.02 ohms) acts as a shunt or near short circuit to the back-EMF voltages.

I mentioned Damping Factor earlier and I wanted to wait until I discussed Source Impedance before I covered it more thoroughly.

Up until now I have been talking about the impedances offered by the loudspeaker load on the amplifier. The loudspeaker load impedance is often referred to as the output impedance of the amplifier; however, it is more correct to call this the amplifier load impedance. This is because amplifiers have an internal output or "source impedance."

The ratio of the source impedance to the load impedance is the amplifier's Damping Factor rating number. The damping Factor number can be obtained by dividing the loudspeaker load impedance by the internal output or source impedance of the power amp. A typical power amplifier source impedance is 0.02 ohms. If I were to divide an 8 ohm speaker load by 0.02 ohms, I would have a Damping Factor number of 400.

As you can see the impedance of the load affects the damping factor of the amplifier. The same amplifier would have a damping factor of 200 into a four ohm load (4 / 0.02 = 200).

The damping factor is the ability of the amplifier to control the loudspeaker load. Another word for control is regulation. The control of the load is a function of the ability of the power amplifier's regulation of the load. If you have a precise millivolt scale on a digital voltmeter, you can calculate the percentage of regulation by measuring the output voltage of the amplifier without a load (open circuit), then place the load resistance value on the amplifiers output and measure the voltage. It will have dropped a very small amount.

If you then take the No Load Voltage and subtract the Full Load Voltage from it, and then divide that number by the Full Load Voltage, you will have calculated that amplifier's percentage of regulation. If you now take the reciprocal of that percentage of regulation, you will have the Damping Factor rating number of that amplifier into that load value.

NLv - FLv / FLv = % Regulation

1 / % Regulation = Damping Factor

or DF = 1 / (NLv - FLv / Flv)

Note: You can't really measure Damping Factor at full power because that amplifier will not be able to maintain its regulation, but as an example let's say you are measuring a CS-800X into an eight ohm load with 6 dB of head room. Your open circuit (NL) voltage is measured at 20 volts, you place an eight ohm load in the circuit (you better use a dummy load or a speaker will be awfully loud), then you measure a (FL) voltage of 19.95 volts, your math would now be:

20 - 19.95 = 0.05 / 19.95 = 0.0025

% of Regulation would be .25%

The reciprocal of 0.0025 = 1 / 0.0025 = 400

DF = 400

Source Impedance (Z source) would then be calculated from an inversion of the previous formula for damping factor (DF = Z Load / Z Source) would now become:

Z Load / DF = Z Source or

8 / 400 = 0.02 ohm Source Impedance

This, ladies and gentlemen is what damping factor is all about. Remember the resistance of the load affects the amplifier's ability to control its load. We have all heard that the professional method of loudspeaker cable connections in audio is use to a heavy gauge cable and the shortest possible cable run. Losses in loudspeaker cable runs are due to the friction, or heat, caused by the high level of electron current flow. Most manufacturers provide an American Wire Gauge (AWG) ## 18 in a 25 foot length as a standard loudspeaker cord. But the electrons flow back and forth in a 50 foot circuit. The speaker wire itself opposes current flow because it has a resistance value.

Let's use an example of an 8 ohm loudspeaker connected directly to the output terminals of a power amplifier:

102 � 8 = 100 � 8 = 12.5 watts

Now let us suppose we are practicing very poor audio and have a loudspeaker connected at the end of 153.6 ft of ## 18 gauge copper wire. AWG ## 18 wire has a resistance of 6.51 ohms per 1000 ft (1000 / 6.51 = 153.60), which means that 153.6 ft of ## 18 copper wire will have a resistance of 1 ohm. Since a loudspeaker wire has two conductors, there would actually be 2 ohms of resistance in series with an 8 ohm speaker connected via 153.6 ft of two conductor AWG ## 18 copper wire. Now our power amplifier looks out at the load and sees the 2 ohms of wire resistance, in series with 8 ohm loudspeaker impedances. So the load is now actually 10 ohms instead of 8 ohms.

102 � 10 = 100 � 10 = 10 watts

At first glance you may say that you are only losing 2.5 watts (which is a 20 percent power loss). However, you are actually losing 36% power. Of the 10 watts now produced by the amplifier, 2 watts is dissipated in the wire, while only 8 watts gets to the loudspeaker.

If you think this is not cool, let's examine what this would do to the amplifier's ability to control or dampen the loudspeaker load. The loudspeaker actually sees the 2 ohms of wire resistance in series with the amplifier's internal output or source impedance. So instead of a Damping Factor of 400, you would have:

DF = Load Z / Source Z

DF = 8 ohm / (.02 + 2 ohm) = 8 / 2.02 = 3.96 DF

We started out with a potential damping factor of 400 and because of our poor choice of 153.6 ft of wire, we have destroyed the amplifier's ability to dampen or control the loudspeaker load. Can you see now why those who know, employ the professional method of putting the power amplifier as close to the loudspeaker system as possible and then use the heaviest gauge wire that will fit the loudspeaker connector. If you haven't been doing this, you need to start, as you are no longer ignorant regarding the importance of damping factor.

Before I give up on damping factor, I would like to make one more point. In the above example I stated that the source impedance of a CS-800X was .02 ohms; therefore, the DF was 400 when driving an 8 ohm load. Well, I don't usually promote products in a paper intended to educate the customer, but I just must make an exception. Beginning with our recently introduced power amplifier model CS-800S, we have included circuitry (patent applied for) that automatically maintains a high damping factor. This is really an ingenious and simple circuit that our chief of analog engineering, Jack Sondermeyer, came up with.

There is a circuit that measures the small change in output voltage when the load impedance changes, and through a feedback network, the circuitry maintains a constant output voltage as the voltage neither increases or decreases with a change in load impedance. You can almost think of it as a negative source impedance so the Damping Factor remains high. It is still affected by the resistance in the wire, so you still would be wise to practice the professional method of short runs and heavy duty loudspeaker wire. The CS-800S amplifiers coming off of our production line at Peavey consistently spec out at greater than 2000 DF, and that is only because that is the highest number our system can measure.

This paper is on Impedance, and in the course of this paper's unfolding I segued into source impedance and used it as a means of explaining damping factor. Source impedance also applies when you are interfacing components within the audio system. With loudspeakers, we are trying to match the loudspeaker load impedance to the output of the power amplifier to obtain maximum power. When we are only trying to transfer signal from one device to another within the audio chain, we are not trying to accomplish any work, so we are not trying to produce significant levels of current. We are just trying to pass or transfer the audio signal. There is, of course, current flow, of course, current flow, as electrons are moving back and forth, but the intention is to pass the signal as a voltage and not produce high levels of current and power. However, each signal processor in front of the power amplifier sees the input impedance of the next device as a load on its output.

Years ago, during the Jurassic period of audio, they attempted to transfer audio signal into 600 ohm loads. This is no longer valid today. The typical input impedance of a modern power amplifier is 20,000 ohm or 20 k. However, the internal output impedance (Source Z) of audio devices can be anywhere from 50 ohms to 2,000 ohms. In order to transfer the signal without introducing major deviations in level and frequency response, the Source Z to Load Z should have a ratio of 10:1; some people accept 7:1, but I hold to the 10:1 ratio.

The source impedance is often overlooked by the non-technician sound system operator. Ignorance may be bliss, but getting bitten on the behind is not pleasant. There are many signal processors, equalizers, and crossovers that do an adequate job in certain applications, but these same devices can cause many problems when the source-to-load impedance becomes reduced.

The best and first example I am going to use is in interfacing a number of power amplifiers in larger systems. There is a limit to how many power amplifier inputs can be paralleled. The limit is determined by the source impedance of the mixer output, the equalizer, or the electronic crossover.

Using the math associated with Ohm's Law, we can calculate what the load impedance will be when we parallel power amplifier inputs. Two 20,000 ohm inputs in parallel becomes a 10,000 ohm load to the signal source. Dividing the input Z by the number of amplifiers whose inputs are in parallel will give the resultant load Z that the signal source sees. Thus ten power amplifiers with their inputs in parallel would be 20,000 ohms divided by 10, or 2,000 ohms.

This means that if the internal output or source impedance of the signal source were 200 ohms, we could successfully transfer the electrical audio signal with no problems. But if the Source Z were 330 ohms we would be below the stated 10:1 Z ratio.

In large scale professional audio it is very important to consider the capability of products to drive long lines and/or loads that represent multiple impedances in parallel. There are many mixers, equalizers, and crossovers that are priced economically, and they work fine in certain simple applications. These products can present problems in large systems, however.

If you want to know how many power amplifiers can be driven by a signal source, multiply the internal output impedance of the source by 10, and divide the result into the source impedance of the power amplifiers. For instance, in our product line we have two series of graphic equalizers, the EQ series and the Q series. The EQ series exhibits a 75 ohm source impedance while the less expensive Q series has a 330 ohm source impedance.

75 x 10 = 75020,000 / 750 = 26

330 x 10 = 3,33020,000 / 3,330 = 6

You can now see that a Peavey EQ-31 can drive 26 CS amplifiers with their inputs in parallel, while the Q series could only drive 6. Thus, in applications such as small systems, the Q series could do a fine job, but there is a limit and now you know the boundaries.

I know of one mixer manufacturer that has a source impedance in their mixer's channel inserts of 1,000 ohms. This is not a real problem if you come out of the mixer with a five to eight foot shielded signal patch cable to interface some processor. But there are many users of this product that have them in studios where the inserts are permanently wired through lengthy cable that is run beneath the floor across the studio to a patch bay. They don't realize that the mixer channel is now rolling off the high frequencies significantly because of the capacitance of the cables and the high source impedance.

The cable itself becomes a low pass filter. The amount of high frequency roll-off is determined by the value of the source impedance. You can find the point where the frequency begins to roll off by taking reciprocal (1/X) of the source impedance (R) times the capacitance (C) in the cables, 1 / (R x C). Let's say, for example, that the cable is long enough to offer 0.2 mfd of capacitance (a microfarad is mathematically 0.000,001 farad).

1 / 100 x 0.000,000,2 = 1 / 0.000,02 = 50,000 Hz or 50 kHz

1 / 1,000 x 0.000,000,2 = 1 / 0.000,2 = 5,000 Hz

The signal processor hooked up to the mixer with an insert with a 100 ohm source impedance would pass signals out to 50 kHz, while the mixer with the 1,000 ohm source impedance in its insert would have significant roll-off above 5 kHz.

We have come to the end of this lengthy paper on Impedance. I believe we have pretty much thoroughly covered the subject. Some of the things I just shared with you took me fifteen years or more to understand as I now do. I don't know about you, but I am still learning. If you are learning, you are growing. When you stop growing you cease to produce quality.

Below, you�ll find a chart relating source-to-load impedances and the number of amplifiers that can be driven with the inputs wired in parallel. There is also a chart on loudspeaker wire.

(in ohms) 1 K ohm 2 K ohm 10 K ohm 20 K ohm
75 1 2 13 26
100 1 2 10 20
330 0 0 3 6
1000 0 0 1 2
2000 0 0 0 1

Copper Wire Guage
AWG## Dia
22 25.35 0.6438 642.4 0.000504 0.33 18.52 60.75 3    
18 40.30 1.024 1624 0.001276 0.82 46.8 153.6 5 150W 10 Ft
16 50.82 1.291 2583 0.002028 1.31 74.47 244.26 7 280W 15 Ft
14 64.08 1.628 4107 0.003226 2.08 118.4 388.35 9 400W 25 Ft
12 80.81 2.053 6530 0.005129 3.31 188.3 617.7 12 800W 40 Ft
0 101.9 2.588 10380 0.008155 5.26 299.5 982.32 17 2,000W 65 Ft

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