IMPEDANCE IN AUDIO TECHNOLOGY(cont.)
WHEN FOUR OHMS IS NOT FOUR OHMS
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.
ARE YOU READY FOR MORE?
I mentioned Damping Factor earlier and I wanted to
wait until I discussed Source Impedance before I covered it
more thoroughly.
SOURCE IMPEDANCE
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.
WE ARE NOT DONE YET!
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.
| SOURCE
Z |
LOAD
IMPEDANCE |
| (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
mils |
Dia
mm |
Cir
mils |
Square
inches |
Sq
mm |
Meter/
ohm |
Feet/
ohm |
Audio
amps |
Max
pwr |
Length
DF<50 |
| 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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