R-C Filter Calculator - Capacitor As Main Component Crossovers CAMCC
Voltage And Current Drive and Compression Driver Protection Capacitors
This Audio Crossover Calculator would not be complete if we did not provide a history of public
address systems, and the transition from 70 volt systems to more MODERN ones. But as you read this, remember that MODERN is not the same class as DECO, and
that OLD SCHOOL does not always rise to the top of the 'visible' marketing pile like New Wave or Techno-Rap big box retailing does.
However, there really is a LOT of diverse technologies involved. Calculating a first order filter, that is,
a single capacitor for unbalanced one line driven (Or 2 lines driven Balanced with 2 caps),
may appear at first glance to be a trivial task. However, because we sell an amplifier
that does both voltage and current drive, this turns out to have a longer story to the tale.
You can think of transducers as falling into one of three general catagories:
1) High impedance transducers i.e. compression drivers
2) Medium impedance transducers i.e. paper cone lightweight moving coil
3) Low impedance transducer i.e. auto, 2 and 4 ohm, plastic cones
They all seem to have approximately equal impedances Z - 16, 8, 4 (or DC 14,6.4,3) the nominal by law being within 20% actual.
Actually the're intended to match up to very different output impedances. The automobile system speaker would be more full range,
hence the plastic cone to avoid loses of paper when the center of a paper cone is at high frequency at the same or immediately before
or after a low note has sounded. In the low impedance coupled speaker, the output impedance must be below the speaker, that is
if a capacitor or C/O network is not placed between amp' and speaker. Large magnets may be found on low Z speakers for more voltage feedback.
Likewise a high impedance output is intended for use with a transformer, which allows the opportunity to balance the poles, and which
allows extreme small high frequency movement oscillation by way of driving two wires in opposite poles and using the transformer as isolation so that
the voltage generated by the moving coil does not feed back into the output and then the input (Neg FB) of the amplifier, just the opposite of low Z transducers.
The low Z type is intended for an active, more sophisticated or modern, solid state system that senses the feedback voltage from the voice coil.
The high impedance (Z) type, like the low, are assumed to exist as an independent target, without other secondary transducers to consider.
The medium impedance transducer is optimal for tube type amplifiers which historically could drive multiple speakers down to a chain
in parallel of 2 or 4 eight ohm transducers in parallel or more 16 ohm transducers in series and or parallel.
While a tube amplifier may have used low output impedance to control speakers, it could also us capacitive coupling
or invent a more exotic feedback control system more like those seen on today's modern solid state amplifiers.
Compression drivers come in one or two inch size of voice coils. In each size the customer
can choose to replace an existing 8 ohm coil with a 16 ohm one, and vice versa. The 16 ohm
diaphgragm has some advantages similar to the advantage of 2 inch over 1 inch size coils.
That is, the lower end of the spectrum from 500 to 1800 hertz is reproduced with less distortion
and more harmonics. It results in a 'fatter / flatter' overall curve and no gap between a large speaker
that for instance, in 18 inch, begins to cancel out frequencies above 500 hertz.
There is also a time versus applied power tradeoff - but we may not have any time or space
to even begin to cover that - the calculator gives at least some adjustment based on magnet weight.
The older 70 volt public address systems were standardized for tube amplifiers. A solid state amplifier
can be either voltage or current 'drive', but tube amplifiers, depending on the feedback type,
tended to use voltage 'driven' into higher impedance 'loading'. This is a generalization like saying that
car amplifiers use 4 ohm low impedance, partly because as the impedances fall lower in a
voltage driven system by adding tweeters, the power supplied falls off very exponentially.
And they increase exponentially if the loading is changed to higher impendances also making precise contol difficult.
Thus, desiging a low ohm speaker to begin with limits the possible sound system degradation.
Furthermore, because initial
current always increases at a rate of V/L the lower inductance L offers more headroom.
That is why a 16 ohm voice coil in compression drivers really should be crossed over at lower F than an 8.
I will start simple to help those follow some of this, but it becomes more complex as we go.
The long distance lines of older PA systems needed step up and step down transformers, both
for noise reduction and to keep limited the loss of voltage (and hence current) over long speaker
to amplifier distances. So, a transformer had multiple taps for different 'Wattage' loads.
The load is just the calculated result of one speaker plus others getting the feed in parallel or serial.
Voltage X Voltage
_____________ = Impedance (ohms)
That is voltage SQUARED divided by Wattage is the line transformer's output side Impedance. Today, with short runs, that impedance
is just either the 16 ohm or 8 ohm - that is if only one compression driver is being fed, which for simplicity, we will assume is the case.
Because a 160 Watt transformer tap was common, the Kennedy amplifier, if you haven't guessed, was designed
to put out a 55 MAXIMUM volt signal, so that there is a good match to prior existing patents and systems.
For instance a 70.7 volt line and 160w is 30 ohms impedance.
Then in a modern system 55 volts at a little over half voltage, 35 volts, at 160 Watt load, has the same impedance.
The 160 Watts in the formula would be the output inpedance or transformer 'tap' such as an older PA terminal marked 160 ohms.
Because its a high impedance system, the output impedance can exactly match or greatly exceed the 16 ohm voice coil impedance (or 8).
But because we need to select a capacitor that will protect a VERY sensitive 116dB 1 Watt 1 meter coil, we must
now use 55 volts in the formula above. When we do that and we choose 400 hertz, the lowest
choice for 2 inch 16 ohms we get a capacitor of 24uf to 26 uf in practical values due to variation in production.
Most one inch coils only go down to 1200 to 1800 hertz. To drive them with a capacitor designed for half that
value would risk early burn up of the coils. Capacitance is equal to one over the quantitiy
6.28 times Cutoff (400) times (16) ohm.
If we did not know
that we have a voltage and current driven amplifier, if may not be possible to select so low
of a crossover value. We would, with a voltage amplifier, choose 800 hz for better control. That, conversely, would
give us a 12uf capacitor. This, as you may expect, cuts the loudness in half, but a big loss to protect the voice coil.
Now, for transformer chains - like a tube pre-amp using a phono input and a guitar pickup feeding either a solid state
or a tube or current amp - that feeds another line transformer that balances the line (high) voltage output, we want to use
instead the 30 ohm Z value, not the 16 ohm voice coil Z.
It reminds us that the ancient symbol of a pyramid with an eye
on top of a pyramid. Does it say HIeye Zees? To see high impedance = old school exotic deco visionary power.
Now, as shown in the table, a 16 ohm compression driver gets a 6.6uf at 800 hertz and 13.0uf at 400 hertz.
See table below
The leftmost column is for a 160 Watt tap in the table which is a table for 70.7 volts, but because we would run two speakers on
the same signal - one bass and one compression driver - that is 80 Watts per leg, over the limit for almost any compression driver RMS.
Therefore the voltage is generally split before going into the line transformer and it is dedicated to the compression driver.
One may want to consider two 26 microfarad capacitors in series to get more ripple current, but it requires four capacitors per Cdriver.
When you use a transformer backwords- 8 ohm primary unbalanced to 10k ohm max balanced, you want the transformer after it.
It if difficult to find the better 16 ohm transducer side line matching coil, but here is a picture of one.
Above is a Stancor A-8097
So far the compression driver 'crossover' is fairly simple, although vastly different from a speaker coil with the same impedance.
There are several important reasons. First, acoustic loading. The compression driver often uses a cone shape in an
inverted capture chamber to catch the initial wave and expell it sideways out the exit port.
Then, a horn that forces a larger volume of air to be actuated by a narrowing column also increases the virtual density
or thickness or viscousity of air, making more responsive to a very small displacement moving lightweight diaphragm.
Secondly, there are resonances and sometime system impedance changes as noted above, and the way that the power
either is increased or decreased as a comparison to the previous state depends on the amplifier's feedback design and
its voltage level (Tubes are whle high SS is low usually, not always) and power supply transformer - large versus small - as well as the time
that transformer is called upon to deliver more or less power and the leveling capacitor's ability to keep it steady.
Also the type of transistors used, the number of them, their quadrature and so forth makes a difference.
However, we want to illustrate the advantage of voltage and current drive at a basic level here.
As you can see from the table below, a pro audio amplifier for PA use has about twice the voltage that
a common consumer stereo has. In addition we should say that converting the signal going into a compression
driver from unbalanced to balanced is a good idea, not only for protection but sound quality and fidelity.
Most line level converters only handle 35 Watts. That turns out not to be a problem, because, although
they, the manufacturers of speakers, don't like to publish the fact, many expensive large format drivers do not really hande all that much RMS Wattage.
Even if they did in a multiple transducer arrangement - only half at most of the signal goes to the
upper end transducer - although making that assumption can get you into trouble - we seek to give a general and
practical guide here to crossover capcitor selection. See tabel below. Wattage label on transformer refers conservatively to primary
Use CRTL-MINUS keys to size down the text below to see the table properly::: [CTRL][-]:
This table illustrates why you should use the TAP wattage for the primary rather than transformer rating on box or other labeling
.........................................................if Line Transf.....If 160 ohm................No Line T...No Line T
.........................................................30 ohm xxW.....Line Tap 30W.....Below Recommended /w SS Current Amps Only
Bass Speaker Size Crossover Target | Pro Amplifier...Home Stereo | C-Driver; 16 Ohms | 8 ohm
Note- <~ 1000hz is for 2 inch V.C. (not inexpensive 1 inch and less coil diameter) unless using a serial parallel crossover instead of a simple capacitor or +/- pair.
Also if using a BALANCED stereo Power amp + PRE-amp or Unbalanced To Balanced transformer w/ pre-amp, Use WITH LINE T columns.
You then want to add an inductive line transformer, which will work better the higher voltage your system operates at.
Consider driving compression drivers from a seperate amplifier (bi-amping). Without high voltage they sound best with a little
negative impedance if you are using a low wattage tube amplifier or can control the output impedance on a current amplifier.
Most dedicated loudspeaker static systems are optimised for voltage drive, or another way of saying it is that the voltage created by the movement of a
voice coil inside a magnet produces voltage by iteself as feedback, and the only way to control the movement is to keep the amplifier
output impedance very low. The most efficient power transfer is when the output impedance nearly matches, well at least it can't go over, the speaker impedance.
While its a mathamatical truth that when they are equal, the coupling is most efficient, that would risk positive feedback into the amplifier instead of negative feedback,
and that would mean a loud noisy feedback loop and everything blows up! A fart like sound can sometimes be heard too. Here we use the impedance to efficiently couple the primary coil
with the capacitor following the secondary coil; the secondary coupled by matching the ohms impedence of the speaker following the capacitor.
This way the resonance of the speaker voice coil matches the resonance in the circuit that drives it - like a capacitively coupled low impedence current amplifier.
In current drive systems, also called 'voltage amplifier' or 'class-A'
if the impedance increases either at resonance peaks or
because of a new voice coil or a blown out tweeter - the voltage amplifier keeps the same voltage, adjusting the current drive. This means
that the power falls in half if the impedance increases by two times as much. A guitar tube combo for example, of simple push pull design would just sound a little less loud.
But in current amps, (Voltage Driven) like an auto amplifier which varies the voltage, the speaker would suddenly get FOUR TIMES the WATTAGE
The current amp gets four times louder while the voltage amplifier's volume is half the expected loudness. It just depends on the amplifier design.
Obviously, buying one hundred dollar diaphragms for a replacement in a solid state class D amp, one does not want to make the mistake
of replacing an 8 ohm compression driver with a 16 ohm one - and maybe that is why you don't see many in automobiles these days, in spite of
the fact that auto systems have finally been getting factory installs of sound systems of fair quality that they deserve. It is also likely
that small guitar amplifiers wish to improve reliability and reduce confusion and are therefore often lacking in upper register sound entirely.
The kennedy solid state amplifier is the best all around answer to changing states of touring and portable set-up systems like those
used by DJ's or event center sound reinforcement and amplification.
Now, the OLD SCHOOL way of marking the Watts that are used in formula #1. First,the 70 volt system is only theoretical at 70 volts.
Any primary winding in a line transformer for the old 70 volt PA can take more then 70 volts and output at least 10 Watts.
The wires for primary coils are Blue and Black, sometimes marked at 0.62 Watt, not 60 Watts.
In that convention 70 volts divided by 0.62 Watts is 8K ohms impedance which is optimal for most
tube power amplifier systems. This Wattage is calulated differently as 70V*70V / 8000 which is 0.62
This amount of power can output 10 Watts while at idle, that is without getting warm and wasting energy.
For single output tube amplifiers, brown and blue primary wire go to the plate and B+ on the output tube.
For a balanced push pull amplifier the brown/blue goes to both plates and the 2.5 Watt tap to B+.
For higher voltages such as 130 volt, and they can go up to 400 volts or more and still be considered
to be a 70 volt system, a higher impedance than 8000 to 10,000 ohms may be used, with different plate connections.
The usual line transformer used with a compression driver may have an adjustment, which all the way turned
left would be 10K and as you turn right, it lowers the primary coil impedance. A single ended triode tube
would have a typical output impedance of only 3 ohms. It may produce only 70 volts with a load, and is
not considered to be a 70 volt system power amplifier. It would use a 1000 ohm load and be used as a
preamplifier. The preamplifier tube handles the dips and rise in impedances. For treble tones,
An 8 ohm speaker can typically have an impedance rise to 20 ohms and a dip to 4 ohms in the upper bass frequencies.
This causes the high frequencies to be over twice as loud as the bass (Plus 3.7dB) because
the minimum impedance is the easiest pathway to the flow of power, or the control impedance.
For these tubes the ratio of the primary to secondary output coils is divided by the target
transducer impedance, but the usual assumption is 8 ohms, not 16 ohms. This can cause the
preamplifier to have an output impedance greater than 4 ohms. For a 300B with a plate of
7K ohms for instance a 3K primary and 8 ohm secondary: 3K/8=375 and 7K/375 is 2.13 ohms.
Such an amplifier cannot connect directly to a 16 ohm speaker, without changing the transformer.
The only way to allow 8 ohm speakers turns out to be to feed back negatively the some output.
As a result, 70 volt systems did not usually use a preamplifier but rather a power amp exclusively.
Each speaker in multiple speaker systems had its own transformer, but at least one had to receive
70 volts for the others to work properly, which is how the system got it's name, the others receive
less than 70 volts in a distribution power amplifier, or more in single target transducer setups.
Without the pre-amplifier, compression drivers tend to suffer the loud treble explained above.
A USA standard 25V 70V line transformer would have a secondary 8 ohm coil and taps on the primary of:
Due to variations in international standards, a 160 Watt tap (30 ohm) is not always present. Be sure to use actual
voltage especially if that voltage exceeds the 70 volt standard assumed rail output in either Class A
mode or if switched in class B mode for your amplifier and transformer. The main thing to be sure to
remember is that a higher impedance primary causes the voltage supplied to be increased, so you need a
smaller capacitor to be safe even though your power amplifier may be rated at lower total Watts RMS output.
After all this, the reader should now consider that finding a transformer for, say the kennedyaudio 55 volt
amplifier can be a challenge. The photo above of a line transformer does not offer a 100 watt tap, that would
be needed to bring the 3025 volt (55v times 55v) down to 30 ohms, which give a 400 hertz crossover with a 13uf cap.
If we actually planned to put a full 55 volts into only one primary coil at 2.5 watts, this would calculate to be at
400 hertz between a 0.1uf and 0.3uf capacitor. The 250 ohms in 25V theoretical is 2000 ohms theoretical 70.7 volt.
If you can find a 20 watt version you could use a 2.6uf capacitor. However, it is lower than most people would
like to see due to the fact that such a low value capacitor puts substantial capacitive reactance impedance into the
line at the lower frequencies being discussed here (400hz). The impedance is matched, that is to say one divided by
2 x pi x frequency x capacitance is 150 ohms, but the loss to the secondary coil due to efficiency is going to be no
less than a 50 percent loss. Voltage determines velocity and current actually moves the voice coil. Compression drivers
don't need nearly as much current due the their Beryllium or Titanium or Aluminum lightweight construction. Still, dynamic
range becomes restricted. A second problem is that at higher frequencies, that capacitive reactance is very low, making the
power spectrum slant upwards when many musical instruments have a downward sloping power spectrum. A S-132X triad offers a
125 ohm primary option and 4/8/16 out. However this model has a retail suggested price of 253.75. They are fortunately
available on eBay.com for much less..
It would be used to cross at 400 hertz using a 5uf to 13uf bi-polar capacitor or any combination that approximates 5uf.
Note however that with the kennedy amplifier being discussed, it is not actually 70.7 volts but 55 volts out.
Then we can calculate that the 125 ohm tap is actually a 39.2 watt tap. This gives us a 77 ohm, not 125 ohm
primary which results in a crossover capacitor of 1/193847 = 5 uf instead of 33uf (on each input plus and minus).
Therefore as a general rule I would buy four bipolar 10uf and use two in series on each pole to the 16 ohm driver.
The option is there to use the 250 ohm tap, which would be calculated as 70*70 theoretical / 250 = 19.6 watts
Now remember here that the wattage going to the upper branch cannot exceed 20 watts instead of 40 watts, so
your amplifier's wattage output should be in parallel with a crossover that draws substantial wattage.
In the Kennedy 500 watt RMS you would want to use a mono amp to feed both sides of dual stage loaded
woofers with horns in parallel so that each side draws 250 watts total, the majority of that being
drawn by the 18 or 21 inch woofer - or a very robust crossover network, perhaps with both the
midrange and the woofer ouput taps going into the bass driver speaker. For a smaller amplifier here,
then 19.6 times 400 times 2Pi is 492352 and 1/492352 is a capacitor value of 2uf.
It important to understand that in high impedance systems, the Watts flowing to the transducer are
being controlled by the impedance of the coupling transformer/capacitor link.
Hi C means less Z at the Cap, but less Z means more V at the Tap
If you looked at the transformer we selected, Triad S with a 125 and 250 ohm tap,it is really not
a 70.7 volt transformer at all, but a 25 volt (home stereo standard) one with 5 watts at 125 ohms.
This works for us on two levels - if the amplifier we use tends to vary voltage to control loudness
then at half of full loudness, even on a big power amplifier like the Kennedy 500, we are at 5 watts.
So, we feel reasonably secure in protecting the transducer unless we approach full output or raise
the sensitivity or use a powerful gain on a preamp. So you see, nothing is absolute or etched in stone.
Likewise using the 250 ohm tap would tend to limit current times voltage (Watts) at 2.5 watts.
Some experience is involved, but IF you DO blow a diaphragm - don't get discouraged. It comes
with the high impedance territory, perhaps more so than the low and medium types. But because
it is more counterintuitive, always make a note of the settings and system state on the inside
of the box so that the loading is documented at the time of failure - along with preamplification
and number of channels being mixed, they type of transistors in the power amp, music versus vocal,
ported or completely closed box, ambient temperature and so forth. Eventually you will get it right.
Because so many more variables are involved, it is a much greater achievment to optimize in the
high impedance domain than it is in the low impedance and paper cone technician's domain.
As a general rule, the voltage rating for an inductor is equal to it's number of turns.(primary)
The current is approximately equal to one over the number of turns. Coils limit rate of change of current.
So, a 70 volt coil is rated for 14 milliamps while a 25 volt coil is rated 40 milliamperes.
The wattage rating is equal to Amperage squared times Impedance; sometimes DC Resistance in ohms, however
the maximum power DISSIPATED in the control coil is impedance or resistance times amperage squared.
Note that in our solution proposal here, we would obtain dissipation between 141 and 282 milliwatts.
To be efficient, as Hi Impedance systems were intended to be, the coil should operate near is full
or maximum power dissipation. We are operating under the 400 milliwatt rating for a 25 volt coil.
That is much better than operating over the 50ma for a 70 volt rated coil, based on number of turns.
At the time 70 volt systems were designe, the 'skin effect' or tendency of voltage to ride on the
outer surfaces of wires, was not well understood. With today's science, 70 volt systems are rare.
However, stadiums that need many speakers at remote locations still use them, because they allowy
there to by any number of speakers running from the same source, as long as the wire gauge, length
and number of such windings of the output transformer
This is where the method of using ohms that is NOT the ohms of the capacitor but the inductor
is derived from in H.I. systems, or whenever the output impedance is greater than voice coil.
And then, you can call yourself a real Pro-Audio soundman.
Back To the Kennedyaudio.com
For background on Guitar TONE Capacitor Selection See
This discussion of guitar crossovers, filters and bypass capacitors.