Written by Joris van den
Heuvel, TalkBass name "Joris", e-mail: Joris.bass@planet.nl
This document is a vast
collection of technical facts a bass guitar player might want to know about his
or her amplification equipment. It does not cover the bass guitar itself.
Publication of this document - or parts of it - prohibited without prior written permission of the author.
Parts printed in blue are being edited.
1. Types
of bass amplifiers
Below is a schematic of a basic bass amplifier system in its simplest form. All setups incorporate these subsystems.
|
bass |
- |
preamp |
- |
tone
controls |
- |
master
volume |
- |
power amp |
- |
loudspeaker |
1.1.
Combo
The most
commonly used type of bass amplifier is the combo. One unit contains all of the
above subsystems:
·
Preamplifier, also known as input amplifier, often
with gain knob. The term "preamplifier" is often used to describe
both the preamplifier and the signal processor. Technically, these are separate
parts. See 2.1
·
Signal processor: tone knobs or equalizer, effects, master
volume knob. See 2.2
·
Additional features may of may not be built in:
effects loop (2.3), compressor (2.7.1.2), tuner output, DI output (2.4).
·
Power amplifier. See section 5
·
Loudspeaker cabinet. See section 6
A combo is
the least flexible way to amplify a bass. If you don't like one specific part
about it, you have no choice but to replace the whole unit.
1.2.
Head
A head is
everything that's in a combo, except for the loudspeaker cabinet. A head may
have its own casing or may be in a 19" chassis, leaving it fairly
unprotected. If you play gigs on a regular basis, it would be wise to put it in
a 19" rack case for protection.
1.3.
Cabinet
Obviously,
when you want to use a head, you'll need a separate loudspeaker cabinet. The
cabinet is connected to the head with a loudspeaker cable (see 7.3),
which differs from a signal cable in many ways. Some cabinets have a built-in
rack space, in which you can put a 19" chassis head. You could say you
built your own combo. But with one advantage: you'll be able to interchange
parts.
1.4.
Rack system
One step
further. Preamplifier/signal processor and power amplifier are separate units
mounted in a rack case, stacked on top of one or more loudspeaker cabinets.
Hence the nickname "stack". Countless combinations exist, and
components can be added to suit individual needs. Signal processors, effects
units, tuners, power conditioners, multiple power- and preamplifiers,
compressors, crossovers, you name it. Often functions are combined into one
unit, like with multi effects processors, which could incorporate a compressor,
equalizer, chorus, overdrive, delay, reverb etc. More on this in section 2.
2. Signal
processing and effects
The first
thing in every bass amplification system is the preamplifier. It takes the
signal from the bass, which is low-current (in the 10 μA range),
low-voltage (in the 100 mV range), and boosts it to medium-current (apx. 10
mA), medium-voltage (apx. 2 V). This is necessary to keep noise and
interference minimal. The term "preamplifier" is often used to
describe the unit that houses the preamplifier and the signal processor.
Technically, these are separate parts. But in case if a tube preamp, the preamp
section itself has its own "sound", so an important part of the tone
shaping takes place there. Some transistor amps may have an input section with
a saturation circuit, to simulate the characteriscs of a tube preamp.
This is
where part of the tone shaping takes place. The term "equalization"
originates from the PA field where equalizers are used to obtain an even
frequency response in a given room. Because every room is different and sounds
different, a device is needed to correct these differences, in other words: to
equalize the response. For bass guitar use, the device should really be named
"tone controller" instead of equalizer, but that aside. The working
principle is simple: certain frequency ranges can be cut or boosted. Mainly
three types exist:
·
Tone controls: rotary knobs labeled "bass",
"mid" and "treble" control fixed frequency ranges. Other
labels may exist and more knobs may be present. Some equalizers have
"pre-shape" or "tone matrix" or other controls. In essence
they are equalizer presets. They preset an equalizer setting that has proven to
be the preference of many bass players.
·
Graphic EQ: sliders labeled with frequencies control
cut and boost (aka "gain") of the frequency range with the labeled
frequency as a center. Each slider controls a socalled "band". The
frequencies are fixed. As is the width of each band ("bandwidth").
·
Parametric EQ: this type lets you control all aspects
of each band through separate controls. Frequency, bandwidth (also designated
"Q"), and gain. Some parametric equalizers have additional shelving
bands. They control everything below (low shelf) or above (high shelf) their
center frequency.
When using
a head or combo together with additional effects pedals or rack units, it is
desirable to first have preamplification and equalization, then the effects
kick in, and then the whole thing is power amplified. Heads and combos don't
have a separate preamp and power amplifier unit, in between which you would
connect your effects. Instead, many of them provide an "effects
loop", which consists of an output (send) and an input (return). The
signal from the preamp is tapped and sent out, in other words you
"send" it to your effects, and then "return" it back to the
power amplifier section. Some heads and combos have switchable signal levels,
usually you have a choice of –10 dB (line) or +4 dB (pro/studio). A rule of
thumb is: pedals use –10 dB and rack units use +4 dB, but some rack units are
also switchable. Always choose the higher level, but everything has to match.
In order to
connect your amplifier to a PA or a studio mixer, a DI is used. A DI device
(which is often built into the amplifier) provides a level adjusted,
electrically isolated, balanced connection. Signal levels and balanced signals
are discussed in 7.1.
The electrical isolation is a way to prevent ground loops and related dangers.
With many different devices, some with very high power consumption, connected
to the mains system in a building, voltages appear across the mains wiring.
These voltages contaminate the ground (zero volts) level, for instance when a
signal cable (very low power) goes from the main mixer to the bass amplifier on
stage, along with the ground conductor from the mains, where the power
amplifiers get their juice from (very high power). This leads to a difference
in ground level, and this is called a "ground loop". A very loud,
system-wide hum is the result. The electrical isolation has the additional
advantage of safety. When something blows, chances of you getting mains voltage
across your body (and your equipment) are reduced.
2.5.
MICing to a PA
Of course,
YOUR bass sounds the way YOU want, played through YOUR amp (else you wouldn't
have bought it, duh!). You want your audience to hear YOUR sound. You could use
a DI to go directly to the mixing table. This is a very reliable way to get
your signal to be amplified by the PA. But A DI taps the signal before it
reaches your amplifier, so your sound stays with you only, as the audience only
hears the sound of the bass without your amplifier. Putting a microphone in
front of your amplifier is the only way. But there are drawbacks. Mics also
have a sound of their own; they alter the sound. And in general, 1 close mic is
used for your whole rig. That single mic hardly captures the sound (that
doesn't mean it can't sound good, though). A 2x10 bass cabinet has, say, 2 10
inch speakers, a horn tweeter and a bass port. To capture everything, you would
have to mic 2-3 feet away, but the influence of other musicians' sounds may
seriously affect sound quality, and feedback from the PA can easily occur. Or
use 3 mics close up (one for one of the speakers, one for the horn and one for
the port). If you put a 1x15 underneith, get ready for 2 more mics (one for the
speaker and one for the port). Only pros will have these kinds of demands, as
it takes a lot of time to sound check the rig this way. Time you don't have at
a medium gig.
2.6.
Analog/digital
The
processing of signals can be done in two ways: analog or digital. Real-world
signals are analog, so processing them with analog electronics is the most
obvious, and before digital signal processing (DSP) was possible, the only way.
When DSP became available, possibilties grew immensely, and are still growing,
because the limit is determined only by the speed of the applied digital
processor(s), while computing speed doubles every 18 months nowadays. Digital
processing requires highly complex designs, and still some analog circuitry,
because the real-world signals have to be converted to digital signals
(sampling or ADC) first, then processed by the actual processor, and afterwards
converted back to analog (DAC). ADC, in short, is meauring the signal voltage
many times per second, too fast to be descerned by the human ear, and
describing each measurement with a number. DSP, in short, is applying complex
math to the acquired digital stream. DAC, in short, is putting all the digital
values back in sequential order, while each number represents a voltage.
Charateristics
of each type are in the table below:
|
Analog |
Digital |
|
Extremely
simple designs are possible to achieve the end result. |
Designs
require a minimum level of (high) complexity. |
|
More
complex designs generally require more electronics. |
More
complex designs hardly need more electronics. The opposite seems to be true:
as science progresses, systems become more compact, but with improved
capability. |
|
Susceptible
to noise and interference |
Once
digital, much less noise is added, but strong interference may lead to hard
failure. |
|
Capabilities
are limited |
Only the
designer's imagination and the current computing speed limit capabilities.
There's a trade-off between sound quality and capability. |
2.7.
Signal processors and effects
2.7.1.
Dynamics based
These are
signal processors that, in one way or another, react to and/or alter the
playing volume. The basis of all dynamics controllers is the envelope follower.
What it does is take a look at the input signal, and then output a signal which
perfectly tracks the volume of the input. With that signal the actual effect is
controlled, as if you were turning an effect knob while you're playing. In
advanced multi-effects processors it can be found as a separate module with its
own controls, and can be linked with different effects, like a wah-filter or a
phaser.
2.7.1.1. Noise
gate
As the name
implies, it's main use is prevent noise from being heard. This is accomplished
by muting the sound when the volume is below a certain level (called
"threshold"). The idea is: if you're not playing, then why listen to
the internal processes of your equipment? (Hmm, sounds like a good idea after a
good Mexican meal ;-) ) More sophisticated noise gates may have several
controls:
·
Threshold level: the volume level at which the gate
opens
·
Attenuation: how much the volume is being cut when
below the threshold level
·
Attack: the time it takes for the gate to go from the
attenuation value to fully "on"; prevents popping
·
Hold time: the minimal "on" time; prevents
constant opening and closing of the gate, for instance when playing short,
separate notes.
·
Decay or release: the time it takes for the gate to
go from "on" to the attenuation value; prevents popping
Note: a
noise gate can't block all noise. If the power amplifier section puts noise on
the speakers when no signal is present, a noise gate can't suppress that noise,
because a power amplifier can't be muted. Also, when there's noise while you
play, obviously the noise gate won't have any effect on that.
This device
is used to make volume changes less dramatic. It gradually turns down the
volume when playing louder and resets it when playing with less intensity.
Controls are:
·
Theshold: the volume level at which the compressor
will engage.
·
Compression ratio: how much the volume is cut. Say
you have a given rise of input volume. A 2:1 ratio will increase the ouput
volume only half of that, as soon as the volume level exceeds the threshold
level. A 4:1 ratio will only increase the output for a quarter of that.
·
Attack: the time it takes for the compressor to
adjust the volume. With a larger attack time, you can keep sudden peaks in the signal.
For slap playing this may be desirable.
·
Release: the time it takes to return to the normal
volume.
·
Gain: an extra gain stage is used to bring back the
compressed signal to counteract the cut volume.
2.7.1.3. Limiter
A variation
of the compressor. A limiter usually has a fixed high compression ratio, a high
threshold, and a very fast attack and release. Its purpose is to avoid very
high peaks that would, for instance, overload an amplifier or recorder.
Professional amplifiers have this feature built-in. An advanced compressor can
be used as a limiter with the proper control settings.
2.7.1.4. Envelope
filter
A filter
changes its frequency at command of the envelope follower. The most common type
is the touch-wah, which is an envelope-controlled low-pass filter with a peak
just before cut-off. When playing softly, the wah is closed, giving a very
muffled sound, and playing louder gradually sweeps the wah to a higher cut-off
frequency, giving a more "ah"-type sound. The touch-wah is best used
with very dynamic playing, causing the device to continuously shift from low to
high frequency cut-off and back.
2.7.2.
Time based
A lot of
different effects can be obtained by recording a signal, storing it for a
period of time, and then playing it back. The recording time can vary from .001
seconds to a few seconds, or actually virtually infinite, in which case you
have a recording device - hardly a sound effect. With very short recording
times, time based effects begin to overlap with frequency based effects.
2.7.2.1. Delay
Back in the
early days, delay machines consisted of a tape recorder with a circular (i.o.w.
endless) tape. The signal was recorded onto the tape, spun round and played
back just before being recorded again. Delay time could be varied by changing
the tape speed or length. This type of delay gave a characteristic sound,
mainly due to saturation (overdriving) of the tape, comparable to tube
saturation. For some time, solid state analog delays have been around. They
apply a socalled bucket brigade delay (BBD). An analog memory array of up to a
few thousand cells is constantly cycled. Compact chorus and flanger pedals
still use this technology.
Repeating,
fading echoes can be created by feeding the attenuated output of the delay back
into the input ("feedback").
A delay is
the most basic application of a digital processor. The first fully digital
sound processors were delays (Lexicon were the first). A simple delay doesn't
require a DSP, which were incredibly expensive at that time. Due to the nature
of digital systems, storing and recalling information without loss is a piece
of cake. If we simply continuously record, store, and playback, we have an
outstanding delay. Maybe too good. That's why nowadays, modern delays have some
sort of built-in signal degradation to make them sound more like good-ol' tape
machines, only 10 times as cheap, and with much less noise…
2.7.2.2. Reverb
A reverb
creates the sense of room acoustics and reverberation. The spring reverbs of
old are still quite popular, because of their low cost. More modern reverbs use
digital technology: the signal is input in a mathematically created virtual
room, and the sound of the "room" is sent out. Before life-like
reverbs like these were possible, the only way to get the desired reverb was to
actually record in a room that had that desired sound. Many close harmony
groups recorded their LPs in bathrooms.
Digital
reverberation requires very complex mathematical functions to be performed by
the DSP. In the table above, there was mention of "a trade-off between
sound quality and capability". Because reverb requires a fast and accurate
DSP, only costly reverb units that meet those requirements, provide life-like
reverb. A good example is the legendary Lexicon PCM-90, which uses all of its
processing power, just to create reverb. Inexpensive units, and especially most
multi effect units, may sound artificial and cold, and may lack definition.
Reverb is
rarely used for bass.
2.7.2.3. Chorus
/ flanger
A chorus is
a short delay (5 – 50 milliseconds) with its delay time slightly varied over
time ("modulation"). This creates a light shimmering effect, because
the pitch of the delayed signal is constantly changing. The delay creates a
doubling effect, while the modulation makes it seem as if two different
instruments are playing the same notes, instead of just one original and an
exact copy.
A flanger
is essentially the same device, but part of the delay output can be fed back
into the input (just like a normal delay), causing a phaser like sound. At
extreme settings, a flanger can sound like you're playing in a pool or a
rotating tunnel. When the feedback control of a flanger is set to 0, you have a
chorus device.
Flangers
used to be created by applying finger pressure to the flange of the reel of a
tape delay machine. Hence the name "flanger".
2.7.3.
Frequency based effects (filters)
These
effects alter the frequency characteristic of the sound they process. Below is
a detailed explanation of many different kinds of basic filters and variations.
In the graphs, both the gain and the frequency axis are logarithmic.
Low
pass. The most basic of all filters is the low pass. It
rolls off all frequencies above its cut-off frequency with a certain slope. In
today's electronic music, this filter, with a steep slope, is often used on the
total mix to create a kind of varying fidility.
High
pass. The inverse of the low pass is the high pass. Mostly
used to keep unwanted low frequencies out of a signal. Very low frequencies
can't be heard, but can damage loudspeakers and amplifiers, as they will effortlessly
try to reproduce them.
Band
pass. A band pass filter only puts out a narrow range of
frequencies. The loudest frequency is
called the "center" frequency, the sharpness of the top is called
"Q", and the rate at which the surrounding frequencies fall off is
called "slope".
Band
stop /notch. The band stop filter cuts a certain frequency range.
This is not the inverse of the band pass, but a low pass and a high pass
together. The notch filter is a relative of the resonance filter. It's a
special type of band stop, and filters one frequency or a very narrow band out
of the signal. For instance to radically cancel hum a 60 Hz notch filter can be
applied.
Resonance.
The purpose of the resonance filter is to isolate one frequency or a very
narrow band. An example of this filter is the tuning section of a radio
receiver. You (usually) only want to hear one station, and isolating its
frequency is therefor necessary.
When applied on an audio
signal, a resonance filter sounds like a phaser, but less apparent.
High
shelf. Often parametric equalizers have additional shelving
filters. Much like a high pass filter, a high shelf deals with everything above
a certain frequency, but doesn't cut everything. There's a minimum gain, which is
the actual gain setting. A high shelf can also be set to boost the high range,
but this is hardly ever needed.
Low
shelf. The inverse of the high shelf.
Although
not really an effect, the creative mind could use it as such. It is described
in section 2.2.
The graph shows different settings:
Solid lines each band separately
boosted.
Dot/dash
line all bands boosted
(bands influence each other)
Dashed line each band separately attenuated
Dotted line all bands attenuated (bands
influence each other)
2.7.3.2. Phaser
A
phaser consists of a socalled comb filter. The graph clearly shows how it got
its name. You could think of it as a short delay (0.1 – 2 milliseconds) which
causes ripples in the frequency characteristic, when mixed back with the
original sound. You can create phasing effects while moving your flat hand
closely towards your mouth while making an "FFFFFF"-like sound.
Because of the delay-like setup in a phaser, it falls in between the time based
and frequency based effects. Digital effects processors will often create a
phaser with a slightly modulated delay (like a flanger), analog phasers almost
always use a comb filter (which is actually a delay. In fact, every filter is a
delay, but an explanation is beyond the scope of this document).
2.7.3.3. Wah-wah
A
foot controlled steep low pass filter, sometimes with adjustable resonance.
This resonance is put just before the cut-off point of the low pass filter, and
moves along with that cut-off frequency. The sound of this effect does its name
honour.
2.7.3.4. Touch
filters
An
adjustable filter is controlled by an envelope follower. The most common type
is the T-wah or touch-wah. It sounds of course much like the wah-wah, but the
filter is controlled by playing volume.
2.7.3.5. Triggered
filters
An
adjustable filter is controlled by a trigger, which, in turn, is controlled by
playing notes. When triggered (a note is played) the filter opens or closes at
a preset rate. In a way a trigger is an envelope follower with just an
"on" and an "off" state.
2.7.4.
Wave form based effects
The last
group of effects are the socalled "unlinear effects". They all alter
the waveform one way or another, or create a totally different one, controlled
by the original waveform.
2.7.4.1. Distortion
The most
obvious waveform effect is distortion. Originally distortion was created by
just turning up an amplifier too far, so the power section ran out of headroom
(hit the ceiling) and chopped off (clipped) the tops of the signal. Slight
distortion is often described as "growl". Some bass amplifier brands
are known for this sound. For electric guitars, usually a lot more than a growl
is sought for, and hence clipper circuits are used. A clipper circuit
deliberately chops off most of the signal producing sounds from rumbling to
roaring to squeeking to fuzzing. Nowadays, countless amplifiers and stomp
pedals exist, each claiming to have their own distinct sound, but they all rely
on the same principle: clipping.
For bass
amps, distortion is often introduced in the loudspeaker cabinet. The drivers
have a limited linear excursion (see 6.13), and when driven beyond their linear range, they
will distort gradually as volume increases. This is also part of the
"growl" mentioned above.
2.7.4.2. Rectifier
Another
form of distortion is rectifying, a method of converting AC to DC, applied in
practically every power supply. The negative half of the signal is flipped over
to the positive side.
2.7.4.3. Wave
shaping
When a
transfer function is applied to a musical signal, sounds ranging from
brass-like to ring modulation can be created. This is called wave shaping. A
lot of different transfer functions exist, and these effects are mainly
incorporated in small digital pedal boards. Often it creates a distortion-like
sound.
2.7.4.4. Harmonic
enhancer
Another
variation of the distortion. The signal is high-pass filtered at a few kHz,
then distorted, and mixed back to the signal. It creates the sense of increased
brightness and clarity. It is often applied on female vocals to give them a
breath-ey sound.
2.7.4.5. Octave
doubler
By
half-cycle rectifying the signal, its frequency can be divided by two, creating
a sound one octave below the original pitch. This is often used to fatten up
solos and other parts played high up the neck. This effect is known to overload
amplifiers when used on low bass lines. Usually, the effect can't be used on
it's own, but can only be mixed in.
2.7.4.6. Pitch
shifter
While the
octave doubler can only divide the input signal's pitch by two, this effect can
change the pitch over a large range, usually –2 octaves to +2 octaves.
2.7.4.7. Ring
modulator
The
amplitude (envelope) of the signal is modulated (controlled) with a high
pitched frequency. The resulting sound is an unmusical, bell-like ringing,
hence the name. Some ring modulator features a controllable frequnecy, be it
from an envelope follower, or from a rocker pedal.
2.7.4.8. Synthesizer
This is the
most radical form of altering the sound of a musical instrument. The pitch of
the signal is determined. With this information, a synthesizer is controlled,
creating its own sounds. Some synthesizers feature MIDI note out capability, so
you can hook up MIDI syntheziser modules to create virtually every synth
instrument. Ever dreamed of playing the piccolo on a bass guitar? With this
kind of stuff you can.
3. Necessary
physics
3.1.
Voltage, current, power and resistance
If we're
gonna talk about electric basses, some basic knowledge about electricity is
essential. Although we could stick to the absolute essentials, we don't. For
all electric equipment to operate, a voltage is needed. For example, a wall
outlet supplies 120 volts (US) or 240 volts (Europe), and a car battery 12
volts. Once a device is connected (and switched on) current will start to flow,
and power is generated. The amount of power is dependent on the voltage of the
source and the resistance of the load. Before we start to describe everything
in detail, we first we have to make some conventions:
|
|
Symbol |
Unit |
Unit symbol |
|
Voltage |
V |
volt |
V |
|
Current |
I |
ampère |
A |
|
Power |
P |
watt |
W |
|
Resistance |
R |
ohm |
Ω = Greek capital Omega, rarely the symbol W
is used |
|
Frequency |
f |
hertz |
Hz |
In the equations these
standard mathematical operators are used:
x·y multiplication
x/y division
xy x raised to the power of y
10log
x the 10-base logarithm of x
(scientific calculators have this function built in under the "log"
key)
Right, now
we've established that, here we go. The relationship between voltage, current
and power is best illustrated by an equation:
P = V·I Power equals Voltage times Current.
Math is easy ain't it?
Example 1:
What's the current through an electric heater that's 115 volts, 1800 watts?
Filling in the equation P = V·I gives 1800W = 115V·I, I = 1800W/115V = 15.65A
(Note: this is very close to the trip point of the circuit breaker)
Example 2:
What's the maximum power generated by a car generator, rated 14.4V, 70A? P =
V·I = 14.4V·70A = 1008W. Must be serious car, then.
Resistance
is another basic aspect of electricity. It determines how much current will
flow though a certain load at a certain voltage level. To be more precise: 1
Volt is generated when 1 Ampere flows through a 1 Ohm load. In an equation it
looks like this:
V = I·R Voltage equals current times
resistance.
Example:
What's the current through a 10Ω resistor connected to a 12V battery? V =
I·R gives 12V = I·10Ω, I = 12V/10Ω = 1.2A
If we
combine the two above equations we get:
P = I2·R (P = V·I, substitute V by I·R)
P = V2/R (P = V·I, substitute I by V/R)
A useful
help, when working with these equations, is to put them in triangles, like
this:
P V P V2
V I I R I2 R P R
Knowing two
variables out of three, you can find the missing one by multiplying or dividing
them. If the two known numbers are horizontal, multiply them. If they're
vertical, divide the top number by the bottom one.
When values
become very large or very small, we can decide to put a prefix in front of the
unit symbol, to indicate the magnitude of the number. That way we don't have to
write down all the zeros that precede or trail the value. The most common
prefix is kilo, as in kilogram (kg), kilowatt (kW), kilohertz (kHz). Below is a
list of all prefixes and their multipliers.
|
Prefix |
Symbol |
Magnitude multiplier |
|
|
Power |
Absolute |
||
|
atto |
a |
10-18 |
,000000000000000001 |
|
femto |
f |
10-15 |
,000000000000001 |
|
pico |
p |
10-12 |
,000000000001 |
|
nano |
n |
10-9 |
,000000001 |
|
micro |
μ |
10-6 |
,000001 |
|
milli |
m |
10-3 |
,001 |
|
centi |
c |
10-2 |
,01 |
|
deci |
d |
10-1 |
,1 |
|
- |
- |
100 |
1 |
|
deca |
D |
101 |
10 |
|
hecto |
h |
102 |
100 |
|
kilo |
k |
103 |
1,000 |
|
mega |
M |
106 |
1,000,000 |
|
giga |
G |
109 |
1,000,000,000 |
|
tera |
T |
1012 |
1,000,000,000,000 |
|
peta |
P |
1015 |
1,000,000,000,000,000 |
|
exa |
E |
1018 |
1,000,000,000,000,000,000 |
Example:
What's the current through a 10kΩ resistor connected to a 250mV (line
level) source, and how much power is generated?
V = I·R P
= V·I
I = V/R P
= .25V·.000025A
I = .25V/10,000Ω P =
.00000625W = 6.25μW
I = .000025A = 25μA
Calculating
series resistances isn’t very hard. You can just add up their values to find
the substitute value Rs:
Rs =
R1+R2+R3+….+Rn (n
resistors in series)
With
parallel connections it gets more complicated: say you have two resistors R1
and R2. Their substitute value Rs will be:
Rs =
(R1·R2)/(R1+R2) (2
resistors in parallel)
The
following is a more general equation, in which you can put as many resistors as
you like in parallel:
Rs =
1/(1/R1+1/R2+1/R3+….+1/Rn)) (n
resistors in parallel)
Due to of
the characteristics of our hearing (explained in more detail in chapter 4), sound
pressure levels (SPL) are expressed in decibels, symbol dB. Initially, this
scale was introduced as the Bel, but the deciBel seemed more practical (1 B = 10
dB). The dB is not a unit, like, for instance, the volt. Rather, it describes
the magnitude ratio of two numbers along a logarithmic scale, meaning adding
dBs actually means multiplying the numbers. This is in such a way that adding
10 dB means multiplying the sound pressure (and the necessary amplifier
power) by 10. Consequently, adding 20 dB is a multiplication by 100, 30 dB is
times 1,000 etc. As said before, only power ratios (P1/P2) can be
expressed. There's always need for a reference level. For instance, when
calculating the maximum SPL of a loudspeaker, the reference level would be the
efficiency rating (sometimes called "reference efficiency"). In
mathematical terms (told you so, we don't stick to the basics):
PdB
= PdBref+10·10log(P) and back:
P = 10((PdB-dBref)/10) Reference
in dB
PdB
= 10·10log(P/Pref) and back:
P = Pref·10(PdB/10) Reference
in watts
Example 1:
you have a speaker with a reference efficiency of 96 dB (1W at 1m), and a
maximum input power of 250 watts. The maximum achievable SPL is: SPL = 96+10·10log(P)
= 96+10·10log(250) = 96+24 = 120 dB. So, the speaker produces 96 dB
at 1W of input power. This is the reference. We want to multiply the
power by 250. This adds 24 dB to the total SPL.
Example 2:
an amplifier's maximum output is 300 Watts. You need more power and decide to
purchase a 500 watts amplifier. That way you have 500/300 = 1.67 times as much
power available. SPL will increase by: SPL = 10·10log(500/300) = 2.2
dB.
A list of
dB conversions:
|
Increase
in dB |
Power
multiplication factor (rounded) |
|
3 |
2 |
|
6 |
4 |
|
9 |
7.9 |
|
10 |
10 |
|
12 |
15.8 |
|
14 |
25.1 |
|
20 |
100 |
|
24 |
251 |
|
27 |
501 |
|
30 |
1000 |
|
100 |
10,000,000,000 |
It was
mentioned before: power equals voltage square divided by resistance (P = V2/R).
Because of the square in the equation, signal levels, which are voltages,
require another method of determining dBs. With signal levels, a rise of 20 dB
(instead of 10) is multiplication by ten. This is how we recognize the squared
voltage on a logarithmic scale. The number in dBs increases twice as much,
compared to power dBs.
VdB = 20·10log(V/Vref)
and back: V = Vref·10(VdB/20) Reference in volts
VdB
= VdBref+20·10log(V) and back:
V = 10((VdB-dBref)/20) Reference
in dB
For audio
signal levels, the reference (Vref in the equation) is .775 V. This is
a standard value, called 0 dBm.
Example 1:
An effects pedal accepts a signal level of –10 dB. This is a very common value
and is called "line" level. Converting this value to a voltage gives:
V1/V2 = .775·10(-10/20) = .775 · .316 = .25 V
Example 2:
A rackmount effects unit accepts a signal level of +4 dB. Again, this is a very
common value, sometimes called "studio" or "professional"
level. In volts this is: V = .775·10(4/20) = .775·1.585 = 1.23 V
Example 3:
When measuring a test sinewave with a digital voltmeter, the display reads 1.00
volts. Determining the signal level in dBs: VdB = 20·10log(1.00/.775)
= 2.21 dB
4.1.
Sound perception
Especially
for bass players it's important to know how the brain interprets low
frequencies. The fact that our hearing is insensitive to low frequencies is
somewhat counteracted by the brain. If the brain detects two different pitches,
the difference is perceived as a third pitch. If, for instance the two first
harmonics of a bass guitar note are heard, but the fundamental frequency of the
string is omitted, the brain will "fill in" the missing fundamental.
The difference with the real thing is feeling. A very low frequency can be
felt, rather than heard. But we do perceive it, even if it isn't there.
This is
common knowledge to bass cabinet designers. The lowest frequencies are not very
important, as opposed to a high sound pressure level. More on this in section 6.
4.2.
Sound pressure
The human
hearing is a piece of art from Mother Nature. It is capable of processing
frequencies that are a factor 500 to 1,000 apart, and sound pressure levels
that are a factor 10,000,000 apart! There's no audio technology on this earth
that can beat the human ears. So you better be careful with them!
Techtalk.
Because our ears can determine vast changes in volume, sound pressure is
measured in decibels, a logarithmnic scale (see 3.3). If you double power (twice
the watts) the sound becomes 3 dB louder. However, an increase of as much as 10
dB is perceived as a doubling of volume. This equals ten times the
power. So in order for you to play twice as loud, you need an amplifier with 10
times as much power.
More on
this in section 5.2
4.3.
A-weighting
Our ears
don't have the same sensitivity for each frequency. The lower the frequency,
the less sensitive, and the same goes for higher frequencies. The midrange,
which is around 1 kHz, is the most sensitive range. This is where most of the
human voice is. Scientists have measured the hearing sensitivity for different
frequencies of thousands of people. The cross-section of these measurements is
called the A-curve. Applying this curve is called A-weighting.
4.4.
Hearing damage and protection
Playing on
a live stage with a band almost always means high sound pressure levels. Especially
when there's PA support for the whole band including drums. At close range (3
feet), a medium powered bass amplifier (200 watts) produces an average sound
pressure level of around 100 dB, crest factor (see 5.2) considered. Every other
musician adds roughly 2 dB to that. The drummer could easily add another 3-6
dB. Then there's the backfire from the PA - especially the bass range.
Reason
enough to wear ear protection. The simplest form is foam rubber plugs. Squeeze,
put in, throw away after use. Cost less than a buck. But often these simple
plugs will hurt when worn for long periods of time. And often they seal your
inner ear from the outside air. For a little more cash ($10-25) special
musician's ear plugs are made that adapt to the shape of your inner ear, often
with one or several ventilation channels, allowing your inner ear to breathe
and sweat. The most advantageous, and of course the most expensive ($50 and
up), are customly molded silicone plugs.
A power
amplifier is in essence an AC to AC power converter. It draws power from the
wall socket with a fixed voltage and frequency, and converts it to a variable
voltage with variable frequency, exactly mimicing the input signal (to a
certain extent). In theory, only the power level will have increased.
5.1.
Power amplifier specifications
There's much more to a power amplifier than its power
rating. On top of that, power can be measured in many ways. Not every company
will specify the maximum output power of their amps the same way. There are no
laws that dictate how power should be measured. Some will specify max power at
1% THD, some at 10% THD (true for most car amps), some will measure short-term
power, others will specify long-term burst power, etc. etc. There's no right or
wrong, they're just ways to measure. Often companies that offer low budget
equipment choose a method that boosts their figures.
|
Term |
Unit |
Description |
Good |
Bad |
|
Sensitivity |
dB |
Input voltage needed to achieve full output power. Useful
for level matching. |
- |
- |
|
Noise |
dB |
Noise produced by the amplifier itself with master
volume set to 0 |
-80dB |
-50dB |
|
SN ratio |
dB |
Signal to Noise ratio |
100dB |
60dB |
|
THD |
% |
Total Harmonic Distortion; describes how much the
output signal resembles the input signal |
0.05% |
0.25% |
|
IMD |
% |
InterModulation Distortion; describes how large
signals (low frequencies) influence smaller signals (higher frequencies) |
0.05% |
0.25% |
|
Slewrate |
V/μs |
The maximum rate at which the output voltage is
able to change |
50V/μs |
20V/μs |
|
Channel separation |
dB |
Crosstalk between channels of a stereo amplifier |
60 dB |
30 dB |
|
Voltage gain |
dB |
Input-to-output voltage gain with master volume at
maximum |
- |
- |
|
Power consumption |
W |
Mains power consumption. Typically an amplifier
requires twice its output power from the mains when operating at full power . |
1.5x output power |
3x output power |
5.2.
Understanding amplifier power
There's
only so much an amplifier can drive. It is designed for a specific minimum load
impedance. This is not the actual output impedance of the amp itself (discussed
in 5.4),
but a rating for the load that can be safely connected to the amplifier. This
has to do with the maximum output current the amplifier can deliver, as a
low-impedance load draws more current than a higher-impedance load. It may be
hard to understand why it's called minimum load, but as described above
and in 3.1, amplifier load increases when impedance decreases.
5.4.
Output impedance and damping factor
As with all
electricity supplying components, amplifiers have an output impedance. You
could look at it as a resistor in series with the output of the amplifier,
representing the imperfection of that amplifier's output stage. Directly
related to output impedance is the damping factor. This is a measure for the
control an amplifier has over a speaker cabinet. A given transistor amplifier
may have an output impedance of .02 ohms. If the connected load has nominal
impedance of 4 ohms, the damping factor is calculated by dividing the load
impedance by the output impedance: 4 / .02 = 200. Not bad. Obviously, the
higher this factor, the better. Especially the low bass response will be
tighter. This is exactly why it's important that loudspeaker cables should be
made of large copper diameter wire. You don't want to lower the damping factor
by connecting the speaker cabinet with a thin cable with a relatively high
series resistance. The speaker cabinet's internal crossover may also add to
this series resistance. The woofer is usually crossed over by one or two series
inductors, that have a resistance of their own. However, usually, the
performance of the cabinet won't be affected because the designer should have
taken the crossover losses into account.
Tube amplifiers usually have
a much higher output impedance. This is where part of their characteristic
sound comes from. Because the amplifier has less control over the connected
load, the sound will have one or two pronounced resonance peaks around the port
frequency of the cabinet. This is often described as the "warm" sound
of tube amplifiers. Other factors are at play here, but this is definitely one
of them.
5.5.
Frequency response
Frequency
response is not much of an issue for solid state amplifiers. A typical range is
10 Hz – 100 kHz. However, if not explicitly mentioned in the specifications,
this is measured at low power. The curve could change significantly when
measuring at full power. This is called "power bandwidth". Low
frequencies demand more from the power supply capacitors, since low frequencies
draw current for longer periods of time than high frequencies. High frequencies
demand more from the electronics' slew rate (see 5.1), since fast changes of the output level are
required. Both these limitations result - obviously - in distortion, but even
then, a good amplifier will perform its duties over far greater frequency range
than that of the human ear.
5.6.
Distortion, clipping
When a
power amplifier is forced past its maximum output power, it will clip. This
means the output voltage of the amp is equal to the supply voltage from the
power supply and can't go any further. The peaks (positive as well as negative)
of the signal are clipped off, hence the term "clipping". Clipping in
itself isn't bad, neither for the amplifier nor the connected speaker(s). It's
the compression of the signal that causes problems. When a signal is compressed
(by clipping it) its average power increases, and may be over the amplifier's
maximum thermal capabilities. Furthermore, a clipped signal loses low frequency
content, due to the fact that low frequencies usually have a larger amplitude.
Low frequencies get clipped first, so to speak. This means the high frequency
content increases relatively, and this can damage tweeters (horns).
Now a more
technical story. A side effect of clipping that is often overlooked is the DC
decoupling instability. Most amplifiers can't amplify DC signals (why would
they need to?), so they are DC decoupled. This has a huge advantage for
designers: the output offset adjustment can be done automatically by the
amplifier itself, instead of adjusting it by hand at the time of manufacture.
This self-adjustment relies on the fact that the amplified signal always has an
average value of zero (equal power in both the positive and negative half of
the signal). If the signal is non-symmetrical, as is the case with many musical
instrument signals, clipping will occur at only one half (positive or negative)
of the signal. As a result, the output offset adjustment starts to shift, as
the amplifier will keep its output at a zero average. In turn, this causes a
very low frequency (that of the adjustment cycle) at the output. This is often
visible as a strong waving of the speaker cones. Needless to say, a speaker cone
that moves this much, is prone to damage.
5.7.
Volume control
It's a
common misconception to believe the master volume control of the power section
to control the output power from 0-100% when it is turned from 0 to 10. The
volume control of a power amplifier is an attenuator and thereby attenuates the
(obviously) too strong input signal. It gives you the possibility to turn down
from maximum power. If the input level (from the preamp/signal processor) is
too low, maximum power will not be achieved. If the input level is very high,
maximum output power is reached long before the master volume control is set to
its maximum.
5.8.
Amplifier topologies
Due to the
nature of loudspeakers, amplifiers have to be designed so that a loudspeaker
can move in (negative) and out (positive) the cabinet. In practise, this means
separating the amplifier in two halves: one for each half of this movement. A
problem occurs when the two halves have to take over from each other. At
near-zero current, both tubes and transistors are non-linear. It means they
will not reproduce the signal well (aka "crossover distortion"). This
problem returns every half cycle of the waveform, as a waveform crosses zero
twice each cycle.
Another
problem occurs when the output devices of the amplifier are not fully
"on". Because a music signal is of a constantly changing amplitude,
this is practically always the case. The connected load of the amplifier
receives part of the output voltage, while the output section gets the
remainder of the supply voltage. This remainder is converted to waste heat.
When an amplifier is working somewhat below its maximum power, more heat than
output power is produced, even if the amplifier is theoretically ideal.
There are
several ways to address these problems. They're called "classes". Not
every amplifier class is suited for audio (there are more purposes for
amplifiers). Only those who are, are listed below.
·
Class A: Maximum current flows through the output
stage at all times. This way the near-zero current is avoided, and thereby
crossover distortion eliminated. An unavoidable side-effect is, when no signal
is present, power consumption is at maximum, and the amplifier will run hot
when no sound is produced. Better still, the amplifier will cool down when
operating at moderate to high output power.
·
Class B: The opposite of class A. No current flows
through the output stage when in rest. Stand-by power consumption is nearly
non-existent, but crossover distortion is eminent, be it acceptible for some
applications (like speech or sirens).
·
Class AB: The best of both worlds. A small stand-by
current keeps the crossover distortion at a low level, and when silent, power
consumption is only a fraction of the maximum power. Nearly all conventional
power amps are class AB.
·
Class D: As mentioned above, heat is produced when an
amplifier output device is not fully "on". Class D amplifiers use
digital technology to rapidly and constantly switch the output devices on and
off, effectively avoiding the "in-between" state. By filtering (averaging)
the switching frequency out of the output, the intended amplified signal
appears on the output. This class is a.k.a. switching amplifiers. It won't be
before long when every amplifier uses class D topology ('cept for them good-ol'
tube amps, but then again, ya never know). When combined with a switching power
supply, instead of a conventional heavy mains transformer, weight, mains power
and cooling requirements can be drastically reduced.
·
Class G: This topology uses two sets of output
transistors and two supply voltages. One set controls low-to-medium power
signals, keeping power consumption and heat at a moderate level. When high
power is needed (during signal peaks), the second transistor set takes over and
provides the higher voltages, fed by the higer supply voltage. As soon as the
peak is over, the first set gets back to work.
·
Class H: Much like class G, this system uses two
stages. Only now the supply voltage is temporarily increased (switched) to deal
with the peaks. The advantage is: you only need one set of (expensive) output
transistors, and the switching can be done by much cheaper electronic switches.
5.9.
Transistor or solid state amplifiers
Most
amplifiers use solid state technology, a.k.a. semiconductors. A transistor is a
semiconductor. This means its conduction can be controlled. A small current
at the input will result in a higher current at the output, supplied by
the power supply. This current gain is the building block for an amplifier. A
transistor's current gain is limited. This is especially true for high power
transistors. This is why several stages are used to increase the input current
about 1 million times and the input voltage about 100 times. Each stage
amplifies the signal a bit more, and the final stage drives the loudspeaker. A
more recent development is the MOSFET (=Metal Oxide Semiconductor Field Effect
Transistor). A semiconductor also, but with a different working principle. Its resistance
can be controlled by an input voltage. This makes for more efficient
(read: cheaper) amplifier design, because high power MOSFETs have a higher gain
and can be driven with less stages. Another development is the IGBT (Insulated
Gate Bipolar Transistor): a regular power transistor is driven by a smaller
MOSFET, combined in the same housing.
In a
transistor amplifier, the mains input is first transformed to a lower AC
voltage (and at the same time electrically isolated from the mains) by a
transformer, then rectified by diodes, and then buffered (to get an
almost-perfect DC voltage) by one or more pairs of very large capacitors. These
are the energy storage units for when the AC voltage is crossing zero and thus
not able to supply current. These large capacitors are of huge importance. With
a high current, a small capacitor will easily be drawn almost empty every
cycle. The voltage drops and the amplifier will clip more easily. Another
side-effect of this is hum, because even when running idle, the supply voltage
will drop every rectified half-cycle.
5.10.
Transistor amplifier maintenance
Apart from
keeping the amplifier dust free, there's not much you can do. The main cause of
failure of transistor amps is overheating, so cooling air must be able to flow
freely. Obviously, overloading an amplifier will certainly overheat it, as the
heat sink(s) and, if applicable, the cooling fan(s) weren't designed to be
overloaded.
5.11.
Tube or valve amplifiers
5.12.
Tube amplifier maintenance
When powers
increase, passive crossovers (see 6.6) become very expensive, and even then, power losses
are unacceptable. This is the point where one decides to bi-amplify. It means
that low frequencies and high frequencies are separated by an active crossover
at signal level, and then each frequency range is amplified by a separate
amplifier and separate speaker(s). This is especially advantageous for
subwoofer setups as a passive subwoofer crossover requires very large and
expensive inductors.
A schematic
of a bass guitar bi-amplified setup:
|
|
|
|
|
crossover |
high output |
- |
amplifier |
- |
cabinet |
|
bass |
- |
preamp /
eq / effects |
- |
|
|
|
|
|
|
|
|
|
|
|
low
output |
- |
amplifier |
- |
cabinet |
5.14.
Stereo amps and bridging
Most power
amplifiers have two channels. The intended application for a 2-channel amp is a
stereo setup, as it is desirable to have two absolutely identical amplifiers
for left and right. However, amplifying a monaural bass guitar in stereo is
hardly ever needed. Several possibilities exist:
|
Setup |
Application |
|
Dual mono |
The same
signal is fed to both amps, each amplifier drives a cabinet |
|
Bridged |
Most
2-channel amps provide a possibility to link up both channels into one
channel with double power. However, the minimum load impedance (see 5.3) is also doubled |
|
Bi-amped |
An active
crossover is put in the signal chain; one channel amplifies the low
frequencies, the other channel gets the high frequencies (see 5.13) |
|
Stereo |
Obviously
for use with two (identical) cabinets. Some effects processors create stereo
effects from a monaural source, and in this case a stereo setup may be
interesting |
Below is a
schematic cross section of a loudspeaker:
a permanent ring magnet
b back pole plate
c front pole plate
d vented pole piece
e voice coil former
f voice coil inside flux gap or air gap
g basket
h mounting flange
k spider
m spider support
n cone
p dust cap
q surround
r voice coil wires
s cone punch tubes
t connection terminal support
u cone wires
And this is
how it all works: the permanent magnet (a) provides an extremely strong
magnetic field (symbol B, a.k.a. as flux, typically 1 Tesla) inside the air gap
(f). The magnetic field is directed there by the pole plates (b/c) and the pole
piece (d). The better part of the voice coil (f) is inside this circular slot,
and is held there by the tubular voice coil former (e), which is held in place
by the spider (k). Electric current through the voice coil will induce a
magnetic field, and, by Lorentz' law, a force is the result. The coil puts the
cone in motion, which will, with its large surface, move air. The spider's
second task is to provide most of the cone suspension (symbol Cms).
It makes the cone move back to its resting position. The cone itself is
centered by the surround (q), which is usually made of rippled impregnated
cloth. The surround also provides a part of the suspension and damps the
unwanted surface vibrations of the cone.
A close-up
of the motor section:
In
this case, the voice coil is overhung, and the coil overhang (the part of the
coil that extends out from the air gap) is the distance the coil can move
linearly, give or take 10%. This figure is known as xmax. Once the xmax
is crossed, any further movement will be increasingly non-linear, as a smaller
part of the coil is covered by the air gap, and thus motor force is gradually
reduced. Distortion is the result. When the coil has moved fully out of the
front pole plate, motion almost stops, and clipping occurs, comparable to
amplifier clipping. With an unproperly constructed spider and surround, the
coil former could end up slamming onto the pole piece and front pole plate or onto
the back pole plate. This will obviously lead to severe damage of the coil, possibly
short-circuiting the connected amplifier. This phenomenon is known as
over-excursion or Xdamage (see 6.7.2).
6.2.
Cabinets
Bass
loudspeakers can't operate in free air. They need a cabinet to absorb the sound
radiated from the back of the loudspeaker, or else it would cancel out the
sound radiated from the front. A properly designed cabinet drastically improves
the bass response of the loudspeaker. Below is a list of common ways to achieve
this:
|
Principle |
Description |
|
Closed |
A closed
system is a cabinet with nothing more than an enclosed air volume, in which
the compliance of the driver and the damping of the air interact to improve the
bass response. |
|
Open-backed |
The
driver is mounted in a cabinet, but the back of the cabinet is left open for
the better part. This type of cabinet won't provide much bass. Most guitar
cabinets are constructed this way. |
|
Ported |
This type
is defined by the use of a port, a hole in the cabinet wall; often a tube or
rectangular channel, extending into the cab, is attached. This port will make
the cabinet resonate at a certain frequency. This frequency is chosen just
below the point where the loudspeaker's response starts to roll off,
effectively improving the bass response. The far majority of (bass guitar) cabinets
apply this principle. It has numerous advantages over a closed system. It is,
however, much harder to design. |
|
Horn loaded |
|
|
Transmission line |
|
6.3.
Configurations
Bass
speakers come in different sizes. Standardised sizes are 8, 10, 12, 15 and 18
inch. Often smaller speakers are used in multiples. Below is a table of common
configurations.
|
Size |
Common
multiples |
|
8" |
2
– 4 – 8 |
|
10" |
1
– 2 – 4 – 8 |
|
12" |
1
– 2 – 4 |
|
15" |
1
– 2 |
|
18" |
1 |
A general
rule is: the larger the speaker, the lower the bass response, the smaller the
speaker, the better the treble response.
6.4.
Frequency response
The frequency
response of a cabinet is the range where it supplies an almost even loudness.
The roll-off points are those frequencies where the loudness drops
considerably. However, "considerably" is a relative term. Most
cabinet manufactorers will specify their limits at -3dB, a clearly noticable
drop in volume, which also equals half the acoustical output power. Others may
use -6, -8 or even -10dB. This rather specifies the "usable range" of
a cabinet: the range at which it produces significant output. Neither way is
good or bad, it's just ways to measure. Just like amplifier output power. As a
consumer, however, you will have to constantly pay attention to how
specifications are obtained.
Resistance was
discussed earlier in section 3.2. The calculations given are also applicable to
loudspeaker impedances. Connecting two cabinets on one amplifier (channel) always
means parallel connection, unless explicitly mentioned. Connecting different cabs
in series is generally not recommended, as it may give unpredictable results.
Identical cabs can be series connected without any problems. A special "series-Y"
cable may be needed.
Impedance,
however, is a different phenomenon. It describes the resistance of a load connected
to AC (Alternating Current) instead of DC (Direct Current). Resistance should
be seen as impedance at a frequency of 0 Hz. Adding the variable of frequency
complicates matters. If a loudspeaker were a simple resistor, its impedance
would be a constant throughout its frequency range. But this is not the case.
Its impedance changes with different frequencies. Around its resonance
frequency (see 6.13) the graph shows a high peak, and with higher
frequencies, the impedance gradually rises. The specified impedance is really a
nominal impedance, measured at 1 kHz. That's exactly why an ohmmeter
will never show the true impedance of a cabinet. An ohmmeter measures (DC)
resistance. Typically for loudspeakers, their DC resistance is about 80% of their
rated impedance.
There are
few speakers that can reproduce the entire audible range. The ones that can are
likely to be fit into high-end audiophile systems. Normal people resort to
using different drivers optimized for a certain frequency range, and fitting
them into the same cabinet. Two-way systems are the most common, as they are
relatively easy to design and give good results at low cost.
Using
optimized drivers means having to split up the frequency range into bands (much
like equalizer bands). The separation range is called the crossover frequency.
One driver's output rolls off, while the next one gradually takes over. The
rate at which this takeover is done is called slope. Slopes are 6, 12, 18 or 24
dB per octave.
6.7.
Power handling
There are
two types of power handling for a speaker. Thermal and mechanical:
6.7.1.
Thermal power handling (Pth)
The only electrical part of a loudspeaker is the voice coil. It is usually made of thin copper wire on a high-temperature resistant coil former. The thermal power handling (Pth) is the maximum average power the coil can dissipate (heat conduct), before the coil wire or the glue, with which the coil is attached, will melt. Because the rise in temperature due to high power is fairly slow, short, high power peaks (in the order of tenths of seconds) will be averaged by the thermal sloth. A rule of thumb: peak power (Ppeak) equals twice the continuous power. Professional drivers are often able to withstand peaks of four times their rated continuous power. Some even 10 times.
6.7.2.
Mechanical power handling (Xdamage)
A
loudspeaker is an electro-mechanical device. The mechanical part can, just like
the electrical part, be overloaded. The cone suspension system is limited in
its excursion (movement). Please note: this is not the figure of Xmax,
which is the maximum linear excursion of the cone (see 6.1). The cone
should be able to move considerably more than Xmax.
6.8.
Damage
6.9.
Protection
6.10.
Efficiency and sensitivity
6.11.
Phasing and distortion
6.12.
Placement
In the past, two engineers, Thiele and
Small, have developed a measurement standard for loudspeaker characteristics.
The Thiele/Small parameters, T/S parameters in short, are what defines a
loudspeaker. These parameters are a list of figures of mechanical and
electrical constants:
|
Para-meter |
US unit |
Eur. unit |
Description |
Interpretation |
|
Fs |
Hz |
Hz |
Free air resonance frequency |
Specifies the the top of the resonance peak of the driver in free air, floating in an infinite space. |
|
Qms |
- |
- |
Mechanical Q factor |
These three figures describe how the driver resonates. The bandwidth of the resonance is split into motional resonance (Qms) and electrical resonance (Qes). Their value is combined in Qts. This value is of great importance to cabinet design. |
|
Qes |
- |
- |
Electrical Q factor |
|
|
Qts |
- |
- |
Total Q factor |
|
|
Vas |
ft3 |
dm3 |
Equivalent air volume |
See 6.1 |
|
Cms |
in/N |
mm/N |
Suspension compliance |
See 6.1 |
|
B |
T |
T |
Magnetic field strength |
Strength of the magnetic field inside the air gap |
|
BL |
N/A |
N/A |
Force factor |
Specifies how much force the voice coil will apply to the cone at a given current |
|
Xmax |
in |
mm |
Maximum linear cone displacement |
See 6.1 |
|
Xdmg |
in |
mm |
Maximum cone displacement |
See 6.7.2 |
|
μ0 |
dB |
dB |
Reference efficiency |
See 6.10 |
|
Sens |
dB |
dB |
Sensitivity |
See 6.10 |
|
Pth |
W |
W |
Thermal power |
See 6.7.1 |
|
Ppeak |
W |
W |
Peak power |
See 6.7.1 |
6.14.
Cabinet DIY
6.14.1. Tools
6.14.2. Materials
6.14.3. Design trade-offs
6.14.4. Measurements
6.14.5. Cost
6.14.6. Literature and software
7. Signals,
connectors, cables
Signal
type
|
Description |
|
Microphone |
Low
impedance (150Ω), low level (10mV) |
|
Instrument |
High
impdeance(1MΩ, low level (100mV) |
|
-10 dB
line |
Medium
impedance (15kΩ), medium level (250mV) |
|
+4 dB
line |
Medium
impedance (15kΩ), high level
(1.25V) |
All of the
above signals can be balanced. This means that the signal is split in
two, and one of them is inverted (put in counterphase). The original signal is
called positive or hot, while the inverted signal is called negative
or cold. Both signals are sent across the cable, each through their own
conductor. At the reception side, the negative signal is inverted back and both
signals are added together, effectively cancelling any noise, hum or
interference that both signals may have picked up in the cable.
Although
not really a signal type as such, this is what an amplifier puts out:
|
Amplifier
output |
Very low
impedance (0.01Ω), very high level (50V) For
instance: 100 Wrms,
8Ω load = 28.3Vrms 600 Wrms,
4Ω load = 49.0Vrms |
7.2.
Connector types
Connector
type
|
Signal
type |
Application |
|
¼" jack |
signal,
speaker |
Instrument,
speaker |
|
TRS
(3-contact ¼" jack) |
signal |
stage,
studio |
|
XLR |
signal,
speaker |
stage,
studio, microphone |
|
Cinch |
analog / digital
signal |
home
stereo, digital audio, video |
|
Speakon |
speaker |
professional
speakers |
|
Banana /
4mm |
speaker |
home/semi-pro
speakers |
|
Binding
posts |
speaker |
home/semi-pro
speakers |
|
5-pole
DIN |
digital
control signal |
MIDI |
|
signal |
A small
diameter core, shielded by copper mesh, along with metal foil or carbon
screen. Shielding prevents interference. |
|
balanced
signal |
A
conductor pair, shielded by copper mesh, along with metal foil or carbon
screen. Shielding prevents interference. Balanced signals see 7.1. |
|
balanced
multi signal |
Many
pairs of conductors, each with their own shielding provide fast and flexible
connection of a mixing console to multiple signal sources on a stage. |
|
speaker |
Large
copper diameter conductor pair, unshielded. |
|
digital |
75 ohms
coaxial cable of low capacitance. One cable for stereo connection. |
|
digital
optical |
Plastic
light conductor. One cable for stereo connection. |
8. Frequencies
of note pitches
Open string frequencies for an 8-string bass guitar
tuned F# – B – E – A – D – G – C – F are bold. Other standard string
tunings are a subset of those. The rectangle indicates middle A.
|
Octave Note |
-5 |
-4 |
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |
|
A |
|
27,50 |
55,00 |
110,00 |
220,00 |
440,00 |
880,00 |
1760,0 |
3520,0 |
|
A# |
|
29,14 |
58,27 |
116,54 |
233,08 |
466,16 |
932,33 |
1864,7 |
3729,3 |
|
B |
|
30,87 |
61,74 |
123,47 |
246,94 |
493,88 |
987,77 |
1975,5 |
3951,1 |
|
C |
|
32,70 |
65,41 |
130,81 |
261,63 |
523,25 |
1046,5 |
2093,0 |
4186,0 |
|
C# |
|
34,65 |
69,30 |
138,59 |
277,18 |
554,37 |
1108,7 |
2217,4 |
4434,9 |
|
D |
|
36,71 |
73,42 |
146,83 |
293,66 |
587,33 |
1174,7 |
2349,3 |
4698,6 |
|
D# |
|
38,89 |
77,78 |
155,56 |
311,13 |
622,25 |
1244,5 |
2489,0 |
4978,0 |
|
E |
20,60 |
41,20 |
82,41 |
164,81 |
329,63 |
659,26 |
1318,5 |
2637,0 |
5274,0 |
|
F |
21,83 |
43,65 |
87,31 |
174,61 |
349,23 |
698,46 |
1396,9 |
2793,8 |
5587,7 |
|
F# |
23,12 |
46,25 |
92,50 |
185,00 |
369,99 |
739,99 |
1480,0 |
2960,0 |
5919,9 |
|
G |
24,50 |
49,00 |
98,00 |
196,00 |
392,00 |
783,99 |
1568,0 |
3136,0 |
6271,9 |
|
G# |
25,96 |
51,91 |
103,83 |
207,65 |
415,30 |
830,61 |
1661,2 |
3322,4 |
6644,9 |