UNIVERSITY OF NAIROBI
SCHOOL OF ENGINEERING
DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING
FINAL YEAR PROJECT REPORT
PROJECT NUMBER: PRJ 098
SPEAKER DRIVE SELECTION FOR 2-WAY AND 3-WAY FOR 50WATTS AND
100WATTS SYSTEMS.
BY
WANJOHI DENNIS KAHIKO
REGISTRATION NUMBER: F17/22922/2008
SUPERVISOR: MR. S.L. OGABA
EXAMINER: MR. SAYYID AHMED
SUBMITTED ON 24TH APRIL 2015
This project report was submitted as a partial fulfillment of the requirement for the
award of Bachelor of Science degree in Electrical and Information Engineering from
University of Nairobi.
DECLARATION AND CERTIFICATION
This is my original work and has not been presented for a degree award in this or any other
university.
…………………………………………………
WANJOHI DENNIS KAHIKO.
F17/22922/2008
This report has been submitted to the Department of Electrical and Information Engineering, The
University of Nairobi with my approval as supervisor:
………………………………………………….
MR. S.L. OGABA
Date: ……………………………………
ii
DEDICATION
I dedicate this to both of my parents for the love and support for seeing me this far, also to my
dear brother who has always been there, to you I say thank you and may the LORD GOD grant
you your every need and desire. Thank you.
iii
ACKNOWLEDGEMENTS
I would like by first thanking GOD for seeing me throughout the entire course granting me the
knowledge I needed to pass my examinations and also throughout this project.
Also thank my supervisor, Mr. S.L. Ogaba, for giving me the guidance I needed to carry out this
project, not forgetting all the lectures.
I would like to acknowledge Mr. Rotich, Mr. Wayoike Mr. Kariuki, the lab technicians who
made time to assist me throughout the project.
Lastly I would thank my classmates for their inputs and opinions and wish them prosperity in the
job market and in their future lives at large.
iv
Contents
DECLARATION AND CERTIFICATION.............................................................................................................. ii
DEDICATION ................................................................................................................................................. iii
ACKNOWLEDGEMENTS ................................................................................................................................ iv
ABSTRACT...................................................................................................................................................... 1
CHAPTER 1 .................................................................................................................................................... 2
1.1.
Problem Definition ........................................................................................................................ 2
1.2 Objectives............................................................................................................................................ 3
CHAPTER 2 .................................................................................................................................................... 4
2. LITERATURE REVIEW ............................................................................................................................... 4
2.1
Sound ............................................................................................................................................ 4
2.1.1 Propagation of sound ................................................................................................................... 4
2.2
Working principle of a speaker ..................................................................................................... 6
2.2.1
Loudspeakers ........................................................................................................................ 6
2.3 Filters................................................................................................................................................. 11
2.3.1 Classification of filters ................................................................................................................ 12
2.3.2 Cut-off frequency ....................................................................................................................... 16
2.4
Audio crossover .......................................................................................................................... 19
2.4.1 Active crossover ......................................................................................................................... 20
2.4.2 Passive crossover ...................................................................................................................... 22
2.4.3 Classification based on filter order or slope .............................................................................. 24
2.4.4
Theory of Operation of a Passive Crossover Network ........................................................ 27
2.4.5 Equalization Networks Incorporated in the Passive Crossover Network .................................. 29
CHAPTER 3 .................................................................................................................................................. 31
3. DESIGN ................................................................................................................................................... 31
3.1 Design of 2-way and 3-way crossover networks............................................................................... 31
3.1.1 Choosing of the crossover point ................................................................................................ 31
3.1.2 Inductor and capacitor values.................................................................................................... 32
3.1.3 Calculated inductor and capacitor values .................................................................................. 32
3.1.4 Crossover network Designs ........................................................................................................ 34
v
3.2 Cabinet design................................................................................................................................... 35
CHAPTER 4 .................................................................................................................................................. 38
4. RESULTS AND ANALYSIS ..................................................................................................................... 38
4.1 Computer simulation results............................................................................................................. 38
4.1.1 AC analysis results .................................................................................................................... 38
4.1.2 Frequency response using the bode plotter tool....................................................................... 40
4.1.3 Analysis of the AC analysis graph ............................................................................................... 44
4.1.4
Circuit implementation and speaker system ..................................................................... 46
CHAPTER 5 ................................................................................................................................................... 47
5
CONCLUSION AND RECOMMENDATIONS....................................................................................... 47
5.1
CONCLUSION ............................................................................................................................... 47
5.2
RECOMMENDATIONS.................................................................................................................. 47
REFERENCES ................................................................................................................................................ 48
APPENDICES ................................................................................................................................................ 48
vi
ABSTRACT
Most music systems have very low sound quality, where individual loudspeaker- drives are
incapable of covering the entire audio spectrum from low frequencies to high frequencies,
therefore overworking/stressing an individual drive.
Crossover networks spilt the audio signal into separate frequency bands namely:
Low pass frequency

Band pass frequency

High pass frequency
These respective frequencies are routed to their respective drives for optimization of those
bands.
In modern multi-drive music systems in most cases active crossovers are used which are very
expensive to manufacture, buy and repair. This is countered by the use of passive crossover
networks which are cheap, readily available, simple and easy to replace or repair.
In order to get a clear non-distorted sound from loudspeaker drives proper selection of
speaker wattage rating must be chosen for the specifications of the system and also the cost
incurred when buying them.
1
CHAPTER 1
1. INTRODUCTION
Audio crossover networks are a class of electronic filters used in audio applications. Most
individual loud speaker drives are incapable of covering the entire audio spectrum with
acceptable relative volume and absence of distortion.
Crossovers split the audio signal into separate frequency bands that can be separately routed to
loudspeakers optimized for those bands; low pass, band pass, high pass.
There are two types of crossover networks:
Active crossover networks

Passive crossover networks
Active crossovers are distinguished from passive crossovers in that they divide the audio signal
prior to amplification.
The passive crossovers they are distinguished further which are:
Two way passive crossover networks

Three way passive crossover networks
Two way passive crossover networks include a tweeter and a woofer which are employed and a
three way passive crossover network include a tweeter, a mid-range and a woofer.
In order to understand crossover networks we need to start from the basics and understand sound
as a wave and how its frequency offsets its energy which corresponds to its amplitude and how
to correlate this concept with the working principle of different speaker wattages.
1.1. Problem Definition
To come up with speaker drives selection for 2way and 3way for 50watts and 100watts. The
reasons for this are to:
To minimize the power wastage which is not consumed by the speaker drives.
2

To minimize the cost of buying expensive speaker drives which are of higher wattage.
The method used to come up with specific speaker drives to simulate the network using a
suitable program, getting the crossover points and exporting the AC analysis to Microsoft excel
if the program used is multisim. Where the magnitude is calculated using the summation of yaxis of the AC analysis where the different ratios of speaker drives are calculated.
1.2 Objectives
The objectives of this project were to come up with speaker drive selection for 2-way and 3-way
for 50watts and 100watts systems for:
Design for 2-way and 3-way crossover networks.

2-way speaker drives (woofer, tweeters) for 50watts and 100watts system selection.

3-way speaker drives (woofer, mid-range, and tweeters) for 50watts and 100watts
systems selection.
3
CHAPTER 2
2. LITERATURE REVIEW
2.1
Sound
Sound is a vibration that propagates as a mechanical wave of pressure and displacement, through
some medium (such as air or water). Sometimes sound refers to only those vibrations with
frequencies that are within the range of hearing for humans or for a particular animal.
2.1.1 Propagation of sound
Sound propagates through compressible media such as air, water and solids as longitudinal
waves and also as a transverse waves in solids. The sound waves are generated by a sound
source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations
in the surrounding medium. As the source continues to vibrate the medium, the vibrations
propagate away from the source at the speed of sound, thus forming the sound wave. At a fixed
distance from the source, the pressure, velocity, and displacement of the medium vary in time. At
an instant in time, the pressure, velocity, and displacement vary in space. Note that the particles
of the medium do not travel with the sound wave.
This is intuitively obvious for a solid, and the same is true for liquids and gases (that is, the
vibrations of particles in the gas or liquid transport the vibrations, while the average position of
the particles over time does not change). During propagation, waves can be reflected, refracted,
or attenuated by the medium.
The behavior of sound propagation is generally affected by three things:
•
A relationship between density and pressure. This relationship, affected by temperature,
determines the speed of sound within the medium.
•
The propagation is also affected by the motion of the medium itself. For example, sound
moving through wind. Independent of the motion of sound through the medium, if the medium is
moving, the sound is further transported.
4
• The viscosity of the medium also affects the motion of sound waves. It determines the rate at
which sound is attenuated. For many media, such as air or water, attenuation due to viscosity is
negligible.
When sound is moving through a medium that does not have constant physical properties, it may
be refracted (either dispersed or focused).
The mechanical vibrations that can be interpreted as sound are able to travel through all forms of
matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the
medium. Sound cannot travel through a vacuum [3].
2.1.1.1 Sound wave characteristic and properties
Sound waves are often simplified to a description in terms of sinusoidal plane waves, which are
characterized by these generic properties:
•
Frequency, or its inverse, the period
•
Wavelength
•
Wave number
•
Amplitude
•
Sound pressure
•
Sound intensity
•
Speed of sound
•
Direction
2.1.1.2 Frequency and Amplitude
An audio frequency (abbreviation: AF) or audible frequency is characterized as a periodic
vibration whose frequency is audible to the average human. It is the property of sound that most
determines pitch and is measured in hertz (Hz) [3].
5
The generally accepted standard range of audible frequencies is 20 to 20,000 Hz, although the
range of frequencies individuals hear is greatly influenced by environmental factors. Frequencies
below 20 Hz are generally felt rather than heard, assuming the amplitude of the vibration is great
enough. Frequencies above 20,000 Hz can sometimes be sensed by young people. High
frequencies are the first to be affected by hearing loss due to age and/or prolonged exposure to
very loud noises [1]. The amplitude of a sound wave is specified in terms of pressure hence a
logarithmic dB amplitude scale used. The quietest sound that humans can hear has amplitude of
20µPa or a sound pressure level of 0dB. Sound pressure level (SPL) is the local pressure
deviation from ambient atmospheric pressure caused by a sound wave measured in Pascal [4].
2.2
Working principle of a speaker
Technically we can define speaker, as a component which converts the electrical signals into the
equivalent air vibrations to make audible sound.
To understand the working of a speaker, we first need to understand the concept of sound. A
sound is nothing but vibrations in air particles. When a sound source generates a sound, it
generally makes a vibration in its surrounding air particles which finally reaches to our
eardrum. Sound is characterized by the parameters like frequency, speed, fluctuation, pressure,
etc.
The speaker works on the same concept. It produces vibrations in air particles in order to
generate a sound [2].
2.2.1 Loudspeakers
A loudspeaker (or "speaker", or in the early days of radio "loud-speaker") is an electro acoustic
transducer that produces sound in response to an electrical audio signal input. In other words,
speakers convert electrical signals into audible signals.
The term "loudspeaker" may refer to individual transducers (known as "drivers") or to complete
speaker systems consisting of an enclosure including one or more drivers. To adequately
reproduce a wide range of frequencies, most loudspeaker systems employ more than one driver,
particularly for higher sound pressure level or maximum accuracy. Individual drivers are used to
6
reproduce different frequency ranges. The drivers are named subwoofers (for very low
frequencies); woofers (low frequencies); mid-range speakers (middle frequencies); tweeters
(high frequencies); and sometimes super tweeters, optimized for the highest audible frequencies.
The terms for different speaker drivers differ, depending on the application. In two-way systems
there is no mid-range driver, so the task of reproducing the mid-range sounds falls upon the
woofer and tweeter. When multiple drivers are used in a system, a "filter network", called a
crossover, separates the incoming signal into different frequency ranges and routes them to the
appropriate driver. A loudspeaker system with n separate frequency bands is described as "n-way
speakers": a two-way system will have a woofer and a tweeter; a three-way system employs a
woofer, a mid-range, and a tweeter. Loudspeakers were described as "dynamic" to distinguish
them from the earlier moving iron speaker, or speakers using piezoelectric or electrostatic
systems as opposed to a voice coil that moves through a steady magnetic field [2].
The most common type of driver, commonly called a dynamic loudspeaker, uses a lightweight
diaphragm, or cone, connected to a rigid basket, or frame, via a flexible suspension, commonly
called a spider, that constrains a voice coil to move axially through a cylindrical magnetic gap.
When an electrical signal is applied to the voice coil, a magnetic field is created by the electric
current in the voice coil, making it a variable electromagnet. The coil and the driver's magnetic
system interact, generating a mechanical force that causes the coil (and thus, the attached cone)
to move back and forth, thereby reproducing sound under the control of the applied electrical
signal coming from the amplifier.
Figure 2-1: Cross-section of a standard loudspeaker
7
2.2.1.1Woofer
A woofer is a driver that reproduces low frequencies. The driver combines with the enclosure
design to produce suitable low frequencies. Some loudspeaker systems use a woofer for the
lowest frequencies, sometimes well enough that a subwoofer is not needed. Additionally, some
loudspeakers use the woofer to handle middle frequencies, eliminating the mid-range driver. This
can be accomplished with the selection of a tweeter that can work low enough that, combined
with a woofer that responds high enough, the two drivers add coherently in the middle
frequencies. It is commonly used to produce low frequency sounds, typically from around 40
hertz up to about a kilohertz or higher. The most common design for a woofer is the
electrodynamics’ driver, which typically uses a stiff paper cone, driven by a voice coil which is
surrounded by a magnetic field.
Figure 2-2: A pair of woofers
2.2.1.2 Mid-Range
A mid-range speaker is a loudspeaker driver that reproduces middle frequencies. Mid-range
driver diaphragms can be made of paper or composite materials, and can be direct radiation
drivers (rather like smaller woofers) or they can be compression drivers (rather like some tweeter
designs). If the mid-range driver is a direct radiator, it can be mounted on the front baffle of a
loudspeaker enclosure, or, if a compression driver, mounted at the throat of a horn for added
output level and control of radiation pattern. A mid-range speaker is a loudspeaker driver that
reproduces sound in the frequency range from approximately 300 to 5000 Hz. It is also known as
a squawker.
8
Mid-range drivers are usually cone types or, less commonly, dome types, or compression horn
drivers. The radiating diaphragm of a cone mid-range unit is a truncated cone, with a voice coil
attached at the neck, along with the spider portion of the suspension, and with the cone surround
at the wide end. Cone mid-range drivers typically resemble small woofers. The most common
material used for mid-range cones is paper, occasionally impregnated and/or surface-treated with
polymers or resins in order to improve vibration damping.
A mid-range driver is called upon to handle the most significant part of the audible sound
spectrum, the region where the most fundamentals emitted by musical instruments and, most
importantly, the human voice, lie. This region contains most sounds which are the most familiar
to the human ear, and where discrepancies from faithful reproduction are most easily observed. It
is therefore paramount that a mid-range driver of good quality be capable of low- distortion
reproduction.
Figure 2-3: A pair of mid-range
2.2.1.3 Tweeter
A tweeter is a high-frequency driver that reproduces the highest frequencies in a speaker system.
A tweeter is a special type of loudspeaker (usually dome or horn-type) that is designed to
produce high audio frequencies, typically from around 2,000 Hz to 20,000 Hz (generally
considered to be the upper limit of human hearing). Specialty tweeters can deliver high
frequencies up to 100 KHz. The name is derived from the high pitched sounds made by some
birds, especially in contrast to the low woofs made by many dogs, after which low- frequency
drivers are named (woofers).
9
Nearly all tweeters are electrodynamic drivers, using a voice coil suspended within a fixed
magnetic field. These designs operate by applying current from the output of an amplifier circuit
to a coil of wire, called a voice coil. The voice coil produces a varying magnetic field, which
works against the fixed magnetic field of a magnet around which the cylindrical voice coil is
suspended, forcing the voice coil—and the diaphragm attached to it—to move. This mechanical
movement exactly resembles the waveform of the electronic signal supplied from the amplifier's
output to the voice coil. Since the coil is attached to a diaphragm, the vibratory motion of the
voice coil transmits to the diaphragm; the diaphragm in turn vibrates the air — thus creating air
motions or audio waves, which we hear as high sounds.
Figure 2-4: A pair of tweeters
2.2.1.4 Speaker Enclosure
A loudspeaker enclosure is a purpose-engineered cabinet in which speaker drivers and
associated electronic hardware, such as crossover circuits and amplifiers, are mounted.
Enclosures may range in design from simple, rectangular particle-board boxes to very complex
cabinets that incorporate composite materials, internal baffles, ports and acoustic insulation.
The primary role of the enclosure is to prevent sound waves generated by the rearward-facing
surface of the diaphragm of an open driver interacting with sound waves generated at the front of
the driver. Because the forward- and rearward-generated sounds are out of phase with each other,
any interaction between the two in the listening space creates a distortion of the original signal as
it was intended to be reproduced. Additionally, because they would travel different paths through
the listening space, the sound waves would arrive at the listener's position at slightly different
times; introducing echo and reverberation effects not part of the original sound.
10
The enclosure also plays a role in managing vibration induced by the driver frame and moving
air mass within the enclosure, as well as heat generated by driver voice coils and amplifiers
(especially where woofers and subwoofers are concerned). Sometimes considered part of the
enclosure, the base may include specially designed "feet" to decouple the speaker from the floor
[2].
2.2.1.5 Relationship between speaker power, sound and frequency
Why a subwoofer must have a large diameter? Why can't it have the same diameter as a tweeter?
This is a very common thing that people think, it also yields statements like "you can't ever get
low bass out of headphones because the drivers are so small" or that there is some kind of
relationship between the diameter of the driver and the largest wavelength (lowest frequency) it
can reproduce. Low-frequency drivers are large and high-frequency drivers are small. This is due
to the energy carried by the sound waves. Frequency is directly proportional to energy hence, a
very high-frequency wave has very high energy, and it only takes relatively little amplitude to
carry a lot of energy. Low frequency waves are not very energetic due to this, and hence require
very high amplitude to have the same energy.
In order to be loud, you need a lot of low-frequency amplitude, and relatively little highfrequency amplitude. So high-frequency drivers don't need to displace a whole lot of air and
create a lot of pressure, so they can be small. Additionally, high frequencies obviously require
very fast motion, which requires a driver with very little mass [5].
Power (P) delivered by an amplifier to a loudspeaker is determined by dividing the voltage (v)
squared by the impedance of the speaker (z). This voltage corresponds to amplitude of the sound
wave since the electrical signal is converted to equivalent air vibration to create audible sound.
i.e. P= V2/Z [6].
2.3 Filters
Electronic filters are analog circuits which perform signal processing functions, specifically to
remove unwanted frequency components from the signal, to enhance wanted ones, or both [7].
11
Electronic filters can be classified into;
•
Passive or active
•
Analog or digital
•
High-pass, low-pass, band pass, band-reject (band reject; notch), or all-pass.
•
Discrete-time (sampled) or continuous-time
•
Linear or non-linear
•
Infinite impulse response (IIR type) or finite impulse response (FIR type)
The most common types of electronic filters are linear filters, regardless of other aspects of their
design.
2.3.1 Classification of filters
2.3.1.1 Passive filters
Passive implementations of linear filters are based on combinations of resistors (R), inductors (L)
and capacitors (C). These types are collectively known as passive filters, because they do not
depend upon an external power supply and/or they do not contain active components such as
transistors.
Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do
the reverse. A filter in which the signal passes through an inductor, or in which a capacitor
provides a path to ground, presents less attenuation to low-frequency signals than high-frequency
signals and is therefore a low-pass filter. If the signal passes through a capacitor, or has a path to
ground through an inductor, then the filter presents less attenuation to high-frequency signals
than low-frequency signals and therefore is a high-pass filter. Resistors on their own have no
frequency-selective properties, but are added to inductors and capacitors to determine the timeconstants of the circuit, and therefore the frequencies to which it responds.
12
The inductors and capacitors are the reactive elements of the filter. The number of elements
determines the order of the filter. In this context, an LC tuned circuit being used in a band- pass
or band-stop filter is considered a single element even though it consists of two components.
At high frequencies (above about 100 megahertz), sometimes the inductors consist of single
loops or strips of sheet metal, and the capacitors consist of adjacent strips of metal. These
inductive or capacitive pieces of metal are called stubs.
2.3.1.2 Active filters
Active filters are implemented using a combination of passive and active (amplifying)
components, and require an outside power source. Operational amplifiers are frequently used in
active filter designs. These can have high Q factor, and can achieve resonance without the use of
inductors. However, their upper frequency limit is limited by the bandwidth of the amplifiers.
2.3.1.3 High-pass filters
A high-pass filter (HPF) is an electronic filter that passes high-frequency signals but attenuates
(reduces the amplitude of) signals with frequencies lower than the cutoff frequency. The actual
amount of attenuation for each frequency varies from filter to filter. A high-pass filter is usually
modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut
filter. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero
average voltages or RF devices. Capacitor blocks the low frequencies while inductor shunts them
opposing all currents having a frequency lower than its specified frequencies. A capacitor that is
used in series with the source of both high and low will respond differently to high- frequency,
low-frequency, and direct currents.
It will offer little opposition to the passage of high frequency currents, great opposition to the
passage of low frequency currents, and completely block direct currents .The value of the
capacitor must be chosen so that it allows the passage of all currents having frequencies above
desired value, and opposes those having frequencies below the desired value.
Then, in order to shunt the undesired low-frequency currents back to the source, an inductor is
used.
13
Figure 2-5: A passive first order high-pass filter.
Figure 2-6: An active high-pass filter
Figure 2-7: Capacitor block low frequencies
Figure 2-8: Inductor shunts low frequencies back to the source.
14
2.3.1.4 Low-pass filter
A low-pass filter is a filter that passes low-frequency signals and attenuates (reduces the
amplitude of) signals with frequencies higher than the cutoff frequency. The actual amount of
attenuation for each frequency varies depending on specific filter design. It is sometimes called a
high-cut filter, or treble cut filter in audio applications. A low-pass filter is the opposite of a
high-pass filter.
Low-pass filters exist in many different forms, including electronic circuits (such as a hiss filter
used in audio), anti-aliasing filters for conditioning signals prior to analog-to-digital conversion,
digital filters for smoothing sets of data, acoustic barriers, blurring of images, and so on. The
moving average operation used in fields such as finance is a particular kind of low-pass filter,
and can be analyzed with the same signal processing techniques as are used for other low-pass
filters. Low-pass filters provide a smoother form of a signal, removing the short-term
fluctuations, and leaving the longer-term trend. In this case the inductor in series with the load is
used to block high frequencies and capacitors in parallel to shunt high frequencies back to the
source.
2.3.1.5 Band-pass filters
A band-pass filter is a device that passes frequencies within a certain range and rejects
(attenuates) frequencies outside that range.
Figure 2-9:: Bandwidth measured at half-power
points (gain -3 dB, √2/2, or about 0.707 relative to peak) on a diagram showing magnitude
transfer function versus frequency for a band-pass filter.
15
These filters can be created by combining a low pass filter with a high pass filter into a single
filter. The filter bandwidth is simply the difference between the upper and lower cut off
frequencies
Figure 2-10: Block diagram showing high and low filters in cascade.
2.3.2 Cut-off frequency
From our discussion above, the term cut-off frequency has been mentioned severally. What is
cut-off frequency? A cutoff frequency, corner frequency, or break frequency is a boundary in a
system's frequency response at which energy flowing through the system begins to be reduced
(attenuated or reflected) rather than passing through.
Typically in electronic systems such as filters and communication channels, cutoff frequency
applies to an edge in a low-pass, high-pass, band-pass, or band-stop characteristic – a frequency
characterizing a boundary between a pass-band and a stop-band. It is sometimes taken to be the
point in the filter response where a transition band and pass-band meet, for example as defined
by a 3 dB corner, a frequency for which the output of the circuit is −3 dB of the nominal passband value. Alternatively, a stop-band corner frequency may be specified as a point where a
transition band and a stop-band meet: a frequency for which the attenuation is larger than the
required stop-band attenuation, which for example may be 30 dB or 100 dB.
In the case of a waveguide or an antenna, the cutoff frequencies correspond to the lower and
upper cutoff wavelengths.
16
Fig 2.11: A bode plot of the Butterworth filter's frequency response, with corner frequency
labeled. (The slope −20 dB per decade also equals −6 dB per octave.)
Another definition is cutoff frequency or corner frequency is the frequency either above or
below which the power output of a circuit, such as a line amplifier, or electronic filter has fallen
to a given proportion of the power in the pass band. Most frequently this proportion is one half
the pass band power, also referred to as the 3 dB point since a fall of 3 dB corresponds
approximately to half power. As a voltage ratio this is a fall to √1/2 ≈ 0.707of the pass band
voltage [8].
2.3.2.1 Filter orders
In all cases, at the cutoff frequency, the filter attenuates the input power by half or 3 dB. So the
order of the filter determines the amount of additional attenuation for frequencies higher than the
cutoff frequency [7].
•
A first-order filter, for example, reduces the signal amplitude by half (so power reduces by
a factor of 4), or 6 dB, every time the frequency doubles (goes up one octave); more precisely,
the power roll-off approaches 20 dB per decade in the limit of high frequency. The magnitude
Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a
diagonal line above the cutoff frequency. There is also a "knee curve" at the boundary between
17
the two, which smoothly transitions between the two straight line regions. If the transfer function
of a first-order low-pass filter has a zero as well as a pole, the Bode plot flattens out again, at
some maximum attenuation of high frequencies; such an effect is caused for example by a little
bit of the input leaking around the one-pole filter; this one-pole–one-zero filter is still a firstorder low-pass.
•
A second-order filter attenuates higher frequencies more steeply. The Bode plot for this
type of filter resembles that of a first-order filter, except that it falls off more quickly. For
example, a second-order Butterworth filter reduces the signal amplitude to one fourth its original
level every time the frequency doubles (so power decreases by 12 dB per octave, or 40 dB per
decade). Other all-pole second-order filters may roll off at different rates initially depending on
their Q factor, but approach the same final rate of 12 dB per octave; as with the first-order filters,
zeroes in the transfer function can change the high- frequency asymptote.
•
Third- and higher-order filters are defined similarly. In general, the final rate of power
roll-off for an order- ‘n’ all-pole filter is 6n dB per octave (i.e., 20n dB per decade).
On any Butterworth filter, if one extends the horizontal line to the right and the diagonal line to
the upper-left (the asymptotes of the function), they intersect at exactly the cutoff frequency. The
frequency response at the cutoff frequency in a first-order filter is 3 dB below the horizontal line.
The various types of filters (Butterworth filter, Chebyshev filter, Bessel filter, etc.) all have
different-looking knee curves. Many second-order filters have "peaking" or resonance that puts
their frequency response at the cutoff frequency above the horizontal line. Furthermore, the
actual frequency where this peaking occurs can be predicted without calculus, as shown by
Cartwright. For third-order filters, the peaking and its frequency of occurrence can too be
predicted without calculus as recently shown by Cartwright.
The meanings of 'low' and 'high'—that is, the cutoff frequency—depend on the characteristics of
the filter. The term "low-pass filter" merely refers to the shape of the filter's response; a highpass filter could be built that cuts off at a lower frequency than any low-pass filter—it is their
responses that set them apart. Electronic circuits can be devised for any desired frequency range,
right up through microwave frequencies (above 1 GHz) and higher.
18
What do we mean by 6dB per octave? In electronics, an octave is a doubling or halving of a
frequency [7]. Along with the decade, it is a unit used to describe frequency bands or frequency
ratios.
A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio:
Octaves=log2 (f2/f1)
An amplifier or filter may be stated to have a frequency response of ±6dB per octave over a
particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor
of 4 in power), when the frequency changes by a factor of 2. This slope, or more precisely 1log10
(4) =6.0206 decibels per octave, corresponds to an amplitude gain proportional to frequency,
which is equivalent to ±20dB per decade (factor of 10 amplitude gain change for a factor of 10
frequency change). This would be a first-order filter.
2.4
Audio crossover
Audio crossovers are a class of electronic filter used in audio applications. Most individual
loudspeaker drivers are incapable of covering the entire audio spectrum from low frequencies to
high frequencies with acceptable relative volume and absence of distortion so most hi-fi speaker
systems use a combination of multiple loudspeakers drivers, each catering for a different
frequency band. Crossovers split the audio signal into separate frequency bands that can be
separately routed to loudspeakers optimized for those bands.
The need for a crossover can be attributed to the inability of most drivers to reproduce the entire
musical spectrum smoothly and efficiently hence because of this most speaker systems are
comprised of several drivers each of which is dedicated to the reproduction of a specific range of
frequencies.
These frequencies are routed to the appropriate driver by a crossover network. This audio device
divides frequencies into two or more frequency bands. A crossover network also prevents
potentially damaging low frequency energy (woofer) from reaching the midrange or tweeter [9].
There are two types of audio crossovers based on their location in the audio signal path:
19
•
Active crossover.
•
Passive crossover
2.4.1 Active crossover
Active crossovers are distinguished from passive crossovers in that they divide the audio signal
prior to amplification. Active crossovers come in both digital and analog varieties. Digital active
crossovers often include additional signal processing, such as limiting, delay, and equalization.
An active crossover contains active components (i.e., those with gain) in its filters. In recent
years, the most commonly used active device is an op-amp; active crossovers are operated at
levels suited to power amplifier inputs in contrast to passive crossovers which operate after the
power amplifier's output, at high current and in some cases high voltage. On the other hand, all
circuits with gain introduce noise, and such noise has a deleterious effect when introduced prior
to the signal being amplified by the power amplifiers.
Figure 2-12: Active crossover
Active crossovers always require the use of power amplifiers for each output band. Thus a 2way active crossover needs two amplifiers—one each for the woofer and tweeter.
This means that an active crossover based system will often cost more than a passive crossover
based system. Despite the cost and complication disadvantages, active crossovers provide the
following advantages over passive ones:
20
•
A frequency response independent of the dynamic changes in a driver's electrical
characteristics.
•
Typically, the possibility of an easy way to vary or fine tune each frequency band to the
specific drivers used. Examples would be crossover slope, filter type (e.g., Bessel, Butterworth,
etc.), relative levels.
•
Better isolation of each driver from signals handled by other drivers, thus reducing
intermodulation distortion and overdriving.
•
The power amplifiers are directly connected to the speaker drivers, thereby maximizing
amplifier damping control of the speaker voice coil, reducing consequences of dynamic changes
in driver electrical characteristics, all of which are likely to improve the transient response of the
system.
•
Reduction in power amplifier output requirement. With no energy being lost in passive
components, amplifier requirements are reduced considerably (up to 1/2 in some cases), reducing
costs, and potentially increasing quality.
2.4.1.1 Advantages and disadvantages of Active Crossover
2.4.1.1.1 Advantages
•
They lack inductors, thereby reducing the problems associated with those components.
•
The op amp-based active filter can achieve very good accuracy, provided that low- tolerance
resistors and capacitors are used.
•
They can easily be made tunable; that is, controls can be added to vary the cut off frequency
which is a very useful facility in difficult communication situations where only the minimum
bandwidth for intelligible communication is required. A relatively recent development in the
control of the response of active filters involves the switching capacitors and resistors at high
frequency, varying the effective values of these components.
•
The active filter crossover components will not change to the short term due to internal
heating.
21
•
They are cheap since they have no inductors which are very expensive.
2.4.1.1.2 Disadvantages
• Active filters generate noise due to their amplifying circuitry.
•
High power consumption unlike passive filters.
2.4.2 Passive crossover
A passive crossover is different from active crossover since its location in the audio signal path is
after the amplifier i.e. between the amplifier and the drivers and it is also made entirely of
passive components, arranged most commonly in a Cauer topology to achieve a Butterworth
filter. Passive filters use resistors combined with reactive components such as capacitors and
inductors. Very high performance passive crossovers are likely to be more expensive than active
crossovers since individual components capable of good performance at the high currents and
voltages at which speaker systems are driven are hard to make. Polypropylene, metalized
polyester foil, paper and electrolytic capacitors are common. Inductors may have air cores,
powdered metal cores, ferrite cores, or laminated silicon steel cores, and most are wound with
enameled copper wire. Some passive networks include devices such as fuses, PTC devices, bulbs
or circuit breakers to protect the loudspeaker drivers from accidental overpowering. Modern
passive crossovers increasingly incorporate equalization networks (e.g., Zobel networks) that
compensate for the changes in impedance with frequency inherent in virtually all loudspeakers.
The issue is complex, as part of the change in impedance is due to acoustic loading changes
across a driver's pass-band.
On the negative side, passive networks may be bulky and cause power loss. They are not only
frequency specific, but also impedance specific. This prevents interchangeability y with speaker
systems of different impedances. Ideal crossover filters, including impedance compensation and
equalization networks, can be very difficult to design, as the components interact in complex
ways. Crossover design expert Siegfried Linkwitz said of them that "the only excuse for passive
crossovers is their low cost. Their behavior changes with the signal level dependent dynamics of
the drivers. They block the power amplifier from taking maximum control over the voice coil
motion. They are a waste of time, if accuracy of reproduction is the goal.
22
Alternatively, passive components can be utilized to construct filter circuits before the amplifier.
This is called passive line-level crossover.
Figure 2-13: A passive crossover network.
2.4.2.1 Advantages and disadvantages of Passive Crossover
2.4.2.1.1 Advantages
• No power supply required.
•
It can handle large currents and high voltages.
•
Requires least number of components for a given filter
•
Very reliable
•
They are not restricted by the bandwidth limitations of op amps; they can work well at very
high frequencies.
•
They generate little noise when compared with circuits using active gain elements. The noise
that they produce is simply the thermal noise from the resistive components.
2.4.2.1.2 Disadvantages
• High cost. Inductors are very expensive since they are coiled using copper wire.
• Large components (inductors and capacitors).
•
Limited ability to adjust the circuit as desired due to limited choice of high power level
components.
23
• Cause substantial overall signal loss and a significant reduction in damping factor between
voice coil and cross-over.
Since my point of focus is passive crossover networks, I will discuss it in detail. These networks
are comprised of inductors, capacitors, or a combination of each.
An inductor, also known as a "coil" or "choke", is a coil of wire which may or may not have an
iron or ferrite core. Inductors with an iron core are called "iron core inductors" while those
without are called "air core inductors". The basic characteristics of both types are the same. As
the frequency passing through an inductor increases, so does the inductive reactance of the coil.
This rise in impedance at higher frequencies allows us to use the inductor as a filter that passes
low frequencies but chokes off high ones.
Capacitors do just the opposite. As frequency decreases, the capacitors reactance increases. That
is, capacitors pass high frequencies and filter out low ones. These capacitors are generally nonpolarized electrolytes, polypropylene, or Mylar and consist of interleaved layers of foil and
insulating material.
One common myth pertaining to passive crossovers is that they "soak up" the power that is not
used for each particular driver. While there is some insertion loss, the filtering action actually
takes place due to the impedance mismatch created by the network.
2.4.3 Classification based on filter order or slope
Just as filters have different orders, so do crossovers, depending on the filter slope they
implement [8]. The final acoustic slope may be completely determined by the electrical filter or
may be achieved by combining the electrical filter's slope with the natural characteristics of the
driver. In the former case, the only requirement is that each driver has a flat response at least to
the point where its signal is approximately −10dB down from the pass-band. In the latter case,
the final acoustic slope is usually steeper than that of the electrical filters used. A third- or fourthorder acoustic crossover often has just a second order electrical filter. This requires that speaker
drivers be well behaved a considerable way from the nominal crossover frequency, and further
that the high frequency driver be able to survive a considerable input in a frequency range below
its crossover point. This is difficult in actual practice. In the discussion below, the characteristics
24
of the electrical filter order is discussed, followed by a discussion of crossovers having that
acoustic slope and their advantages or disadvantages.
Most audio crossovers use first to fourth order electrical filters. Higher orders are not generally
implemented in passive crossovers for loudspeakers, but are sometimes found in electronic
equipment under circumstances for which their considerable cost and complexity can be
justified.
2.4.3.1 First order
First-order filters have a 20 dB/decade (or 6 dB/octave) slope. All first-order filters have a
Butterworth filter characteristic. First-order filters are considered by many audiophiles to be
ideal for crossovers. This is because this filter type is 'transient perfect', meaning it passes both
amplitude and phase unchanged across the range of interest. It also uses the fewest parts and has
the lowest insertion loss (if passive). A first-order crossover allows more signals of unwanted
frequencies to get through in the LPF and HPF sections than do higher order configurations.
While woofers can easily take this (aside from generating distortion at frequencies above those
they can properly handle), smaller high frequency drivers (especially tweeters) are more likely to
be damaged since they are not capable of handling large power inputs at frequencies below their
rated crossover point. In practice, speaker systems with true first order acoustic slopes are
difficult to design because they require large overlapping driver bandwidth, and the shallow
slopes mean that non-coincident drivers interfere over a wide frequency range and cause large
response shifts off-axis.
2.4.3.2 Second order
Second-order filters have a 40 dB/decade (or 12 dB/octave) slope. Second-order filters can have
a Bessel, Linkwitz-Riley or Butterworth characteristic depending on design choices and the
components used. This order is commonly used in passive crossovers as it offers a reasonable
balance between complexity, response, and higher frequency driver protection. When designed
with time aligned physical placement, these crossovers have a symmetrical polar response, as do
all even order crossovers.
25
It is commonly thought that there will always be a phase difference of 180° between the outputs
of a (second order) low-pass filter and a high-pass filter having the same crossover frequency.
And so, in a 2-way system, the high-pass section's output is usually connected to the high
frequency driver 'inverted', to correct for this phase problem. For passive systems, the tweeter is
wired with opposite polarity to the woofer; for active crossovers the high-pass filter's output is
inverted. In 3-way systems the mid-range driver or filter is inverted. However, this is generally
only true when the speakers have a wide response overlap and the acoustic centers are physically
aligned.
2.4.3.3 Third order
Third-order filters have a 60 dB/decade (or 18 dB/octave) slope. These crossovers usually have
Butterworth filter characteristics; phase response is very good, the level sum being flat and in
phasequadratue, similar to a first order crossover. The polar response is asymmetric. In the
original D'Appolito MTM arrangement, a symmetrical arrangement of drivers is used to create a
symmetrical off-axis response when using third-order crossovers.
Third-order acoustic crossovers are often built from first- or second-order filter circuits.
Figure 2-14: 1st order, 2nd order and 3rd order for high-pass, low-pass and band-pass filters
A first order crossover is often what you will find in PA systems. You will often find a second
order (12db per octave) in studio monitors and many higher end home speaker systems. The
reasons for this are many. There are major differences between the actual speakers found in a PA
system versus those used in a Studio monitor or home speaker system. Studio monitor systems
26
components are tightly controlled and everything is matched specifically to the enclosure and is
made to give as flat a frequency response as possible; this is done using speakers that are of
lower efficiency. PA speakers tend to be of very high output. You can use second order
crossovers in PA systems, many of the integrated multi- speaker cabinets available today have
them.
2.4.4 Theory of Operation of a Passive Crossover Network
If we place a capacitor in series with a 4 ohm tweeter, we have created a first order (6 dB/octave)
high pass filter. As frequency goes down, the capacitive reactance of the capacitor goes up. At
the crossover point, the impedance presented by the capacitor will be equal to the impedance of
the tweeter. Since the capacitor is in series with the tweeter, the effective load impedance "seen"
by the amplifier is 4 + 4 or 8 ohms. This rise in load impedance causes a 3 dB reduction in
output power at the amplifier. As the frequency continues to go down, the effective impedance of
the network continues to rise and the output of the amplifier continues to be reduced at a rate
determined by the slope of the crossover. In our example, the roll-off rate would occur at 6
dB/octave because it is a first order network.
The number of inductors and capacitors in a network determines its order. For example, if a
network consisted of one component it would be a first order network. Two components would
comprise a second order network and so on. Final response roll off rates occur in multiples of 6
dB/octave, according to the order of the filter. Consequently, a first order network would have a
slope of 6 dB/octave; a second order network would have a slope of 12 dB/octave; and so on.
It is generally accepted that 1st order networks should only be used for low-pass filters because a
6 dB/octave roll off rate will not provide adequate protection for midrange and tweeter drivers.
On the other hand, slopes greater than 18 dB/octave tend to suffer from poor transient response,
audible ringing, phase disparity among the drivers, and excessive insertion loss.
Insertion loss is a term used to account for the power that is lost when a passive crossover
network is used. The most significant power loss occurs in the inductor due to the resistance of
the wire. Some inductors can have dc resistances as high as 1 ohm. This can rob almost 20
27
percent of the power intended for the drivers. Although this may seem high, 20 percent is only
about a 1 dB drop in output level.
Resistance in the crossover network also degrades the damping ability of the amplifier. Since the
damping factor is the ratio of the load impedance to the output impedance of the amplifier,
adding any resistance to the output impedance of the amp will greatly reduce the ability of the
amp to control cone movement. The result of this could be bass that lacks definition or sounds
muddy.
In order to reduce these problems, you must be very careful when selecting the components for
your passive crossover network. The best sounding (and most expensive) capacitors are the
Mylar and polypropylene high-voltage variety. These should always be used for high-pass filters
because they are series components.
For low-pass filters, any type of capacitor can be used; however, the choice of inductor is more
critical since it is the series element. Air core inductors are better sounding because of their
lower distortion figures; unfortunately, they tend to have a higher dc resistance than iron core
varieties.
Of all the variables involved in crossover design, the crossover point is the most ambiguous.
Factors affecting the selection process are size of the drivers used, roll off slope, and the number
of crossover points in the system [10].
28
Figure 2-15: A twoway and three-way 1st order crossover networks and their frequency response.
2.4.5 Equalization Networks Incorporated in the Passive Crossover Network
2.4.5.1 Zobel network
An Impedance Equalization Circuit, also known as a Zobel circuit, can be used to counteract the
rising impedance of a voice coil caused by inductive reactance. The cause of this impedance rise
is due to the speaker's voice coil inductance (Le). A schematic of an impedance equalization
circuit (Zobel) is shown below. The impedance equalization circuit is usually placed after the
crossover circuitry.
Figure 2-16: An example of a Zobel network.
2.4.5.2 Speaker L-pad
A speaker L pad is a special configuration of rheostats used to control volume while maintaining
constant load impedance on the output of the audio amplifier. It consists of a parallel and series
resistor in an "L" configuration. As one increase in resistance, the other decreases, thus
maintaining constant impedance, at least in one direction. To maintain constant impedance in
both directions, a "T" pad must be used. In loudspeakers it is only necessary to maintain
impedance to the crossover; this avoids shifting the crossover point.
29
A constant-impedance load was important in the days of vacuum tube power amplifiers, because
such amplifiers often did not work efficiently when terminated into impedance greatly different
than their specified output impedance. This was only true of full range speakers. Most modern
applications for full range speakers use tapped transformers. Maintaining constant impedance is
less important to modern amplifiers using solid state electronics.
In high frequency horns, the L Pad is seen by the crossover, not the amp. L pads may not
necessarily use infinitely variable rheostats, but instead a multi-position rotating selector switch
wired to resistors on the back. Tapped transformers are not L pads—low-end manufacturers to
the contrary; they are auto formers. L-pads can also be used at line level, mostly in proapplications
30
CHAPTER 3
3. DESIGN
3.1 Design of 2-way and 3-way crossover networks
This where we designed 2-way and 3-way crossover networks using the theory learnt before,
where the 2-way spilt the frequency into two bands of frequency and the 3-way spilt the
frequency into three bands of frequency. In the design of crossover networks crossover points are
very critical when being chosen. Keeping in mind that all the crossover networks were of 1st
order.
3.1.1 Choosing of the crossover point
The speaker impedance were found to be:
Woofer- 8Ω

Mid-range- 4Ω

Tweeter- 8Ω
For the 2-way 50 watts the first crossover point was at (fc1) = 604.56 HZ.
For the 2-way 100 watts the first crossover point was at (fc2) = 906.86HZ.
For the 3-way 50 watts the crossover points were: First crossover point (fc1) = 490HZ.
 Band pass crossover points (FL) =602.86HZ and (FH) = 2.122KHZ.
 Second crossover point (fc2) = 2.926KHZ.
For the 3-way 100watts the crossover points were: First crossover point (fc1) = 1.061KHZ.
 Band pass crossover points (FL) = 1.205KHZ and (FH) = 3.183KHZ.
 Second crossover point (fc2) = 4.232KHZ.
31
3.1.2 Inductor and capacitor values
From the chosen crossover points, the theory learnt before and deriving the capacitor and
inductor formulas from first principle we were able to calculate the capacitor and inductor values
and compared them to standard values which are in the market.
Knowing the cross-over points and the speaker impedance, reactance of an inductor from first
principles is given by:
XL= 2πfL from this we can get:
 L=
Reactance of a capacitor from first principles is given by:
 Xc =
from this we can get:
C=
for this case, at the cross-over point the reactance is equal to the
speaker impedance= Zo.
L=
and C=
Where fc is the cross-over frequency.
3.1.3 Calculated inductor and capacitor values
2-way 50 watts
Low pass section
L1 = 8 / 2Π*604.56 = 2.1mH
High pass section
C1 = 1 / 2Π*604.56*8 = 33µF
2-way 100 watts
Low pass filter section
L1 = 8 / 2Π*906.86 = 1.4mH
High pass filter section
C1 = 1 / 2Π*906.86*8 = 22µF
32
3-way 50 watts
Low pass filter section
L1 = 8 / 2Π*490 = 2.6mH
Band pass filter section
C1 = 1 / 2Π*602.86*4 = 66µF
L2 = 4 / 2Π*2122 = 300µH
High pass filter section
C2 = 1 / 2Π*2926*8 = 6.8µF
3-way 100 watts
Low pass filter section
L1 = 8 / 2𝛱*1061 = 1.2mH
Band pass filter section
C1 = 1 / 2Π*1205*4 = 33µF
L2 = 4 / 2Π*3183 = 200µH
High pass filter section
C2 = 1 / 2Π*4232*8 = 4.7µF
For the inductor, it was coiled manually and a formula that was researched from the internet
was used but it was a little bit tedious.
L (µH) = 31.6*N2*r12 / 6*r1+9*L+10*(r2-r1)
Where…
L (µH) = Inductance in micro Henries
33
N = Total Number of turns
R1= Radius of the inside of the coil in meters
R2= Radius of the outside of the coil in meters
L = Length of the coil in meters
3.1.4 Crossover network Designs
3.1.4.1
2- way cross over network designs
Figure 3-1: 2-way 50 watts crossover design
Figure 3-2: 2-way 100 watts crossover design
34
3.1.4.2 3way crossover network design
Figure 3-3: 3-way 50 watts crossover design
Figure 3-4: 3-way 100watts crossover design
3.2 Cabinet design
The cabinet was designed using Bass Box Pro software where it calculated the power of the
woofer and giving us the measurements of the cabinets. They were as follows and all
measurements’ are in inches:-
35
30”
11”
12”
Figure 3-5 schematic drawing of the 2-way and 3- way 100 watts system selection.
23”
10”
12”
Figure 3-6 schematic diagram of the 2-way and 3- way 50 watts system selection.
36
Figure 3-7: Early stages of the cabinets being built.
37
CHAPTER 4
4. RESULTS AND ANALYSIS
4.1 Computer simulation results
In manual simulations where it involves obtaining results using the crossover network and an
oscilloscope for accuracy where this becomes an issue. Therefore in order to overcome this
challenge we used a computer simulation in order to obtain AC analysis of the crossover circuits
used.
From the AC analysis it observed how power gain for the different drives varied with frequency.
For example for woofer, power gain covered the largest area with respect to the frequency range
followed by the power gain of the mid-range and then tweeter which covered the smallest area.
In the literature review, it was researched that theoretically woofer wattage is more than that of
the tweeter. For a multi- drive music system, energy of the sound waves from all the drives
should be same so there should be a kind of a balance between the drives. For example for a
woofer it compensates for its low frequency energy by having high amplitude which then
corresponds to voltage of the audio signal which then means woofer will have the highest power
rating.
4.1.1 AC analysis results
The following are the AC analysis for the cross-over designs. The vertical scale was changed
linear scale from logarithmic scale to observe the responses accurately. Computer simulation was
done using MULTISM 11.0 software. The analysis was done for frequency range of 10Hz to 10
KHz.
38
Figure 4-1: AC analysis for 1st order 2-way crossover for 50 watts speaker system.
Figure 4-2: AC analysis for 1st order 2-way crossover for 100 watts speaker system.
Figure 4-3: AC for 1st order 3-way crossover for 50 watts speaker system.
39
Figure 4-4: AC for 1st order 3-way crossover for 100 watts speaker system.
From the different AC analyses we observe the different curves for the different wattages for the
2-way and 3-way.
4.1.2 Frequency response using the bode plotter tool
The roll-offs and the -3db point can be observed better using the bode plotter tool in the
simulation tool. The bode plotter was connected across the output. The following are the
responses observed for the implemented circuit:
4.1.2.1- 1st order 2-way 50 watts cross-over network
4.1.2.1.1- Low Pass Section
Figure 4-5: bode plot 1st order 2-way 50 watts crossover network low pass.
40
4.1.2.1.2- High Pass Section
Figure 4-6: bode plot 1st order 2-way 50 watts crossover network high pass.
4.1.2.2- 1st order 2-way 100 watts cross-over network
4.1.2.2.1- Low Pass Section
Figure 4-7: bode plot 1st order 2-way 100 watts crossover network low pass.
4.1.2.2.2- High Pass Section
Figure 4-8: bode plot 1st order 2-way 100 watts crossover network high pass.
41
4.1.2.3- 1st order 3-way 50 watts cross-over network
4.1.2.3.1- Low Pass Section
Figure 4-9: bode plot 1st order 3-way 50 watts crossover network low pass.
4.1.2.3.2- Band Pass Section
Figure 4-10: bode plot 1st order 3-way 50 watts crossover network band pass.
4.1.2.3.3- High Pass Section
Figure 4-11: bode plot 1st order 3-way 50 watts crossover network high pass.
42
4.1.2.4- 1st order 3-way 100 watts cross-over network
4.1.2.4.1- Low Pass Section
Figure 4-12: bode plot 1st order 3-way 100 watts crossover network low pass.
4.1.2.4.2- Band Pass Section
Figure 4-13: bode plot 1st order 3-way 100 watts crossover network band pass.
4.1.2.4.3- High Pass Section
Figure 4-14: bode plot 1st order 3-way 100 watts crossover network high pass.
43
4.1.3 Analysis of the AC analysis graph
From the computer simulation we got the AC analysis which will enable us to get the individual
speaker drive wattages i.e. the power of the mid-range and the tweeter. This is done by
exporting the magnitudes of the power to Microsoft excel .i.e. the y-axis. These ratios help us
calculate the power of these drives represented by the areas under these curves. The following
are the ratios calculated;
For 1st order 2 way 50 watts;
 Woofer = 2.805
 Tweeter = 2.259
Ratio = 2.805:2.259
For 1st order 2 way 100 watts
 Woofer = 2.524
 Tweeter = 2.103
Ratio = 2.524:2.103
For 1st order 3 way 50 watts
 Woofer = 2.143
 Mid-range = 2.079
 Tweeter = 1.948
Ratio = 2.143:2.079:1.948
For 1st order 3 way 100 watts
 Woofer = 2.563
 Mid-range = 1.883
 Tweeter = 1.748
Ratio = 2.563:1.8829:1.748
Now for the calculation the woofer ratio was the base ratio as it was the maximum wattage of the
speaker drives.
For the 2-way 50Wrms;
Woofer = 50Wrms
Tweeter = 2.259/2.805*50 = 40.26Wrms
44
For the 2-way 100Wrms
Woofer = 100Wrms
Tweeter = 2.103/2.524*100 = 83.32Wrms
For the 3-way 50Wrms
Woofer = 50Wrms
Mid-range = 2.079/2.143*50 = 48.5Wrms
Tweeter = 1.948/2.143*50 = 45.5Wrms
For the 3-way 100Wrms
Woofer = 100Wrms
Mid-range = 1.883/2.563*100 = 73.5Wrms
Tweeter = 1.748/2.563*100 = 68.2Wrms
From the calculated values did not match practical values of the speakers which are in the market
so the nearest value of the speakers where bought and compared to the theoretical values and the
errors were calculated.
Drives
Theoretical Wattages
Practical Wattages
Error (%)
Woofer
50Wrms
50Wrms
0%
Tweeter
40.26Wrms
40Wrms
0.65%
Woofer
100Wrms
100Wrms
0%
tweeter
83.32Wrms
75Wrms
9.99%
Table 1: Comparisons of theoretical and practical values of 2-way networks of 50Wrms and
100Wrms.
Drives
Theoretical Wattages
Practical Wattages
Error (%)
Woofer
50Wrms
50Wrms
0%
Mid-range
48.5Wrms
40Wrms
17.5%
Tweeter
45.5Wrms
35Wrms
23.1%
Woofer
100Wrms
100Wrms
0%
Mid-range
73.5Wrms
60Wrms
18.4%
Tweeter
68.2Wrms
50Wrms
26.7%
Table 2: Comparisons of theoretical and practical values of 3-way networks of 50 and 100Wrms
45
The errors found in the calculation were found to be acceptable since the efficiency of the
crossover networks was still high enough so fabrication of the circuits was to start.
4.1.4 Circuit implementation and speaker system
The final step was to implement the four circuits on PCB’s and also the fabrication of the speaker
drives onto their cabinets. The sound was sampled with and without the crossover networks and
quality of the sound could be heard that there was a big difference as the distortion had subsided.
Below are photographs of the speaker drives and the four crossover networks.
Figure 4-15: 2-way and 3-way speaker systems.
Figure 4-16: 2-way and 3-way cross-over networks on one board.
46
CHAPTER 5
5
CONCLUSION AND RECOMMENDATIONS
5.1
CONCLUSION
The main objectives of this project were to come up with speaker drive selection for 2-way and
3-way for 50watts and 100watts systems for:
Design for 2-way and 3-way crossover networks.

2-way speaker drives (woofer, tweeters) for 50watts and 100watts system selection.

3-way speaker drives (woofer, mid-range, and tweeters) for 50watts and 100watts
systems selection.
These objectives were met and the designs were implemented also speaker drives were calculated
and also implemented. The audio output of the speakers was of high quality since each speaker
drive operated on its specified frequency band hence producing the best sound quality on the
basis of their capability. I was able to design first order circuits of the two different wattages and
compare their responses using the AC analysis and also compare the different sound qualities
using the different crossover networks.
The experimental errors of the project were at a minimal since compared to the old ways of
speaker selection and fabricating crossovers which was done manually with a lot of estimations
here we calculated the possible outcomes and minimized the errors hence coming up with a solid
piece of engineering equipment that can be fabricated in large scale for a wider consumer use.
5.2
RECOMMENDATIONS
For easier selection of speaker drives in the future I propose the following recommendations: Choice of the speaker drive should be a little bit larger compared to the ones specified
because they were of a smaller value and were not in the market.
 Inductor design to be simplified for easier design of inductors if they were to be designed
in large scale.
 Inductors to be made a solenoid core instead of an air core in order to minimize the
number of windings hence reduce the material used and cost of the material.
47
REFERENCES
1. Chris D’ambrose. Frequency Range of Human Hearing ‘The Physic
Book’, 2003
2. David b. Weems, Designing, Building and Testing your Own Speaker
System with Projects, 3rd edition.
3. Olson, Harry F. Autor, Music, Physics and Engineering, 1967.
4. Bies, David A and Hansen, Colin, Engineering Noise Control, 2003
5. AVS Forum> audio> speakers.
6. www. prestonelectronics.com
7. William, Arthur B & Taylor, Fred J, Electronic Filter Design
Handbook, 1995. Mc Graw-Hill. ISBN 0-07-070441
8. Internet- Wikipedia
9. Linkwitz Siegfried, Crossovers, 2009
APPENDICES
1. Hz= Hertz
2. dB = Decibel
3. SPL= Sound Pressure Level
4. Pa = Pascal
5. KHz =Kilo Hertz
6. µ = micro
7. m = milli
8. H = Henries
9. F = Farads
10. Ω = Ohms
11. Π = 3.14
12. R = Resistance
13. L= Inductance
14. C = Capacitance
48
15. Zo= Impedance
16. fc = Cross over frequency/ Cut off frequency
17. V= Voltage
18. P = Power
19. f = frequency
20. LPF = Low pass filter
21. HPF = High pass filter
22. BPF = Band pass filter
23. FL= Lower cut off frequency
24. FH = Upper cut off frequency
25. W= Watts
26. Rms = root mean square.
49
50