Design of an Audio Multitone Refiner, Simulation of Audio Frequencies & Analysis Using Active Filter

Oyebola, Blessed Olalekan

Design of an Audio Multitone Refiner, Simulation of Audio Frequencies & Analysis Using Active Filter

Summary

The indispensable need for alignment and optimization of sound systems has prompted this study. It tries to answer questions such as: What constitutes audio and frequency response components? Are they pragmatic? What are filters in this context?
The work mainly focuses on improving an input audio signal to be free from shape glitch in order to circumvent unwanted audible peaks or anomalies in the final sound. Additionally, this study tries to offer operational flexibility per definition of an Audio Multitone Refiner.
Because of their versatility, the signal analyzing tools Laplace transform, Fourier series, D.C. and transient analysis were employed to ascertain the realization of all constructed circuits in this study. ‘Casio fx7400G’ language was used during programming of the band pass filter, as were active filters.

Excerpt

FOREWORD

This work was a research work in all its facets that involved laboratory findings typically

designed and constructed; with rigorous mathematical analysis, programming, circuit synthesis

and stimulation; bearing in mind the necessities to add to the world of audio production.

CHAPTER ONE

INTRODUCTION

The dispensable needs of alignment and optimization of sound systems has prompted this

project. In concise answer would be provided to question such as what constituted audio and the

frequency response components. Are they pragmatic? What are filter and the rest?

The main focus of this work was to improve an input audio signal to be free from shape

glitch in order to circumvent unwanted audible peaks or anomalies in the final sound and offer

operational flexibility hence the definition of an Audio Multitone Refiner.

1.1

What Is Filter?

A filter is a device that passes electric signals at certain frequencies of frequency ranges while

preventing the passage of other. Filter circuits are used in a wide variety of applications. In the

field of telecommunication, band-pass filters are used in audio frequency range (0 kHz to 20

kHz) for modems and speech processing. High frequency band-pass filters (several hundred

MHz) are used for channel selection in telephone central offices. Data acquisition systems

usually require anti-liaising low-pass filter as well as low-pass noise filters in their preceding

signal conditioning stages. System power supplies often use band-rejection filters to suppress the

50 or 60-H line frequency and high frequency transients. In addition, there are filters that do not

filter any frequencies of a complex input signal, but just add a linear phase shift to each

frequency component, thus contributing to a constant time delay. These are called all-pass filters.

At high frequencies (> 1 MHz), all of these filters usually consist of passive components such

inductors (L), resistors (R), and capacitors (C). They are then called LRC filters. In the lower

frequency range (1 Hz to 1 MHz), however, the inductor value becomes very large and the

inductor itself gets quite bulky, making economical production difficult. In these cases, active

filters become important. Active filters are circuits that use an operational amplifier (op amp) as

the active device in combination with some resistors and capacitors to provide an LRC-like filter

performance at low frequencies (Fig. 1a & b). Inductor based circuits are heavy, expensive to

produce and suffer from low frequency distortion and induced hum.

(a)

(b)

Figure 1. Second-order passive low-pass and second-order active low-pass

1uF

1uH

Inductors have always been a problem in electronics (audio), as they are by nature relatively

large, tends to pick up mains hum as well as other noise in the electromagnetic spectrum. An

inductor could be simulated and placed on chips; nevertheless, it has limited Q unlike the real

inductor, but very high Q is rarely needed in audio. L=C

-R

) most pronounced limitation

are that one end of the simulated inductor is earthed, floating ones are expensive and rare; R

minimum allowed is 100ohm (series resistance equivalent to wire "real inductor" resistance), it

does not have the same energy storage. The simulated inductor will still try to meet real

properties but quit not the same.

The operational amplifier was initially a vacuum tube circuit used in the early 1940s in

analog computers. It was so called because it could be used as a high gain dc "amplifier"

performing mathematical "operations". Op-Amp's internal circuit is simply a combination of

class A, class B and class AB amplifiers. These circuits function together to give a very high

gain output.

1.2

Fundamentals of Filters (Low-Pass)

The simplest filter is the passive RC low-pass network where the complex frequency variable

allows for any time variable signals. For pure sine waves, the damping constant becomes zero;

for a normalized presentation of the transfer function, s is referred to the filter's corner

frequency, or -3 dB frequencies. With the corner of the low fc = 1/2RC, for frequencies w >> 1,

the roll off is 20 dB/decade. For a steeper roll off, n filter stages can be connected in series to

avoid loading effects, op amps, operating as impedance converters, separate the individual filter

stages.

Passive band-pass filter involve all the well-known problems of using inductors. In

addition, if constant-Q behavior is to be maintained, their outputs require buffering from the

loading effects of the slider. Gyrators may be substituted for the inductors; however, at least two

operational amplifiers per section will be required (Bohn, 1976). This brings up the next category

of active tow-pole RC filters. Requiring only one operational amplifier per section, they

represent the most cost-effective approach. While this category of filters is more sensitive to

component tolerances than the state-variable approach, the cost advantages are overwhelming.

For significantly less money than the cost of the additional two or three operational amplifiers,

some very precise passive components can be bought, with precision parts.

Selection from among the various configurations of active RC two-pole bandpass filters

is no easy task. Two circuits, however, emerge as time-tested and worthy of further study. Both

have been derived from the monumental work of Sallen and Key (14). The first is the well-

known voltage-controlled voltage source (VCVS) bandpass filter credited to Kerwin and

Huelsman (15) and Multiple feedback Band pass (MFB). It is the most popular non-inverting

configuration and features a low spread of element values. A definite advantage is the ability to

precisely set the gain of the filter with resistors without upsetting the center frequency. This

circuit drops right into BP block shown in Fig. 2.

1.3

Superiority of Active Filters over Passive Filters

Op-Amp provides gain hence the input signal passed to the output will not be attenuated, and

therefore better response curves can be obtained. The high input impedance and low input

impedance of the Op-Amp means that the filter circuit does not interfere with the signal source

or lad. Also, because active filters provide gain, resistor can be used instead of inductors and

therefore active filters are generally less expensive. Signal is not affected as much as with

passive crossovers, since everything is done in low voltage. There is much more flexibility since

all that is needed to adjust crossover frequencies is to turn a knob, while on passive, the

component have to be replaced. The problem is that more amplifier channels are needed to go to

all the speakers. Passive crossovers work after the amplifiers, receiving high signal cutoff

frequencies and filter dB/octave simile.

Cut-off frequency is quite different from octave frequencies. The octave or decade

frequencies are basically used for filter topologies, stages or orders contract or definition. Slope

or gain drop at octave depends or varies from filter (order) to filters dissipated in Tables. At

octave or decade is the standard "checkpoint" frequency to examine attention (or boost) incur on

signal frequencies by various filter orders.

Cut-off frequency (wc

or wc

) is not defined by octave or decade frequencies `scale'

since cut-off frequencies is expected to be less than that octave frequency point; at cut off

speaker receives half power as compared to the maximum possible power at the center frequency

in the circuit. Since half power different in audio amount to about -3dB power which is the

maximum tolerable change for human audible frequencies, if the dB loss is greater than or equal

to 3dB than this will be clear and wide sparity of sound of different level and to make a quick or

faster `dieing' of the unwanted frequencies attenuation beyond 3dB equivalent frequency has to

be more tense has the beauty of the higher order filter is to provide strong more effective

`killing' of the undesired frequencies.

The passive filters have high signal levels since all the frequency splitting is done after

the amplifier channel obtaining maximum power by playing with the resistances `seen' by the

amplifier and since an inductor stores current while capacitor stores voltage they act as short and

open at low frequencies relatively. The more component added, he more effectively the filter

would be. The capacitors and inductors also dissipate power, wasting energy that speakers could

be using; inductors are more expensive than capacitor so that passive crossover can get really

expensive especially at low frequency of high power applications. Passive also introduce phase

shifts (which is often ignored for practical purposes) which put voltage and current out of phase

with respect to each other hence affecting the delivered power to the speaker and affecting the

delivered power to the speaker and affecting the delivered power to the speaker nad affecting

overall speaker `timing'. A 6dB/octave (which is either a series capacitor or a series inductor

filter) has a phase shift of 90 degrees; 12dB/octave (which resulted from a series inductor-

capacitor filter) gives 270 degrees phase shift. Anyway! Even order crossover filter would or

should be adhered to since this hock up the speakers out of phase (+ to and to +).

1.4

Basic Op-Amp and Feedback Theory

No current flows into or out of the input terminals and when negative feedback is applied the

differential input voltage is reduced to zero. The voltage follower is extremely useful for

buffering voltage sources and for impedance transformation. The impedances of the two inputs

should be equal to reduces offsets due to bias currents.

Table 1.1 Filter order and their rate of attenuation (in dB)

ORDER SECTION NOMINAL ROLLOFF

First I 6db/ octave

Second 2 12db/ octave

Third 3 18 db / octave

Fourth 4 24db /octave

"n" n>4 6db/octave /section

In audio, the first four are common since the transient response become worse and phase for

higher orders. Low and high pass filters are usually conventional enough but band pass and band

stop filter can be made in many different ways hence a few basic filter alignments (Table 1.1).

Butterworth is common in audio while Chebyshev alignment is very common in acoustical filters

but it is not generally considered desirable in electronic filter for crossover or other purposes

(Franko, 1988).

Speech fundamental as dealt with in this project occur over a fairly limited range between

about 125HZ and 250HZ. Vowels essentially contain the maximum energy and power of the

voice, occurring over the range of 350HZ to 2000HZ. Consonants occurring over the range of

1500HZ to 4000Hz contain little energy but are essential to intelligibility. The frequency range

from 63 to 500Hz carries 60% of the power of the voice and yet contributes only 5% to the

intelligibility. The 500Hz to 1 kHz region produces 35% of the intelligibility, while then from 1

to 8 kHz produces just 5% of the power of 60% of the intelligibility, by rolling off the low

frequencies and accentuating the range from 1 to 5 kHz, (see chapter three).

1.5

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CHAPTER TWO

LITERATURE REVIEW

Active device (operational amplifier op amp) supersedes inductor in audio processing industries;

conversely op amp was at the outset a vacuum tube circuit used in the early 1940 in anlog

computer. It was so called because it could be used as a high gain dc amplifier performing

mathematical operation op amp's internal circuit is simply a combination of class A class B and

class AB amplifiers (Franko, 1988). These circuit functions together to give a very high output

gain.

Inductors have always been a problem electronic audio however as they are by nature

relatively large tend to pick up mains hum as well as other noise in the electromagnetic

spectrum. An inductor is stimulated to be placed on chip; nevertheless, it has limited Q unlike the

real inductor but very high Q is rarely needed in audio. With gyrator, the valve of an inductor

could be calculated by: L=R1R2C1, more accurately (due to Seigfried linkwitz) is L=C

) most pronounced limitation are that one end of the simulated inductor is earthed, floating

ones are expensive and rare; R1 minimum allowed is 100ohm (series resistance equivalent to

wire real inductor resistance), it does not have the same energy storage. The stimulated inductor

will still try to meet real properties but quit not the same. L along with C1make up a turned

circuit which is connected to the pot so that the turned circuit can be moved from the positive to

negative input to vary the gain at the turned frequency. The frequency that the circuit is tuned for

can be calculated by:

f =

, R

)

Instead of using MFB filter the more common gyrator tuned circuit can be used. Cauer

(elliptical) filter exhibit equiripple characteristic in both the passband and the stopband. Phase

information may be gleaned from the transfer functions by separating them in to real and

imaginary parts and then using the relationship:

Phase: o = tan

-1

Group delay is defined as the negative of the first derivative of the phase with respect to

frequency.

Type Properties:

Butterworth

· Maximally flat near the center of the band.

· Smooth transition from pass to stopband.

· Moderate out of band rejection

· Low group delay variation near center of band.

· Moderate group delay variation near band edges

· Table of poles for N=1 to 10

· Butterworth has monotonic amplitude response with a maximally flat passband, less phase

shift, and better transient results; in conclusion,

· It is the preferred choice (in this project it was only be used in cross over design which was

not constructed due to time and financial constrain).

Chebychev

· Equiripple in passband

· Abrupt transition from passband to stopband.

· High out of band rejection.

· Rippled group delay near center of band

· Large group delay variation near band edges.

· Table of poles for N=1 to 10.

· The cherbyshev approximation to an ideal filter has a much more rectangular response in the

region near cutoff than has the Butterworth family.

Bessel

· Rounded amplitude in passband

· Gradual transition from passband to stopband

· Low out of band rejection

· Very flat group delay near center of band.

· Flat group delay variation near band edges

· Tables of poles for N= 1to 10

Ideal

· Flat in the passband.

· Step function transition from passband to stopband.

· Infinite out of band rejection.

· Zero group delay everywhere.

Outline

Butterworth Advantages maximally flat magnitude response

in the passband. Good all round performance

pulse response better than chebyshev. Rate of

attenuation better than Bessel.

Disadvantages some overshoot

and. Ringing in step response.

Chebyshev Advantages better attenuation Beyond the pass

band than Butterworth pass-band than

Butterworth advantages best step response

Disadvantages ripple in pass

band. Considerable ringing in

step response

Bessel

Advantages best step response very little

overshoot or ringing

Disadvantages slower rate of

attenuation beyond the pass

band than Butterworth

2.1

Transfer Functions

Transfer function is created in three forms, standard, cascade, and parallel. Cascade and parallel

transfer functions consist of first and second order terms that are cascaded or summed in parallel

together. The cascade and parallel transfer are used to create the active filters. Cascade transfer

function generate the filter composed of Thomas biquads, positive gain single amplifier biquads,

negative gain single amplifier, biquads and GIC biquads, parallel transfer function are

implemented with a summation of positive gain and negative gain single amplifier biguads.

Typical transfer functions are below:

( 2)

2 + + 2)( + 4)

Cascade transfer function

")(

Parallel Transfer function

Thomas Biquads

Their primary advantage is that it provides very high Q second order stages.

Akerberg-Mossberg Biquads

The Akerberg-Mossberg biquad exceeds the performance of the Thomas biquads for Opamp

imperfections and matches the Thomas 2 biquad notch performance in the presence of element

valve errors. This increased performance is obtained by replacing the positive integrator in the

Thomas 2 biquad second and third Opamps with a Miller integrator. The Miller integrator uses

two matched op amp in a configuration that tends to cancel errors due to Opamp imperfections.

The Akerberg-Mossberg biquad may absorb a third pole.

Positive Gain Single Amplifier Biquads

"The advantages of positive Gain SAB'S, except for Twin T stages are always gain changeable,

and there is usually no reversal of sign. The disadvantages are they are more susceptible to

element imperfections than negative Gain SAB's. All pass and even notch positive Gain SAB's

with injector resistor have assigned reversal"

Negative Gain Single Amplifier Biquads

Negative gain single amplifier biquads (SAB's) require only one op amp for first, second, and

sometimes third order amplifiers. Second and third order Negative Gain SABs use the Bridge T

or MFB circuit configuration for the feedback path. Filter light does not support third order

stages. "The advantages of Negatives Gain SAB;s is that they are generally higher resistant to

imperfect elements than positive gain SAB's. The disadvantages is that are generally more

susceptible to op amp imperfections than positive gain SAB's and the gain for all pass notch

stages is fixed"

Parallel Active Filters

The summation circuit may be optionally active or passive. The advantage of doing this is that

performance degradation due to op amp imperfections is not amplified through successive

cascade stages. The disadvantage is the filter design may be physically very large and notches

tend to be poor quality.

Leapfrog Filters

Leapfrog filter are passive LC ladder simulations. The advantage is that errors due to element

values or op amps tend to be distributed across the filter instead of concentrated at a specific

biquad. This generally makes them more robust. Filter solutions supports leapfrog filters for low

pass and band pass all pole designs; Table 2.1 illustrate quick view of the above discusses stages.

Band Pass Architectures

Band pass filter may be created with multiple integrated band pass stages, or high and low pass

stages. Odd order filters of the high/ low pass architecture always have a band pass stages in the

center. In general, the integrated band pass architecture works better for narrow band filters, and

the high/ low pass architecture works better for wide band filters.

This is due to potentially huge, undesirable internal gains that may saturate op amps if the wrong

architecture is used.

Stages Type

High Orders That Are Available

Thomas or Akerberg Mossberg Biquads

Third Order

Positive gain all poles single amplifier stages

Third order and fourth order

Positive gain single amplifier stages with

transmission zeros

Third order

Negatives gain all poles single amplifier

stages

Third order and fourth order

Negatives Gain Single Amplifier Stages With

Tranmissinon zeros

Usually Third Order

GIC

Third Order

Twin T

Third Order In The Form Of An

Rc Pole Following the Op Amp

Fundamentals of low pass filters

The simplest low pass filter is the passive RC low pass network shown in Fig. 3

A(s) =

___________________

Figure 3. First order passive RC Low-Pass and its transfer function

Where the complex frequency variable, s=jw+0, allows for any time variable signals; for pure

sine waves, the damping constant, 0, becomes zero and

s=jw.

For a normalized presentation of the transfer function, s is referred to the filter's corner

frequency, or -3 dB Frequency,

c, and has these relationship:

= =jw

With the corner frequency of the low- pass in Figure 2.1 being fc=1/wRC, s becomes S= sRC

and the transfer function A(s) result in:

A(S)=

The magnitude of the gain response is |A|=

The frequencies n>>1, the rolloff is 20 Db/decade. For a steeper rolloff, `n' filter stages can be

connected (James, 1999) in series as shown in Fig.4. To avoid loading effects, op amps,

operating as impedance converters, separate the individual filter stages.

1uF

Figure 4. Fourth order passive RC Low pass with Decoupling Amplifiers

The resulting transfer function is:

(S)

(

)(

)...(

)

In the case that all filters have the same cut-off frequency, fc, the coefficients become

a1=a2=...an=a=

2 - 1 and fc of each partial fiter is 1/ times higher than fc.

Fig. 3 shows the results of a fourth order RC low-pass filter. The roll off of each partial fiter(

curve 1) is- 20 dB/ decade, increasing the roll-off of the overall filter (curve 2) to 80 dB/ \decade.

2.2

Butterworth Low Pass Filters

The Butterworth low pass filter provides maximum pass band flatness. Therefore, a Butterworth

low pass is often used as anti-aliasing filter in data converter applications where precise signal

levels are required across the entire pass band. Fig. 4 plots the gain response of different orders

of Butterworth low pass filters versus the normalized frequency axis (=f/fc); the higher the

order, the longer the passband flatness

2.3

Tschebyscheff Low Pass Filters

The Tschebyscheff low pass pass filters provide an even gain rolloff above Fc; however, the

passband gain is not monotony, but contains ripples of constant magnitude instead. For a given

filter order, the higher the passband ripples, the higher the filter's rolloff. With increasing filter

order, the influence of the ripple magnitude on the filter rolloff diminishes. Each ripple accounts

for one second-order filters with order numbers generate ripples above the 0-dB line, while

filters with odd numbers create ripple below 0 dB. Tschebyscheff filters are often banks, where

the frequency content of a signal is of more important than a constant amplification.

2.4

Bessel Low Pass Filters

The Bessel low pass filters have a linear phase response over a wide frequency range, which

results in a constant group delay in that frequency range. Bessel low pass filters, therefore,

provide optimum square- wave transmission behavior. However, the passband gain of a Bessel

low pass filter is not as flat as that of the Butterworth low pass, and the transition from passband

to stop band is by far not a sharp as that of a Tschebyscheff low pass filter.

2.5

Quality Factor Q

The quality factor Q is an equivalent design parameter to the filter order n, instead of designing

an nth order Tschebyscheff low pass; the problem can be expressed as designing a Tschebyscheff

low pass filter with a certain Q. the band pass filter, Q is defined as the ratio of the mid

frequency, f m, to the bandwidth at the two -3dB points:

(

For low pass and high pass filters, Q represents the pole quality and is defined as

High Qs can be graphically presented as the distance the 0-dB line and the peak point of the

filter's gain response.

2.6

Précis

The general transfer function of a low pass filter is:

A(s)=

(

)

The filter coefficients ai and bi distinguish between Butterworth, Tschebyscheff, and Besssel

filters Tab book inc., 1982). The coefficients for all three types of filters could be found in filter

Table; in addition, the ratio

is defined as the pole quality. The higher the Q valve, the more a

filter inclines to instability.

2.7

Low Pass Filter Design

The transfer function of single stage is:

A(s)=

(

)

For a first order filter the coefficient b is always zero (b1=0), thus yielding:

A(s)=

The first order and second order filter stages are the building blocks for higher-order filters.

Often the filter operate at unity gain (A O=1) to lessen the stringent demands on the op amp's

open loop gain. Figure 2.8 shows the cascading of filter stages up to the sixth order. A filter with

an even order number include number include an additional first order stage at the beginning.

Details

Pages

Type of Edition

Erstausgabe

Year

2017

ISBN (PDF)

9783960676355

ISBN (Softcover)

9783960671350

File size

1.5 MB

Language

English

Publication date

2017 (March)

Grade

B (4 of 5)

Keywords

Audio Filteration Active filter Low pass filter Tone control Multiple feedback Band pass filter Amplifier Audio multi-tone refiner

Author

Blessed Olalekan Oyebola (Author)

Design of an Audio Multitone Refiner, Simulation of Audio Frequencies & Analysis Using Active Filter

Summary

Excerpt

Table Of Contents

Details

Author

Blessed Olalekan Oyebola (Author)