05-signal level and units of measurements

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Signal Level andUnits of Measurements

ECE-41724

NATIONAL BROADCASTING NETWORK (NBNNATIONAL BROADCASTING NETWORK (NBN--4)4)NATIONAL BROADCASTING NETWORK (NBNNATIONAL BROADCASTING NETWORK (NBN--4)4)

John Achilles Denna

The Decibel

- dB always describes a ratio of two

quantities that are most often related to

power (but not exclusive to).

- it expresses large quantities into smaller

figures to simplify its expression.

Basic Equation

For Power related figures:

For Voltage/Current related figures:

=

Po

PidB log10

Pi = information power

Po = reference power

Ei = information voltage

Eo = reference voltage

=

Eo

EidB log20


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Problem 1

What is the ratio, in dB, of 2 watts to 1

watt?

Solution:

dB = 10log(P1P0)

= og

dB = 10log(2)

dB = 3

Note: whenever one power is twice another, it is 3dB

greater (or if it is half the power, it is 3dB less)

Problem 2

What is the ratio, in dB, of 100 watts to 10

watts?

Solution:

dB = 10log(P1P0)

= og

dB = 10log(10)

dB = 10

Note: whenever one power is ten times another, it is 10dB

greater (or if it is 1/10 the power, it is 10dB less)

Power-Voltage-Current Relationship

R

EP

2

=

RIP 2=

PRE =

R

PI =

Compare 10V and 100V assuming load impedance of 8.

Po = 10/8 = 12.5W ; Pi = 100/8 = 1,250W

In terms of Power ratio ; = 10 Log (1,250/12.5)

= 20dB

In terms of Voltage ratio ; = 20 Log (100/10)

= 20dB


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dB TablePOWER VALUE

(Watts)Level in dB

relative to 1WattLevel in dB relative

to 1mW

1 0.00 dB 30.00 dBm

10 10.00 dB 40.00 dBm

100 20.00 dB 50.00 dBm

200 23.01 dB 53.01 dBm

400 26.02 dB 56.02 dBm

800 29.03 dB 59.03 dBm

1000 30.00 dB 60.00 dBm

2000 33.01 dB 63.01 dBm

4000 36.02 dB 66.02 dBm

8000 39.03 dB 69.03 dBm

10000 40.00 dB 70.00 dBm

20000 43.01 dB 73.01 dBm

40000 46.02 dB 76.02 dBm

80000 49.03 dB 79.03 dBm

100000 50.00 dB 80.00 dBm

1000000 60.00 dB 90.00 dBm

John Achilles Denna

Relative vs Absolute LevelsdB in itself, has no absolute value. It needs standard

reference value to describe a specific quantity.

Example:

The audio consoles maximum output level is +20dB.

Question : What does this expression give you?

The First Statement is meaningless because it doesnt

specify the reference.

Adding additional information actually tells us that the

console is capable of delivering 100milliwatts into someload.

ove m wa .

dB to Electrical Signal Relationship

dBm an expression ofelectrical power level referenced

to 1milliwatt.

Therefore, 0dBm = 1mW

as no re erence o e er vo age or mpe ance s perInstitute of Radio Engineers (IRE) Volume 28.

The typical circuit in which dBm was measured when the term wasfirst devised was a 600 telephone line. Which results to a voltagedissipation of0.775Vrms.

Note : it does not necessarily mean that 0dBm automaticallyequates to 0.775Vrms, this expression only applies if the loadimpedance is 600, but 0dBm always mean 1milliwatt.


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Example

* The audio consoles maximum output level is

+20dBm.

** The audio consoles maximum output level is

+20dBm into a 600 load.

What is now the dB relationship in terms of voltage and

power of this expression ? assuming load impedance

of 600.

Ans. Max. output voltage = 7.75Vrms

Max. Power output = 100mW

Decibel and Sound Level

Most modern audio equipment (consoles, tape decks,

signal processors, etc.) are sensitive to voltage levels

in which Power output is not really a consideration

except for Power Amplifiers driving loudspeakers in

which Watts are a common expression.

The term dBm expresses power ratio, so how does it

relate to voltage?

Ans: no direct relationship, although voltage can be calculated

if the impedance is given.

To minimize complications in the various expressions

in dB of Power and Voltage, another dB term wasproposed,that is..

dBu

It is the term more appropriate in expressing output

or input voltage.

an expression ofoutput / input voltage, which implies

that 0dBu is equal to 0.775V, however dBu value

is not dependent on the load.

The voltage represented by dBu is equal to dBm if

and only if the dBm figure is derived with 600

load!

The u in dBu stands for unloaded


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Example

* The consoles maximum output level is

+20dBu into a 10K or higher impedance

load.Comparing this question to the previous,

** The audio consoles maximum output level is

+20dBm into a 600 load.20dBu = 7.75V on a load equal or greater than 10K

while 20dBm=7.75V into a 600 load. There is a

mismatch in impedance.

The 2nd example specifies for a 600 load to be the

same with the 1st. However, if the 1stexample is made

to be connected to a 600 termination, the output would

probably drop in voltage, increase distortion andburn

out!.

dBV and dBv

dBu is a recent relative voltage referenced term,

and for many years, dBV denoted a voltage-

referenced, with 0 dBV = 1 Vrms.

In this case the NAB ado ted the used of lower

case v to denote the voltage value

corresponding the power in dBm (i.e. dBv was

a voltage-related term with 0 dBv = 0.775 volts)

Relating Level to Voltage


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Example

1. The nominal output level is +4dBv

2. The nominal output level is +4dBV

These two statements seems to be identical, but if

youll notice the units are not the same.

The 1st statement will deliver a nominal output of

1.23 Vrms

The 2nd statement will deliver a nominal output of

1.6 Vrms

Example

1. The nominal output level is +4dBv

2. The nominal output level is +4dBu

These two statements are the same, and the only

difference is that, the latter is the preferable

usage today.

Note: the only difference between dBu (or dBv) and

dBV is the actual voltage chosen as the

reference for 0dBV and dBu or dBv, that is 1 volt

and 0.775Vrms respectively.

Conversion of units


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Relating dBV to dBu and dBm to Specs

The standard for Phono jack inputs and outputs are

rated in dBV (1 Volt reference)

Note:Typical line level phono jack inputs and outputs are

intended for used with high impedance equipment, which

is basically sensitive to voltage rather than power, thus

their nominal level is -10dBV.

XLR connectors and some phone jack output levels

are rated in dBm (1mW reference) or dBu

(0.775Vrms reference)

Note:

XLR are intended for low or high impedance equipment

which has a nominal level of +4dBu (sound

reinforcement) and +8dBu (recording for broadcasting)

dbW and dB SPL

dBW

0 dBW is 1 Wat

This unit is referenced to 1 watt

dB SPL

Where: Pa= actual pressure level

Pr= 0.00002N/m2= 0.0002dyne/cm2

=

reference

actualSPL

P

PdB log20

Volume, Gain, and Level

Three most often misused terms in audio:

Volume

Defined as the power level

Gain

If not specified, it refers to be transmission gain,

which is the power increase of a signal,

expressed in dB.

Level

Defined as the magnitude of a quantity in relation

to an arbitrary reference value (e.g. SPL)


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Equal Loudness Contours

Equal Loudness Contours

The Figure shows the relationship betweenphons

and decibels, and illustrates the well-known

Robinson-Dadson equal loudness contours.

Note:

Phons and decibels share the same numerical

value only at 1000 Hz.

In general, the ear becomes less sensitive to

sounds at low frequencies, thus it takes more sound

pressure at lower frequencies and at a very high

frequencies for us to believe a sound is equally loud

as a sound at 1000Hz.

Loudness Control


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Area of Audibility

Hearing Response

Using the Equal loudness contour, the peak hearing

sensitivity comes between 3000 and 4000Hz in

which is the resonant frequency range of the outer

ear canal

The small size of the ear drum also affects the

(long wavelength).

With the equal loudness contour, it generally tell us

that the hearing ability of a human is not linear.

Dynamic Range

- It is the difference between the loudest and most

silent portion of a program signal (sound)

- For sound systems, it is the difference between

the peak output level and the electro-acoustic

noise-floor.

Dynamic Range (dB) = Loudest part of the

sound noise floor

Dynamic range has nothing to do with dBm, dBu, or

dB SPL as it is typically referenced to dB to

denote the range of audible sounds in a particular

program


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Example 1

Examine a typical rock concert:

The sound levels at the microphones (not in the

audience) may range from 40 dB SPL (theaudience, wind, and traffic noise at the mic during a

very quiet momentary pause) to 130 dB SPL

Dynamic Range (dB) = 130 dB SPL 40 dB SPL

= 90 dB

Example 2 (Electrical Dynamic Range)

When the sound level reach 130 dB SPL at the mic,

the maximum line levels (at the mixing consoles

output) may reach +24 dBu (12.3V). Similarly when

the sound level falls to 40 dB SPL, the minimum line

level falls to -66 dBu (388 micro volts)

Dynamic Range (dB) = +24 dBu (-66 dBu)

= 90 dB

Acoustical Dynamic Range

Acoustical dynamic range deal mostly with

loudspeakers

This specify the response of the speaker (i.e. if the

speakers arent capable of such range, then the

output signal is distorted which lead to serious

Program dynamic range deal with microphones

Electrical dynamic range deal with audio consoles

and power amplifiers


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Acoustical Dynamic Range

What are the actual sound levels that must be

produced?

Ans:

That all depends on the distance between the

audience and the loud speakers and how loud the

sound one wants to be at the audience.

The peak sound level we might accept as

reasonable facsimile for this excitement is

120dBSPL

Dynamic Range

Dynamic range of the system can be increase by:

Increasing the sound system maximum sound level

capability

Making the environment quieter (good acoustical

treatment) in which it also cut down the excess

Note:

for every 3dB increase in sound level requires exactly

twice the capability in both power amplifiers and

speakers (this leads to another cost)

Dynamic Range

When dynamic range of the program material

exceeds the dynamic range capability of the sound

system, some combination of the following will

result:

Program peaks will be distorted due to clipping and/orloudspeaker break-up

Quiet passage will not be heard because they will be

below the electrical and/or acoustic noise floor.


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Dynamic Range (Compressor)

Compressor

A signal processing device that cuts down the

dynamic range into a certain level

Compression side effects:

Makin uiet breath soundslouder

Creating a pumping effect

Increasing the distortion of low frequency signals

Note:

distorting on peaks is not acceptable either, thus we may

use compression only above a given threshold,

otherwise not at all.

The key to understanding compressors is always

to think in terms ofincreasing level changes indB above the threshold point.

Compressor

.From the example, for every 1.6 dB increase

above the threshold point the output only

increases 1 dB. In this regard, compressors

make loud sounds quieter. If the sound gets

louder by 1.6 dB andthe output only increases

by 1 dB, then the loud sound is now quieter.


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Compression above a threshold

Reduce the dynamic range of a vocal to enable

it to remain present and audible in a mix when

competing with other amplified instruments.

Used when mixing both live and recorded

material.

Compressor Applications

Reduce dynamic range of vocalists and other

musical instruments that exceed the recording or

reproduction capability.

Prevent clipping and distortion in live sound

systems or recording chains.

Produce louder recordings for broadcast.

Control the creation of sound. When used in

conjunction with microphones and instrument

icku s com ressors hel determine the final

Compressor Applications

timbre by selectively compressing specific

frequencies and waveforms.

Common examples are fattening drum sounds,

increasing guitar sustain, vocal smoothing, and

bringing up (punching) specific sounds in the mix.


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Limiters

Permits compression to be applied above a set

threshold level

An electronic device that limits the output level

from rising any higher, with infinite compression, or

very much higher, with 10:1 compression,

regardless of further increases in input signal

Typical compression ratio is from 8:1 to 20:1

Example

Suppose the threshold is set to +15dBu, and the

compression ratio is 10:1, so long as the input to

compressor is below +15dBu, the limiters output

level exactly matches its input


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Compander

A noise reduction system (companders) which

allows the original program dynamics to be

maintained throughout the recording and playbackprocess by compressing the program dynamic

range before it goes onto tape , and complimentary

expan ng e ynam c range as e program s

retrieved from the tape

Headroom

It is the average electronic line level in the concert

sound (+4dBu), corresponding to an average

sound level of 110dBSPL at the microphone.

A.K.A. Nominal program level

The difference between the nominal and highest

(peak) level in a program


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Headroom

Headroom = Peak Level Nominal level

= 130dBSPL 110dBSPL

= 20dB

Headroom = Peak Level Nominal level

= +24dBu (+4dBu)

= 20dB

Why Headroom is Important

As specification, it tells us the ability of the sound

system to handle loud program peaks

Sound systems with greater headroom will be

able to handle louder peaks before distorting or

destroying itself

Headroom Requirements

Choice on headroom figure depends on:

Type of program material

The Application

Available budget for amplifiers

Typical Headroom Values

15 to 20dB for musical application in which high fidelity is

the ultimate consideration

10 dB for sound reinforcement application (in which

compressor or limiter can help hold the

program peaks within the chosen headroom

value, thus avoid clipping problems)


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Dynamic Range and Headroom

References

Yamaha Sound Reinforcement Handbook

Master Handbook of Acoustics

JBL Sound System Design

Thank you for yourThank you for your

attention.attention.


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John Achilles Denna

05-signal level and units of measurements

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