VU Meter Myths. Best practices in getting the clean sound

7/29/2019 VU Meter Myths. Best practices in getting the clean sound

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where P is the average power and A is the

amplitude when signal and noise are measured

across the same impedance.

Signal-to-Noise ratio can be expressed in dB as:

10 1010log 20logSIGNAL SIGNAL

dB

NOISE NOISE

SIGNAL dB NOISE dB

P ASNR

P A

P P

= = =

=

Figure 2 shows a generic device. Signal-to-

Noise Ratio is generally different at input and

output ports. If this device has gain G, input noise

can be defined as:

OUTIN NN

G=

and it represents the so-calledfloor noise.

The output signal is of course:

OUT IN S G S=

Consider an ideal multi-stage device, such as a

never-clipping mixing console (distortion will be

introduced later). Figure 3 (page 3) shows a 3-stage signal path: pre-amplifier (gain), channel

amplifier (channel fader) and master amplifier

(master fader). A signal generator Sv (including

its source resistance SR ) is connected to the pre-

amplifier (stage 1). In Figure 12

TSv represents

the thermal noise generated by SR .

This circuit can be simplified by transformingall noise sources as Thevenins equivalent voltage

generators as shown in Figure 4 and 5 for a

generic stage k:

( )

( ) ( )

1

1 1

ek S k

Nk Nk NkTS k S k

R R

e v v i R

=

= + +

The resulting power gain for stage kis:

( )( )( )

2

2

1

1

/ /INkk mk Ok IN kINkS k

RG g R R

R R+

= +

where OkmkINk

ig

v= is the transconductance for

stage k.

The mean squared output signal is:

2 2 2 2 2

1 2 3OUT SS v G G G=

The mean squared output noise is:

( )2 2 2 2 21 1 2 32 2 2 2 2

2 2 3 3 3

4OUT S N

N N

N kTR e G G G B

e G G B e G B

= + +

+ +

where B is the bandwidth over which noise is

measured, k is Boltzmanns constant and T is

temperature (generally 290T K= ).

The resulting SNR, referred to Figure 5, is:

2

2 22 2 3

1 2 2 2

1 1 2

4

SOUT

N NS N

v BSNR

e ekTR e

G G G

=

+ + +

Figure 2 Generic Device

Figure 4 Thevenins equivalent generator andresistance for the k-th stage


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Tips to get a higher OUTSNR are:

- Having a louder input signal level- Having higher G in all stages, esp.

1G , if

2

Nke are fixed, the resulting decrease of

OUTSNR with respect to

INSNR is of lesser

extent

- Narrowing bandwidth B to signalbandwidth (obtained by filtering)

- Having lowS

R

(connecting a DI Box

between source and mixer does not help,

because the problem moves one stage

before).

Since bandwidth is included in the formula, its

clear that adding filters (Equalizer section) to the

path changes SNR as well.

Stages are usually not done all the same way. Thenoisiest amplifiers are mostly found at the end of

the chain. So the lowest noise amplifier is placed

in the headstage position as it is supposed to give

the bulk of gain.

3. TOTAL HARMONIC DISTORTION +NOISE

When taking distortion into account, we may

describe the systems behavior through Total

Harmonic Distortion (THD)and Total Harmonic

Distortion and Noise (THD+N).

THD is defined as:

2

1

n

n

P

THDP

==

where nP is the power of the n-th harmonic and

1P is the power of the fundamental frequency. In

a real system higher harmonics are a finite

number, as they decay to zero with increasing

frequency.

THD is also defined as:

2

2

1

n

n

V

THDV

==

Both definitions are used in audio applications.

THD is given in percent as distortion factor or in

dB relative to the fundamental frequency as

distortion attenuation.

THD+N is defined as:

2

1

n NOISE

n

P P

THDP

=

+

=

Figure 3 3-Stage Amplifier [2]

Figure 5 3-stage generic amplifier with Thevenins equivalent noise generators


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What is distortion? Active circuits are seat of

different kinds of distortion. In this article we

focus on harmonic distortion (HD) and

intermodulation distortion (IMD).

Harmonic Distortion

Harmonic distortion seems to be what worries

sound engineers to the greatest degree. First of

all its good to establish some definitions:

Signal dynamics: the gap between the quietest

level and the loudest level of the signal

Amp dynamics: the gap between the floor noise

level of the amplifier and the maximum level

accepted related to a certain THD percentage.

Another looseness in audio theories is often told

to student sound engineers as follows:

Input signal will be clipped, so keep it low

In reality its the output signal that will be

clipped! (Its apparent if looking at dynamics

issues from bottom to top of the signal path)

So, be sure the input signal is low enough to

prevent clipping even when gain is at minimum or

if its quiet at the start beware when raising up the

gain!

Which is the maximum level for low enough?

The measurement of THD is not an easy

enterprise without a proper instrumentation, such

as a spectrum analyzer or a specific

instrumentation with smaller THD and greater

dynamics than the device under test.

Clipping anyway is audible, so low enough is set

below the clipping level. Figure 6 gives a hint to

choose the optimal level for the output signal.

Figure 6 (b) shows that a real amplifier does not

clip abruptly, but the amps trans-characteristic,

after rising linearly, gradually deflects from

linearity and reaches an upper/lower limit thus

causing a compression of the signal right below

the ceiling and clipping when the limit is crossed.

Compression and limiting add higher harmonics

to the signal.

Intermodulation Distortion

Non-linear electronic devices, such as transistors

or diodes, may work as multipliers. The output

signal, because of the amps non-linear behavior,

is composed of higher order terms:

2 3

0 1 2 30

OUT n IN IN IN IN n

v a v a a v a v a v

== = + + + +

L

So, for a composite input signal (e.g. sum of 2

Figure 6 (a) Asymptotic trans-characteristic. The picture shows how peaks above the limits are cut off (b) A realistic trans-

characteristic. An amplified signal is kept within the amps linear zone. Q indicates the amplifiers polarization point [3].


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cosines):

1 1 2 2cos cosINv V t V t = +) )

the output signal is:

0 1 1 1 2 2

2

2 1 1 2 2

cos cos

cos cos

OUTv a a V t V t

a V t V t

= + + +

+ + +

) )

) )

L

From trigonometry:

( ) ( )1

cos cos cos cos2

= + +

( ) ( )

2

2 1 1 2 2

2 2 2 2

2 1 2 2 2 1 2 21 2

2 2

2 1 2 1 2 1 2

cos cos

cos 2 cos 22 2 2 2

cos cos

a V t V t a V a V a V a V

t t

a V V t t

+ =

= + + + +

+ + +

) )

) ) ) )

) )

Finally non-linearity produces:

- a term in 0= - terms in

1 2

,n m with n, m = 1,2,

- Intermodulation Products in( ), 1 2n m n m = with n, m = 1,2,

4. STANDARD OPERATING LEVELSo, which is the relationship among SNR,

Distortion and VU Meters? The only relationship

concerns the reason meters were invented for:

metering the level of the signal. Measuring the

output level could be a way to get information

about the degree of THD in a given device and

backward information about the input signal level.

Beside this, monitoring levels is important in

order to feed the next stage in the audio path with

a signal of adequate level, for example connecting

the mixers master outputs to power amplifiers.

Input and output min and max levels are basic

specifications for all electronic devices, so the

need for standard levels arose.

A VU Meter is an indicator of the averagepower of the waveform. The average power for a

periodic signal (with period T) is defined as:

( )0

1T

AVP p t dt

T=

where p(t) is the instantaneous power:

( ) ( ) ( )p t i t v t=

For a purely resistive load average power can be

expressed as:

2

RMS

AV RMS RMS

L

VP V I

R= =

The ear integrates audio power over time, so

reading a VU meter would be quite natural in that

sense.

The Peak Power Meter (PPM) monitors the

power peaks of the waveform. So, even thoughloudness information is not well-rendered, the

measure is more accurate in order to avoid

clipping. Because of the wide range of levels and

the highly variable peaks, the dynamic range of

the signal on a PPM is usually compressed

through a logarithmic amplifier prior to display,

so that the needles or the LEDs swings are more

readable [4].

The scales of VU Meters and Peak Meters are

mostly expressed in dB, since the perceived

loudness of the signal varies logarithmically with

signal power.

So, an increase of 3dB is easily translated into a

doubling of the power and so on.

Instrumentation has to be carefully calibrated

according to a particular standard.

Three renowned standard line-up levels are listed

below:

PPM4 = 0 dBu = 0.775 V RMS (UK broadcasters)

0VU = +4 dBu = 1.23 V RMS (commercial equipm.)

0VU = -10 dBV= 316 mV RMS (consumer/prosumer

equipm.)

Two examples of how Analog and Digital line-

ups are related follow:

0VU = +4 dBu = -20 dBFS (SMPTE RP155)

PPM4 = 0 dBu = -18 dBFS (EBU R64-1992)

Figure 7 compares all standard levels.


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Some useful definitions:

1020log

1

RMS

RMS

VdBV

V

regardless of load impedance

10 1010 log 20 log

1 0.775

RMS RMS

RMS RMS

P VdBu

mW V =

regardless of load impedance (u = unloaded)

10 1010 log 20 log

1 0.775

RMS RMS

RMS RMS

P VdBm

mW V =

load resistance = 600 (Radio applications: 50

1020log

0.224

RMS

RMS

V

V

)

Note: dB is referred to a dimensionless quantity,

for example:

( ) ( )10 10

8

4

10log 8 10log 4

9 6 3

OUT

IN

dB

P mWG

P mW

G

dBm dBm dB

= =

=

=

dBFS (dB relative to full scale) is an amplitude

relative unit in digital systems. 0 dBFS refers to

the maximum possible digital level (all signals,

whose peak levels cross this limit, will be

clipped). Peak measurements produce negative

numbers.

RMS measurements in the digital domain still

present some ambiguities [5]:

if 0 dBFS is assigned to the RMS value of a full-

scale sine wave, then a full-scale square wave willbe at +3dBFS (AES17-1998 and IEC 61606, e.g.

Dorrough meters).

if 0 dBFS is assigned to the RMS value of a full-

scale square wave, then a full-scale sine wave will

be at -3dBFS (e.g. Euphonix meters).

Remember, for a sine wave:

2

PEAKRMS

VV =

5. SUMMARYVU meters or Peak meters on mixing consoles

assist sound engineers in monitoring respectively

the RMS level or peak level of the signal during

recording, mixing, live sessions etc.

Standard Operating Level has to be taken into

account, especially when working with different

categories of equipment (commercial or

consumer). The needle pointing at 0 VU does not

say SNR is the best: paragraph 2 explains that the

relationship among all parameters is morecomplicated. When the equipment we use is not

known, bringing the signal to 0 dB could be a safe

area, since manufacturers should at least

guarantee a linear functioning of the device at

Standard Operating Level to make sure continuity

in the signal path is not compromised.

6. REFERENCES[1] Hermann A. Haus, Richard B. Adler Circuit theory of

linear noisy networks, Technology Press of MassachusettsInstitute of Technology, 1959

[2] W. Marshall Leach, Jr. On the Calculation of Noise in

Multistage Amplifiers, IEEE Transactions on Circuits and

Systems Fundamental theory and applications, vol. 42, no

3, march 1995

[3] A. S. Sedra and K. C. Smith Microelectronic Circuits

New York: Oxford University Press, 2004

[4] Richard Brice Recording Consoles, from Audio

Engineering Know it all, Newnes Elsevier 2009

[5] Euphonix System 5 Metering: Peak vs. Average, 2002

Figure 7 Standard Levels compared [4]

VU Meter Myths. Best practices in getting the clean sound

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