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'[EE]: What is the relationship between gain and dB'
2001\07\15@233925 by Mathew

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I have read somewhere that 40 dB of gain is approximately 200 times gain. Does anyone know if this is true and what the formula is to have work out the relationship.

Thanks in advance

Matt
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2001\07\16@003659 by jim

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Matthew,

If you're talking about power gain, 40db is a gain of 10000.  If you're
talking
voltage gain, you're talking about a gain of 100.  This can be calculated by
using the formulas for powewr and voltage as shown below.

Pg (db) = 10log(Po/Pi)

where Pg is power gain
         Po is output power
         Pi is input power
  and log is the logarithim

and for voltage...

Vg(db) = 20log(Vo/Vi)

where  Vg is voltage gain
          Vo is the output voltage
          Vi is the input voltage
   and  log is the logarithim.

Hope this helps you out.

                                   Regards,

                                       Jim



{Original Message removed}

2001\07\16@090654 by Olin Lathrop

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> I have read somewhere that 40 dB of gain is approximately
> 200 times gain. Does anyone know if this is true and what
> the formula is to have work out the relationship.

A "Bell" (named after Alexander Graham Bell) is a means of quantifying the
power ratio of two signals.  The scale is logarithmic, with an increase of 1
Bell denoting in increase in the power ratio by a factor of 10.  A factor of
10 is a rather large jump, so deciBells are almost universally used instead
of Bells.  A deciBell, abbreviated "dB", is a tenth of a Bell.  Therefore 10
dB denote a relative increase in power by a factor of 10, and 40dB therefore
denotes a relative increase in power by 10**4 = 10,000.  Note that this is
power, not voltage.  If an amplifier had a gain of 40dB and its input and
output impedence were the same, then it would have a voltage gain of
SQRT(10,000) = 100.

A few quick rules of thumb to remember.  A voltage gain of 10 at the same
impedence increases the power by 20dB, and similarly a voltage gain of 2
results in an increase of Log10(2**2) = Log10(4) = 6dB.


********************************************************************
Olin Lathrop, embedded systems consultant in Littleton Massachusetts
(978) 742-9014, .....olinKILLspamspam@spam@embedinc.com, http://www.embedinc.com

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2001\07\16@103412 by Douglas Butler

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If dB are confusing try to remember they are deci-Bells, invented I
believe by Alexander Grahm himself.  Convert deci-Bells to Bells and
things make more intuitive sense.  4 Bells of gain increase the power by
4 decimal places.

Bell worked with the deaf and only indirectly with electricity, so power
was a measure of sound level.  Voltage was only important if you
happened to be using electrical aparatus.  So for voltage you have to
make a correction.

Sherpa Doug

> {Original Message removed}

2001\07\16@111721 by David VanHorn

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Jim, any chance you could correct your PC clock from 2007 to 2001?
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I would have a link to http://www.findu.com/cgi-bin/find.cgi?KC6ETE-9 here
in my signature line, but due to the inability of sysadmins at TELOCITY to
differentiate a signature line from the text of an email, I am forbidden to
have it.

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2001\07\16@130003 by James Paul

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All,

I don't know where that dat came from.  I've checked both of my
machines, and both have the correct date set.   Maybe it's a
function of the server system.

                                           Regards,

                                             Jim





On Mon, 16 July 2001, David VanHorn wrote:

{Quote hidden}

jimspamKILLspamjpes.com

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2001\07\16@184540 by Alexandre Domingos F. Souza

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>A "Bell" (named after Alexander Graham Bell) is a means of quantifying the
>power ratio of two signals.  The scale is logarithmic, with an increase of 1
>Bell denoting in increase in the power ratio by a factor of 10.  A factor of

       Olin, isn't the unit called BEL???


---8<---Corte aqui---8<----

Alexandre Souza
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2001\07\16@185354 by David VanHorn

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At 07:47 PM 7/16/01 -0300, Alexandre Domingos F. Souza wrote:
> >A "Bell" (named after Alexander Graham Bell) is a means of quantifying the
> >power ratio of two signals.  The scale is logarithmic, with an increase of 1
> >Bell denoting in increase in the power ratio by a factor of 10.  A factor of
>
>         Olin, isn't the unit called BEL???

Yes, but it's inconveniently large, so we use deci-bels
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I would have a link to http://www.findu.com/cgi-bin/find.cgi?KC6ETE-9 here
in my signature line, but due to the inability of sysadmins at TELOCITY to
differentiate a signature line from the text of an email, I am forbidden to
have it.

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2001\07\16@202720 by Andy N1YEW

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i know its a bel!

BEL not BELL

andy
----- Original Message -----
From: Alexandre Domingos F. Souza <EraseMEtaitospam_OUTspamTakeThisOuTTERRA.COM.BR>
To: <PICLISTspamspam_OUTMITVMA.MIT.EDU>
Sent: Monday, July 16, 2001 6:47 PM
Subject: Re: [EE]: What is the relationship between gain and dB.


>A "Bell" (named after Alexander Graham Bell) is a means of quantifying the
>power ratio of two signals.  The scale is logarithmic, with an increase of
1
>Bell denoting in increase in the power ratio by a factor of 10.  A factor
of

       Olin, isn't the unit called BEL???


---8<---Corte aqui---8<----

Alexandre Souza
@spam@taitoKILLspamspamterra.com.br
http://planeta.terra.com.br/lazer/pinball/

---8<---Corte aqui---8<----

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2001\07\19@080304 by Angelos Gonias

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dB=10*log(G), G = gain, make sure you use log base 10

-Angelos

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[KILLspamPICLISTKILLspamspamMITVMA.MIT.EDU]On Behalf Of Mathew @ Everythingit
Sent: 16 July 2001 01:48
To: RemoveMEPICLISTTakeThisOuTspamMITVMA.MIT.EDU
Subject: [EE]: What is the relationship between gain and dB.


I have read somewhere that 40 dB of gain is approximately 200 times gain.
Does anyone know if this is true and what the formula is to have work out
the relationship.

Thanks in advance

Matt

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2001\07\19@120622 by Olin Lathrop

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> dB=10*log(G), G = gain, make sure you use log base 10

Note that this is power gain.  Power gain is proportional to the square of
the voltage gain.  Therefore an incremental increase in voltage gain of 10
increases the output signal by 20dB.


********************************************************************
Olin Lathrop, embedded systems consultant in Littleton Massachusetts
(978) 742-9014, RemoveMEolinspamTakeThisOuTembedinc.com, http://www.embedinc.com

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2001\07\21@035354 by Peter L. Peres

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> dB=10*log(G), G = gain, make sure you use log base 10
>
> -Angelos

Just remember that you need to specify power or voltage gain. Most low
frequency systems up into HF specify gain in voltage. Above that all gains
are specified in power gain terms. The difference is a multiplier of 2 in
dB (power is proportional to voltage squared - i.e. raised to the 2nd
power). The formula is then:

db=20*log(G)

Peter

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