The truth about decibels

[Larry Brasfield]

"Guy Macon" <_see.web.page_@_www.guymacon.com_> wrote
in message news:11c33e45vljsr58@corp.supernews.com...

John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...

Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com
Above views may belong only to me.

 

[Pooh Bear]

Guy Macon wrote:

John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...

No - I don't think he does ! And you're a stinking troll btw !

In fact it was one of the best contributions I've ever seen to a thread
that came 'out of the blue'. Full of excellent info that it would be
hard to find by any other method !

Thanks, John !

Don't let clowns like Guy Macon put you off ! Your contribution was
certainly very informative as far as I'm concerned.

Graham

 

[Pooh Bear]

John Perry wrote:

Pooh Bear (and others) wrote:

600 ohms working was only ever needed for long 'land lines' - and how many
of
them still exist ? It's all concentrated at the local exchange and
distributed digitally via optic fibre these days !

Actually, in some sparsely populated rural US areas there are still the
ancient 600-ohm lines in use. You can recognize them by the bare wires
held up on glass insulators and twisted every few hundred feet by
dropping one to a lower crosstie so it can swap places on the next
crosstie with its return wire.

I can believe that.

< snip >

The true nature of twisted-pair's characteristic impedance becomes
obvious when you apply a TDR (time-domain reflectometer). These devices
use variations in the line's characteristic impedance to find crimps,
breaks, shorts, etc. in a long transmission line.

Looking for 'echoes' ?

They are also important to FDM on both 600- and 100-ohm lines, because
improperly terminated long lines can have enough reflection to corrupt
the higher-frequency multiplexed channels.

And they were important to teletype (is this even used any more?)

Maybe someone has one somewhere ! ;-) Maybe in Russia ?

I recall as a youngster the first 'Glass Teletype'. That ages me !

because improperly terminated 100-ohm twisted pair limited the baud rate
possible over long subscriber lines.

Part of my job 35 years ago as a toll office tech was troubleshooting
these things . So some details may be distorted by faulty memory and
subsequent education. But the gist is correct.

And your contribution is appreciated.

Graham

 

[Spehro Pefhany]

On Tue, 28 Jun 2005 12:19:14 -0700, the renowned "Larry Brasfield"
<donotspam_larry_brasfield@hotmail.com> wrote:

"Guy Macon" <_see.web.page_@_www.guymacon.com_> wrote
in message news:11c33e45vljsr58@corp.supernews.com...
John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...


Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

Doesn't even have to be infinitely long, just long enough that the
reflection from the unterminated end doesn't make it back before
you've got your measurement.


Best regards,
Spehro Pefhany
--
"it's the network..." "The Journey is the reward"
speff@interlog.com Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com

 

[Keith Williams]

In article <qd93c1hn4v58le1kc7g5um250hnbio800f@4ax.com>,
speffSNIP@interlogDOTyou.knowwhat says...

On Tue, 28 Jun 2005 12:19:14 -0700, the renowned "Larry Brasfield"
donotspam_larry_brasfield@hotmail.com> wrote:

"Guy Macon" <_see.web.page_@_www.guymacon.com_> wrote
in message news:11c33e45vljsr58@corp.supernews.com...
John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...


Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

Doesn't even have to be infinitely long, just long enough that the
reflection from the unterminated end doesn't make it back before
you've got your measurement.

Then it's not DC. ;-)

--
Keith

 

[John Larkin]

On Tue, 28 Jun 2005 15:33:10 -0400, Spehro Pefhany
<speffSNIP@interlogDOTyou.knowwhat> wrote:

On Tue, 28 Jun 2005 12:19:14 -0700, the renowned "Larry Brasfield"
donotspam_larry_brasfield@hotmail.com> wrote:

"Guy Macon" <_see.web.page_@_www.guymacon.com_> wrote
in message news:11c33e45vljsr58@corp.supernews.com...
John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...


Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

Doesn't even have to be infinitely long, just long enough that the
reflection from the unterminated end doesn't make it back before
you've got your measurement.

If the DVM takes a normal amount of time to make a reading, the ohmic
drop of the cable will mess up the measurement. RG58 is 50 ohms, but
if you take a full second to measure the resistance, you're going to
add the resistance of 186,000 miles of center conductor!

John

 

[Kevin Aylward]

tlbs wrote:

Pooh Bear wrote:
1. A measuring system first used in telephony (Martin, W.H.,
"DeciBel -- the new name for the transmission unit. Bell System
Tech. J. January, 1929), where signal loss is a logarithmic function
of the cable length.

I have actually read that original paper by Martin. I have also read
another white paper with comments similar to your own, and have tried
(in my own circle of influence) to educate people about the proper use
of the dB.

In it's purest (and according to Martin) use, the Bel or deciBel is to
be used ONLY for power comparisons at one point in a circuit.

I, and most others, don't care a bloody toss about how the Bell
originally came about. Its simply irrelevant. As I have said. On has to
move on with the times.

Being able to see the general, from what was a specific instance is
actually, and possible a brilliant, insight.

For example, Einstein, when he realised that the Lorentz transformation
originally used as a kludge and *specifically* for Maxwell's Equations,
that had time being dependant on velocity, was *general* for the whole
of mechanics.

There are many more examples where people have recognised that a
specific first off idea was just a subset of a more useful and general
idea. The ability to spot such ideas is to be admired. Those that cant
open their eyes to the bigger picture, are those that are surly stuck in
the mud.

That
is, signal 1's power was measured at point-X in a system, and signal
2's power was measured at the SAME POINT in the system. The
base-10-log of the ratio of the 2 powers were compared and that
number was given the unit "Bel".

Later, it was determined that the power of a single signal could be
measured at 2 different points in a system AS LONG AS THE CIRCUIT
IMPEDANCE WAS THE SAME AT THOSE 2 MEASURING POINTS, then the
base-10-log of the ratio could also be expressed in units of Bels.

Here is an example of BAD usage of the dB:
If you ever find an OpAmp datasheet that charts its' gain vs.
frequency, and the Y-axis is expressed in dB, that's bad.

Complete and utter nonsense. I can't see how any experienced analogue
designer, who actually uses such graph as a matter of course on a daily
basis, could ever come up with such drivel as this, and I mean absolute
drivel. What is the world coming too.

Yeah, I'm on the rag on this. This debate is so daft as to be unreal.

Why?
because the input impedance of an Op Amp is nearly infinite, while
the output impedance is nearly zero. The impedances are NOT the
same, therefore you cannot express the gain ratio in terms of dB.

Yes we can. We don't care about power gain. What part of the definition,
as in how it is used by the overwhelming majority of professional
engineers today, "it is a simple log of a ratio" do you not understand?

I used to see this all the time in the 70's and occasionally in the
80's.

Pardon.!!! Its *the* de-facto stranded way of presenting gain plots.
Period. Its how one universally does feedback stability analysis. One
looks at the gain slope in dB and ensures that it goes through the 0 dB
point at 20 db/dec. Jesus wept dude. Do you do any real design at all?

The CORRECT

Nope.

y-axis units is Volts/Volt, and if they want to
express it as a logarithm, 20*log(Vout/Vin) that's perfectly fine, but
it is NOT a dB. I repeat that is NOT a dB.

Yes it is. Now get this, we have made a definition of dB that is
different to that as it was originally conceived. It makes sense to do
so, it is consistent with a more general definition, so we have done so.

Here is an example of GOOD usage of the dB:
The examples of RF components from Mini-Circuits given above and their
use of dB, or dBm IS PERFECTLY OK.

{snip irrelevant historical use}

I have designed quite a few RF circuits in my time -- this is how it's
done.

And little else it would seem.

Units like dBc generally fall within the original definition of the
Bel and dBel, because the power levels of the carrier and the
modulating signal can be measured at the same point in the circuit.

Look mate. The definition of the dB, today, is 20 log(Q1/Q2). End of
story. Get over it.

Kevin Aylward
informationEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Pooh Bear]

Adrian Tuddenham wrote:

Pooh Bear <rabbitsfriendsandrelations@hotmail.com> wrote:

decibel Abbr. dB Equal to one-tenth of a bel. [After Alexander Graham
Bell.]

1. A measuring system first used in telephony (Martin, W.H., "DeciBel --
the new name for the transmission unit. Bell System Tech. J. January,
1929), where signal loss is a logarithmic function of the cable length

That looks like a fairly up-to-date reference, I'm pleased to see that
it reiterates the 1929 definition of the decibel and there is no
indication that it has been re-defined as others have claimed.

You apparently missed

AES-R2
IEC 60027-3
IEC 60268-2

But then I know you have a fuckwit's closed mind so I expected no more !

Graham

p.s. in any event it *never* had to be 're-defined' anyway ! The equations
simply fall out of the sums.

 

[Pooh Bear]

tlbs wrote:

Pooh Bear wrote:
1. A measuring system first used in telephony (Martin, W.H., "DeciBel --
the new name for the transmission unit. Bell System Tech. J. January,
1929), where signal loss is a logarithmic function of the cable length.

I have actually read that original paper by Martin. I have also read
another white paper with comments similar to your own, and have tried
(in my own circle of influence) to educate people about the proper use
of the dB.

The relevant 'education' is now adopted by the AES ( Audio Engineering Society
) who write the standards on this matter. Their standards are adopted by
bodies such as the IEC, ANSI and ISO

In it's purest (and according to Martin) use, the Bel or deciBel is to
be used ONLY for power comparisons at one point in a circuit. That is,
signal 1's power was measured at point-X in a system, and signal 2's
power was measured at the SAME POINT in the system. The base-10-log of
the ratio of the 2 powers were compared and that number was given the
unit "Bel".

But he failed to mention in that paper that Bell Labs knew that 0dBm - i.e
1mW - was not a sufficiently large signal to ensure adequate volume for
clarity of conversation over the phone.

Therefore Bell Labs 'invented' the VU ( volume unit ) meter.

I reckon most ppl in the developed world have seen a VU meter even if only a
miniature version on their cassette recorder.

The VU meter was calibrated such that '0' on the VU scale - normally referred
to as '0 VU' was a *voltage* equivalent to +4dBm ( 600 ohms ) in the load.

Note *voltage*. The VU meter was / is simply a moving coil meter with a
rectifier ( copper oxide in early examples - germanium in more recent ) and
therefore a *voltage* driven instrument.

The VU meter had / has an internal impedance of 3900 ohms and was used with an
external fixed series resistor of 3600 ohms to provide a load of 7500 ohms.
The '0 VU' mark was calibrated to be equivalent to +4dBm ( 600ohms ) i.e.
1.228 V.

So........ All the time that Bell Labs were supposedly saying that the dB was
only 'pure' if considered as power - they were *ACTUALLY* measuring it as a
*VOLTAGE* !

Now go play elsewhere ! And take your idiotic preconceptions with you !


Graham

 

[Tim Wescott]

John Larkin wrote:

On Tue, 28 Jun 2005 15:33:10 -0400, Spehro Pefhany
speffSNIP@interlogDOTyou.knowwhat> wrote:


On Tue, 28 Jun 2005 12:19:14 -0700, the renowned "Larry Brasfield"
donotspam_larry_brasfield@hotmail.com> wrote:


"Guy Macon" <_see.web.page_@_www.guymacon.com_> wrote
in message news:11c33e45vljsr58@corp.supernews.com...

John Perry wrote:


In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...


Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

Doesn't even have to be infinitely long, just long enough that the
reflection from the unterminated end doesn't make it back before
you've got your measurement.




If the DVM takes a normal amount of time to make a reading, the ohmic
drop of the cable will mess up the measurement. RG58 is 50 ohms, but
if you take a full second to measure the resistance, you're going to
add the resistance of 186,000 miles of center conductor!

John


Dang lossy cable!

--
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

 

[Adrian Tuddenham]

Kevin Aylward <see_website@anasoft.co.uk> wrote:


[...]

Look mate. The definition of the dB, today, is 20 log(Q1/Q2). End of
story. Get over it.

If only we had realised this years ago - then audio designers could have
dispensed with valves, transistors and all the problems that come with
amplifiers. All you need is a step-up transformer between the
microphone and the loudspeaker.


--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

 

[Adrian Tuddenham]

tlbs <tlbs101@excite.com> wrote:

Pooh Bear wrote:
1. A measuring system first used in telephony (Martin, W.H., "DeciBel --
the new name for the transmission unit. Bell System Tech. J. January,
1929), where signal loss is a logarithmic function of the cable length.

I have actually read that original paper by Martin. I have also read
another white paper with comments similar to your own, and have tried
(in my own circle of influence) to educate people about the proper use
of the dB.

In it's purest (and according to Martin) use, the Bel or deciBel is to
be used ONLY for power comparisons at one point in a circuit. That is,
signal 1's power was measured at point-X in a system, and signal 2's
power was measured at the SAME POINT in the system. The base-10-log of
the ratio of the 2 powers were compared and that number was given the
unit "Bel".

Later, it was determined that the power of a single signal could be
measured at 2 different points in a system AS LONG AS THE CIRCUIT
IMPEDANCE WAS THE SAME AT THOSE 2 MEASURING POINTS, then the
base-10-log of the ratio could also be expressed in units of Bels.

Here is an example of BAD usage of the dB:
If you ever find an OpAmp datasheet that charts its' gain vs.
frequency, and the Y-axis is expressed in dB, that's bad. Why? because
the input impedance of an Op Amp is nearly infinite, while the output
impedance is nearly zero. The impedances are NOT the same, therefore
you cannot express the gain ratio in terms of dB.

I used to see this all the time in the 70's and occasionally in the
80's. The CORRECT y-axis units is Volts/Volt, and if they want to
express it as a logarithm, 20*log(Vout/Vin) that's perfectly fine, but
it is NOT a dB. I repeat that is NOT a dB.

Here is an example of GOOD usage of the dB:
The examples of RF components from Mini-Circuits given above and their
use of dB, or dBm IS PERFECTLY OK. Why? because their components are
all 50 Ohm and 75 Ohm systems and are explicitly stated as such. 50
Ohm inputs, 50 Ohm outputs. 75 Ohm inputs, 75 Ohm outputs. The gains
or attenuations listed assume (properly) that the source impedance and
load impedances connected to the devices sold are also of the same
impedance as the devices sold. So if it states that a device has a
gain of 13 dB, it has a gain of 13 dB in an implicit 50 Ohm (or 75 Ohm
for that part number) system. If the output is stated at +33 dBm, then
it will produce 10 V across 50 Ohms and 2W into 50 Ohms.

I have designed quite a few RF circuits in my time -- this is how it's
done.

Units like dBc generally fall within the original definition of the Bel
and dBel, because the power levels of the carrier and the modulating
signal can be measured at the same point in the circuit.

Thank you for that interesting information and brilliantly clear
exposition. I only wish you had written some of the modern textbooks,
then we wouldn't have the present misunderstandings.

(Sadly, though, we'd probably still have to put up with the occasional
objectionable and obstreperous individuals who disgrace the profession
and its institutions)


--
~ Adrian Tuddenham ~
(Remove the ".invalid"s and add ".co.uk" to reply)
www.poppyrecords.co.uk

 

[Pooh Bear]

Adrian Tuddenham wrote:

Kevin Aylward <see_website@anasoft.co.uk> wrote:

[...]

Look mate. The definition of the dB, today, is 20 log(Q1/Q2). End of
story. Get over it.

If only we had realised this years ago - then audio designers could have
dispensed with valves, transistors and all the problems that come with
amplifiers. All you need is a step-up transformer between the
microphone and the loudspeaker.

Look here plonker.... It was actually the transistor that caused all this
fuss. Not to mention the damn IC !

If, like you, we still lived back in the 1930s there wouldn't be this
problem. And we would be listening to 'chamber music' on the BBC third
service for our entertainment !

Graham

 

[Pooh Bear]

Adrian Tuddenham wrote:

Thank you for that interesting information and brilliantly clear
exposition. I only wish you had written some of the modern textbooks,
then we wouldn't have the present misunderstandings.

(Sadly, though, we'd probably still have to put up with the occasional
objectionable and obstreperous individuals who disgrace the profession
and its institutions)

Hmmmm.. damn shame about *accepted industry practice* isn't it ?

Not to mention International Standards bodies !

Yeah - you ignore the lot of them and we'll ignore you. Fair deal ?

Graham

 

[Robert]

"Pooh Bear" <rabbitsfriendsandrelations@hotmail.com> wrote in message
news:42C0DEBC.BF071D14@hotmail.com...

"James T. White" wrote:

"Joerg" <notthisjoergsch@removethispacbell.net> wrote in message
news:WZYve.421$0V3.386@newssvr13.news.prodigy.com...
Hello Graham,

dBm all over the place...

Plus dBi and dBd for antennas!
--
James T. White

Did I *not*say that the RF guys adopted the dB ? ;-)

Since you mention them - us LF Luddites ;-) would be quite interested as
to how you RF guys use the dB !

The measures you mention are new to me.

I'd heard of dBc - third order intercept ( whatever that is ! ) but it
never related to my area of interest so I didn't pay enough attention.

dBc is a usually used to specify the dB relationship of signals to a Carrier
frequency which has it's own absolute signal level (a lot of the time in
dBm).

The distortion measurement I think you're talking about is the 3rd order
intermodulation non-linearity test and is given as a (Output or Input) dBm
level itself.

That level is where you stick in two tones into a nonlinear device and get
the tones out plus 2xf1-f2 and 2xf2-f1. You get other nonlinear products out
as well but these are the ones closest to being inband.

You increase the level of input tones and since the intermod products are
3rd order they increase 3dB for every 1dB increase in input tones. You just
plot them on a graph and look where they intersect for the 3rd order
intercept level in dBm.

Robert

 

[Guy Macon]

Larry Brasfield wrote:

Guy Macon wrote...

John Perry wrote:

In fact, twisted pair is around 100 ohms from DC to microwave,

Are you sure you don't want to change "DC" to some low AC frequency?
At DC the insulation resistance is a bit higher than 100 Ohms...

Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

(Homer Simpson voice) D'OH!

As soon as I read the above I realized that you are correct and that
I was assuming a finite cable length.

If I am not mistaken (again), if you spend, say, 10 minutes or less
making your measurement, you cannot distinguish between an infinitely
long cable and one that is a mere 11 light-minutes long.

 

[Guy Macon]

Adrian Tuddenham wrote:

Kevin Aylward <see_website@anasoft.co.uk> wrote:

Look mate. The definition of the dB, today, is 20 log(Q1/Q2). End of
story. Get over it.

If only we had realised this years ago - then audio designers could have
dispensed with valves, transistors and all the problems that come with
amplifiers. All you need is a step-up transformer between the
microphone and the loudspeaker.

I worship your wit and wisdom, O Great One.

 

[Don Bowey]

On 6/28/05 1:52 PM, in article 42C1B8A8.42C55756@hotmail.com, "Pooh Bear"
<rabbitsfriendsandrelations@hotmail.com> wrote:

tlbs wrote:

Pooh Bear wrote:
1. A measuring system first used in telephony (Martin, W.H., "DeciBel --
the new name for the transmission unit. Bell System Tech. J. January,
1929), where signal loss is a logarithmic function of the cable length.

I have actually read that original paper by Martin. I have also read
another white paper with comments similar to your own, and have tried
(in my own circle of influence) to educate people about the proper use
of the dB.

The relevant 'education' is now adopted by the AES ( Audio Engineering Society
) who write the standards on this matter. Their standards are adopted by
bodies such as the IEC, ANSI and ISO

In it's purest (and according to Martin) use, the Bel or deciBel is to
be used ONLY for power comparisons at one point in a circuit. That is,
signal 1's power was measured at point-X in a system, and signal 2's
power was measured at the SAME POINT in the system. The base-10-log of
the ratio of the 2 powers were compared and that number was given the
unit "Bel".

But he failed to mention in that paper that Bell Labs knew that 0dBm - i.e
1mW - was not a sufficiently large signal to ensure adequate volume for
clarity of conversation over the phone.

Put a telephone headphone up to your ear and listen to a one-mW signal. You
may change your mind.

Therefore Bell Labs 'invented' the VU ( volume unit ) meter.

Horsepucky - the Volume Unit meter was designed to be used *after* a
facility was properly aligned with a "dB meter." to observe voice and music.
As I recall, it was slightly dampened.

I reckon most ppl in the developed world have seen a VU meter even if only a
miniature version on their cassette recorder.

The VU meter was calibrated such that '0' on the VU scale - normally referred
to as '0 VU' was a *voltage* equivalent to +4dBm ( 600 ohms ) in the load.

It appears you may be, incorrectly, implying the "V" means Voltage, not
"Volume."

Note *voltage*. The VU meter was / is simply a moving coil meter with a
rectifier ( copper oxide in early examples - germanium in more recent ) and
therefore a *voltage* driven instrument.

The VU meter had / has an internal impedance of 3900 ohms and was used with an
external fixed series resistor of 3600 ohms to provide a load of 7500 ohms.
The '0 VU' mark was calibrated to be equivalent to +4dBm ( 600ohms ) i.e.
1.228 V.

So........ All the time that Bell Labs were supposedly saying that the dB was
only 'pure' if considered as power - they were *ACTUALLY* measuring it as a
*VOLTAGE* !

More horsepucky. Only a complete moron would assume that.

Don

 

[Guy Macon]

Larry Brasfield wrote:

Cable impedance at DC is a perfectly sensible concept. To measure
it is simple: Apply your Ohm meter to an infinitely long sample of it.

Spehro Pefhany wrote:

Doesn't even have to be infinitely long, just long enough that the
reflection from the unterminated end doesn't make it back before
you've got your measurement.

John Larkin wrote:

If the DVM takes a normal amount of time to make a reading, the ohmic
drop of the cable will mess up the measurement. RG58 is 50 ohms, but
if you take a full second to measure the resistance, you're going to
add the resistance of 186,000 miles of center conductor!

Don Bowey wrote:

You may want to re-think that.
Here are some specs for non-loaded 26G pic cable; a common Exchange
Cable type: Resistance per mile from 1 Hz to 15kHz = 441 Ohms.
Beyond that freq the skin effect starts increasing the resistance.
At 1MHz it's 463 Ohms, and at 5 MHz it's 2044 Ohms. Approximate
Z per mile at 1 Hz is 20,562 Ohms, and is up to 2057 Ohms at 100 Hz.
In the band from 300 Hz to 3 kHz the Z runs from 1189 Ohms to 383
Ohms. At 5Mhz the Z is 96 Ohms/mile.

This is the best thread I have read in a long time.

 

[Don Bowey]

On 6/28/05 1:32 PM, in article
9tiwe.35546$Vo6.4966@fe3.news.blueyonder.co.uk, "Kevin Aylward"
<see_website@anasoft.co.uk> wrote:

(snip typical Kevin blustery posturing)

But I strongly suspect Einstein stole his best ideas from his wife. You
should get a wife to help you get on track.

By the way 10log P1/P2 is still much in use, your authoritative declarations
not withstanding.

Don