[bill ramsay]

On Fri, 17 Aug 2007 16:30:46 GMT, "jim Gregory"
wrote:

Does this mean, traditionally, telephone cable tx loss should be measured
with
a stimulus of centre freq @ 800Hz (near enough to 5000/2pi) in preference to
using 1kHz?
I seem to remember that in '80s-'90s, BT's Private Wires testers often
measured atten of lines at 800Hz.
Jim

"The Phantom" wrote in message
.. .
On Wed, 15 Aug 2007 08:59:48 +0300, "Iain Churches"
wrote:

From e-mail I receive, it seems to me that
the decibel is a misunderstood and widely
abused term.

I have added a page to my website on the
subject mainly constructed from my dog-eared
student notes from the third quarter of the last century.
The page cannot yet be accessed
from the index page, but can be found at:

http://www.kolumbus.fi/iain.churches...heDecibel.html

Any comments or suggestions/additions would
be welcome. I am grateful for the help of my
pals Jim and Richard in the UK for their contributions.

Regards to all
Iain

The second paragraph is a little off. You say:

"The basic unit chosen was the power loss in a standard telephone line
over
the distance of one mile, at 1kHz. This was called the Transmission Unit,
but was renamed, after the inventor of the telephone, and became known as
the bel..."

Let me quote from page 9 of the book, "Transmission Circuits for
Telephonic Communication", published by Bell Labs in 1925.

"Three different units have been used to express telephonic volume
efficiencies:

(1) The natural attenuation unit, also designated as a napier or as a hyp;

(2) The mile of standard cable or simply a mile;

(3) The so-called transmission unit or TU."

Regarding a mile of standard cable, they say:

"Standard cable is defined as a cable having uniformly distributed
resistances of 88 ohms per loop mile and uniformly distributed shunt
capacitance of .054 microfarad per mile. Its series inductance and shunt
leakance are assumed to be zero.*

* In England it has been customary to assume an inductance of .001 henry
per loop mile--which assumption reduces the attenuation constant of the
cable by approximately 3 per cent."

A cable with a resistance of 88 ohms per loop mile is made of standard 19
gauge wire. Later in the book they talk of long distance line composed of
10 or even 8 gauge wires spaced a foot apart.

"The mile of standard cable is based upon the constant percentage
decrease in current (or in power) per mile which takes place when an
e.m.f.
of a frequency, such as f cycles (f = w/2pi = 5000/2pi), is impressed at
one end of an infinite length of such a cable."

The measurement frequency here is 796.4 Hz (w = 5000).

They also say:

"Due to the objection that the attenuation constant of standard cable
varies with frequency and also to the fact the use of a frequency of 796.4
Hz is not universally agreed upon, there has recently been adopted a new
transmission unit which (1) does not vary with frequency, (2) is of a
convenient size or magnitude--avoiding one of the chief objections to the
napier or natural attenuation unit--and (3) has a simple physical
significance so that its eventual universal adoption would appear
probable.

This new transmission unit (referred to for the sake of convenience as a
TU) is defined by the relation

Ntu = 10*LOG10(W1/W2)

in which Ntu is the number of TU by which any two powers W1 and W2 are
said
to differ."

They apparently had not yet decided to call it a decibel, and of course,
one Bel = 10 TU. This text was written in 1924 and published in 1925.

There is a table of conversions:

Relations between various types of units

Multiply by to obtain

miles .947 TU
miles .109 napiers
napiers 9.175 miles
napiers 8.686 TU
TU 1.056 miles
TU .115 napiers
---------------------------------------------------

So, we see that the attenuation of a mile of standard cable was not
called a transmission unit; it was just called a "mile". The transmission
unit (TU) was what would later be called a decibel; it was not a Bel, it
was a tenth of a Bel.

The Wikipedia article says, "Devised by engineers of the Bell Telephone
Laboratory to quantify the reduction in audio level over a 1 mile
(approximately 1.6 km) length of standard telephone cable, the bel was
originally called the transmission unit or TU." This is wrong, as the
quotations I've given show.

The TU was indeed devised to quantify the reduction in audio level, but
it wasn't intended to represent the attenuation in one mile of cable, as
you can see from the conversion table. The TU was defined as
10*LOG10(W1/W2), which wasn't the attenuation of a mile of cable; it was
close (1 mile = .947 TU), and that is why a TU was defined as
10*LOG10(W1/W2) and not just LOG10(W1/W2). They wanted a conveniently
sized unit.

From the conversion table we see that a mile was an attenuation of .947
decibels, to answer John Byrns' question.