# linear model Hioki - Telecommunications

B

#### Brian

Jan 1, 1970
0
Greetings,

I am requesting clarification and assistance from the scientific
community, if anyone can offer it, on Hioki's, "Telecommunications"
Fourth Edition.

If you have a copy of the text, you will have noticed many of the errors,
most notably the editors did not catch an error with Ohms law and Joules
law on page 12. After that, my confidence in this text was shot, but I
am stuck with it for class.

My question is regarding the use of the linear model for Signal out and
Noise out Chapter 2.2.3, example 2.11 page 17.

Hioki (and my instructor) have stated that Signal is the combination of
the intelligence and noise such that.

So = Signal Out
Si = Signal In
No = Noise Out
Ni = Noise In
Ap = Amplification
Nr = Noise added by the equipment such as an amplifier

No = Ni * Ap + Nr
So = Si * Ap

However, it seems odd that the formula for No is not applied to So. Hioki
left off the Nr. Now if Signal includes the Noise, this does not make
sense.

provide references to a text I can use to further clarify the situation
as this text has absolutely no credibility at this point.

Thank-you,
Brian

R

#### Robert Baer

Jan 1, 1970
0
Brian said:
Greetings,

I am requesting clarification and assistance from the scientific
community, if anyone can offer it, on Hioki's, "Telecommunications"
Fourth Edition.

If you have a copy of the text, you will have noticed many of the errors,
most notably the editors did not catch an error with Ohms law and Joules
law on page 12. After that, my confidence in this text was shot, but I
am stuck with it for class.

My question is regarding the use of the linear model for Signal out and
Noise out Chapter 2.2.3, example 2.11 page 17.

Hioki (and my instructor) have stated that Signal is the combination of
the intelligence and noise such that.

So = Signal Out
Si = Signal In
No = Noise Out
Ni = Noise In
Ap = Amplification
Nr = Noise added by the equipment such as an amplifier

No = Ni * Ap + Nr
So = Si * Ap

However, it seems odd that the formula for No is not applied to So. Hioki
left off the Nr. Now if Signal includes the Noise, this does not make
sense.

provide references to a text I can use to further clarify the situation
as this text has absolutely no credibility at this point.

Thank-you,
Brian

I have no references that i can cite.
However, signal and noise are never separate.
That said, there is a concept that two or more signals can be analyzed
as if they were separate; sort of a 1+2 = 2+1 and (1)+(2) = (1+2) etc.
Well, sort-of true - *IF* and only if the system is perfectly linear,
and a good approximation if the system (for all cases of the signals in
question) is "reasonably" linear (say 1% or better for similar accuracy
in results).
So, the amplifier "sees" (Si+Ni+Nr) as a *composite* signal, as
amplifier noise is almost always referred to its input.
That one convention "destroys" the usability of the relationships you
gave.
Now, the amplifier has a gain of Ap, so AS LONG AS THE AMPLIFIER IS
LINEAR FOR THE SIGNALS GIVEN (emphasis is on purpose), then at the
output one has: (So+No) = Ap * (Si+Ni+Nr).
That is to say, the complete signal at the input, which one may be
able to estimate the actual signal level Si and the actual noise that is
in that signal Ni, and measure the amplifier noise Nr, will total to the
composite (Si+Ni+Nr).
That is what the amplifier works with or "sees".

Now the signal Si or the noise Ni or the amplifier noise Nr OR THE
TOTAL AT ANY GIVEN INSTANT IN TIME may drive the amplifier into
non-linearity that is sufficient to *create* harmonics of a magnitude as
to "noticeably" add to the output signal.
Such added information can be considered as "noise", even tho it is
not random (noise is usually considered to be a random signal).
So here we get into semantics.
One can have a Si of 100KHz pure sine wave, which is the signal of
interest and wanted.
One can "pipe" it thru a coax cable that is rather long, and have a
truck drive over the cable at an extremely regular interval - creating
bursts of noise, said bursts being very regular.
In fact, short the input (no generator) and measure the noise and put
it thru a spectrum analyzer.
Oooh! Look at that low frequency "spike". Nice Ni.
Now replace that long cable and truck with a *second* generator that
puts out pulses at that same rate; twiddle the rise, width and fall
times to get a similar spectrum. Almost identically looking Ni.
But one used a *signal generator* (!).
Too bad; it is !!NOISE!! because, like a weed, it is UNWANTED.
((As an aside, to measure amplifier noise, one uses a NOISE GENERATOR
(that is to say, a special signal generator that creates a known level
and *spectrum* of noise) to drive the amplifier input.
In this case a "real" signal is UNWANTED and the *noise* is desired.))

Now i have never heard anyone calling distortion at the *output* of an
amplifier as being named "noise".
It certainly is not Si or Ni or Nr amplified, but it is (normally)
UNWANTED.

So that is a semantics problem that conventional terminology created.
The extra output is called distortion, and not noise.
Never mind that the Ap * (Si+Ni+Nr) is *not* equal to the output,
never mind that it may be almost impossible to recognize even one
component of the input; the convention is that one has Ap * (Si+Ni+Nr)
plus distortion.

*********
Hopefully, i have not confused you, and instead partly clarified the
situation.

In any event, do not argue in class; *ask* polite questions about the
discrepancies in the book and couch them as errors caused by the
publisher.
The writer of the book is "never" wrong - most especially if (s)he has
one or more degrees!
If the instructor brushes off your careful and plitew queries, or sas
or implies that you are wrong, then shut up about it and cease the
queries.
Else you may get a very bad grade that you did not earn (at minimum).
Just find other texts (older ones are probably better; look up what
Shannon had to say about communications over a noisy channel; one can
say that he"defined" information theory) for more enlightenment.
And filter out the "noise" of those errors; your brain becomes a
different kind of a non-linear "amplifier" that gives (Si+Ni+Nr) ---> So
= Ap*Si.

B

#### Brian

Jan 1, 1970
0
Robert,

Thank-you for the information, and the advice on keeping cool in class.

I will look up Shannon.

Brian

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