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linear model Hioki - Telecommunications

Discussion in 'General Electronics' started by Brian, Mar 16, 2005.

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  1. Brian

    Brian Guest


    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

    Please provide explanation if Hioki is correct. Either way, please
    provide references to a text I can use to further clarify the situation
    as this text has absolutely no credibility at this point.

  2. Robert Baer

    Robert Baer Guest

    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
    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)

    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

    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
    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
    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.
  3. Brian

    Brian Guest


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

    I will look up Shannon.

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