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Homework Help: Transfer Function Notation

  1. Jun 29, 2006 #1
    Just a quick question about some notation used in my book.

    The proper form of the transfer function used in my book is as follows:

    [tex] \bar H(j\omega) = \frac{K_0(j\omega)^{\pm N} (1+j\omega\tau_1)(1+2\zeta_3(j\omega\tau_3)+(j\omega\tau_3)^2)\cdot\cdot\cdot }{(1+j\omega \tau_a)(1+2\zeta_b(j \omega \tau_b)+(j \omega \tau_b)^2 )\cdot \cdot \cdot}[/tex]

    I'm kinda just being picky here, but I would like to understand the convention that they used.

    Why the jump from [itex] \tau_1 [/itex] to [itex] \tau_3 [/itex], the choice of starting with [itex] \zeta_3 [/itex] in the numerator. Just curious if someone could shed some light on this.

    Thank you
     
    Last edited: Jun 29, 2006
  2. jcsd
  3. Jun 30, 2006 #2

    FredGarvin

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    Science Advisor

    Is this in circuits, controls, vibrations...? What is the topic?

    By the looks of it, it's a formulation from an infinite series.
     
  4. Jul 1, 2006 #3
    Woops I forgot about this post :blushing:

    Sorry, I should have specified where this came from. This is from a basic circuit engineering course, specfically from the book: "Basic Engineering Circuit Analsysis" 8th Edition, Irwin/Nelms.

    It looks like an expansion of some sort. The lecture notes have been very good, so I haven't been reading chapters like I typically do, just skimming them...it looks like I missed a page or two.

    [tex] \bar H(s) = \frac{N(s)}{D(s)}=\frac{K_0(s-z_1)(s-z_2)\cdot \cdot \cdot(s-z_m)}{(s-p_1)(s-p_2)\cdot\cdot\cdot(s-p_n)} [/tex] (1)

    where:
    [tex] s= j\omega [/tex]
    [tex] N(s) =[/tex] a polynomial of degree m
    [tex] D(s) =[/tex] a polynomial of degree n

    Also, it says that in general (1) can be expressed in the form that I gave in the OP. Hope that helps clear things up.
     
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