Poles with Increasing Phase

Discussion in 'Homework Help' started by jegues, Feb 2, 2014.

  1. jegues

    Thread Starter Well-Known Member

    Sep 13, 2010
    735
    43
    I'm having trouble understanding the bode plot for,

    G(s) = \frac{1}{2s-1}

    Usually when I am drawing bode plots for either real poles or zeros, I simply solve for the break frequency knowing that a zero/pole will give me a +/-20dB/decade asymptote after the break frequency on my magnitude plot, and a +/-90° phase shift across two decades, with the center (i.e. the +/-45° point) at my break frequency on my phase plot.

    This has always worked when I have,

    (s+a) \quad a>0

    but it seems to change when,

    (s - a) \quad a>0 \quad \text{or, } \quad (-s+a) \quad a>0

    I can't wrap my head around why a pole has an increasing phase that starts at -180°. I was expecting a phase decrease from 0° to -90°.

    Can someone explain what I am misunderstanding?
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Perhaps if you re-cast the transfer function in the complex frequency domain

    G_{(j \omega)}=\frac{1}{(-1+j2\omega)}

    Then rationalise the function ....

    G_{(j \omega)}=-\frac{1}{(1+4 {\omega}^2)}-j \frac{2\omega}{(1+4{\omega}^2)}

    What is the initial phase as ω approaches zero?
     
  3. LvW

    Active Member

    Jun 13, 2013
    674
    100
    jegues, do you realize that the pole is real and in the right half of the s-plane?
    Thus, it belongs to an unstable non-realizable system.
     
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