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Transfer function on a circuit

  1. Apr 11, 2013 #1
    I'm tinkering with a software called LTspice. The user can insert circuits and simulate them. After doing some Bode plots I started to wonder what the transfer function looked like. I usually don't bother about this when I build amplifiers, but this LTspice software got me curious.

    I looked through some old note I have and came up with this, sort of.

    H = Y/X
    Where Y(s) is the laplace tranformation of y(t), likewise for x(t) and in-signal.
    Impedance of a capacitor [itex]Z_c = \frac{1}{i ω C}[/itex] and the resistor [itex]Z_R = R[/itex]. I guess the impedances should be written with [itex]iω = s[/itex] if a proper Laplace tranformation is to be done.

    Can any one show me how to derive Y and X for this circuit:
     

    Attached Files:

  2. jcsd
  3. Apr 11, 2013 #2
    I forgot the inner resistance of the triode/tube. The inner resistance is between the input connection and the top/plate connection.

    My fumbling attempts:
    [itex]\displaystyle X(s) = \frac{\frac{R_c+\frac{1}{sC}}{R_c \frac{1}{sC}}+R_c}{\left( \frac{R_c+\frac{1}{sC}}{R_c \frac{1}{sC}} \right)R_c}[/itex]


    [itex]Y(s) = \frac{R_c+\frac{1}{sC}}{R_c\frac{1}{sC}}+r_a[/itex]
     
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