© François Le Coat
©Karl Samyn

Last modified :
         09 mar 1998

5. The curves of Bode


a. System theory

  • 1. Basic knowledge

  • 2. Harmonic analyse of a linear system

b. Filters with OPAMs

  • 1. OPAM

  • 2. Determination of H(p)

  • 3. Band passage filter

c. More examples

(all formulas also available as *.fmu file in directory /bode)
  • 1. Filter using 2 OPAM's

    The circuit drawn in fig. 4.3.1 gives this for H(p) :

    [figure 4.3.1]

    [formula example 1]
         with : T1 = R1C1
                  T2 = R2C2
                  R1 = R2 = 1 Mega Ohm
                  C1 = 1 micro F
                  C2 = 0.063 micro F

    This gives us a "low pass filter" with an amplification of -24 dB. Try to draw this curves yourself. Both curves are suplied in the /bode directory. It are /bode/bode_a1.img and /bode/bode_f1.img.
  • 2. Filter from a telephone central

    This filter has next H(p) :

    [formula example 2]

    The files are /bode/bode_a2.img and /bode/bode_f2.img.
  • 3. Special case

    Here we have a H(p) that can not be transformed to the form like formula 4.2.1.

    [formula example 3]

    The general form is this one :

    [formula 4.3.1]

    In all the above cases we had dzeta = 1. The curve of the amplitude (/bode/bode_3a.img) we get here, looks similar to the curves from a spring (see mechanics). So does the formula.