INTRODUCTION



    Filters are the fundamental circuits for obtaining frequency selection; transmitting some signals without attenuation while blocking other signals. In a radio frequency environment care must be taken to achieve low
VSWR
Voltage Standing Wave Ratio.
in the passband frequencies while obtaining sufficient
attenuation
The attenuation depends on the order n of the filter : 20n dB/decade.
in the stopband region. We assume that the components used are ideal. A realistic design must take care of : The parisitic effect of the components, cicuit board capacitance and trace inductances. We implemented the interface to design both : Butterworth and Chebyshev filter topologies for low pass, high pass and band pass filters. We will soon add the band reject type for both topologies.


BASIC TOPOLOGIES IN FILTER DESIGNS


1-BUTTERWORTH:The equations used for the low pass design are shown below :


Equations for Butterworth Low Pass Filter

Where :
  • f : is the cut-off or corner frequency in Hz.
  • R
    In the Butterworth design the load is always matched to the source.
    : is the source load and it must be equal to the load value in Ω.
  • n
    In the simulator n is ≦15.
    : is the order of the filter and it is equal to the number of components.
  • i : is the component number, odd for shunt capacitor and even for series inductor.

2-CHEBYSHEV:The equations used for the low pass Chebyshev design are more complex than the Butterworth type. We have used a mathematical model provided by Peter Vizmuller in his book RF Design Guide : Systems, Circuits and Equations. The equations used in the simulation are shown below :


Equations for Chebyshev Low Pass Filter

Where :
  • f : is the
    ripple frequency
    Not the cut off frequency
    in Hz .
  • R
    In the Chebyshev design the load is matched to the source when the order of the filter is odd.
    : is the source resistance value in Ω.
  • n : is the
    order
    In the simulator n is ≦15.
    of the filter and it is equal to the number of components.
  • i : is the component number, odd for shunt capacitor and even for series inductor.
  • Ar : is the pass band ripple in dB.