### BASIC TOPOLOGIES IN FILTER DESIGNS

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

##### 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 :

##### 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.