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LOW-PASS FILTER
A network which passes all the
frequencies upto ωH and stop or
attenuated all other frequencies is
called low-pass filter.
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HIGH-PASS FILTER
A network which passes all the
frequencies from ωL and stop or
attenuated all other frequencies before
ωL is called high-pass filter.
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BAND-PASS FILTER
A network which passes all the
frequencies between ωH and ωL and stop
or attenuated all other frequencies is
called band-pass filter.
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BAND-REJECT FILTER
A network which stop all the
frequencies between ωH and ωL and
passes all other frequencies is called
band-stop filter.
7. Filter Transmission, Types and Specification
Transfer Function
T s( )
Vo s( )
Vi s( )
The Filter Transmisson found by evaluating T(s) for physical frequencies
s j ω⋅ T jω( ) T jω( ) e
jφ ω( )
⋅
Gain Function
G ω( ) 20 log T jω( )( )⋅ dB
Attenuation Function
A ω( ) 20− log T jω( )( )⋅ dB
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transfer function zeros or transmission zeros
T s( )
aM s z1−( )⋅ s z2−( )⋅ s z3−( )⋅ ⋅ ⋅ ⋅ s zM−( )⋅
s p1−( ) s p2−( )⋅ s p3−( )⋅ ⋅ ⋅ ⋅ s pN−( )⋅
transfer function poles or the natural poles
Pole Zero Plot of LPF
11. Transmission specifications for a bandpass filter. The magnitude response of a filter that just meets
specifications is also shown. Note that this particular filter has a monotonically decreasing
transmission in the passband on both sides of the peak frequency.
Band Pass Filter
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12. Pole-zero pattern for the bandpass filter whose transmission is shown. This filter is of the sixth order (N = 6.)
BPF Transfer Function
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13. Summary of General First-Order Filter
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