1996 - 2016
BSEE - KB3UON
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An infinite number of filter transfer functions exist. A handful are commonly used as a starting point due to certain characteristics. The table following the plots lists properties of the filter types shown below. Not given - due to complex numerical methods required - are the Cauer (Elliptical) filters that exhibit equiripple characteristic in both the passband and the stopband.
Phase information may be gleaned from the transfer functions by separating them in to real and imaginary parts and then using the relationship:
Phase: θ = tan-1 (Im / Re)
Group delay is defined as the negative of the first derivative of the phase with respect to frequency, or
|Type||Properties||Transfer Function (Lowpass)|
| Filters with a large BW will exhibit sloped group delay across the band. This usually is not a problem since group delay deviation tends to be specified for variation in some subsection of the band.|
|These equations are used to convert the lowpass prototype filter equation into
equations for highpass, bandpass, and bandstop filters. They work for all three functions - Butterworth, Chebyshev,
and Bessel. Simply substitute the highpass, bandpass, or bandstop transformation of interest for the fr
term in the lowpass equation.
by Robert J. Wenzel
This CD-ROM course contains approximately 12-hours of instruction on the fundamentals of microwave filters, couplers and matching networks. Included is a thorough review of the common types of filter responses and calculations, filter realization, and various methods of filter design, including bandpass, network theory and Kuroda. Subsequent sessions cover the fundamentals of directional couplers. A final session describes distributed element matching networks and a matching network design example.
|Related Pages on RF Cafe
- Filter Transfer Functions
- Filter Equivalent Noise Bandwidth
- Filter Prototype Denormalization
- Filter Design Resources
- Bessel Filter Poles
- Bessel Filter Prototype Element Values
- Butterworth Lowpass Filter Poles
- Butterworth Filter Prototype Element Values
- Chebyshev Lowpass Filter Poles
- Chebyshev Filter Prototype Element Values
- Monolithic Ceramic Block Combline Bandpass
- Coupled Microstrip Filters: Simple Methodologies for