RF Cafe Software

RF Cascade Workbook 2005 - RF Cafe
RF Cascade Workbook

Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel
RF & EE Symbols Word
RF Stencils for Visio

About RF Cafe

Kirt Blattenberger - RF Cafe WebmasterCopyright
1996 - 2016
Webmaster:
Kirt Blattenberger,
 BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:
 AirplanesAndRockets.com

Try Using SEARCH
to Find What You Need. 
There are 1,000s of Pages Indexed on RF Cafe !

Electronics World Cover,TOC,and list of posted Popular Electronics articles QST Radio & TV News Radio-Craft Radio-Electronics Short Wave Craft Wireless World About RF Cafe RF Cafe Homepage RF Cafe in Morse Code Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs Twitter LinkedIn Crosswords Engineering Humor Kirt's Cogitations Engineering Event Calendar RF Engineering Quizzes AN/MPN-14 Radar 5CCG Notable Quotes App Notes Calculators Education Magazines Software,T-Shirts,Coffee Mugs Articles - submitted by RF Cafe visitors Simulators Technical Writings RF Cafe Archives Test Notes RF Cascade Workbook RF Stencils for Visio Shapes for Word Thank you for visiting RF Cafe!

Filter Transfer Functions

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

Group Delay:      RF Cafe: Group delay formula

RF Cafe - Filter comparative responses chart

Type Properties Transfer Function (Lowpass)
Butterworth
  • Maximally flat near the center of the band.
  • Smooth transition from passband to stopband.
  • Moderate out-of-band rejection.
  • Low group delay variation near center of band.
  • Moderate group delay variation near band edges.
  • Table of poles for N=1 to 10.

RF Cafe - Butterworth filter prototype transfer equation


Chebyshev
  • Equiripple in passband.
  • Abrupt transition from passband to stopband.
  • High out-of-band rejection.
  • Rippled group delay near center of band.
  • Large group delay variation near band edges.
  • Table of poles for N=1 to 10.

RF Cafe - Chebyshev filter prototype transfer equation


Bessel
  • Rounded amplitude in passband.
  • Gradual transition from passband to stopband.
  • Low out-of-band rejection.
  • Very flat group delay near center of band.
  • Flat group delay variation near band edges[1].
  • Table of poles for N=1 to 10.

RF Cafe - Bessel filter prototype transfer equation

Note: BN, PN, and boN must be placed
          in a loop from 0 through N.


Ideal
  • Flat in the passband.
  • Step function transition from passband to stopband.
  • Infinite out-of-band rejection.
  • Zero group delay everywhere.

RF Cafe - Ideal filter prototype transfer equation
(Heaviside step function)

[1] 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.
Band Translations
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.

RF Cafe - Filter translation equations lowpass highpass bandpass bandstop

Click for more detailMicrowave Filters, Couplers and Matching Network

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
  Filters Design
- Coupled Microstrip Filters: Simple Methodologies for
  Improved Characteristics