TABLE OF CONTENTS The ideal filter transfers all incident energy at passband frequencies to the filter output termination. In practice, energy is lost by reflection at the filter ports, dissipation within the filter and/or radiation from the filter [1]. These topics are considered in this chapter.
Reactive filters provide transition region and stopband rejection by reflecting energy at the input and returning that energy to the source. Certain filter transfer functions, such as Chebyshev, reflect some energy even at frequencies well into the passband in order to achieve greater transition region steepness (selectivity).
Passband reflections may also occur unintentionally. For example a mismatched output termination may reflect energy which passes back through the filter and is lost in the source termination.
If only the source or load is mismatched, the mismatch loss, L m, for a purely reactive network is
| (1) |  |
where ? is the reflection coefficient. For example, the mismatch loss of an ideal lowpass filter terminated at the output in 100 ohms instead of a nominal 50 ohms is -10 times the base 10 logarithm of 1-.333 2 which is 0.51 dB. The reflection coefficient is ( VSWR-1)/( VSWR+1) where the VSWR is 100/50 or 2.0. Equation (1) may also be used to relate the passband reflection coefficient ripple in a Chebyshev filter to the attenuation ripple in decibels.
[1] We will use the term insertion loss to signify lost energy which does not arrive at the output termination...
