(iii) Attain equal ripple behavior at the passband for optimum loss performance.
The filtering function has frequency dependent term in the denominator which will distort the equal ripple characteristic and bandwidth of filter.
In order to generate the filter coefficients for equal ripple response, let the denominator of (2) equal to Q,
During each test, the input/output resonators are gradually trimmed off at the open end until the input and output VSWR have reached an optimum valve, resulting in equal ripple
performance across the passband.
The EPFILTER software package is based on the equal ripple optimization technique. An actual filter implementation also is presented, including comparisons between calculated and measured filter performance.
This approximate design was used as a starting point for the equal ripple optimization.
In a practical design, this is more desirable than an equal ripple
design(6) since the decreasing reflection coefficient compensates for the typically increasing reflections with increasing frequency from other parts of the circuit, such as input and output connectors.
The designs were synthesized with a proprietary CAD program to give a theoretic |+ or -~0.1 dB equal ripple
response covering the 10 to 50 GHz band.
For example, for an equal ripple octave (2:1) bandwidth, a midband coupling of -2.7 dB is indicated, resulting in the curves shown in Figure 3.
Here, one readily can see the reduction in equal ripple bandwidth from the nominal octave to a much lesser value of under 1.5:1.
The general synthesis for both designs is to derive the G values for the desired filters depending on their response, maximally flat (Butterworth) or equal ripple