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| Keywords: Mm'-Derived Low-pass Image Impedance.svg image impedances of prototype low-pass mm'-derived filter m-derived filter and constant-k filter in the region immediately below <var>ω</var> <var>ω</var><sub>c</sub> 1 The parameters of the mm'-derived filter are <var>m</var> 0 7230 <var>m'</var> 0 4124 <var>mm'</var> 0 3 The parameter of the m-derived filter is <var>m</var> 0 6 These filters both have the optimum impedance matching for their types <math>Z_ iT mm' \frac \sqrt 1-\omega 2 \left 1- 1-m 2 \omega 2 \right 1-\left \omega/\omega_\infin\right 2 </math> where <math>\omega_\infin \frac \omega_c \sqrt 1- mm' 2 </math> <math>Z_ iT m \frac \sqrt 1-\omega 2 1-\left \omega/\omega_\infin\right 2 </math> where <math>\omega_\infin \frac \omega_c \sqrt 1-m 2 </math> <math>Z_ iT \sqrt 1-\omega 2 </math> own 2009-11-26 Inductiveload Mathematica Code <pre><nowiki> wc 1; mm'-derived m1 0 7230; m2 0 4134; mm m1 m2; winfmm wc/Sqrt1 - mm 2; zitmmw_ Sqrt1 - w 2 1 - 1 - m1 2 w 2 / 1 - w/winfmm 2 ; m-derived m 0 6; winfm wc/Sqrt1 - m 2; zitmw_ Sqrt1 - w 2/ 1 - w/winfm 2 ; constant-k zitw_ Sqrt1 - w 2 Plot zitmmw zitmw zitw w 0 6 1 PlotRange -> All </nowiki></pre> M-Derived filters Mm'-Derived filters Constant-k filters Image impedance | ||||
