## Overview

#### The six pole filter has the unexpected result L1=L3. This gives it an important cost advantage since only two different inductor types are required. The four and eight pole filters do not have this feature. Also note that C1=sin(90°/6)=sin 15° and L6 is 6 sin 15°. This leads to the author's conjecture for which he would be grateful for a proof. It holds for zero input impedance filters and is known to hold for filters of two thru ten poles. The last element in an n pole filter is sin(90°/n). The first element is n·sin(90°/n). As n becomes large, this value therefore approaches π/2=1.5707. The sum of the inductors/capacitors (even/odd) is 1/[sin(90°/n)]. The sum of the capacitors/inductors (even/odd) is [(n-1)/n][sin(90°/n)]. The product of all the values is 1.Knowing these rules make it possible to derive the values for the two, four, and six pole filters without laborious mathematical calculations. To derive the six pole values by this method, you must make use of the fact that the first two inductors are equal. Since sin(90°/7) and sin(90°/9) cannot be expressed exactly in radicals, the values for seven and nine pole filters can only be a decimal approximation. This is true for most of the higher order filters. As a good rule of thumb, inductors for filters cost ten times as much as capacitors and are several times larger in size. Good filter design will minimize the number of inductors used. Filters designed to be driven by a zero input impedance with an odd number of poles require one more inductor than capacitor. If the extra inductor is used, it makes sense to add another capacitor on the output. This will turn it into an even pole filter of substantially better performance with only a small increase in cost. If a filter is driven by a current source, its first element must be a capacitor. An odd number of poles should be chosen for this filter since it uses one more capacitor than inductor. Much better performance will again result with only a small increase in cost.

10:00 AM 3/25/2010 πθ°Ωω±√·