[a]: 291 The definition and synthesis of leapfrog filters is described by Temes & LaPatra,[1]: 281–291 Sedra & Brackett,[3][b]: 713 Chen[4] and Wait, Huelsman & Korn.
The arrangement of feedback loops in the signal flow-graph inspired the name leapfrog filter.
This manipulation is can be accomplished by a simple procedure: The signal-flow graph is suitable for implementation.
The individual components in parallel or series can be combined into general impedances or admittances.
One strategy is to open the feedback loops so that the remaining filter structure is a simple cascade design.
These stages may be designed with a large, but finite Q so that they can be tuned while the feedback loops are open.
A low-pass ladder filter and its signal flow graph
Generic ladder filters with either (a) voltage input/voltage output, (b) current input/voltage output, (c) voltage input/current output or (d) current input/ current output. The output may also be the voltage across or the current through an internal component of the last element.
Four element ladder filter with voltage input and voltage output
Three stages of signal-flow graph development of a four element ladder filter with voltage input and voltage output.
A schematic for a passive band pass electronic filter
The signal flow-graph representation of the ladder filter equations.
The signal flow-graph representation of the ladder filter equations with impedances scaled by
R
, an arbitrary resistance.
The signal flow-graph representation of the ladder filter equations with impedances scaled by R, an arbitrary resistance. The signs of the gains have been manipulated so that all gains feeding into a node have the same signs.
Modified Tow-Thomas active biquad filter with summing inputs and complimentary band pass outputs suitable for use in a leapfrog filter. V
BP
is the bandpass output, V
BPI
is the inverted bandpass output, V
LPI
is the inverted lowpass output.
