Frequency-dependent negative resistor

A frequency-dependent negative resistor (FDNR) is a circuit element that exhibits a purely real negative resistance −1/(ω2kC) that decreases in magnitude at a rate of −40 dB per decade.

The element is usually implemented from a generalized impedance converter (GIC) or gyrator.

The definition and application of frequency-dependent negative resistors is discussed in Temes & LaPatra,[1]: 275, 282–286  Chen[2] and Wait, Huelsman & Korn.

The transformed ladder filter realizes the DC transfer gain as the ratio of two capacitors.

Finally, if Ra and Rb are large with respect to the other resistors there is little effect on the filter's transition band and high frequency behavior.

The electronic symbol for a frequency-dependent negative resistor. The symbol is intended to evoke a double capacitor.
A low pass ladder filter and an implementation using frequency dependent negative resistors (FDNR). Ra and Rb are added for practical reasons.
Schematic of a frequency dependent negative resistor.