A method of stabilizing a variable filter for an analog electromagnetic signal against circuit oscillation includes the steps of: providing a signal loop comprising a signal input, a signal output, and a plurality of variable circuit elements connected in the signal loop, the plurality of variable circuit elements comprising an adjustable resonator and an adjustable gain block, the signal loop having a variable frequency response that is characterized by a central frequency, a frequency passband, a response Q, and an operating point and a resonator response curve that are plottable in a Cartesian s-plane having an origin, a real axis, and an imaginary axis; and maintaining stability of the variable filter within an operating range by controlling the adjustable resonator and the adjustable gain block such that, in the Cartesian s-plane, the resonator response curve satisfies an orthogonality stability condition.

A variable filter and method of switching a resonant frequency of the variable filter from an initial frequency to a desired frequency, where the variable filter has a tunable frequency and a variable Q. With the variable filter operating at the initial frequency and an initial Q, the variable filter is Q-spoiled toward a low-Q state. The variable filter is tuned toward the desired frequency and the tunable resonator is Q-enhanced from the low-Q state to achieve a desired filter response.

A variable filter and method of switching a resonant frequency of the variable filter from an initial frequency to a desired frequency, where the variable filter has a tunable frequency and a variable Q. With the variable filter operating at the initial frequency and an initial Q, the variable filter is Q-spoiled toward a low-Q state. The variable filter is tuned toward the desired frequency and the tunable resonator is Q-enhanced from the low-Q state to achieve a desired filter response.

A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

A method of stabilizing a variable filter for an analog electromagnetic signal against circuit oscillation includes the steps of: providing a signal loop comprising a signal input, a signal output, and a plurality of variable circuit elements connected in the signal loop, the plurality of variable circuit elements comprising an adjustable resonator and an adjustable gain block, the signal loop having a variable frequency response that is characterized by a central frequency, a frequency passband, a response Q, and an operating point and a resonator response curve that are plottable in a Cartesian s-plane having an origin, a real axis, and an imaginary axis; and maintaining stability of the variable filter within an operating range by controlling the adjustable resonator and the adjustable gain block such that, in the Cartesian s-plane, the resonator response curve satisfies an orthogonality stability condition.

A variable-frequency LC filter that has sharp attenuation characteristics and that does not increase the size of a substrate and a high-frequency frontend module using such a variable-frequency LC filter are provided. A first variable capacitor and a second variable capacitor are disposed on a principal surface such that strength of magnetic field coupling caused between a first inductor and a third inductor is greater than strength of magnetic field coupling caused between a second inductor and the first inductor and than strength of magnetic field coupling caused between the second inductor and the third inductor.

A variable-frequency LC filter that has sharp attenuation characteristics and that does not increase the size of a substrate and a high-frequency frontend module using such a variable-frequency LC filter are provided. A first variable capacitor and a second variable capacitor are disposed on a principal surface such that strength of magnetic field coupling caused between a first inductor and a third inductor is greater than strength of magnetic field coupling caused between a second inductor and the first inductor and than strength of magnetic field coupling caused between the second inductor and the third inductor.

A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.

A variable filter has a signal loop defined between a signal input and a signal output. A plurality of circuit elements connected in the signal loop, the plurality of circuit elements comprising a frequency tunable resonator, and an adjustable scaling block that applies a gain factor that is adjustable in a range that comprises a positive gain and a negative gain. A controller is connected to 1) tune the frequency tunable resonator; and to 2) adjust the gain factor of the adjustable scaling block between a negative gain factor to a positive gain factor providing for variable Q independent of frequency.