Single amplifier frequency dependent negative resistor

Claim 2

A circuit including an input terminal and further comprising an amplifier having first and second inputs and an output, a conductance G 2 coupling the output to the first input, a capacitance C 1 coupling the input terminal to the first input, a conductance G C coupling the input terminal to the second input, conductances G 7 and G D , respectively, coupling the first and second inputs to ground, a capacitance C 2 directly coupling the output to the input terminal, and a conductance G Y directly connecting the output to the input terminal, wherein an admittance Y IN between the input terminal and ground equals Ds 2 , where D is a real number and s is a complex frequency variable.

Claim 3

A circuit in accordance with claim 1 wherein the conductance G 2 equals (C 1 C 2 G D )/D(G C +G D ), the conductance G C equals (G Y )(C 1 /C 2 +G Y D/C 2 2 )/(1-G Y 2 D/C 2 2 G D ), the conductance G 7 equals (G D )[1+(1+C 2 /C 1 )(G 2 /G Y )]/(1+G Y /G 2 ), the conductance G Y and the capacitance C 2 are selected so that G Y 2 D/C 2 2 G D < 1, and the real number D equals (C 1 C 2 G D )/(G C +G D )(G 2 ).

Claim 4

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the FDNR input terminal and to the second input terminal of the amplifier; a first capacitance connected to the FDNR input terminal and to the first input terminal of the amplifier; a second capacitance directly coupling the output terminal of the amplifier to the FDNR input terminal; a third conductance connected to the first input terminal of the amplifier and to the reference terminal; a fourth conductance connected to the second input terminal of the amplifier and to the reference terminal; and a fifth conductance directly connecting the output terminal of the amplifier to the FDNR input terminal.

Claim 5

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the FDNR input terminal and to the second input terminal of the amplifier; a first capacitance connected to the FDNR input terminal and to the first input terminal of the amplifier; a second capacitance directly coupling the output terminal of the amplifier to the FDNR input terminal; a third conductance connected to the first input terminal of the amplifier and to the reference terminal; a fourth conductance connected to the second input terminal of the amplifier and to the reference terminal; and a fifth conductance directly connecting the output terminal of the amplifier to the FDNR input terminal.

Claim 6

A circuit including an input terminal and further comprising an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitor C 1 connected between the input terminal and the first input, a conductance G 6 coupling the input terminal to the first input, a conductance G C coupling the input terminal to the second input, conductances G 7 and G D , respectively, coupling the first and second inputs to ground, a conductance G 5 coupling a node between the conductance G 4 and the capacitor C 1 to ground, a capacitor C 2 directly coupling the output to the node, and a conductance G Y directly connecting the output to the input terminal, wherein an admittance between the input terminal and ground equals Ds 2 , where D is a real number and s is a complex frequency variable.

Claim 7

A circuit including an input terminal and further comprising an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitor C 1 connected between the input terminal and the first input, a conductance G 6 coupling the input terminal to the first input, a conductance G C coupling the input terminal to the second input, conductances G 7 and G D , respectively, coupling the first and second inputs to ground, a conductance G 5 coupling a node between the conductance G 4 and the capacitor C 1 to ground, a capacitor C 2 directly coupling the output to the node, and a conductance G Y directly connecting the output to the input terminal, wherein an admittance between the input terminal and ground equals Ds 2 , where D is a real number and s is a complex frequency variable.

Claim 8

A circuit in accordance with claim 4 wherein the admittance between the input terminal and ground equals (ν 2 s 2 +ν 1 s+ν 0 )/(d 2 s 2 +d 1 s+d 0 ), where ν.sub.2 = (C.sub.1 C.sub.2 G.sub.D)(G.sub.4 +G.sub.C +G.sub.6 +G.sub.Y), ν.sub.1 = (g.sub.4 +g.sub.c +g.sub.6 +g.sub.y)[(c.sub.1 +c.sub.2)(g.sub.2 g.sub.d -g.sub.7 g.sub.b)-c.sub.1 g.sub.5 g.sub.b ] + (c.sub.2)(g.sub.4 +g.sub.y)(g.sub.6 g.sub.d -g.sub.7 g.sub.c) + (c.sub.1 g.sub.y [(g.sub.d)(g.sub.4 +g.sub.6) - (g.sub.c)(g.sub.5 +g.sub.7)], ν.sub.0 = (g.sub.1)(g.sub.6 +g.sub.c +g.sub.y)(g.sub.2 g.sub.d -g.sub.7 g.sub.b) + (g.sub.4 g.sub.5)(g.sub.2 g.sub.a -g.sub.3 g.sub.b) + (g.sub.1 g.sub.y)(g.sub.6 g.sub.d -g.sub.7 g.sub.c), d.sub.2 = C.sub.1 C.sub.2 G.sub.A, d.sub.1 = (C.sub.1 +C.sub.2)(G.sub.2 G.sub.A -G.sub.3 G.sub.B) - (G.sub.1 G.sub.B C.sub.1), d.sub.0 = (G.sub.1)(G.sub.2 G.sub.A -G.sub.3 G.sub.B), g.sub.a = g.sub.c + g.sub.d, g.sub.1 = g.sub.4 + g.sub.5, g.sub.3 = g.sub.6 + g.sub.7, and G.sub.B = 0, G.sub.4 = ∞, G.sub.5 = 0, and G.sub.6 = 0.

Claim 9

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the amplifier output terminal and to the first input terminal of the amplifier; a second conductance connected to the amplifier output terminal and to the second input terminal of the amplifier; a circuit branch comprising a serial connection of a third conductance and a first capacitance, the conductive terminal of the circuit branch connected to the input terminal of the FDNR circuit and the capacitive terminal of the circuit branch connected to the first input terminal of the amplifier; a second capacitance directly coupling the amplifier output terminal to the circuit branch at a node intermediate the third conductance and the first capacitance; a fourth conductance connected to the FDNR input terminal and to the first input terminal of the amplifier; a fifth conductance connected to the FDNR input terminal and to the second input terminal of the amplifier; a sixth conductance connected to the first input terminal of the amplifier and to the reference terminal; a seventh conductance connected to the second input terminal of the amplifier and to the reference terminal; an eighth conductance connected to the circuit branch at the node intermediate the third conductance and the first capacitance and to the reference terminal; and a ninth conductance directly connecting the output terminal of the amplifier to the FDNR input terminal.

Claim 10

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the amplifier output terminal and to the first input terminal of the amplifier; a second conductance connected to the amplifier output terminal and to the second input terminal of the amplifier; a circuit branch comprising a serial connection of a third conductance and a first capacitance, the conductive terminal of the circuit branch connected to the input terminal of the FDNR circuit and the capacitive terminal of the circuit branch connected to the first input terminal of the amplifier; a second capacitance directly coupling the amplifier output terminal to the circuit branch at a node intermediate the third conductance and the first capacitance; a fourth conductance connected to the FDNR input terminal and to the first input terminal of the amplifier; a fifth conductance connected to the FDNR input terminal and to the second input terminal of the amplifier; a sixth conductance connected to the first input terminal of the amplifier and to the reference terminal; a seventh conductance connected to the second input terminal of the amplifier and to the reference terminal; an eighth conductance connected to the circuit branch at the node intermediate the third conductance and the first capacitance and to the reference terminal; and a ninth conductance directly connecting the output terminal of the amplifier to the FDNR input terminal.

Claim 11

A circuit including an input terminal and further comprising, an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitance C 1 connected between the input terminal and the first input, a conductance G C coupling the input terminal to the second input, conductances G 7 and G D , respectively, coupling the first and the second inputs to ground, a capacitance C 2 directly coupling the output to a node between the conductance G 4 and the capacitance C 1 , and a conductance G Y directly connecting the output to the input terminal, wherein an impedance between the input terminal and ground equals R + (1/Ds 2 ), where R is a resistance, D is a real number, and s is a complex frequency variable.

Claim 12

A circuit including an input terminal and further comprising, an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitance C 1 connected between the input terminal and the first input, a conductance G C coupling the input terminal to the second input, conductances G 7 and G D , respectively, coupling the first and the second inputs to ground, a capacitance C 2 directly coupling the output to a node between the conductance G 4 and the capacitance C 1 , and a conductance G Y directly connecting the output to the input terminal, wherein an impedance between the input terminal and ground equals R + (1/Ds 2 ), where R is a resistance, D is a real number, and s is a complex frequency variable.

Claim 13

A circuit in accordance with claim 7 wherein a constant K 4 ≧ 1, g.sub.y > 1/(rk.sub.4)(1+c.sub.1 /c.sub.2), g.sub.4 = (k.sub.4 g.sub.y)(1+c.sub.1 /c.sub.2), g.sub.c = g.sub.y {k.sub.4 c.sub.1 +c.sub.2 +drg.sub.4.sup.2 /(c.sub.1 +c.sub.2)}/(c.sub.2)(k.sub.4 -1), g.sub.d = g.sub.c /{(r)(g.sub.4 +g.sub.c +g.sub.y) - 1}, g.sub.b = c.sub.2 (g.sub.c +g.sub.d)(c.sub.1 +c.sub.2)/(rdg.sub.4.sup.2), g.sub.7 = [(g.sub.c /c.sub.1){(c.sub.1 +c.sub.2)/(g.sub.4 g.sub.d)+(c.sub.2)/(g.sub.y g.sub.d +g.sub.b /r)}].sup.-1, and G.sub.2 = C.sub.2 {C.sub.1 G.sub.4 +G.sub.7 (C.sub.1 +C.sub.2)}/(G.sub.4.sup.2 DR).

Claim 14

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired impedance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the output terminal of the amplifier and to the second input terminal of the amplifier; a series branch circuit including a third conductance and a first capacitance connected between the FDNR input terminal and the first input of the amplifier; a fourth conductance coupling the FDNR input terminal to the second input of the amplifier; fifth and sixth conductances, respectively, coupling the first and second inputs of the amplifier to the reference terminal; a second capacitance directly coupling the output to a node between the third conductance and the first capacitance; and a seventh conductance directly connecting the output to the FDNR input terminal.

Claim 15

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired impedance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the output terminal of the amplifier and to the second input terminal of the amplifier; a series branch circuit including a third conductance and a first capacitance connected between the FDNR input terminal and the first input of the amplifier; a fourth conductance coupling the FDNR input terminal to the second input of the amplifier; fifth and sixth conductances, respectively, coupling the first and second inputs of the amplifier to the reference terminal; a second capacitance directly coupling the output to a node between the third conductance and the first capacitance; and a seventh conductance directly connecting the output to the FDNR input terminal.

Claim 16

A circuit including an input terminal and further comprising, an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitance C 1 connected between the input terminal and the first input, a conductance G C coupling the input terminal to the second input, a conductance G D coupling the second input to ground, a capacitance C 2 directly coupling the output to a node between the conductance G 4 and the capacitance C 1 , and a capacitance C 7 coupling the first input to ground, wherein an admittance between the input terminal and ground equals G + Ds 2 , where G and D are real numbers and s is a complex frequency variable.

Claim 17

A circuit including an input terminal and further comprising, an amplifier having first and second inputs and an output, means coupling the output by way of a conductance G 2 to the first input and by way of a conductance G B to the second input, a series branch circuit including a conductance G 4 and a capacitance C 1 connected between the input terminal and the first input, a conductance G C coupling the input terminal to the second input, a conductance G D coupling the second input to ground, a capacitance C 2 directly coupling the output to a node between the conductance G 4 and the capacitance C 1 , and a capacitance C 7 coupling the first input to ground, wherein an admittance between the input terminal and ground equals G + Ds 2 , where G and D are real numbers and s is a complex frequency variable.

Claim 18

A circuit in accordance with claim 10 wherein K > 1, g.sub.a = g.sub.c + g.sub.d = k(1+c.sub.1 /c.sub.7), α = (c.sub.7)(c.sub.1 +c.sub.2).sup.2 /(c.sub.1 c.sub.2)(c.sub.1 +c.sub.7), g.sub.2 = (g.sub.c)(k-1)/α, g.sub.4 = (g.sub.c)(k-1), and G.sub.B = (C.sub.1 C.sub.2 G.sub.A)/(C.sub.7)(C.sub.1 +C.sub.2).

Claim 19

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the output terminal of the amplifier and to the second input terminal of the amplifier; a series branch circuit including a third conductance and a first capacitance connected between the FDNR input terminal and the first input of the amplifier; a fourth conductance coupling the FDNR input terminal to the second input of the amplifier; a fifth conductance coupling the second input of the amplifier to the reference terminal; a second capacitance directly coupling the output to a node between the third conductance and the first capacitance; and a third capacitance coupling the first input of the amplifier to the reference terminal.

Claim 20

A frequency dependent negative resistor (FDNR) circuit which utilizes a single amplifier to provide a desired admittance function between an input terminal of the FDNR circuit and a terminal having a fixed reference potential, the circuit comprising: a differential amplifier having first and second input terminals and having an output terminal; a first conductance connected to the output terminal of the amplifier and to the first input terminal of the amplifier; a second conductance connected to the output terminal of the amplifier and to the second input terminal of the amplifier; a series branch circuit including a third conductance and a first capacitance connected between the FDNR input terminal and the first input of the amplifier; a fourth conductance coupling the FDNR input terminal to the second input of the amplifier; a fifth conductance coupling the second input of the amplifier to the reference terminal; a second capacitance directly coupling the output to a node between the third conductance and the first capacitance; and a third capacitance coupling the first input of the amplifier to the reference terminal.