Negative capacitance synthesis

1. A negative capacitance circuit, comprising:

a first transistor (Qn 1 , Qp 1 , Mn 3 or Mp 3 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the first transistor connected to a first voltage rail (Vsp or Vsm);

a second transistor (Qn 2 , Qp 2 , Mn 4 or Mp 4 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the second transistor connected to the control terminal (base or gate) of the first transistor, and the control terminal (base or gate) of the second transistor receiving a bias voltage;

a first bias current source (Ibias) connected between the second current path terminal (emitter or source) of the first transistor and a second voltage rail (Vsm or Vsp);

a second bias current source (Ibias) connected between the second current path terminal (emitter or source) of the second transistor and the second voltage rail (Vsm or Vsp);

a capacitor (C 1 ) connected between the second current path terminal (emitter or source) of the first transistor and the second current path terminal (emitter or source) of the second transistor; and

a resistor (R c ) including a first resistor terminal and second resistor terminal, the first resistor terminal connected to the control terminal (base or gate) of the first transistor and to the first current path terminal (collector or drain) of the second transistor, and the second resistor terminal forming the input node of the negative capacitance circuit.

2. The negative capacitance circuit of claim 1 , wherein:

the first and second transistors are bi-polar NPN transistors;

the control terminals of the first and second transistors are bases;

the first current path terminals of the first and second transistors are collectors; and

the second current path terminals of the first and second transistors are emitters.

3. The negative capacitance circuit of claim 2 , wherein:

the first voltage rail is a positive supply voltage; and

the second voltage rail is a negative supply voltage or ground.

4. The negative capacitance circuit of claim 1 , wherein:

the first and second transistors are bi-polar PNP transistors;

the control terminals of the first and second transistors are bases;

the first current path terminals of the first and second transistors are collectors; and

the second current path terminals of the first and second transistors are emitters.

5. The negative capacitance circuit of claim 4 , wherein:

the first voltage rail is a negative supply voltage or ground; and

the second voltage rail is a positive supply voltage.

6. The negative capacitance circuit of claim 1 , wherein:

the first and second transistors are NMOS transistors;

the control terminals of the first and second transistors are gates;

the first current path terminals of the first and second transistors are drains; and

the second current path terminals of the first and second transistors are sources.

7. The negative capacitance circuit of claim 6 , wherein:

the first voltage rail is a positive supply voltage; and

the second voltage rail is a negative supply voltage or ground.

8. The negative capacitance circuit of claim 1 , wherein:

the first and second transistors are PMOS transistors;

the control terminals of the first and second transistors are gates;

the first current path terminals of the first and second transistors are drains; and

the second current path terminals of the first and second transistors are sources.

9. The negative capacitance circuit of claim 8 , wherein:

the first voltage rail is a negative supply voltage or ground; and

the second voltage rail is a positive supply voltage.

10. A negative capacitance circuit, comprising:

a first transistor (Qn 1 , Qp 1 , Mn 3 or Mp 3 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the first transistor connected to a first voltage rail (Vsp or Vsm);

a second transistor (Qn 2 , Qp 2 , Mn 4 or Mp 4 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the second transistor connected to the control terminal (base or gate) of the first transistor, and the control terminal (base or gate) of the second transistor receiving a bias voltage;

a first bias current source (Ibias) connected between the second current path terminal (emitter or source) of the first transistor and a second voltage rail (Vsm or Vsp);

a second bias current source (Ibias) connected between the second current path terminal (emitter or source) of the second transistor and the second voltage rail (Vsm or Vsp);

a capacitor (C 1 ) connected between the second current path terminal (emitter or source) of the first transistor and the second current path terminal (emitter or source) of the second transistor;

a resistor R c ) including a first resistor terminal and second resistor terminal, the first resistor terminal connected to the control terminal (base or gate) of the first transistor and to the first current path terminal (collector or drain) of the second transistor, and the second resistor terminal forming the input node of the negative capacitance circuit; and

a voltage offset device (Voffset);

wherein the capacitor (C 1 ) includes a first capacitor terminal and a second capacitor terminal;

wherein the voltage offset device (Voffset) is connected between the second current path terminal of the first transistor and the first capacitor terminal;

wherein the second capacitor terminal is connected to the second current path terminal of the second transistor; and

wherein the bias voltage provided to the control terminal of the second transistor is equal to or substantially equal to the offset voltage, provided by the voltage offset device (Voffset), plus a voltage drop across the resistor (R c ).

11. A negative capacitance circuit, comprising:

a first transistor (Qn 1 , Qp 1 , Mn 3 or Mp 3 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the first transistor connected to a first voltage rail (Vsp or Vsm);

a second transistor (Qn 2 , Qp 2 , Mn 4 or Mp 4 ) having a control terminal (base or gate) and a current path including a first current path terminal (collector or drain) and a second current path terminal (emitter or source), the first current path terminal (collector or drain) of the second transistor connected to the control terminal (base or gate) of the first transistor, and the control terminal (base or gate) of the second transistor receiving a bias voltage;

a first bias current source (Ibias) connected between the second current path terminal (emitter or source) of the first transistor and a second voltage rail (Vsm or Vsp);

a second bias current source (Ibias) connected between the second current path terminal (emitter or source) of the second transistor and the second voltage rail (Vsm or Vsp);

a capacitor (C 1 ) connected between the second current path terminal (emitter or source) of the first transistor and the second current path terminal (emitter or source) of the second transistor;

a resistor (R c ) including a first resistor terminal and second resistor terminal, the first resistor terminal connected to the control terminal (base or gate) of the first transistor and to the first current path terminal (collector or drain) of the second transistor, and the second resistor terminal forming the input node of the negative capacitance circuit; and

a voltage offset device (Voffset);

wherein the voltage offset device (Voffset) is connected between the control terminal of the first transistor and the first current path terminal of the second transistor; and

wherein the bias voltage provided to the control terminal of the second transistor is equal to or substantially equal to the offset voltage, provided by the voltage offset device (Voffset), plus a voltage drop across the resistor (R c ).

12. A negative capacitance circuit, comprising:

at least two transistors;

a resistor R c ; and

a capacitor C 1 ;

wherein the negative capacitance circuit has an input impedance

Zin

≈

-

1

jω

⁢

⁢

C

1

-

2

gm

+

R

C

,

where

gm is the transconductance of the transistors of the negative capacitance circuit, and

R

C

≈



2

gm



.

13. The circuit of claim 12 , further comprising:

a first bias current source for biasing one of the transistors; and

a second bias current source for biasing another one of the transistors.

14. The circuit of claim 12 , wherein:

the resistor R c including a first resistor terminal and second resistor terminal,

the first resistor terminal is connected to a control terminal (base or gate) of one of the transistors and to a current path terminal (collector or drain) of another one of the transistors; and

the second resistor terminal forms the input node of the negative capacitance circuit.

15. The negative capacitance circuit of claim 1 , wherein the negative capacitance circuit has an input impedance

Zin

≈

-

1

jω

⁢

⁢

C

1

-

2

gm

+

R

C

,

where

gm is the transconductance of the transistors of the negative capacitance circuit, and

R

C

≈



2

gm



.

16. The negative capacitance circuit of claim 1 , wherein the output stage includes an output stage transistor having a gate-source capacitance that causes distortion, and wherein the negative capacitance circuit is connected in parallel with the gate-source capacitance.

17. The negative capacitance circuit of claim 1 , wherein the output stage includes an output stage transistor having a base-emitter capacitance that causes distortion, and wherein the negative capacitance circuit is connected in parallel with the base-emitter capacitance.

18. The negative capacitance circuit of claim 1 , wherein the negative capacitance circuit reduces effects of a parasitic capacitance.

19. The negative capacitance circuit of claim 1 , wherein the negative capacitance circuit compensates for effects of a parasitic capacitance.

20. The negative capacitance circuit of claim 1 , wherein the negative capacitance circuit reduces distortion of an output stage.

21. The negative capacitance circuit of claim 1 , wherein the negative capacitance circuit improves linearity of an output stage.