Method and apparatus for using back gate biasing for power amplifiers for millimeter wave devices

1. An apparatus, comprising:

an input transformer;

a first differential transistor pair comprising a first transistor, a second transistor, and a first direct current (DC) voltage source configured to provide a first back gate bias voltage to the first transistor and to the second transistor;

a second differential transistor pair comprising a third transistor, a fourth transistor, and a second DC voltage source configured to provide a second back gate bias voltage to the third transistor and to the fourth transistor;

a neutralization cap comprising a fifth transistor, a sixth transistor, and a third DC voltage source, wherein the fifth transistor and the sixth transistor are cross-coupled, the fifth transistor is an NMOS transistor, the sixth transistor is an NMOS transistor, and the third DC voltage source is configured to provide a third back gate bias voltage to the fifth transistor and the sixth transistor; and

an output transformer.

2. The apparatus of claim 1 , further comprising a harmonic trap.

3. The apparatus of claim 1 , further comprising at least one stacked transistor pair, wherein each stacked transistor pair comprises a seventh transistor, an eighth transistor, and a fourth DC voltage source configured to provide a fourth back gate bias voltage to the seventh transistor and the eighth transistor.

4. The apparatus of claim 3 , wherein the apparatus comprises two stacked transistor pairs.

5. The apparatus of claim 3 , wherein first transistor, second transistor, third transistor, fourth transistor, fifth transistor, sixth transistor, seventh transistor, and eight transistor each comprise a front gate and a back gate configured to receive a back gate bias voltage.

6. The apparatus of claim 1 , further comprising:

a harmonic trap; and

two stacked transistor pairs, wherein each stacked transistor pair comprises a seventh transistor, an eighth transistor, and a fourth DC voltage source configured to provide a fourth back gate bias voltage to the seventh transistor and the eighth transistor.

7. The apparatus of claim 1 , wherein the first transistor, the second transistor, the third transistor, the fourth transistor, the fifth transistor, and the sixth transistor are each an FDSOI transistor.

8. An apparatus, comprising:

an input transformer;

a first differential transistor pair comprising a first transistor, a second transistor, and a first direct current (DC) voltage source configured to provide a first back gate bias voltage to the first transistor and to the second transistor;

a second differential transistor pair comprising a third transistor, a fourth transistor, and a second DC voltage source configured to provide a second back gate bias voltage to the third transistor and to the fourth transistor;

a neutralization cap comprising a fifth transistor, a sixth transistor, and a third DC voltage source, wherein the fifth transistor and the sixth transistor are cross-coupled, the fifth transistor is a PMOS transistor, the sixth transistor is a PMOS transistor, and the third DC voltage source is configured to provide a third back gate bias voltage to the fifth transistor and the sixth transistor; and

an output transformer.

9. The apparatus of claim 8 , further comprising a harmonic trap.

10. The apparatus of claim 8 , further comprising at least one stacked transistor pair, wherein each stacked transistor pair comprises a seventh transistor, an eighth transistor, and a fourth DC voltage source configured to provide a fourth back gate bias voltage to the seventh transistor and the eighth transistor.

11. The apparatus of claim 10 , wherein the apparatus comprises two stacked transistor pairs.

12. The apparatus of claim 8 , further comprising:

a harmonic trap; and

two stacked transistor pairs, wherein each stacked transistor pair comprises a seventh transistor, an eighth transistor, and a fourth DC voltage source configured to provide a fourth back gate bias voltage to the seventh transistor and the eighth transistor.

13. The apparatus of claim 8 , wherein the first transistor, the second transistor, the third transistor, the fourth transistor, the fifth transistor, and the sixth transistor are each an FDSOI transistor.

14. A method, comprising:

forming an apparatus comprising:

an input transformer;

a first differential transistor pair comprising a first transistor, a second transistor, and a first direct current (DC) voltage source configured to provide a first back gate bias voltage to the first transistor and to the second transistor;

a second differential transistor pair comprising a third transistor, a fourth transistor, and a second DC voltage source configured to provide a second back gate bias voltage to the third transistor and to the fourth transistor;

a neutralization cap comprising a fifth transistor, a sixth transistor, and a third DC voltage source, wherein the fifth transistor and the sixth transistor are cross-coupled, the fifth transistor is a PMOS transistor, the sixth transistor is a PMOS transistor, and the third DC voltage source is configured to provide a third back gate bias voltage to the fifth transistor and the sixth transistor; and

an output transformer;

determining a desired capacitance of the neutralization cap;

determining a desired back gate bias voltage that, when applied to the fifth transistor and the sixth transistor, imparts the desired capacitance to the neutralization cap; and

fixing the third DC voltage source such that the back gate bias voltage is equal to the desired back gate bias voltage.

15. The method of claim 14 , wherein the third DC voltage source provides a back gate bias voltage from 1 V to 5 V.

16. The method of claim 14 , wherein the first transistor, the second transistor, the third transistor, the fourth transistor, the fifth transistor, and the sixth transistor are each an FDSOI transistor.

17. The method of claim 14 , further comprising:

determining a desired efficiency of the apparatus;

determining a desired back gate bias voltage that, when applied to the first transistor and the second transistor, imparts the desired efficiency to the apparatus; and

fixing the first DC voltage source such that the back gate bias voltage provided to the first transistor and the second transistor is equal to the desired back gate bias voltage that imparts the desired efficiency to the apparatus.

18. The method of claim 14 , further comprising:

determining a desired efficiency of the apparatus;

determining a desired back gate bias voltage that, when applied to the third transistor and the fourth transistor, imparts the desired efficiency to the apparatus; and

fixing the second DC voltage source such that the back gate bias voltage provided to the third transistor and the fourth transistor is equal to the desired back gate bias voltage that imparts the desired efficiency to the apparatus.

19. The method of claim 14 , wherein the apparatus further comprises:

at least one stacked transistor pair, wherein each stacked transistor pair comprises a seventh transistor, an eighth transistor, and a fourth DC voltage source configured to provide a fourth back gate bias voltage to the seventh transistor and the eighth transistor; and

the method further comprises:

determining a desired gain of the apparatus;

determining a desired back gate bias voltage that, when applied to the seventh transistor and the eighth transistor, imparts the desired gain to the apparatus; and

fixing the fourth DC voltage source such that the back gate bias voltage provided to the seventh transistor and the eighth transistor is equal to the desired back gate bias voltage that imparts the desired gain to the apparatus.

20. The method of claim 19 , wherein the apparatus comprises two stacked transistor pairs.