Method and apparatus of an input resistance of a passive mixer to broaden the input matching bandwidth of a common source/gate LNA

1. An apparatus, comprising:

a first spiral inductor coupled to a source of a first transistor;

a second spiral inductor coupled to a drain of a second transistor;

a third inductor connecting the first transistor to the second transistor;

a first capacitance coupled in parallel to the third inductor forming a bandpass filter; and

a second capacitance coupled in parallel to the first spiral inductor forming a resonant circuit, wherein the resonant circuit oscillates at a center frequency.

2. The apparatus of claim 1 , wherein the resonant circuit oscillates at a lower frequency than the center frequency when a width of the second transistor is less than a width of the first transistor.

3. The apparatus of claim 1 , wherein the resonant circuit oscillates at a higher frequency than the center frequency when a width of the second transistor is greater than a width of the first transistor.

4. The apparatus of claim 1 , further comprising:

a drain of a third transistor coupled to a gate of a fourth transistor with a first width;

a source of the third transistor coupled to the resonant circuit; and

an oscillator clock configured to operate at a first frequency that enables the third transistor; and

wherein the third transistor presents a first impedance to the resonant circuit, causing the resonant circuit to have a first bandwidth.

5. The apparatus of claim 4 , wherein the resonant circuit has a wider bandwidth than the first bandwidth when either a frequency of the oscillator clock is larger than the first frequency, a width of the fourth transistor is larger than the first width, or both are increased simultaneously.

6. The apparatus of claim 4 , wherein the resonant circuit has a narrower bandwidth than the first bandwidth when either a frequency of the oscillator clock is less than the first frequency, a width of the fourth transistor is less than the first width, or both are decreased simultaneously.

7. A method of operating a circuit, comprising:

coupling a first spiral inductor to a source of a first transistor;

coupling a second spiral inductor to a drain of a second transistor;

connecting a third inductor between the first transistor to the second transistor;

forming a bandpass filter by coupling a first capacitance in parallel to the third inductor; and

forming a resonant circuit by coupling a second capacitance in parallel to the first spiral inductor, wherein the resonate circuit oscillates at a center frequency.

8. The method of claim 7 , wherein the resonant circuit oscillates at a lower frequency than the center frequency when a width of the second transistor is less than a width of the first transistor.

9. The method of claim 7 , wherein the resonant circuit oscillates at a higher frequency than the center frequency when a width of the second transistor is greater than a width of the first transistor.

10. The method of claim 7 , further comprising the steps of:

coupling a drain of a third transistor to a gate of a fourth transistor with a first width;

coupling a source of the third transistor to the resonant circuit; and

configuring an oscillator clock to operate at a first frequency to enable the third transistor; and

presenting a first impedance of the third transistor to the resonant circuit, causing the resonant circuit to have a first bandwidth.

11. The method of claim 10 , wherein the resonant circuit has a wider bandwidth than the first bandwidth when either a frequency of the oscillator clock is larger than the first frequency, a width of the fourth transistor is larger than the first width, or both are increased simultaneously.

12. The method of claim 10 , wherein the resonate circuit has a narrower bandwidth than the first bandwidth when either a frequency of the oscillator clock is less than the first frequency, a width of the fourth transistor is less than the first width, or both are decreased simultaneously.

13. The receiver of claim 10 , wherein energy from the resonant circuit is used to charge the gate of the fourth transistor.