Systems and methods for measuring I-Q mismatch

1. A method of measuring I-Q mismatch in a system having a transmitter, the transmitter comprising an in-phase up-converter, a quadrature-phase up-converter, and a power detector, the method comprising:

measuring an in-phase transmit power at the power detector caused by transmitting an in-phase output signal to the in-phase up-converter;

measuring a quadrature-phase transmit power at the power detector caused by transmitting a quadrature-phase output signal to the quadrature-phase up-converter;

calculating a transmitter-gain-mismatch as a function of the in-phase transmit power and the quadrature-phase transmit power;

measuring an I-Q transmit power at the power detector caused by simultaneously transmitting a gain-mismatch-compensated in-phase output signal to the in-phase up-converter and a gain-mismatch-compensated quadrature-phase output signal to the quadrature-phase up-converter; and

calculating a transmitter-phase-mismatch as a function of the I-Q transmit power,

wherein the step of calculating the transmitter-gain-mismatch comprises solving the equation G 13 m =√{square root over (P I /P Q )}, where G 13 m , is the transmitter-gain-mismatch, P I is the in-phase transmit power, and P Q is the quadrature-phase transmit power.

2. The method of measuring I-Q mismatch in a system of claim 1 , wherein the in-phase output signal is a radio-frequency signal.

3. The method of measuring I-Q mismatch in a system of claim 1 , wherein the quadrature-phase output signal is a radio-frequency signal.

4. The method of measuring I-Q mismatch in a system of claim 1 , wherein the step of calculating the transmitter-phase-mismatch comprises solving the equation

ϕ

=

2

⁡

[

arcsin

⁡

(



Tx_out





M



)

-

45

]

,

where φ is the transmitter-phase-mismatch and Tx 13 out is the I-Q transmit power.

5. The method of measuring I-Q mismatch in a system of claim 1 , the system further comprising a receiver comprising an in-phase down-converter, a quadrature-phase down-converter, an in-phase input, and a quadrature-phase input, the method further comprising:

transmitting a known receiver input signal to the in-phase down-converter and the quadrature-phase down-converter;

measuring an in-phase receive power at the in-phase input and a quadrature-phase receive power at the quadrature-phase input;

calculating a receiver-gain-mismatch as a function of the in-phase receive power and the quadrature-phase receive power; and

calculating a receiver-phase-mismatch as a function of the in-phase receive power, the quadrature-phase receive power, and the receiver-gain-mismatch.

6. The method of measuring I-Q mismatch in a system of claim 5 , wherein the known receiver input signal is a loop-backed output signal of the transmitter.

7. The method of measuring I-Q mismatch in a system of claim 5 , wherein the known receiver input signal is a radio-frequency signal.

8. A method of measuring I-Q mismatch in a system having a transmitter, the transmitter comprising an in-phase up-converter, a quadrature-phase up-converter, and a power detector, the method comprising:

measuring an in-phase transmit power at the power detector caused by transmitting an in-phase output signal to the in-phase up-converter;

measuring a quadrature-phase transmit power at the power detector caused by transmitting a quadrature-phase output signal to the quadrature-phase up-converter;

calculating a transmitter-gain-mismatch as a function of the in-phase transmit power and the quadrature-phase transmit power;

measuring an I-Q transmit power at the power detector caused by simultaneously transmitting a gain-mismatch-compensated in-phase output signal to the in-phase up-converter and a gain-mismatch-compensated quadrature-phase output signal to the quadrature-phase up-converter; and

calculating a transmitter-phase-mismatch as a function of the I-Q transmit power,

wherein the step of calculating the transmitter-phase-mismatch comprises solving the equation

ϕ

=

2

⁡

[

arcsin

⁡

(



Tx_out





M



)

-

45

]

,

 equation where φ is the transmitter-phase-mismatch and Tx 13 out is the I-Q transmit power.

9. The method of measuring I-Q mismatch in a system of claim 8 , wherein the in-phase output signal is a radio-frequency signal.

10. The method of measuring I-Q mismatch in a system of claim 8 , wherein the quadrature-phase output signal is a radio-frequency signal.

11. The method of measuring I-Q mismatch in a system of claim 8 , wherein the step of calculating the transmitter-gain-mismatch comprises solving the equation G 13 m =√{square root over (P I /P Q )}, where G — m is the transmitter-gain-mismatch, P I is the in-phase transmit power, and P Q is the quadrature-phase transmit power.

12. The method of measuring I-Q mismatch in a system of claim 8 , the system further comprising a receiver comprising an in-phase down-converter, a quadrature-phase down-converter, an in-phase input, and a quadrature-phase input, the method further comprising:

transmitting a known receiver input signal to the in-phase down-converter and the quadrature-phase down-converter;

measuring an in-phase receive power at the in-phase input and a quadrature-phase receive power at the quadrature-phase input;

calculating a receiver-gain-mismatch as a function of the in-phase receive power and the quadrature-phase receive power; and

calculating a receiver-phase-mismatch as a function of the in-phase receive power, the quadrature-phase receive power, and the receiver-gain-mismatch.

13. The method of measuring I-Q mismatch in a system of claim 12 , wherein the known receiver input signal is a loop-backed output signal of the transmitter.

14. The method of measuring I-Q mismatch in a system of claim 12 , wherein the known receiver input signal is a radio-frequency signal.