High dynamic range radio architecture with enhanced image rejection

Abstract

A circuit for down-converting an RF signal to a baseband signal includes a trans-admittance amplifier adapted to receive the RF signal and generate in response a pair of differential current signals. The circuit further includes a trans-impedance amplifier having at least four mixers and at least four linear amplifiers. The four mixers frequency down-convert the pair of differential current signals to generate four pairs of differential baseband current signals, wherein each pair of the differential baseband current signals has a different phase and is associated with each of the linear amplifiers. Additionally, the circuit includes a summing block that generates an in-phase signal using a first weighted sum of the four different baseband current signals and a quadrature signal using a second weighted sum of the four different baseband current signals. The circuit further includes an analog-to-digital converter for converting the in-phase and quadrature signals to respective digital representations.

Description

BACKGROUND OF THE INVENTION

The present invention relates to communication systems, and more particularly to a high-linearity low-noise radio.

Generally, a radio uses one or more mixers to down-convert a radio frequency (RF) signal to a baseband signal. A problem with a conventional mixer used in a down-converter is that it generates unwanted harmonics, such as third and fifth harmonics. These harmonics may disturb the radio sensitivity, cause distortion in the RF signal, and/or cause electromagnetic interference. Accordingly, there is a need for improved circuits and methods to eliminate or at least reduce these harmonics.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention provide circuits and methods for eliminating or reducing harmonics in a radio. An embodiment of the present invention provides a circuit for down-converting an RF signal to a baseband signal. The circuit includes a trans-admittance amplifier adapted to receive the RF signal and generate in response a pair of differential current signals. The circuit further includes a trans-impedance amplifier that comprises at least four mixers and at least four linear amplifiers. The at least four mixers frequency down-convert the pair of differential current signals to generate four pairs of differential baseband current signals, wherein each pair of the differential baseband current signals has a different phase and is associated with each of the linear amplifiers. Additionally, the circuit includes a summing block that generates an in-phase signal using a first weighted sum of the four different baseband current signals and a quadrature signal using a second weighted sum of the four different baseband current signals.

In an alternative embodiment, a circuit for reducing harmonics in a received signal includes a trans-admittance amplifier adapted to receive an RF signal and generate in response a pair of differential current signals. The circuit further includes a trans-impedance amplifier that comprises at least four mixers and at least four linear amplifiers. The at least four mixers frequency down-convert the pair of differential current signals to generate four pairs of differential baseband current signals, wherein each pair of the differential baseband current signals has a different phase and is associated with one of the linear amplifiers. Additionally, the circuit includes a summing block that generates an in-phase harmonic signal using a first weighted sum of at least a first three of the four different baseband current signals and a quadrature harmonic signal using a second weighted sum of at least a second three of the four different baseband current signals. The circuit additionally includes an analog-to-digital converter module that converts the in-phase and quadrature harmonic signals to respective digital representation. The circuit also includes a digital processing unit adapted to eliminate or at least reduce the harmonics of one of the differential baseband current signals based on the in-phase and quadrature harmonic signals using a least mean squares algorithm.

In another embodiment of the present invention, a method for providing a baseband signal having reduced harmonics includes receiving an RF signal and generating in response a pair of differential current signals. The method further includes frequency down-converting the pair of differential current signals and generating four pairs of differential baseband current signals. The method also includes generating an in-phase signal using a first weighted sum of the four pairs of differential baseband current signals and generating a quadrature signal using a second weighted sum of the four pairs of differential baseband current signals.

In yet another embodiment of the present invention, a method for providing a baseband signal having reduced harmonics includes receiving an RF signal and generating in response a pair of differential current signals. The method further includes frequency down-converting the pair of differential current signals and generating four pairs of differential baseband current signals. The method also includes generating an in-phase harmonic signal using a first weighted sum of at least a first three of the four pairs of differential baseband current signals and generating a quadrature harmonic signal using a second weighted sum of at least a second three of the four pairs of differential baseband current signals. The method additionally includes canceling harmonics in the baseband based on the in-phase and quadrature harmonic signals. In a specific embodiment, the canceling includes the use of a least mean squares algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate the present invention and, together with the description, further serve to explain embodiments of the invention.

FIG. 1 is a block diagram illustrating a high linearity low noise radio circuit according to an embodiment of the present invention; and

FIG. 2 is a simplified block diagram illustrating a high linearity low noise circuit according to an alternative embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a block diagram of a radio 100 according to one exemplary embodiment of the present invention. Radio 100 is shown as including, in part, a wide-band low-noise trans-admittance amplifier 120 that generates differential output currents I_LNA+ and I_LNA−. In an embodiment, the low-noise trans-impedance amplifier includes a low-noise amplifier 124 having a feedback resistor 122 disposed across its input and output terminals. The feedback resistor is used to provide the required input termination resistance. The low-noise trans-admittance amplifier further includes a gain stage 126 capacitively coupled to the output terminal of the amplifier 124. The low-noise trans-admittance amplifier also includes a gain stage 128 that is capacitively coupled to the input terminal of the amplifier 124. In an embodiment, the noise introduced by amplifier 124 has the same polarity at the outputs of gain stages 126 and 128. This noise is then canceled at the outputs of gain stages 126 and 128 due to the common mode rejection of a following stage.

Radio 100 also includes a trans-impedance amplifier 150 coupled to the trans-admittance amplifier. In an embodiment, the trans-impedance amplifier includes at least four mixers 162, 164, 166, 168 that are configured to receive the differential current signals I_LNA+, I_LNA− from the low-noise trans-admittance amplifier 120 and frequency down-convert them to at least four respective differential output signals 172, 174, 176, 178. Each of the four output signals are coupled to one of the four respective amplifiers 152, 154, 156, 158. In an embodiment, each of the amplifiers is a wide bandwidth amplifier having a differential output and a programmable gain that is digitally controlled. In an embodiment, the bandwidth of the amplifiers may be 4 MHz and higher.

In an embodiment of the present invention, the differential current signals supplied by low noise trans-admittance amplifier 120 remain in the current domain as their frequency is down-converted by mixers 162, 164, 166 and 168 and as they are amplified by amplifiers 152, 154, 156, and 158, to generate signals TZ₀, TZ₄₅, TZ₉₀, TZ₁₃₅, thereby improving the linearity of the low noise trans-admittance amplifier and the mixers. In the embodiment, each of the TZ₀, TZ₄₅, TZ₉₀, TZ₁₃₅ signals is shown as being a differential signal having a differentially positive and a differentially negative signal component. Radio 100 further includes a summation block 180 that is coupled to the amplifiers 152, 154, 156, and 158. In an embodiment, the summation block includes a first summing amplifier 182 and a second summing amplifier 184. Each of the summing amplifiers receives the TZ₀, TZ₄₅, TZ₉₀, TZ₁₃₅ signals and generates a weighted sum of the signals TZ₀, TZ₄₅, TZ₉₀, TZ₁₃₅ to generate an in-phase (I) signal and a quadrature (Q) signal.

Radio 100 further includes an oscillator circuit 190 that provides a reference signal 191 to a multi-phase signal generator 192. In an embodiment, the local oscillator may be a frequency synthesizer and the multi-phase signal generator may include multiple divider by 2 circuits and produces digital signals having the same frequency but different phases for the four mixers 162, 164, 166, 168. In another embodiment, the multi-phase clock generator may be poly-phase filters that may include resistive and capacitive components to produce sinusoidal signals having the same frequency but different phases for the mixers. In yet another embodiment, the multi-phase signal generator 192 may be integrated within the oscillator circuit.

In an embodiment, each mixer uses a 12.5% duty cycle non-overlapping clock to provide four differential baseband outputs. These differential outputs may be described as samples of the RF waveform at four different oscillation phases—0, 45, 90 and 135 degrees. In a conventional down-converter only quadrature outputs at phases of 0° and 90°, called I and Q signals respectively, are available. In accordance with the present invention, however, a weighted sum of four phases are used to generate the I and Q signals.

In accordance with one embodiment of the present invention, the I and Q signals are generated using the weighted sum as shown in Equations (1) and (2) below, each with harmonic rejection of the 3^rd and 5^th harmonics at the RF input.I=TZ₀+(√2+1)TZ₄₅+(√2+1)TZ₉₀+TZ₁₃₅  (1)Q=(√2+1)TZ₀+TZ₄₅+TZ₉₀+(√2+1)TZ₁₃₅  (2)

Numerically, the in-phase signal I comprises 1×TZ₀, 2.41(√2+1)×TZ₄₅, 2.41×TZ₉₀, and 1×TZ₁₃₅. Similarly, the quadrature signal Q comprises 2.41×TZ₀, 1×TZ₄₅, 1×TZ₉₀, and 2.41×TZ₁₃₅.

In an embodiment, the summation block 180 is shown as having a bi-quad gain stage that generates the final I and Q signals. The presence of the op-amp with virtual ground node provides a convenient summing node. Scaling of the baseband outputs is achieved by selecting the appropriate resistors in the trans-impedance amplifier 150. In an embodiment, the composite frequency response of the real pole in the trans-impedance amplifier 150 and the pair of complex poles is a third order Butterworth filter. As is seen from the above description, the signals remain in the current domain even while being frequency down-converted all the way down to the baseband region of operation.

Additionally, radio 100 includes a digital-to-analog converter stage that converts the I and Q signals to a digital representation to provide to a digital front end (DFE) for further processing.

Additional Harmonic Rejection Using LMS

The four signals at the output of trans-impedance amplifier 150 carry an estimate of the desired signals and the unwanted signals at harmonics of the RF frequency. As described above, a weighted sum of these signals is used in accordance with the present invention to provide estimates of the desired I and Q signals.

In an alternative embodiment of the present invention, another weighted sum of the output signals of trans-impedance amplifier 150 is used to provide estimates of the signal at the 3^rd or 5^th harmonic. In one exemplary embodiment, the 3^rd or 5^th harmonics are obtained using the following expression:I_harm=TZ₃₁₅−√2TZ₀+TZ₄₅  (3)Q_harm=TZ₄₅−√2TZ₉₀+TZ₁₃₅  (4)

These signals can be digitized in a relatively simple Analog-to-digital converter (ADC) to generate a digital representation of the complex signal at the harmonic frequency. Using this complex signal as a reference, a least mean square (LMS) algorithm may then be used to detect and cancel the signal leaking into the main path. In one example embodiment, at least a 20 dB improvement in 3^rd and 5^th harmonic rejection is achieved.

FIG. 2 is a schematic diagram of a radio 200 according to an alternative embodiment of the present invention. Radio 200 includes a wideband low-noise trans-admittance amplifier 120 configured to receive an RF signal and produce a pair of differential current signals I_LNA+ and I_LNA−. Radio 200 also includes a trans-impedance amplifier 150 coupled to the trans-admittance amplifier. In an embodiment, the trans-impedance amplifier includes at least four mixers 162, 164, 166, 168 that are configured to receive the differential currents from the low-noise trans-admittance amplifier 120 and frequency down-convert them to at least four respective differential output signals 172, 174, 176, 178. Each of the four output signals are coupled to one of the four respective amplifiers 152, 154, 156, 158. Each of the four amplifiers provides a respective pair of differential signals TZ₀, TZ₄₅, TZ₉₀, TZ₁₃₅. The trans-admittance amplifier and the trans-impedance amplifiers have been described in sections above and will not be further explained for sake of brevity.

Radio 200 further includes a local oscillator 190 configured to produce a reference frequency signal 191 to a multi-phase generator 192 that generates multiple clock signals having the same frequency but with different phases. In an embodiment of the present invention, multi-phase generator 192 will be implemented using divide-by-2 circuits known to one of skill in the art to produce the four differential output signals at four different phases (0, 180), (45, 225), (90, 270), and (135, 315).

Radio 200 includes a summing block 260 that generate an in-phase harmonic signal 272 and a quadrature harmonic signal 274. In an embodiment, summing block 260 includes a summing amplifier 262 that generates the in-phase harmonic signal in accordance with Equation (3) and a summing amplifier 264 that generates the quadrature harmonic signal 274 in accordance with Equation (4) and using the output signals of trans-impedance amplifier 150.

Radio 200 also includes an analog-to-digital converter block 290 that converts the in-phase and quadrature harmonic signals and at least one of the four pairs of differential baseband current signals to their respective digital representations. In a specific embodiment, the at least one of the four pairs of differential baseband current signals may be the one that has the differential phases (0, 180) as shown in FIG. 2. The at least one of the four pairs of different baseband current signals may contain harmonics that can be eliminated based on the in-phase and quadrature harmonic signals in a subsequent digital front end (DFE) module. In a specific embodiment, the elimination of the harmonics in the baseband current signals may use a least mean squares algorithm to detect and cancel the harmonics as described in sections above.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. For example, the detection and cancellation of the harmonics may use other algorithms than the disclosed LMS algorithm. The weighted sum may also use other hardware summing circuits other than the shown summing amplifiers. The difference phases may be generated differently from the disclosed embodiments of the present invention.

The above embodiments of the present invention are illustrative and not limiting. Various alternatives and equivalents are possible. The invention is not limited by the type of integrated circuits in which the present disclosure may be disposed. Other additions, subtractions or modifications are obvious in view of the present invention and are intended to fall within the scope of the appended claims.

Claims

1. A circuit comprising: a trans-admittance amplifier (TAA) receiving a Radio Frequency (RF) signal and in response generating a pair of differential RF current signals at a positive TAA output terminal and a negative TAA output terminal, the trans-admittance amplifier comprising: a low-noise amplifier (LNA) for receiving the RF signal at an input LNA terminal, amplifying the received RF signal, and outputting the amplified RF signal on an output LNA terminal;a first gain stage for receiving the amplified RF signal at a first stage input capacitively coupled to the output LNA terminal, applying a first gain to the amplified RF signal to generate the positive RF current signal of the pair of differential RF current signals, and outputting the positive RF current signal on a first stage output capacitively coupled to the positive TAA output terminal; anda second gain stage for receiving the RF signal on a second stage input capacitively coupled to the input LNA terminal, applying a second gain to the received RF signal to generate the negative RF current signal of the pair of differential RF current signals, and outputting the negative RF current signal on a second stage output capacitively coupled to the negative TTA output terminal;a second amplifier circuit comprising at least four mixers and at least four linear amplifiers, the at least four mixers down-converting a frequency of the pair of differential RF current signals from the positive and negative TAA output terminals to generate four pairs of differential baseband current signals each having a phase corresponding to different phases of a local oscillator signal, and each of the linear amplifiers being associated with a different one of the four pairs of differential baseband current signals; anda summing block configured to: generate an in-phase signal using a first weighted sum of the four differential baseband current signals; andgenerate a quadrature phase signal using a second weighted sum of the four differential baseband current signals; anda processing unit configured to reduce harmonics in at least one of the lour pairs of differential baseband current signals based on the generated in-phase and quadrature harmonic signals.

2. The circuit of claim 1, wherein a first one of the four pairs of the differential baseband current signal has a phase of 0 degree with respect to the local oscillator signal, wherein a second one of the four pairs of the differential baseband current signal has a phase of 45 degrees with respect to the local oscillator signal, wherein a third one of the four pairs of the differential baseband current signal has a phase of 90 degrees with respect to the local oscillator signal, wherein a fourth one of the four pairs of the differential baseband current signal has a phase of 135 degrees with respect to the local oscillator signal.

3. The circuit of claim 2, wherein each of the at least four mixers receives two 12.5% duty cycle non-overlapping clock signals to provide one of the four pairs of differential baseband current signals.

4. The circuit of claim 1, wherein a first pair of the four pairs of differential baseband current signals is defined as TZ0 having a relative phase of 0 degrees, a second pair of the four pairs of differential baseband current signals is defined as TZ45 having a relative phase of 45 degrees, a third pair of the four pairs of differential baseband current signals is defined as TZ90 having a relative phase of 90 degrees, a fourth pair of the four pairs of differential baseband current signals is defined as TZ135 having a relative phase of 135 degrees, and the generated in-phase signal using the first weighted sum of the four differential baseband current signals is substantially equal to: TZ0+(√2+1)TZ45+(√2+1)TZ90+TZ135.

5. The circuit of claim 1, wherein a first pair of the four pairs of differential baseband current signals is defined as TZ0 having a relative phase of 0 degrees, a second pair of the four pairs of differential baseband current signals is defined as TZ45 having a relative phase of 45 degrees, a third pair of the four pairs of differential baseband current signals is defined as TZ90 having a relative phase of 90 degrees, a fourth pair of the four pairs of differential baseband current signals is defined as TZ135 having a relative phase of 135 degrees, and the generated quadrature signal using the second sum of the four differential baseband current signals is substantially equal to: (√2+1)TZ0+TZ45+TZ90+(√2+1)TZ135.

6. A circuit for reducing harmonics in a received signal comprising: a trans-admittance amplifier (TAA) receiving a Radio Frequency (RF) signal and in response generating a pair of differential RF current signals at a positive TAA output terminal and a negative TAA output terminal, the trans-admittance amplifier comprises: a low-noise amplifier (LNA) for receiving the RF signal at an input LNA terminal, amplifying the received RF signal, and outputting the amplified RF signal on an output LNA terminal;a first gain stage for receiving the amplified RF signal at a first stage input capacitively coupled to the output LNA terminal, applying a first gain to the amplified RF signal to generate the positive RF current signal of the pair of differential RF current signals, and outputting the positive RF current signal on a first stage output capacitively coupled to the positive TAA output terminal; anda second gain stage for receiving the RF signal on a second stage input capacitively coupled to the input LNA terminal, applying a second gain to the received RF signal to generate the negative RF current signal of the pair of differential RF current signals, and outputting the negative RF current signal on a second stage output capacitively coupled to the negative TTA output terminal;a second amplifier circuit comprising at least four mixers and at least four linear amplifiers, the at least four mixers down-converting a frequency of the pair of differential RF current signals from the positive and negative TAA output terminals to generate four pairs of differential baseband current signals each having a phase corresponding to different phases of a local oscillator signal, and each of the linear amplifiers being associated with a different one of the four pairs of differential baseband current signals; anda summing block configured to: generate an in-phase harmonic signal using a first weighted sum of at least a first set of three of the four pairs of differential baseband current signals; andgenerate a quadrature harmonic signal using a second weighted sum of at least a second set of three of the four pairs of differential baseband current signals; anda processing unit configured to reduce harmonics in at least one of the four pairs of differential baseband current signals based on the generated in-phase and quadrature harmonic signals.

7. The circuit of claim 6, further comprising: an analog-to-digital converter module configured to convert the at least one of the four pairs of differential baseband current signals and the in-phase and quadrature harmonic signals to respective digital representations.

8. The circuit of claim 6, wherein the processing unit is a digital signal processor configured to eliminate the harmonics out of the at least one of the four pairs of differential baseband current signals using a least means squares algorithm based on the generated in-phase and quadrature harmonic signals.

9. The circuit of claim 6, further comprising: a local oscillator including a multi-phase signal generator configured to produce a plurality of clock signals having a same frequency and different phases, wherein each of the plurality of clock signals is associated with one of the at least four mixers.

10. The circuit of claim 9, wherein the multi-phase signal generator comprises digital circuits.

11. The circuit of claim 6, wherein the first set of three of the four pairs of differential baseband current signals are defined as TZ315 having a relative phase of 315 degrees, TZ0 having a relative phase of 0 degrees, and TZ45 having a relative phase of 45 degrees, and the generated in-phase harmonic signal is substantially equal to: TZ315−√2TZ0+TZ45.

12. The circuit of claim 6, wherein the second set of three of the four pairs of differential baseband current signals are defined as TZ45 having a relative phase of 45 degrees, TZ90 having a relative phase of 90 degrees, and TZ135 having a relative phase of 315 degrees, and the generated quadrature harmonic signal is substantially equal to: TZ45−√2TZ90+TZ135.

13. The circuit of claim 6, wherein each of the at least four mixers receives two 12.5% duty cycle non-overlapping clock signals to provide one pair of the four pairs of differential baseband current signals.

14. A method for providing baseband signals having reduced harmonics, comprising: receiving a Radio Frequency (RF) signal at a low-noise amplifier (LNA) input terminal of a trans-admittance amplifier (TAA);generating, by the trans-admittance amplifier, a pair of differential RF current signals in response to the received RF signal on a positive TAA output terminal and a negative TAA output terminal, and generating the pair of differential RF current signals comprises: low-noise amplifying the received RF signal and outputting the amplified RF signal on an output LNA terminal;receiving the amplified RF signal at a first stage input capacitively coupled to the output LNA terminal, generating the positive RF current signal of the pair of differential RF current signals by applying a first gain to the amplified RF signal at a first gain stage, and outputting the positive RF current signal by a first stage output capacitively coupled to the positive TAA output terminal; andreceiving the RF signal on a second stage input capacitively coupled to the input LNA terminal, generating the negative RF current signal of the pair of differential RF current signals by applying a second gain to the RF signal at a second gain stage, and outputting the negative RF current signal on a second stage output capacitively coupled to the negative TTA output terminal;frequency down-converting the pair of differential RF current signals using at least four mixers for producing four pairs of differential baseband current signals, each of the four pairs of differential baseband current signals having a different phase with regard to a local oscillator signal;generating an in-phase signal using a first weighted sum of the four pairs of differential baseband current signals; andgenerating a quadrature signal using a second weighted sum of the four pairs of differential baseband current signals.

15. The method of claim 14, further comprising: generating a plurality of clock signals having a same frequency and different phases, wherein each of the plurality of clock signals is associated with one of the at least four mixers.

16. The method of claim 14, wherein each of the at least four mixers receives two 12.5% duty cycle non-overlapping clock signals to provide one pair of the four pairs of differential baseband current signals.

17. The method of claim 14, wherein a first pair of the four pairs of differential baseband current signals is defined as TZ0 having a relative phase of 0 degrees, a second pair of the four pairs of differential baseband current signals is defined as TZ45 having a relative phase of 45 degrees, a third pair of the four pairs of differential baseband current signals is defined as TZ90 having a relative phase of 90 degrees, a fourth pair of the four pairs of differential baseband current signals is defined as TZ135 having a relative phase of 135 degrees, and the generated in-phase signal is substantially equal to: TZ0+(√2+1)TZ45+(√2+1)TZ90+TZ135.

18. The method of claim 14, wherein a first pair of the four pairs of differential baseband current signals is defined as TZ0 having a relative phase of 0 degrees, a second pair of the four pairs of differential baseband current signals is defined as TZ45 having a relative phase of 45 degrees, a third pair of the four pairs of differential baseband current signals is defined as TZ90 having a relative phase of 90 degrees, a fourth pair of the four pairs of differential baseband current signals is defined as TZ135 having a relative phase of 135 degrees, and the generated quadrature signal is substantially equal to: (√2+1)TZ0+TZ45+TZ90+(√2+1)TZ135.

19. A method for providing baseband signals having reduced harmonics comprising: receiving a Radio Frequency (RF) signal at a low-noise amplifier (LNA) input terminal of a trans-admittance amplifier (TAA);generating, by the trans-admittance amplifier, a pair of differential RF current signals in response to the received RF signal on a positive TAA output terminal and a negative TAA output terminal, and generating the pair of differential RF current signals comprises: low-noise amplifying the received RF signal and outputting the amplified RF signal on an output LNA terminal;receiving the amplified RF signal at a first stage input capacitively coupled to the output LNA terminal, generating the positive RF current signal of the pair of differential RF current signals by applying a first gain to the amplified RF signal at a first gain stage, and outputting the positive RF current signal by a first stage output capacitively coupled to the positive TAA output terminal; andreceiving the RF signal on a second stage input capacitively coupled to the input LNA terminal, generating the negative RF current signal of the pair of differential RF current signals by applying a second gain to the RF signal at a second gain stage, and outputting the negative RF current signal on a second stage output capacitively coupled to the negative TTA output terminal;frequency down-converting the pair of differential RF current signals using at least four mixers for producing four pairs of differential baseband current signals, each of the four pairs of differential baseband current signals having a different phase with regard to a local oscillator signal;generating an in-phase harmonic signal using a first weighted sum of a first set of three of the four pairs of differential baseband current signals; andgenerating a quadrature harmonic signal using a second weighted sum of a second set of three of the four pairs of differential baseband current signals; andreducing harmonics, by a processing unit, in at least one of the four pairs of differential baseband current signals based on the generated in-phase and quadrature harmonic signals.

20. The method of claim 19, wherein the first set of three of the four pairs of differential baseband current signals are defined as TZ315 having a relative phase of 315 degrees, TZ0 having a relative phase of 0 degrees, and TZ45 having a relative phase of 45 degrees, and the generated in-phase harmonic signal is substantially equal to: TZ315−√2TZ0+TZ45.

21. The method of claim 19, wherein the second set of three of the four pairs of differential baseband current signals are defined as TZ45 having a relative phase of 45 degrees, TZ90 having a relative phase of 90 degrees, and TZ135 having a relative phase of 315 degrees, and the generated quadrature harmonic signal is substantially equal to: TZ45−√2TZ90+TZ135.