阅读说明：本技术 对阻挠者具有高免疫的降频转换器及其方法 (Down converter with high immunity to frustrators and method thereof ) 是由 萨尔肯·希尤斯 梁宝文 林嘉亮 于 2018-10-31 设计创作，主要内容包括：降频转换器包括混频器,该混频器用来接收具有第一端和第二端的射频信号且根据具有第一端和第二端的本地振荡器信号输出包括第一端和第二端的中间信号,本地振荡器信号的第一端和第二端共同形成双相周期信号,其基本频率大致等于射频信号的期许成分的平均频率。降频转换器还包括：运算放大器,用来接收中间信号并输出具有第一端和第二端的输出信号；第一反馈网络,用来将输出信号的第二端耦合到中间信号的第一端；第二反馈网络,用来将输出信号的第一端耦合到中间信号的第二端；辅助混频器,用来接收射频信号并根据本地振荡器信号提供添加到输出信号的补充信号。辅助混频器基于使用与混频器相同的电路但用与电容串联的开关替换混频器中的每个开关。(The down-converter includes a mixer for receiving a radio frequency signal having a first end and a second end and outputting an intermediate signal including the first end and the second end based on a local oscillator signal having a first end and a second end, the first end and the second end of the local oscillator signal together forming a two-phase periodic signal having a fundamental frequency substantially equal to an average frequency of desired components of the radio frequency signal. The down converter further includes: an operational amplifier for receiving the intermediate signal and outputting an output signal having a first terminal and a second terminal; a first feedback network for coupling the second end of the output signal to the first end of the intermediate signal; a second feedback network for coupling a first end of the output signal to a second end of the intermediate signal; an auxiliary mixer is arranged to receive the radio frequency signal and to provide a supplementary signal to be added to the output signal in dependence on the local oscillator signal. The auxiliary mixer is based on replacing each switch in the mixer with the same circuit as the mixer but with a switch in series with a capacitor.)

1. A down converter, comprising:

A mixer for receiving a radio frequency signal including a first terminal and a second terminal and outputting an intermediate signal including the first terminal and the second terminal based on a local oscillator signal including the first terminal and the second terminal, wherein the first terminal and the second terminal of the local oscillator signal together form a bi-phase periodic signal having a fundamental frequency substantially equal to an average frequency of an allowable component of the radio frequency signal;

An operational amplifier for receiving the intermediate signal and outputting an output signal including a first terminal and a second terminal;

A first feedback network for coupling the second end of the output signal to the first end of the intermediate signal;

A second feedback network for coupling a first end of the output signal to a second end of the intermediate signal; and

An auxiliary mixer for receiving the RF signal and providing a supplemental signal added to the output signal based on the local oscillator signal;

Wherein the auxiliary mixer is based on using the same circuit topology as the mixer, but replacing each switch in the mixer with a switch in series with a capacitor.

2. The frequency down-converter of claim 1, wherein the mixer comprises:

A first switch for connecting the first terminal of the radio frequency signal to the first terminal of the intermediate signal when the first terminal of the local oscillator signal is active;

A second switch for connecting the second terminal of the RF signal to the first terminal of the intermediate signal when the second terminal of the local oscillator signal is active;

A third switch for connecting the first terminal of the RF signal to the second terminal of the intermediate signal when the second terminal of the local oscillator signal is asserted; and

A fourth switch for connecting the second terminal of the RF signal to the second terminal of the intermediate signal when the first terminal of the local oscillator signal is active.

3. The frequency down-converter of claim 1, wherein the auxiliary mixer comprises:

a first switch in series with a first capacitor, wherein the first capacitor capacitively couples the first terminal of the RF signal to the second terminal of the output signal when the first terminal of the local oscillator signal is active;

A second switch in series with a second capacitor, wherein the second capacitor capacitively couples the second terminal of the RF signal to the second terminal of the output signal when the second terminal of the local oscillator signal is active;

a third switch in series with a third capacitor, wherein the third capacitor capacitively couples the first terminal of the RF signal to the first terminal of the output signal when the second terminal of the local oscillator signal is active; and

A fourth switch in series with a fourth capacitor, wherein the fourth capacitor capacitively couples the second terminal of the RF signal to the first terminal of the output signal when the first terminal of the local oscillator signal is active.

4. The downconverter of claim 1 wherein the first feedback network comprises a parallel connection of a feedback resistor and a feedback capacitor.

5. The downconverter of claim 1 wherein the second feedback network comprises a parallel connection of a feedback resistor and a feedback capacitor.

6. The frequency down-converter of claim 1, further comprising:

An integrator for receiving the output signal and outputting a filtered signal including a first terminal and a second terminal;

A first feedback resistor for providing feedback from the second end of the filtered signal to the first end of the intermediate signal; and

A second feedback resistor for providing feedback from the first end of the filtered signal to the second end of the intermediate signal.

7. The down converter of claim 6, wherein the integrator comprises an additional operational amplifier, two feed resistors and two feedback capacitors.

8. the downconverter of claim 1 wherein the local oscillator signal is a square wave with a duty cycle of approximately 25%.

9. The downconverter of claim 1 wherein the downconverter is integrated in a zero intermediate frequency receiver.

10. A method of down-conversion comprising:

receiving a radio frequency signal comprising a first end and a second end;

Receiving a local oscillator signal comprising a first terminal and a second terminal, wherein the first terminal and the second terminal of the local oscillator signal together form a bi-phase periodic signal having a fundamental frequency substantially equal to an average frequency of an allowed component of the rf signal;

Mixing the radio frequency signal with the local oscillator signal using a mixer to output an intermediate signal including a first terminal and a second terminal;

Converting the intermediate signal into an output signal including a first end and a second end using an operational amplifier having a negative feedback via a first feedback network and a second feedback network; and

Mixing the radio frequency signal with the local oscillator signal using an auxiliary mixer to create a supplemental signal that is added to the output signal as a supplement;

wherein the auxiliary mixer is based on using a circuit topology identical to the mixer, but replacing each switch in the mixer with a switch in series with a capacitor.

Technical Field

The present invention relates to frequency down-converters (frequency down-converters), and more particularly to a frequency down-converter circuit and method with improved linearity and dynamic range.

Background

As shown in fig. 1A, the conventional down converter 100 includes: a mixer 110 for receiving a Radio Frequency (RF) signal including a first terminal VRF + and a second terminal VRF-and outputting an intermediate signal including a first terminal VX + and a second terminal VX-, according to control of a Local Oscillator (LO) signal including a first terminal VLO + and a second terminal VLO-; an operational amplifier 120 for receiving the intermediate signal and outputting an Intermediate Frequency (IF) signal including a first terminal VIF + and a second terminal VIF-; a first feedback network 130 for providing feedback coupling between VIF-and VX +; and a second feedback network 140 to provide feedback coupling between VIF + and VX-.

as indicated by the reference block COB110, the mixer 110 comprises: a first (second, third, fourth) switch 111(112, 113, 114) for connecting VRF + (VRF-, VRF +, VRF-) to VX + (VX +, VX-) when signal VLO + (VLO-, VLO + -) is asserted (asserted). As indicated by the reference block COB130, the feedback network 130 comprises a parallel connection of a capacitor 131 and a resistor 132. Feedback network 140 is implemented using the same circuitry as feedback network 130, but with VX + and VIF + replacing them, respectively. Since conventional down-converter 100 is well known to those skilled in the art, it will not be described in detail herein.

the prior downconverter 100 is typically used in a zero-intermediate frequency (zero-IF) receiver, where the average frequency of the desired components of the RF signal is exactly equal to, or at least approximately equal to, the fundamental frequency (fundamental frequency) of the LO signal. In this case, the desired component in the IF signal has a low-pass characteristic, and is generally referred to as a baseband (BB) signal. In a zero intermediate frequency receiver, two downconverters and two LO signals (including in-phase and quadrature signals) are required: one of the two downconverters uses an in-phase signal and the other a quadrature signal. Since the concepts of "zero intermediate frequency receiver", "in-phase" and "quadrature" are well known to those skilled in the art, they will not be described in detail herein.

In addition to the desired components, the RF signal (represented by VRF + and VRF-in downconverter 100 of fig. 1A) often contains undesired components in the receiver called "blockers". The frustrator is different in frequency from the desired component, but is down-converted with the desired component. The frustrator can be very harmful. First, the disturber can detrimentally degrade the linearity of the mixer 110 and op-amp 120, thereby distorting the desired components in the IF signal. Second, the frustrator may detrimentally reduce the available dynamic range of the desired component of the signal in the operational amplifier 120 and subsequent circuitry. Although feedback networks 130 and 140 may provide a low pass filtering function that may slightly attenuate undesired components and slightly address the issue of dynamic range, the need to maintain the integrity of the desired components may limit the low pass corner frequency and the filtering effect. Furthermore, the feedback networks 130 and 140 do not effectively mitigate the linearity problem.

To handle the jammer, the bandpass filter 150 shown in fig. 1B can be used to attenuate the jammer of RF signals in a zero intermediate frequency receiver. The band pass filter 150 includes four switches 151, 152, 153, and 154, and four capacitors 155, 156, 157, and 158. When VLO + (VLO-) is active, switch 151(152) is used to shunt VRF + to ground via capacitor 155 (156). When VLO + (VLO-) is active, switch 153(154) is used to shunt VRF-to ground via capacitor 157 (158). The band pass filter 150 belongs to a class of filters known in the art as "N-path filters". For the principles of the N-path filter, reference may be made to the paper published by Klumperink et al in 2017 at Custom Integrated Circuits Conference (CICC): "N-path filters and mixer-first receivers: a review ". In short, the impedance of the band pass filter 150 is approximately inversely proportional to the frequency difference between the RF signal and the LO signal. As such, the band pass filter 150 has a high impedance for the desired component (of the RF signal) but a low impedance for the undesired component (of the RF signal). Thus, the frustrator can effectively shunt to ground and attenuate.

Although the band pass filter 150 can attenuate the frustrator, there are two problems or disadvantages with this configuration. First, the four capacitors 155, 156, 157, and 158 are typically very large and occupy a large physical area in the integrated circuit chip. Second, the impedance of the bandpass filter 150 is not infinite, and therefore, the unwanted component is also shunted to ground, resulting in a loss of the unwanted component of the RF signal. This loss is usually not negligible.

Accordingly, there is a need to implement a down-converter circuit configuration to overcome these disadvantages of conventional systems.

Disclosure of Invention

the present disclosure discloses a method that can be used to alleviate linearity and dynamic range problems caused by the frustrator, but without using a large area and without incurring non-negligible losses to the desired components of the RF signal.

in one embodiment, a down converter includes: a mixer for receiving an RF signal having a first terminal and a second terminal and outputting an intermediate signal having a first terminal and a second terminal in response to an LO signal having a first terminal and a second terminal, wherein the first terminal and the second terminal of the LO signal together form a two-phase periodic signal (tw-phase periodic signal) having a fundamental frequency substantially equal to an average frequency of a desired component of the RF signal; an operational amplifier for receiving the intermediate signal and outputting an output signal including a first terminal and a second terminal; a first feedback network for coupling the second end of the output signal to the first end of the intermediate signal; a second feedback network for coupling a first end of the output signal to a second end of the intermediate signal; and an auxiliary mixer for receiving the RF signal and providing a supplemental signal added to the output signal in accordance with the LO signal, wherein: the auxiliary mixer is based on using the same circuit topology as the mixer, but replacing each switch in the mixer with a switch in series with a capacitor.

In one embodiment, a method comprises: receiving an RF signal comprising a first end and a second end; receiving an LO signal comprising a first terminal and a second terminal, wherein the first terminal and the second terminal of the LO signal together form a two-phase periodic signal having a fundamental frequency substantially equal to an average frequency of desired components of the RF signal; mixing the RF signal with the LO signal using a mixer to output an intermediate signal including a first terminal and a second terminal; converting the intermediate signal into an output signal comprising a first terminal and a second terminal using an operational amplifier with negative feedback via a first feedback network and a second feedback network; and mixing the RF signal with the LO signal using an auxiliary mixer to create a supplemental signal that is added to the output signal as a complement, wherein: the auxiliary mixer is based on using the same circuit topology as the mixer, but replacing each switch in the mixer with a switch in series with a capacitor.

Drawings

Fig. 1A shows a schematic diagram of a conventional down converter.

FIG. 1B shows a schematic diagram of a bandpass filter.

Fig. 2 shows a functional block diagram of a down converter according to an embodiment of the invention.

fig. 3 shows a functional block diagram of a zero intermediate frequency receiver.

Fig. 4 shows a flow chart of a method according to an embodiment of the invention.

Description of the symbols

100. 200, 330, 340 downconverter

110. 210 frequency mixer

111. 112, 113, 114, SW1, SW2, SW3, SW4 switches

120. 220, 252 operational amplifier

130. 230 first feedback network

131 capacitor

132 resistance

140. 240 second feedback network

150 band-pass filter

151. 152, 153, 154 switch

155. 156, 157, 158 capacitors

210A auxiliary mixer

C1, C2, C3 and C4 capacitors

250 additional network

r1, R2 resistance

RP, RN feed-in resistor

CP, CN feedback capacitance

300 zero intermediate frequency receiver

310. 320 buffer

410 to 450 steps

Detailed Description

the present invention relates to a down converter. While the specification describes several exemplary embodiments of the invention, which are considered to be the preferred modes of carrying out the invention, it is understood that the invention may be embodied in many different forms and is not limited to the specific examples described below or to the specific ways of carrying out any of the features of these examples. In other instances, well-known details are not shown or described to avoid obscuring the invention.

those skilled in the art understand the terms and basic concepts associated with microelectronics, such as "signal," "network," "capacitance," "resistance," "switch," "feedback," "negative feedback," "operational amplifier," "buffer," and "integrator," as used in this disclosure. Such terms and basic concepts will be apparent and understood to those skilled in the art and will not be described in detail herein.

In the present disclosure, a switch is a means for conditionally connecting a first signal to a second signal according to the state of a control signal. The control signal has two states: an "asserted" state and a "de-asserted" state. When the control signal is asserted, the switch is turned on and the first signal and the second signal are effectively connected by the switch. When the control signal is inactive, the switch is not conductive and the first signal and the second signal are not connected by the switch.

In the present disclosure, a differential signal is a composite signal including a first constituent signal and a second constituent signal. The first component signal is referred to as a first terminal and the second component signal is referred to as a second terminal.

Fig. 2 shows a functional block diagram of a down-converter 200 according to an embodiment of the present invention. The down converter 200 includes: a mixer 210 for receiving an RF signal including a first terminal VRF + and a second terminal VRF-, and outputting an intermediate signal including a first terminal VA + and a second terminal VA-according to a control of an LO signal including a first terminal VLO + and a second terminal VLO-; an operational amplifier 220 for receiving the intermediate signals (VA + and VA-) and outputting an output signal including a first terminal VB + and a second terminal VB-; a first feedback network 230 for providing feedback coupling between VB-and VA +; a second feedback network 240 for providing feedback coupling between VB + and VA-; and an auxiliary mixer 210A for providing capacitive coupling between the RF signals (VRF + and VRF-) and the output signals (VB-and VB +) in accordance with control of the LO signals (VLO + and VLO-).

VLO + and VLO-form a two-phase periodic signal that mathematically satisfies the following equation:

V(t)＝V(t-T/2) (1)

Here, T denotes a time variable, T is a fundamental period of the biphasic periodic signal, and 1/T is approximately equal to an average frequency of a prospective component of the RF signal. In one embodiment, both VLO + (t) and VLO- (t) approximate a square wave that periodically switches back and forth between a first level and a second level. When VLO + (t) is at a first level, it is referred to as "in effect" and in other cases it is referred to as "not in effect". VLO- (t) works similarly. The duty cycle of VLO + (t) is the percentage of time VLO + (t) "in effect". VLO- (t) works similarly. In one embodiment, VLO + (t) and VLO- (t) both have a duty cycle of approximately 25%. In another embodiment, VLO + (t) and VLO- (t) both have a duty cycle of approximately 50%. In yet another embodiment, VLO + (t) and VLO- (t) both have duty cycles of approximately 33%.

In one embodiment, the mixer 210 is implemented with a circuit shown by the labeled block COB110 in fig. 1. (wherein the signal tag needs to be changed, i.e. "VX +" and "VX-" need to be replaced by "VA +" and "VA-" respectively.

in the embodiment shown in the labeling block COB210A, the auxiliary mixer 210A includes: a first (second, third, fourth) switch SW1(SW2, SW3, SW4) for connecting "VRF +" ("VRF-", "VRF +", "VRF-") to "VB-" ("VB-", "VB +" "VB +") via a first (second, third, fourth) capacitor C1(C2, C3, C4) when "VLO +" ("VLO-", "VLO +") is active. The auxiliary mixer 210A has the same circuit topology as the mixer 210 in terms of circuit topology, with the difference that the auxiliary mixer 210A further includes capacitances C1, C2, C3, and C4 for capacitive coupling. In terms of signal interaction, mixer 210 serves to couple the RF signals (VRF + and VRF-) to the intermediate signals (VA + and VA-), while auxiliary mixer 210A serves to couple the RF signals (VRF + and VRF-) to the output signals VB-and VB +).

In one embodiment, both feedback networks 230 and 240 are implemented using the circuitry shown in the labeling box COB130 in fig. 1. (the signal flags should be changed to suit the application of the circuit, e.g., "VX +" and "VIF-" are replaced with "VA +" and "VB-"). In another embodiment, feedback networks 230 and 240 are both implemented using the circuit shown in reference box COB130 of fig. 1, but with resistor 132 removed.

In one embodiment, which is selected to be adopted, the down-converter 200 further includes an additional network 250, and the additional network 250 includes an integrator 251, a first resistor R1, and a second resistor R2. The integrator 251 includes an operational amplifier 252, two feed resistors RP and RN, and two feedback capacitors CP and CN. The purpose of using the additional network 250 will be explained later. The difference between downconverter 200 and downconverter 100 is that downconverter 200 has an additional auxiliary mixer 210A in addition to additional network 250. The auxiliary mixer 210A effectively implements a band-pass filter that can suppress the jammer component of the RF signal. The conventional N-path filter 150 of fig. 1B shunts the RF signal to ground with a capacitance according to the LO signal; unlike the N-path filter 150, the auxiliary mixer 210A shunts the RF signals (i.e., VRF + and VRF-) to the output (i.e., VB-and VB +) of the operational amplifier 220 using capacitors (i.e., C1, C2, C3, and C4) based on the LO signals (VLO + and VLO-). Since op-amp 220 can provide inverting gain and thus boost the output signal (VB-and VB +), auxiliary mixer 210A can shunt more current from the RF signal than conventional N-path filter 150 in fig. 1B, based on using the same switches and capacitors. This is a principle known as the Miller effect. In accordance with this principle, the capacitors C1, C2, C3 and C4 allow for smaller capacitance values (smaller than those used in the conventional N-path filter 150 of fig. 1B) while achieving the same current splitting capability and filtering performance.

In addition, the conventional N-path filter 150 in fig. 1B will inevitably partially shunt the desired component of the RF signal to ground; unlike the N-path filter 150, the auxiliary mixer 210A will inevitably partially shunt the desired component of the RF signal to the output of the operational amplifier 220. However, the down-conversion occurs together with the splitting action, so that part of the desired component of the RF signal split by the auxiliary mixer 210A is down-converted and becomes part of the desired component of the output signal. In other words, for the desired component of the RF signal, the auxiliary mixer 210A provides only an additional path to the output of the operational amplifier 220 (in addition to directly through the mixer 210 and the operational amplifier 220 with the feedback networks 230 and 240). Therefore, the desired component is hardly lost. Therefore, the auxiliary mixer 210A solves the problem of large capacitance and signal loss of the band pass filter 150 in fig. 1B.

Additional network 250 is operative to receive the output signals (i.e., VB + and VB-) and output a filtered signal including a first terminal VC + and a second terminal VC-, using integrator 251. Operational amplifier 220, integrator 251, feedback networks 230 and 240, and resistors R1 and R2 together form a biquad filter (biquad filter) that provides a second order low pass filtering function. Biquad filters are well known to those skilled in the art and therefore will not be described in detail here. As is well known to those skilled in the art, an integrator (e.g., integrator 251) may be implemented using an operational amplifier (e.g., operational amplifier 252) along with two feed resistors (e.g., R1 and R2) and two feedback capacitors (e.g., CP and CN), and therefore will not be described in detail herein.

fig. 3 shows a functional block diagram of a zero intermediate frequency receiver 300. The zero intermediate frequency receiver 300 includes: a first buffer 310 for receiving an input RF signal including a first terminal VI + and a second terminal VI-and outputting a first buffered signal including a first terminal VRFI + and a second terminal VRFI-; a second buffer 320 for receiving the input RF signal and outputting a second buffered signal including a first terminal VRFQ + and a second terminal VRFQ-; a first downconverter 330 for receiving the first buffered signal and outputting an in-phase baseband signal comprising a first terminal VBBI + and a second terminal VBBI-based on an in-phase LO signal comprising the first terminal VLOI + and the second terminal VLOI-; and a second downconverter 340 for receiving the second buffered signal and outputting quadrature baseband signals including a first terminal VBBQ + and a second terminal VBBQ-according to quadrature LO signals including the first terminal VLOQ + and the second terminal VLOQ-.

Both first downconverter 330 and second downconverter 340 are implemented using downconverter 200 of fig. 2. When implementing the first downconverter 330, VRFI +, VRFI-, VLOI +, and VLOI-should be substituted for VRF +, VRF-, VLO +, and VLO-, respectively, and (if additional network 250 is included) VBBI + and VBBI-for VC + and VC-, respectively, or VBBI + and VBBI-for VB + and VB-, respectively. Similarly, when implementing second downconverter 340, VRFQ +, VRFQ-, VLOQ +, and VLOQ-should replace VRF +, VRF-, VLO +, and VLO-, respectively, and (if additional network 250 is included) VBBQ + and VBBQ-should replace VC + and VC-, respectively, or VBBQ + and VBBQ-should replace VB + and VB-, respectively. VLOI +, VLOQ +, VLOI-, and VLOQ-form a four-phase periodic signal that mathematically satisfies the following equation:

V(t)＝V(t-T/4) (2)

V(t)＝V(t-T/4) (3)

V(t)＝V(t-T/4) (4)

Here, T represents a time variable, T is a fundamental period of a four-phase periodic signal, and 1/T is substantially equal to an average frequency of a desired component of an input RF signal. In one embodiment, VLOI + (t), VLOQ + (t), VLOI- (t), and VLOQ- (t) are square waves that approximate a periodic switching back and forth between a first level and a second level. When VLOI + (t) is at a first level, it is referred to as "in effect" and in other cases it is referred to as "not in effect". VLOQ + (t), VLOI- (t), and VLOQ- (t) are the same. The duty cycle of the VLOI + (t) is the percentage of time that the VLOI + (t) is "in effect". VLOQ + (t), VLOI- (t), and VLOQ- (t) are the same. In one embodiment, VLOI + (t), VLOQ + (t), VLOI- (t), and VLOQ-all have a duty cycle of approximately 25%. In another embodiment, VLOI + (t), VLOQ + (t), VLOI- (t), and VLOQ-all have a duty cycle of about 50%. In yet another embodiment, VLOI + (t), VLOQ + (t), VLOI- (t), and VLOQ-all have a duty cycle of about 33%.

Buffers 310 and 320 provide isolation between downconverters 330 and 340, but they are selected for adoption. When buffers 310 and 320 are not used, both VRFI + and VRFQ + are equal to VI +, while VRFI-and VRFQ-are equal to VI-. Buffers 310 and 320 are preferably used when VLOI + (t), VLOQ + (t), VLOI- (t), and VLOQ- (t) have a duty cycle of approximately 50% to avoid potentially harmful coupling between downconverters 330 and 340. Buffers are circuits that provide good reverse isolation and are well known to those skilled in the art and therefore will not be described in detail herein.

as shown in the flowchart of fig. 4, a method according to an embodiment of the present invention includes: (step 410) receiving an RF signal comprising a first end and a second end; (step 420) receiving an LO signal comprising a first terminal and a second terminal, wherein the first terminal and the second terminal of the LO signal together form a bi-phase periodic signal having a fundamental frequency substantially equal to an average frequency of desired components of the RF signal; (step 430) mixing the RF signal with the LO signal using a mixer to output an intermediate signal including a first terminal and a second terminal; (step 440) converting the intermediate signal into an output signal comprising a first terminal and a second terminal using an operational amplifier having a negative feedback via a first feedback network and a second feedback network; and (step 450) mixing the RF signal with the LO signal using an auxiliary mixer to create a supplemental signal that is added to the output signal as a complement, wherein: the auxiliary mixer is based on using the same circuit topology as the mixer, but replacing each switch in the mixer with a switch in series with a capacitor.

Embodiments of the present invention may also be applied to low intermediate frequency receivers in which the frequency difference between the desired components of the LO signal and the RF signal is not zero, but is substantially smaller than the fundamental frequency of the LO signal.

those skilled in the art will readily observe that numerous modifications and variations may be made in the apparatus and method while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the claims.