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UCSB ECE 145b - CMOS Mixers and Polyphase Filters

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IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 36, NO. 6, JUNE 2001 873CMOS Mixers and Polyphase Filters for LargeImage RejectionFarbod Behbahani, Member, IEEE, Yoji Kishigami, John Leete, Member, IEEE, and Asad A. Abidi, Fellow, IEEEAbstract—This paper presents an in-depth treatment of mixersand polyphase filters, and how they are used in rejecting the imagein transmitters and receivers. A powerful phasor-based analysis isused to explain all common image-reject topologies and their limi-tations, and itisshownhow this can replacecomplex trigonometricequations commonly found in the literature. Practical problems indesign and layout that limit the performance of image-reject up-conversion and downconversion mixers are identified, and solu-tions are presented or limits explained. This understanding is putto work in a low-IF CMOS wideband, low-IF downconversion cir-cuit, which repeatedly rejects the image by 60 dB over the wideband of 3.5 to 20 MHz without trimming or calibration.Index Terms—Analog complex filter, analog polyphase filter,image rejection, quadrature generation, radio receivers.I. INTRODUCTIONOBTAINING adequate image rejection with on-chip cir-cuits poses the main obstacle to full integration of a super-heterodyne wireless receiver (RX). In a zero-IF RX, the imageof one half of a channel is the other half of the same channel;thus it is sufficient to reject the image by, say, 15 dB or so rela-tive to the final required signal-to-noise ratio (SNR), and thisis easily obtained with conventional quadrature downconver-sion. However, zero-IF suffers from several drawbacks such asdc offset and flicker noise, which cannot be easily eliminatedwithout also removing valuable spectral energy around dc in thedownconverted spectrum. By contrast, a low-IF receiver down-converts the desired channel to frequencies beyond the flickernoise corner. Although the IF amplifiers and filters operate atfrequencies substantially the same as in a zero-IF receiver, theimage now consists of some other unrelated channel two timesthe IF away in frequency, which may be substantially largerthanthe desired channel. This unrelated channel might have to besuppressed by up to 60 dB.The image channel may be rejected by filtering prior to down-conversion, or by signal cancellation. However, it is difficult tobuild active filters with sufficient selectivity and dynamic rangeat the high frequencies prior to final downconversion. A prac-tical alternative is to cancel the image, by mixing quadraturephases of RF with the local oscillator (LO), or vice-versa, andfollowing this with a Hilbert filter at the IF. A Hilbert filter re-sponds to the complex representation of a signal, rather than toonly its magnitude. This is relevant here because after downcon-version, the signal and its image lie at the same frequency, butManuscript received July 5, 2000; revised January 17, 2001.The authors are with the Electrical Engineering Department, University ofCalifornia, Los Angeles, CA 90095-1594 USA.Publisher Item Identifier S 0018-9200(01)04136-1.with conjugate complex representations. The ultimate image re-jection is limited by the quadrature accuracy of the mixer inputphases, gain matching of the mixers, and the accuracy of thephase shifts within the Hilbert filter. Without tuning, the repeat-able image rejection of a simple quadrature mixer is limited toabout 40 dB.An interesting extension of the basic structure is the double-quadrature architecture [1]. It uses four mixers with both RFand LO inputs in quadrature phases. This structure is shown tobe much less sensitive to the unbalance in the phase and ampli-tude of the RF and LO inputs of the mixers. The image rejec-tion is now limited by the gain mismatch between mixers, andby inaccuracies in the IF phase shifter. It will be shown that inpractice a carefully designed polyphase filter can repeatedly re-ject the image by 60 dB, comparable to what is possible with anoff-chip IF filter.II. ANALOG POLYPHASE FILTER:EVOLUTION AND PRINCIPLEOFOPERATIONBefore discussing the details of the passive polyphase filter,it is important to understand Hilbert filters in general. A con-ventional bandpass scalar filter is synthesized from a lowpassprototype by the symmetric lowpass-to-bandpass transforma-tion,. It cannot distinguish be-tween an input frequency and its image on the negative fre-quency axis, and offers the same frequency response to both[Fig. 1(a)]. On the other hand, a Hilbert filter creates a bandpassresponse by translating a lowpass prototype with the shift trans-form,, so the frequency response is no longermirrored about zero frequency, and the desired frequency maylie in the passband, while the image frequency lies in the stop-band [Fig. 1(b)].With this in mind, a Hilbert filter may be synthesized to nullthe image while passing the desired frequency. The prototypeis the single-pole RC filter with a notch at dc. The constitutiverelation of the circuit is(1)Applying the shift transform to this equation leads towhen(2)0018–9200/01$10.00 © 2001 IEEE874 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 36, NO. 6, JUNE 2001(a)(b)Fig. 1. (a) Conventional highpass filter with notch at dc. (b) Hilbert filter,which gives asymmetric response to positive and negative frequencies, obtainedby shifting the characteristic of (a) on the frequency axis.Fig. 2. Evolution of the simple CR highpass network into the correspondingHilbert filter.If the input signals are present in differential and quadraturephases, that is, asand , then resistor orcapacitor con-nections between these signals and additional controlled sourcesrealize the filter circuit. Repeating this structure for each of thefour inputs, the circuit naturally extends to a differential quadra-ture topology (Fig. 2). At the image frequency when the filterproduces, the four controlled sources carry zero current.This means that the filter null is unaffected if these sources aredeleted from the circuit. It is easily seen that removing the con-trolled sources only raises the passband gain by. This gain isunimportant as long as it is at least unity. The circuit that remainsafter deletion of the controlled sources is the classic passive RCpolyphase filter [2].The polyphase filter is a symmetric RC network with inputsand outputs symmetrically disposed in relative phases (Fig. 3).Consider applying four inputs, all sinewaves at the same fre-quency but with arbitrary amplitudes and phases as representedby the phasors shown in Fig. 4 (vector


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