J.Semicond.2013,34(9) Wang Xin et al. DCOC DCOC DCOC G=0-54dB G=0-18dB G=0-18dB G=0-18dB Q=0.61 0=1.45 0=5.04 。=0.2-4MHz Biquad 1 Biquad 2 Biquad 3 Fig.1.The filter structure including DCOC R 1+2 Hs)=H。 w C 品 1+-5 vinp von -vop o-RRCC: R w-RRCC. R S3 S2 000000- R R Fig.2.The Tow-Thomas bi-quad structure and O factor.Figure I shows the structure of the filter,includ- the main cause of distortion in the bi-quad is the nonlinearity ing the DC offset cancellation(DCOC)loop at each stage.A of OTAs.As will be shown below,the IIP3 and DC gain of the six order filter is realized by cascading three bi-quads together. OTA determines the IIP3 of the bi-quad.The feedback path Each stage has an 18 dB gain range and the cutoff frequency could also have an impact on the linearity performance.The is tunable.So the filter has a 54 dB gain range in total.Fig- Volterra series is usually used to analyze the linearity perfor- ure 2 shows a detailed schematic of a single bi-quad.All the mance ofa memory system,but it is cumbersome to simplify resistor arrays and capacitor arrays are tunable.A classic net- multiple feedback paths using SFG.In Refs.[7,8],another use- work analysis of the bi-quad reveals the gain,cutoff frequency ful analysis method was introduced and exemplified,but the and O factor,which could change by adjusting Re,Ra and Rd, discussions were mainly restricted to the scaling technique, respectively.To maximize the in-band linearity performance, which needs to scale all the elements using different scaling high-O poles are assigned to the nearby zeros instead of re- factors at the same time.In this paper,employing a similar ap- mote zeros.Figure 3 shows the pole-zero pairing scheme.This proach,a procedure which is used in this design to maximize kind of pole-zero pairing could minimize the amplitude peak the IIIP3 of the bi-quad by normalizing all the passive element of high-O poles near the cutoff frequency.The bi-quads are parameters to a reference resistance and capacitance when the ordered as the O-factor gradually increases to maximize the IIP3 and DC gain of the OTA are fixed is developed. in-band IIP3. Because of balance structure use,the second-order dis- tortion of the bi-quad could be ignored.As shown in Fig.4, 2.2.IIP3 optimization two different kinds of transfer functions,which have been ex- Since passive resistors and capacitors can be very linear, plained in Ref.[8],are used.Hoi is the transfer function from 095007-2J. Semicond. 2013, 34(9) Wang Xin et al. Fig. 1. The filter structure including DCOC. Fig. 2. The Tow-Thomas bi-quad structure. and Q factor. Figure 1 shows the structure of the filter, includ￾ing the DC offset cancellation (DCOC) loop at each stage. A six order filter is realized by cascading three bi-quads together. Each stage has an 18 dB gain range and the cutoff frequency is tunable. So the filter has a 54 dB gain range in total. Fig￾ure 2 shows a detailed schematic of a single bi-quad. All the resistor arrays and capacitor arrays are tunable. A classic net￾work analysis of the bi-quad reveals the gain, cutoff frequency and Q factor, which could change by adjusting Rc, Ra and Rd, respectively. To maximize the in-band linearity performance, high-Q poles are assigned to the nearby zeros instead of re￾mote zeros. Figure 3 shows the pole-zero pairing scheme. This kind of pole-zero pairing could minimize the amplitude peak of high-Q poles near the cutoff frequency. The bi-quads are ordered as the Q-factor gradually increases to maximize the in-band IIP3. 2.2. IIP3 optimization Since passive resistors and capacitors can be very linear, the main cause of distortion in the bi-quad is the nonlinearity of OTAs. As will be shown below, the IIP3 and DC gain of the OTA determines the IIP3 of the bi-quad. The feedback path could also have an impact on the linearity performance. The Volterra series is usually used to analyze the linearity perfor￾mance of a memory systemŒ6, but it is cumbersome to simplify multiple feedback paths using SFG. In Refs. [7, 8], another use￾ful analysis method was introduced and exemplified, but the discussions were mainly restricted to the scaling technique, which needs to scale all the elements using different scaling factors at the same time. In this paper, employing a similar ap￾proach, a procedure which is used in this design to maximize the IIIP3 of the bi-quad by normalizing all the passive element parameters to a reference resistance and capacitance when the IIP3 and DC gain of the OTA are fixed is developed. Because of balance structure use, the second-order dis￾tortion of the bi-quad could be ignored. As shown in Fig. 4, two different kinds of transfer functions, which have been ex￾plained in Ref. [8], are used. H0j is the transfer function from 095007-2