IN high performance digital-to-analog converters (DAC),

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1 A Octuple Sitching Structure ith Code Independent for Frequency Converion of High Performance D/A Converter Wang liguo, Wang zongmin, and Kong ying Abtract A ne itching tructure for decreaing ignal dependent nonlinearity and upconverting in high performance D/A converter i addreed in thi paper. The itching hich receive a digital data input ignal that i defined at data interval can removing any ubtantial data dependency from thi interaction. The logic circuit control the itch to be in one of a normal mode or multi-mixer mode that convert the input digital data ignal into a mixed analog ignal having a mixer frequency that i higher than the data frequency. Simulation reult ho that the ne itch tructure mot extend the uable frequency pectrum into fifth to ixth Nyquit zone beyond conventional DAC. Index Term Differential octuple ithing, direct digital modulation, data independent I. INTODUCTION IN high performance digital-to-analog converter (DAC), noie become an ever more limiting conideration a dynamic range increae and/or a minimum detectable ignal decreae. One particular ource of noie in a mixed digital and analog ignal application i effect on critical analog ignal path of the variou digital circuit. One commonly ued uch critical analog ignal path i the itch or teering of analog reference ignal by control element, hich are themelve activated by digital control ignal. In a phyically realizable ytem, it i impoible to completely iolate thee digital control ignal from analog ignal hich they are controlling becaue of coupling through the analog ignal control element [1], and alo becaue digital circuit conume time-varying poer and caue time-varying loading [], I drop [3], and charge injection, hich in turn caue interaction ith the overall ignal proceing circuit. Thee effect caue change in reference ignal, upply voltage, bia level, clock phae, tranition phae, and ubtrate effect that in turn corrupt the deired analog ignal being proceed. Becaue of inevitable paraitic and non-ideal circuit, thi can caue data dependant loading and puriou coupled ignal modulation []. In thi manner the digital ignal add noie and/or ditortion to the analog ignal. In direct digital modulation ytem, the ignal i upconverted in digital domain, and the modulated digital i converted into a modulated analog form. In thee ytem, a digital-to-analog converter (DAC) hoe converion rate i more than the Nyquit rate of the carrier frequency. A Manucript received June 3, 011; revied July 7, 011. Thi ork a upported by Beijing Microelectronic Tech-Intitution(BMTI). Wang liguo i the potgraduate of Beijing Microelectronic Tech- Intitution, No.. Siyingmen N.d Donggaodi Fengtai Ditrict,Beijing ,China ruixin01@16.com. Wang zongmin and Kong ying are ith Beijing Microelectronic Tech- Intitution(BMTI). Fig. 1. The tructure of octuple itching ide variety of different electronic device ue a ytem that both convert internal digital ignal to analog ignal, and hift the frequency of the reultant analog ignal. For example, conventional cell phone often have a digital to analog chip converter chip that convert a digitally proceed voice ignal into an analog baeband ignal for tranmiion. Before tranmiion, hoever, a mixer chip hift the frequency of the baeband ignal to a frequency that facilitate tranmiion. An effective itching tructure, called differential-octuple itching (DOS) i propoed for the overampling DAC to meet the requirement for direct digital modulation and data independent. Fig.1 i the circuit baed on DOS. Section II give the tructure of octuple itching. Section III dicue the theory of itching. Section IV decribe the control circuit of itching. Section V contain ome concluion plu ome idea for code independent of glitch. Section VI preent the primary experimental reult of the paper and the ection VII i the concluion. II. DIFFEENTIAL OCTUPLE SWITCH Practically, it i not poible to deign a perfect itch ued a a 1-bit DAC. Ordinary differential itching i capable of eliminating many nonlinearitie caued by imperfect itching but till ha ome data-dependent nonlinearitie [5]. Due to the mixed-ignal nature of a DAC, digital data activity on the itch gate ill caue interference in the analog output. Thi become an important performance iue a the tatic and dynamic performance. A pecial cae of data pattern dependent interference come from the varying gate een by the final control ignal hich control the itch to be on or not. The no popular to tranitor itch topology. True and complement of the data are provided to the to input

2 Fig. 3. The time domain ave of itching function (a)zero-order hold pule. (b)z hold pule. (c)pl hold pule. (d)p3l hold pule. (e)pl hold pule Fig.. General ave of DAC output eparately and the DAC output change only hen either of them change. A a multi-bit DAC, the itch changed tate ill produce glitch through the capacitor beteen gate and drain but thoe not changed ill not impact on output, the output glitch depend on data patten. If, hoever, the itch act every clock edge or half a clock cycle or a quarter clock cycle, the frequency of thi noie ill not be in the band of ignal but have a certain relationhip ith the converion clock frequency. The noie frequency either i a ame a the carrier band frequency or tice or four time a high a the carrier band frequency. Thi itching i DOC. Fig.1 i the implified circuit baed on DOC. Each itch i controlled by one ignal that i come from the logic operation of input data and clock, the itch apparatu ha a current ource that tranmit a current to either one of to differential output node Ip and In via one of the eight itche G1-G. To the end, no more than one of eight itche G1-G can be in an on tate at any ingle time. For each quarter DAC clock cycle, one of the eight tranitor change their tate hile the other remain off. The data input to the egment determine hether the current for thi egment i re-routed by thi itching, thereby changing the differential output current level, or only routed through a different tranitor for an unchanged output. III. SWITCHING THEOY According to the ample theorem, a long a e ample fat enough, digital ignal x(n) contain all information of analog ignal x(t). If e hope to recontruct x(t) from x(n) perfectly, e can let g(t) in(π f t), x(t) π f t n x(n) g(t nt S ) But it i very hard to build an analog circuit that doe thi. The mot practical ay of recontructing the continuou time ignal i to imply hold the dicrete time value that i continued either for full period T or a fraction Tp. It i illutrated in Fig.. The proce of hold can be realized through an analog circuit that e can call it itch hoe function i the recontructing. Conider the general cae ith a rectangular pule 0 < T p < T, let the rectangular unit pule i h(t)u(t)- u(t-tp), the time domain ignal follo from convolving the Dirac equence ith it. Becaue of x(t) x(n) h(t nt S ) Xp(f) T p T n Hp(f) T p in(π f T p) e jπ f Tp π f T p in(π f T p ) e jπ f Tp π f T p n X(f n T ) A to a dicrete ignal x(n), the pectrum Xd(f) i Periodically pread of pectrum X(f) hich i Fourier tranform of x(t). So, hen e recontruct the x(t) from x(n), in frequency domain the recontruction function Hp(f) hich e elect filter the Xd(f). A follo, e ill deign the recontructed function hich i realized by DOC and fulfill the recontruction and upconverion of DAC. A. Zero-Order Hold Pule In the normal DAC mode, the recontruction function of itch i zero-order hold pule in Fig.3.(a) We let { 1 0 < t < T P ZH (t) (t) 0 t < 0 or t > T P ZH (t) Laplae tranform L{ (t) u(t) u(t T ) (t)} L{u(t) u(t T )} 1 1 e T Fourier tranform F { F { (t)} 1 e T e j T e j T (t)} T j T j e j T 1 e T P ZH ()

3 Fig.. The ave of itching function in frequency domain (a)zero-order hold pule. (b)z hold pule. (c)pl hold pule. (d)p3l hold pule. (e)pl hold pule in( T P ZH () T ) T e j T T Sa( T T )e j From the figure, e can get hen n r (n z, n 0), the ample function have zero point and the envelope of function drop at the peed of -0dB/Decade or -6dB/Octant. In Fig..(a), number 1 to i the Nyquit zone, the Nyquit frequency i / and the pectrum i the mot trong at 1 Nyquit zone at hich the normal DAC ork and i the baeband zone. the amplitude of other zone pectrum i force to get more decreaed. B. eturn to Zero Pule We can call the return to zero pule double phae ingle polar level(z) in Fig.3.(b) { 1 0 < t < T P ZH (t) (t) 0 t < 0 or t > T P ZH (t) F { (0, T ) (0, T ) (0, T ) (t) u(t) u(t T ) (t)} 1 T e j P ZH () T in( T ) T e j T T Sa( T T )e j From the pectrum of the return to zero in Fig..(b), e can ee that the idth of it increae to double time more than the pectrum of zero-order hold PZ() meanhile the amplitude decreae to one half. So the pectrum amplitude of firt Nyquit zone i retrained but the econd and third zone i trenged relative to the PZH(). C. Biphae Bipolar Level Pule(pL) 1 0 < t < T T P pl (t) (t) (t) 1 < t < T 0 other (0, T ) ( T,T ) P pl (t) u(t) u(t T ) + u(t T ) the ave of time domain i Fig.3.(c), Fourier tranform F {P pl (t)} P pl () T 1 e +e T T 1 e j +e jt j T in ( T ) T e j π j T j P pl () T (1 e j ) j F { (t)} T e j T e j T j T (0, T ) e j T P ZH () T Sa(π )in(π )e j π j T P pl () T in (θ)

4 d(in (θ)) here, let θ π, θ θ0 e can get hen θ θ0 π , PpL (0 ) 0.76T So the pectrum in Fig..(c) abolutely retrain the DC ignal and retrain the firt Nyquit zone pectrum in a large degree, but treng the econd and third Nyquit zone pectrum epecially the econd Nyquit zone pectrum i trenged moothly. To DAC, the realization can be called upconverion. D. Quadphae Triple Level Pule(p3L) The ave of time domain i Fig.3.(d) Q1 Q1 Pp3L (t) (0, T ) (t) (0, T ) (t u(t) u(t F {Pp3L (t)} 1 e (e T T T ) e e T T ) u(t T ) T T +e 3 )(e T e u(t 3 T ) j T ) 3 T e Fig. 5. The control circuit of the itching input ignal Fig. 6. The control circuit of the itching input ignal j Pp3L () T Pp3L () T π T in( ) in( T )ej 3j T T jπ 3j Sa(π )in(π )e T The pectrum of Quad-phae triple level pule in Fig..(d) treng the econd and third Nyquit zone amplitude moothly more than Biphae Bipolar level pule. So it can realize the function of upconverion better. E. Quad-Phae Bipolar Level Pule(pL) The ave of time domain i Fig.3.(e) u(t) u(t PpL (t) T ) T ) + u(t IV. T HE CONTOL CICUIT OF SWITCHING u(t 3 T ) + u(t T ) Fourier tranform F {PpL (t)} 1+e T e T e 3 T +e T (e T e T ) (e T +e T j ) T 3 e j PpL () PpL () T T T in( ) π in( T )co( T )ej j π T T Sa(π )in(π )co(π )ej j T the pectrum of Quad-phae Biphae level i Fig..(e) and trength the fourth and fifth Nyquit zone amplitude pectrum. So it can realize the function of upconverion higher. The control circuit of itching decide hich itch i on tale. Becaue no more than one of eight itche can be on tate at any ingle time, for example, if itch G1 i on, and G-G i off. In that cae, the current flo to output Ip and the current on output node In i zero. The differential output ignal (Ip-In) therefore i +1, hen itch G i on and other are off. The current therefore flo to the output node In, hich produce a differential output ignal of -1. From ection III, in thi paper, e ill introduce five orked mode of DAC. That are eparately zero-order hold mode(normal), return to zero mode(z), Biphae Bipolar level mode(pl), Quad-phae triple level mode(p3l), Quad-phae Bipolar level mode(pl). D i the input data, C i clock and the C 90 i the reult that the clock hift 90 degree. A to the five mode of zero-order normal, pl, pl, Z and p3l. V1-V are the reult of operation of C, C 90 and D, the arithmetic operator i NAND, ee the Fig.5. The TABLE.I enumerate all the tatu of the control ignal

5 TABLE I THE ESULT OF FIVE DAC MODES D C C V V V V V V V V Normal output pl output pl output p3l output Z output and the output reult of five mode. Becaue the operation mode e deign i programmable, e elect a 3 to encode to produce five control ignal hich control eparately five DAC mode. The output D1 repreent Normal mode. D repreent the pl mode that e only need to let V5 to G6, V6 to G5, V7 to G, V to G7. D3 repreent pl mode that e only need to let V3 to G, V to G3, V7 to G, V to G7. D repreent p3l mode that e only need to link V3 and V, V7 and V, let V5 to G6, V6 to G5. D5 repreent return to zero mode that e only need to link V5 and V6, V7 and V. See the Fig.6. V. CODE INDEPENDENT OF GLITCH While the data do not change in to ucceive clock cycle, the operation ill produce the variational data on the itch, but do not bring the change on the output. While the data change in to ucceive clock cycle, the itch that change accord ith data ill bring the change on the output. From thi no matter hether the input data change, the output ignal complemental change all the ay and do not have any relation ith the input data. So the glitch hich i correlated to the input data i tranformed the glitch at a fixed frequency that i four time of the clock, far from the baeband and be filter. With thi cheme, the diturbance to the circuit of thi egment (mot particularly to the ource node of the itche) or adjacent circuit are data-independent, ince one tranitor turn on and other turn off each quarter clock cycle. Thi prevent data dependent pumping of any node. VI. EXPEIMENTAL ESULT The Matlab imulation reult of DOC i illutrated in Fig.7. The input ignal i the digital inuoidal f(n) in(π 10 5 n) + hoe frequency i 100Khz and the reolution i 10 bit. A 0 point FFT i calculated baed on the output ignal. In Fig.7, the normal mode, (a) i ave of the time domain and e can ee that the firt Nyquit zone pectrum i trenged from frequency pectrum (b). In the Fig.7, the Biphae Bipolar level mode(pl), (c) i ave of the time domain and e can ee that the pectrum (d) i retrained the firt Nyquit zone pectrum in a large degree, but trengthed the econd and third Nyquit zone pectrum, o the pectrum i modulated the econd and third Nyquit zone. In Fig.7, Quad-phae Bipolar level mode (pl), (e) i ave of the time domain and e can ee that the pectrum (f) mainly treng the fourth and fifth Nyquit zone thu can realize the more high upconverion. In Fig.7, return to zero mode, (g) i ave of the time domain and e can ee that the econd and third Nyquit zone pectrum i trenged from frequency pectrum (h) meanhile the firt Nyquit zone pectrum i decreae one half, o the pectrum i modulated the econd and third Nyquit zone. In the Fig.7, Quad-phae triple level mode, (i) i ave of the time domain and e can get the econd and third Nyquit zone pectrum (j) hich i compared ith the pl mode i more trenged, o it can be realization of upconverion. VII. CONCLUSION A novel itching tructure called differential octuple itch able to overcome the output nonlinearitie depend on input data and realized to upconverion i propoed. Through the deigned control circuit, it can make the DAC orked at five mode hoe function are modulator and e can elect anyone to achieve the upconverion of the output ignal. EFEENCES [1] A. V. den Boch, M. A. F. Borreman, M. S. J. Steyaert, and W. Sanen, A 10-bit 1-GSample/ Nyquit Current-Steering CMOS D/A Converter, IEEE J. Solid-State Circuit, vol. 36, no. 3, pp , 001. [] G. A. M. V. der Pla, J. Vandenbuche, W. Sanen, M. S. J. Steyaert, and G. G. E. Gielen, A 1-bit Intrinic Accuracy Q andom Walk CMOS DAC, IEEE J. Solid-State Circuit, vol. 3, no. 1, pp , [3] C.-H. Lin, F. M. der Goe, J.. Wetra, J. Mulder, Y. Lin, E. Arlan, E. Ayranci, X. dong Liu, and K. Bult, A 1 bit.9gs/ DAC With IM3-60dBc Beyond 1 GHz in 65nm CMOS, IEEE J. Solid-State Circuit, vol., no. 1, pp , 009. [] D. A. Mercer, LOW POWE APPOACHES TO HIGH SPEED CMOS CUENT STEEING DACS, IEEE Cutom Intergrated Circuit Conference., pp , 006. [5] B. Schafferer and. Adam, LOW POWE APPOACHES TO HIGH SPEED CMOS CUENT STEEING DACS, Proc. Int. Solid-State Circuit Conf., 00.

6 Fig. 7. The time and frequency domain ave of five mode (a)the time domain output of Normal mode. (b)the Fourier thanform reult of Normal mode. (c)the time domain output of pl mode. (d)the Fourier thanform reult of pl mode. (e)the time domain output of pl mode. (f)the Fourier thanform reult of pl mode. (g)the time domain output of Z mode. (h)the Fourier thanform reult of Z mode. (i)the time domain output of p3l mode. (j)the Fourier thanform reult of p3l mode