Study of Parasitic Capacitance Effect on Low Pass CMOS Active Filters Xu Donglin and Ren Junvan ASIC & System State Key Lab, Microelectronics Department, Fudan University, Shanghai, 200433 dl.xii:Ciccc or"
Abstract - This paper clarifies a classic first-order low With the incorrect negligence to input parasitic pass filter could not be considered as the classical one capacitors, it is proved a classical first-order low pass when we take into account the input parasitic filter transfers to a virtual full pass filter (we'll explain capacitance of the CMOS amplifier, which contributes a the name later). Futher discussion clarifies frequency zero into the transfcr function of the low pass filter. response of the open loop operational amplifiers merely Based on that analysis, interestingly a socalled virtual hut uifortunately limits that of the full pass filter. full pass filter is designed using the same structure, This finding is also applied to analysis of high-order Ivhich frequency response is however limited by the low pass filters in section III to examine the influence. open loop transfer function ofthe amplifier. It highlights Then section IV gives a brief sumnialy. the importance of taking into account the parasitics in hieh li-eqitency cii-cui1 design. Analysis ol' parasitic U. Modeling of Classical first-order Low Pass Filter capacitance of high-order low pass filters also proves it mav decrease the order of the filters.'
I Introduction With the growth of wireless conmunication market, CMOS integrated circuits desigm has come into a GHz era. Great interests are devoted to parasitics, device and channel modeling, which previously, in tam of accuracy, pia!, a negligihle role in the relatively lo& speed circuits. Fig. I. Classical first-order low pass filter with input Input capacitance of CMOS operational amplifiers is capacitancc niodcl of thc CMOS anipliticr among the parasitics we neglected in the design of active .4. Transfer jaictioti of classical Jrsr-order low pass analog filteis [I].With the frequency incizase, this small Jlter- capacitance ive believed now give such a great effect to The simplest active filter employing the non-invetting the transfer function of filters that we have to change feedback amplifier is shown in Fig. 1. The amplifier is some classical concepts. assumed to have vel? high open-loop gain A, the circuit The transfer function of a classical first-order low pass gain being contiolled by resisters R, and RI filter is derived in section I1 with the modeling of the [K=lt(R,/R,)]. Filtering action is performed by the input capacitance, to demonstrate that change and show RI-CI frequency selective network, which is cascaded the accm-acy compared to SPICE simulation results. with the amplifier. The analysis above usually neglects the input capacitance ol' the CMOS amplifier when che This work is supported by Shanghai AM R&D Fund, 2001 . frequency conceined is not vely high or the capacitor C, Projrct Codc: 0102.
0-7803-7889-X/03/$17.00@2003 IEEE. 992
Authorized licensed use limited to: MIT Libraries. Downloaded on July 2, 2009 at 12:43 from IEEE Xplore. Restrictions apply. is much la]-ger thnn that of the input parasitic in order of magnitude. In this paper, we analyze the transfer function of this classical first-order low pass filter with the additional influence of the input capacitance of C,", and Cm2.The From now on, the classical low pass filter meeting detail expression for C,, is discussed in [2],but here we equation (9) is intendedly named full pass filter to analyze the effect hvjust adding those to our circuit. And distinguish itself from others. It means the classical from this analysis, we could still see how and when this firs-order low pass filter is no longer a circuit whose effect changes the classical transfer function. name stands for, when input capacitance of the CMOS Nodal analvsis at nodes (a) and @)yields: amplifier comes close to equation (9). If we design a low v -J/ pass filter satisfving equation (9), the transfer function + y>. SC, + 1.: . SC,", = 0 (1) R, becomes into a full pass fonii:
and , which leaves far away fiam OUT design objective. li, r,; =..~(i:-vJ, r3:-vb=---to (3) A C. Firqueiicy msponse Iin~irarion for A large. Using a form of classical first-order low pass filter Therefore r': -5.1.; and combining equations (1) and and the condition descrihed hy equation (9), we could (2) gixs gel an ou(pul signal amplfied by a laclor of K and without any phase shift with respect to thd input signal in (4) a veT wide frequency hand, as shown in Fig.2. It's As espccted; ii'C,,,, and equal to 0, equation (4) pi-ominent that the perlbimance of original low pars coiiies hack to the ti-anzfer function of classical filters shift far aii'ay from expected. The circuit first-older lo\v pass filtei-. But taking into account the parameters are listed in table I. . effect of CjB2produces a left-half-plane zero: Jndeed: this full pass filter cannot really be obtained, for some other parasitics neglected in analysis ahove. Though much smaller than even the input paiasitic capacitance of the aniplifier, an equivalent output E. Design considei.atiom/ior/ii/l pass Jlrer capacitance limits the frequency response of the Using equation (5) and transfer function of classical so-called full pass filter. The output parasitic capacitance fil-st-oi-derIOW pass filter, equation (4) becomes: attenuates the gain A of the amplifier when the frequency increases. It makes the equation (3) obsolete, then the equation (4) and so on. where, Further derivation proves the transfer function of the h- =I +R,/R, full pass filter is:
Assume that PI is cancelled by Z,, transfer function (6) consequentlv ha.; 110 relation with the frequency. And where CO,R, e-e the equivalent output capacitance and so \ve call it a full pass filter. Then it should he met: iesistance of the ampliiiei- respectively. To make
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Authorized licensed use limited to: MIT Libraries. Downloaded on July 2, 2009 at 12:43 from IEEE Xplore. Restrictions apply. conclusion tractable, we have assumed the maintain a full pass filter from that on. ti;msconductance G,. of the amplifier equals to l/RI, On the other hand, Fig.? proves that considering input otherwise poles in equation (11) may change a bit but capacitance gives more accurate expression than that of too complicated to he listed here. the well-accepted analysis to a classical low pass filtet-, Equation (11) returns to classical first-order low pass especially when the circuit satisfy the equation (9), (13). filter only when it meets: The triangle curves in Fig.? are obtained with classical first-order low pass filter analysis without consideration of input capacitance. The real frequency response is The dominant pole locates at P, = -l/[(C, +Cm,)k,] shown by cross cun~es,to which the dash curve derived In the ctse of designing a full pass filter, it should be from our analysis fits vey well. satistied with: More accmate transfer function of full pass filter could he obtained by taking into consideration the other parasitic capacitance like ones connecting the input and , where tirquency response is limited by pole: the output of the amplifier. But for the interest of this paper, it's enough to highlight the effect of the parasitics (14) capacitance when doing filter design. If the gain K is large, pole of the full pass filter approximates that of open loop amplifier. In another Itl. High-order Low Pass Filter Extension words: frequency response of the open loop amplifier limits lhat or the rid1 p liller. Thus, so called I'ull pass filter is indeed a virtual full pass filter.
TABLE I
8 I 11 2 O.5P > 80dB 1 OOM 1, pig. 3. Classical Secood-order lo\\, pass filter with input ...... * capacitance iiiodel of the CMOS oniplifier I .. , .. f . With classical analysis, the second-order low pass 'z , ,.%. ;-:: : filter in Fig.3 gives the transfer function: ! -: *I;*. : 1 ..- !LK. C,C,R,II 11 1K' 1 -, Y S'+5 ..-+-+--- +- C,R CL% CA] C,CIR,% ... ',, ".Ti..l (15) -L,.... . -~. .- -.--..-.i,--~.-J - , where - ~ . .. ..-&E-2 2 Fig. 2. Frequency response ofthc analyzed hill pass tiller K'=I+R,/R, (16) Fig.2 sho\vs the tuning point where the phase of input We note the input parasitic capacitance merely signal and that of output signal shift away, which means changes RJinto a complex form: thc gain ol' ~huamplifier is no longer large enough to
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R, +- R, (17) I + ,SR,C,- Using (I 7); transfer function ( 15) hecomes:
__1.'. i; 1.: I
(18) It shows parasitic capacitance also produces a zero which may cancel a pole in the transfer function using the siillllar desip method discussed in section 11. This results in a first-order low pass filter though the appetti-ance is a classical second-order low pass filter The same derivation can be applied to higher-order Imv pass fillers, which gives the same finding that parasitic capacitance may decrease the order of the low pass filters in celtniii condition.
Iv. Summary Considering Ihc input pmsilic capacilance ol' CMOS amplifier in classical low pass filters gives much more accurate expression than the classical method. To prove this. a full pass filter is designed baxd on analysis this paper derives and the simulation result fits the expected vel? well. And the high-order low pass filters prove the l'inding. too. Thnt difference from the lo\\, pass transfei- function sliwvs [he classical concept on low pass filters is \vorthy ol' considzring in thc high frequency hand. Non-conditional appliance of' the classical anelysis will
result iii eii-ors.
References [I] A. Waters, .4ctive Fiilrer Design, Macmillan Education Ltd. I991 [21 P. J. V Vmdeloo, W. M. C. Sansen, "Modeling of the MOS Transistor for High Frequency Analog Design,"
IEEE Tvaiisnctioiis 011 Corriyiitei~-AidedDesigil, Vol. 8, No. 7; pp. 71372.3, 1989.
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