A method is presented to determine and evaluate the actual tap weight errors in CCD split-electrode transversal filters. It is concluded that the correlated part in the tap weight errors dominates the random errors

Ricco, Bruno

Wallinga, Hans

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Analysis of tap weight errors in CCD transversal filters

University of Twente Research Information

89ANALYSIS OF TAP WEIGHT ERRORS IN CCD TRANSVERSAL FILTERS.Bruno Ricco, Hans Wallinga,AbstractA method is presented to determine and evaluatethe actual tap weight errors in CCD split-electrodetransversal filters. It is concluded that thecorrelated part in the tap weight errors dominatesthe random errors.IntroductionThe effect of device processing random variationson tap weight errors in CTD split-electrodetransversal filters has already been treated inthe available literature [l 3] . The scope of theabove studies is limited to the influence ofrandom tap weight errors on the frequency response.In practice however also physical causes oferrors should be considered. For instance thecharge distribution of a signal charge packetbetween the two parts of a splitted senseelectrode depends on the charge packet magnitudeand on the clock mode and clock waveform. Alsothe external circuitry may affect the overallfrequency response. In the first part of thiscontribution we have investigated whether theseeffects can be reduced to "equivalent" tap weighterrors.Another problem arises when tap weight errors arecorrelated. In practical devices several causesfor correlated tap weight errors can be imagined.Amongst these are:incorrect biasing of the external circuitrymask misalignmentfluctuations in device processing parametersand material parameters (such as under etching,oxide thickness and substrate doping) with adirectional gradient or with aspatial periodicity that exceeds the distancebetween subsequent sensing gates.The second part of this contribution deals withcorrelation tests on experimentally determinedtap weight errors.The interest of the present investigation is firstto check the validity of the theoretical resultsof the studies mentioned above. It adds asignificant, although not yet conclusivecontribution towards the understanding of theseveral phenomena that dominate the transferfunction deterioration in practice.Equivalent tap weight errorsThe transfer function modulus of four samples ofa 16-elements CCD quadrature filter as describedin [4] have been measured. (In order to increasethe .statistical significance this analysis is nowextended to other filters.)B. Riccô is with University of Bologna, Departmentof Electronics, Viale Risorgimento 2, Bologna,Italy.H. Wallinga is with Twente University ofTechnology, Department of Electrical Engineering,P.O.Box 217, Enschede, The Netherlands.The tested devices are from the same slice, sothey had the same mask alignment andtechnological processing. The quadrature filterhas two outputs: a Delay Transform (D.T.) and aHubert Transform (H.T.) output. N(=16) selectedpoints, equally spaced within the frequencyinterval 0 <_ f/f < 1, of the measured transferfunction of each filter output, are used tocompute the Inverse Fourier Transform by means ofa Fast Fourier Transform routine. Here f denotesthe signal frequency and f the clock frequency.This procedure yields a sequence of "equivalent"tap weights h, . In order to check whether thistap weight sequence provides the measured transferfunction, the tap weights are substituted in thewell known expressionH(f) - £ h exp ( - 2 TT jkf/f )k=0 C(1)This results in a "fitted" transfer function. Thedifference between fitted and measured transferfunction is between 0.1% and 1%, so the measuredtransfer function can be considered to be aresult of a purely transversal filter withequivalent tap weights h, .Now equivalent tap weights errors are defined asOh, \'K (2)where h' are the designed tap weights. In the nextparagraph, the analysis of the tap weight errorsis explained.The advantage of the quadrature filter forobtaining the equivalent tap weights is worthmentioning. The designed tap weights of the D.T.,h' have an even symmetry with respect to themiddle of the filter, and the H.T. tap weightshtf have an odd symmetry. They are related withexpressiontn^h¿,DT = (-'> h¿,HT (3)The D.T. and H.T. use the same split-electrodes,so they will suffer from the same equivalenttap weight errors. The actual transfer functionof a filter function with an even, resp. oddtap weight symmetry may be expressed asH (f) = exp (-j (N-l) TT f/f )* (G (f) + OG (f) + j OG (f))* e e o'(4)andH (f) = j exp ( -j (N-l) Ti f/f )o cx (Go(f) + 5Go(f) j 6Ge(f) )(5)90Here G (f) and G (f) are both real, but resp.even and odd functions, representing the amplitudeof the designed transfer functions. <5G (f) andresent the transfer function amplitudesOG (f) repdue to theô h , thatthat everyas a sum oand7. Noticetap weight error sequences 6 h,have even resp. odd symmetry,tap weight sequence can be consideredf sequences with odd and even symmetry,oh, S h1e k <5 h.o k (6)As a second approach, a sort correlation functionN-lC(M) 1 yN "W k=0 6hfOh:k+M (8)has been calculated, where the oh denote thedifference between oh. and the mean valuekN-lN A oh,k=0Since the oh 's are expected to be small, &G (f)in (4) and 6G (f) in (5) can be neglected. Inconsequence the 6 h, and 5 h can be determinedfrom transfer function modulus measurements ofresp. the H.T. and D.T. In this way, with (6),oh can be obtained without the need for veryaccurate phase measurements.The measurements and analysis described abovehave been performed for different clock modesand different slopes of the trailing edge of thetransfer clock. Fig. 1 shows examples ofmeasured and fitted transfer functions. Some dataabout the resulting equivalent tap weight errorshave been presented in table 1, whereThe 6hv have been repeated modulo N-l (i.e.oh* = foi* oh* = oh* etc.).0 N+lr.m.s. - a* Lr1 k=0 (6V (7)represents the average magnitude of the calculatederrors.DiscussionIf the theories for random variable tap weightsin [l] and [2] are applied to the equivalenttap weight errors, they predict a pass-band ripple,significantly greater than the measured one. (Thetheory in [2] predicts for a tolerance T in theorder of 1%, as we have found, a ripple 6%,against a measured value of 1%.) Thisdisagreement might indicate that the hypothesisof random variable oh, fails,kTo investigate this, two different approaches havebeen pursued. First it has been checked whetheror not the oh, belong to some statisticaldistribution, using standard x methods [5].Several distributions have been tried, amongstwhich the Gaussian distribution (used in [2]),a rectangular distribution, a triangulardistribution and some distribution types in betweenthe latter two. The distribution centers have beenmade to coincide with the origin as well as withthe mean oh value. The width W spanned the wholeerror amplitude range. The output of the x testsis the probability that the oh, Ts belong to any ofsuch statistical distributions. The result wastypically 0.2 and never higher than 0.4, whereasa positive result usually requires a probabilityvalue higher than 0.8. The negative result of theX tests fortifies the expectation that the tapweight errors are somehow correlated.For an ergodic process C(M) would becomenegligible at a distance M, indicating thecorrelation interval, and for a purely randomvariable sequence, only C(0) would significantlydiffer from 0. Due to the limited length of thefilter (N=16) the process we deal with is notergodic, and this makes the interpretation ofthe C(M) uncertain. It is however reasonable toassume also here that a finite value of C(M) forM^0 will indicate some correlation. In figure 2an example of a calculated correlation functionC(M) is represented, showing its typical behaviourfor three different clock waveforms. The dependenceof C(M) on the clock waveform is not surprising inview of the dependence of the measured transferfunction on the clock waveform (fig. 1). Itindicates that physical phenomena associated withthe charge transport towards the sensing gatesinfluence the tap weight errors significantlymore than spatially determined factors do.ConclusionsThe quadrature filter turned out to be a verysuitable diagnostic tool for analysing CCDtransversal filter tap weight errors,because onlytransfer function amplitudes have to be measured,and the difficult phase measurements can beavoided. The measured transfer functions H(f) ofthe D.T. and H.T. output of the quadrature filterscan satisfactorily be described by the usualexpression (1), if the equivalent tap weights= h' + oh, are substituted.\Even though no conclusive argument has beenreached, there are convincing indications that thetap weight errors show a strong correlation overthe whole filter, and that it is not allowed totreat those as purely random variables. In generalthe equivalent errors will have a random part aswell as a correlated part. Our results indicatethat the latter component dominates over the randompart, but that it has less effect on the frequencyresponse of the device. This is of interest for thetheoretical evaluation of the filter performance.The theories assuming random tap weight errorspredict for the tap weight error of magnitude thatwe have found (0.2 . 0.3% on average with maximumvalues up to l%),a significantly higher ripple(- 1 dB) in the transfer function than we havemeasured (=0.3 dB). Analysis of the strongcorrelation should help in investigating thephysical causes of the filter performancedegradation.91In order to increase the statistical significanceof the results, more measurement data are providedfor, and the presented method will also be appliedto other transversal filters.References(1). R.D. Baertsch et al.: "The design andoperation of practical charge-transfertransversal filters"; IEEE Journal of SolidState Circuits, SC 11, pp. 65-74, Febr. 1976.(2). 0. Andrisano, L. Calandrino: "Tap weighttolerance effects in CCD transversalfiltering"; Alta Frequenza, XLV, issue no. 12,1976.(3). 0. Andrisano, L. Calandrino, B. Riccö: "Onthe performance of CCD channel filters fortelephone systems"; Alta Frequenza, XLVI,pp. 374-379, Sept. 1977.(4). C. Morandi, H. Wallinga: "A quadruply sensedCCD transversal filter for quadraturephasing"; Proceedings of the 3 InternationalConference on the Applications of Charge-Coupled Devices, Edinburgh, pp. 292-301,Sept. 1976.(5). A. Papoulis: "Probability, random variablesand stochastic processes"; Mc Graw-Hill, 1965.Filter{Filterr.m.s.maxminr.m.s.maxminr.m.s.maxminr.m.s.maxminTj=50 ns0.00210.0047-0.00010.00260.00550.0001T =50 nsii_0.00300.0051-0.00060.00160.0034-0.0009T2=600 ns0.00140.0030-0.00030.00150.0021-0.0004T4=500 ns0.00270.00520.00120.00480.0134-0.0057T3=1.5 ys0.00180.0035-0.00060.00190.00380.0001T5=1.0 ys0.00300.00650.00020.00780.0226-0.0086Table 1 : Calculated tap weight errors for 4different samples (A to D). The clock mode usedfor A and B differs from the mode applied for Cand D. The trailing edge rise time T of the clockis a parameter.1.0Î H.T. transfer function moduluslinear scale (arbitrary units)0.5T = 50 nsT2 600 nsT = 1500 ns0.5normalized frequency1.0f/fFig. 1 : Measured transfer functions of sample Dfor different clock trailing edge rise times T.The fitted transfer function applies for T .Fig. 2: Normalized calculated "correlation function"C(M) for different trailing edge rise times T.

Analysis of tap weight errors in CCD transversal filters

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