A behavioural model for scan converter-based transient digitizers

"deasuremem Vol.

Pll: S0263-2241 (96)00018-8

EI.SEVIER

17, No. 2. pp. 103 114. 1996 Copyright ~¢ 1996 Elsevier Science Ltd Printed in The Netherlands. All rights reserved 0263-2241 96 $15.011 + I)I)0

A behavioural model for scan converter-based transient digitizers P. Arpaia

a, F.

Cennamo

b

p. D a p o n t e c, M. D ' A p u z z o a

Dipartimento di ht,~egneria Elettrica. Universitb di Napoli "Federico 11", via Claudio 21, ,~0125 Naples. Italy b Dipartimento di h!lormatica e Sistemistica, Universitd di Napoli "Federico I1", t'ia C/audio 21. ,~¢0125 Naples, Italy Dip. di ln~,,, dell'h!li~rm, ed lng. Elettrica, Unirersitd di Salerno. cia Ponte don Melillo I. 84084 l:isciano ( SA). hair

Abstract

A model for the non-ideal behaviour of transient digitizers based on the scan conversion principle has been developed. This model allows digitizer behaviour to be investigated under several operating conditions in order to: Ill verify performance enhancement obtained through new digital signal processing techniques, (ii) develop characterization techniques peculiar to scan converters and (iii) illustrate working mechanisms and error sources with educational aims. In this paper the proposed model is described in detail and its validity and application range are illustrated through several examples. Copyright © 1996 Elsevier Science Ltd.

Keywords. Scan converter: Model: A/D converter 1. Introduction

Owing to this working mechanism, apart from the general error sources of an Analog to Digital Converter (ADCI, in scan conversion further particular errors arise from: (i) the writing operations on the diode matrix, (iil the technology of the diodes and, in particular, their time response and (iii) the operations of extracting the digitized signal from the target trace. Such error sources (i) affect mainly the dynamic performance of scan converters; thus digital signal processing algorithms liar error reduction have been developed [3] and (ii) cause traditional ADC tests [4 12] to give an inaccurate performance evaluation [13]: thus the development of specific test techniques is necessary. These twofold aims can be usefully pursued through a software simulation tool. As a matter of fact, in recent years ADC simulation has become more and more widespread and various models have been proposed [13 20]. Among these, three classes, at three different abstraction levels, can be

Scala conversion is one of the methods based on the "'Fast in, Slow Out" concept, where a fast transient signal is first captured and stored in an analog buffer, and then off-line digitized at a slower rate [ I ] . Presently, digitizers based on the scan conversion principle are the main way to measure subnanosecond transient events accurately [2]. in scan converters, a high-bandwidth electron gun acts directly on a target matrix of semiconductor diodes by modifying their potential (Fig. 1~. The corresponding charge distribution (trace) is stored on the target until a reading gun "scans'" the matrix at low speed. The resulting charge levels are digitized, corrected through a reference array and stored in a matrix (linear array). Then a centroid algorithm is applied to each matrix column corresponding to an instant t of the time window acquisition, in order to find the signal amplitude at t. 103

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r"

1

Pixel charge distribution for a single vertical scan

Diode Target

/

--,

I [ I I

r

Single Scan "~

___1

Writing Block

I..

41

/\

ARRAY

);1 /

,.I

Reading Block

Signal P r o c e s s i n g B l o c k

Fig. 1. Block diagram of the scan conversion process.

identified [18]: (i) device level models, where the ADC circuit schematic is analysed in terms of all its effective circuit components, (ii) macromodels, where the ADC is studied in terms of basic element models of equivalent electric circuits and (iii) behavioural models, described by blocks of circuitry considered as black boxes and modelled at a high level using their input-output characteristics. The choice of the modelling level must take into account: (i) the model feasibility, (ii) the availability of model parameter values for specific components and (iii) the ease of model validation techniques. The first two problems are especially serious in de¢ice level modelling of scan converters, where the complexity of the converting circuit and the difficulty of representing error sources in terms of basic components lead to the need for an expensive and time-wasting specific simulation tool. This problem can be solved using macromodels based on general purpose components. However, for scan converters, the number of available general purpose components is fairly limited so the difficulty of building very complex models arises. On the other hand, behavioural modelling allows specific routines to be written easily without any limit to the complexity and accuracy of the model, paying most attention to working operations and the overall functions of each functional block. Such a capability is particularly useful in the scan converter analysis, where error sources are mostly related to the intrinsic working mechanism rather

than to non-ideal characteristics of specific components. In this paper a behavioural model of scan conversion-based transient digitizers is proposed. This model describes the working mechanism of the scan converters, with particular attention to the writing operations on the diode target. Tests on an actual scan digitizer and on its corresponding model devoted to (i) highlighting the model validity and (ii) verifying its parameter sensitivity, are described. The model effectiveness is also evidenced through its application to the development of a digital filter for the enhancement of the dynamic performance of scan converters.

2. Basic working mechanism of scan converters

Recent realizations of scan conversion-based transient digitizers [21] use a tube consisting of two electron guns facing each other with a semiconductor diode target positioned between them, conceptually analogous to two CRTs joined at a common face plate screen. The input signal is applied directly to a high-bandwidth writing electron gun which works in a similar way to a high-performance oscilloscope CRT. The writing electron gun has the vertical plates directly driven by the input signal and the horizontal plates driven by a triggered sweep ramp from the time base. Waiting for an event, the

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reading gun periodically "'refreshes" the target diode potential levels (Fig. 2a). When a high-speed input signal is applied, in order to attain a sufficient level of intensity, the writing gun writes the waveform directly on the target by forward-biasing the target diodes (Fig. 2b). The two-dimensional (2D) charge distribution corresponding to the trace location is stored on the target until it is sensed by the reading gun at a lower rate (Fig. 2c). The reading gun operates similarly to a video camera, continuously scanning the opposite side of the target from top to bottom, left to right, at a rate optimized for the successive digital data transfer. As the reading gun scans a "written" diode, more beam current is required to reversebias the diode. This change in beam current is sensed and the resulting signal is used to attain a low-speed representation of the high-speed input signal. Vinally, the levels sensed by the reading gun from the target on a single vertical scan are converted to digital values (Fig. 1). A reference array provides a map of the diode target allowing corrections for differences in target element charge capability. If an aberration arises in the target and causes error problems, the reference array can be updated at any time. Where the difference between the digitized data of lhe diode target and the corresponding values of the reference array is greater than a minimum charge threshold level (necessary to reject low-level noise), the data are stored in a linear array. When a vertical line is scanned, the charge distribution across that line exhibits a Gaussian trend, since both the electron writing beam and the diode response to the beam action are Gaussian by nature [22]. Then, for each vertical line, in order to lind the charge distribution peak, the corresponding data stored in the linear array are processed by means of a centroid algorithm. The centroid algorithm is a weighted average calculation that transforms ( data (current scan line number), ~1 data (vertical location) and I data (charge intensity)into a single ~lm[~] waveform array of coordinates: .,,.

q m [ ~ ] = i , ~1

,

(1)

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b)

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-.4

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Acceleration

Fig. 2. Working principle. (a) Waiting phase: waiting for an event, I b) writing phase: capturing the writing gun trace location and (c) reading phase: reading the wriUen targel [21 ].

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where N is the number of data points in a vertical scan. The centroid application to each vertical line yields a determination of the charge peak representing the trace centre on that line. This centre corresponds to the value of the input signal in the instant the beam moves across the line. In this way, from the two-dimensional charge distribution on the diode target, the final amplitude versus time digital representation of the input signal is reached.

3. Peculiar error sources in scan converters

The peculiar errors in scan converters arise mainly from the writing mechanism and from the use of the centroid algorithm, since reading gun and ADC operations are carried out at slow speed and, hence, their errors are negligible. In the writing phase the magnitude of the error depends on the way the electron beam stimulates each target diode and which particular diodes are stimulated. As a consequence, the electron beam and the resulting charge distribution on the target have to be dynamically modelled in each instant of the writing phase. For this reason, the main factors influencing the writing mechanism have been analysed: the intensity level of the writing electron beam, the focusing of the beam, the sweep speed and the input signal dynamic and the astigmatism phenomenon. The writing intensity is influenced by the intensity and focus controls, the sweep speed, the instrument operating temperature and the trace slope. An insufficient writing beam intensity will result in target portions not being sufficiently written such as at zero crossing for high-frequency sine waves, whilst an excessive intensity can produce a blooming effect such as near the sine wave peaks. The Jocus determines the concentration of the writing beam and is slightly dependent on the intensity setting. Adjustment of focus is not critical for long time windows, but, for the shortest ones normally required (about 5 ns and 10ns), it is critical for achieving the best writing on the target. The sweep speed and the input signal dynamic also influence the writing operations, owing to the effects of the limited target diode response time on the input signal recording. Such effects become

more and more sensitive according to the reduction of the beam irradiation time across the diode matrix. The astigmatism phenomenon [23] produces a distortion in the trace on the diode target owing to a variation in the internal electric field in the vertical deflection plates. Such variation depends on the influence of the accelerating anode field on the vertical deflection plates. This distortion limits the achievable accuracy [24], in spite of the manufacturer's use of (i) travelling wave deflectors to minimize signal rate distortion [25] and (lit bilinear built-in corrections [-26]. Finally, another possible error source is the centroid algorithm capable of extracting the digitized output signal from data stored in the diode target. In critical acquisition conditions, the centroid algorithm can produce an intrinsic information loss owing to the passage from a 2D charge distribution on the target to a 1D amplitude versus time signal representation. Moreover, the algorithm derived from E q . ( l ) turns out to be very sensitive to the zero baseline adjustment and also to low-frequency noise, which prevents the achievement of highly accurate results in many experimental situations [27].

4. Scan converter behavioural model

The proposed model has been subdivided into three functional blocks corresponding to the three fundamental operating phases of the converter: (i) the writing block, (ii) the reading block and (iii) the signal processing block (Fig. 1).

4.1. Writing block Since writing phase errors are predominant, particular attention has been paid to modelling: (i) the dynamic interaction between the electron beam and the diode target and (ii) the effect of the astigmatism distortion on the beam target impact area.

4.1.1. Electron beam model. In each instant of the motion, the position of the beam trace on the target is identified by (Fig. 3): (i) the coordinates of the trace centre and (ii) the trace main axis,

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X'

Beam qc y + : ~ Y'

",/

pendent parameters, ~rx along the x-axis and or,. along the y-axis and (ii) the law of variation of the c o m p o n e n t s a'x and a~,t along the two axes tangential (x') and normal (y') to the trajectory (Fig. 3). The p a r a m e t e r c~; is at a m i n i m u m and equal to o-.~ for a D C signal: it increases according to the vertical deflection, and consequently, to the signal slope tg :~: cri~= a., x/l + tg2:~.

(2)

Its c o m p o n e n t s in the reference system having as origin C and axes x , y are derived through simple geometrical considerations:

lnput signal trace

o'xx =

q Fig. 3. Orientation of the beam trace on the diode target with respect to the trajectory. assumed to be tangential to the trajectory. The centre coordinates are identified as follows: • the abscissa ~ as the index of the current vertical scan: • the ordinate r/c as the element index of the current vertical scan containing the distribution peak. The tangent (tg :0 to the trajectory at the ith point is identified on the basis of the input signal derivative by c o m p u t i n g a second-order regression on k points. The shape of the b e a m trace is modelled by a G a u s s i a n distribution (Fig. 4). Given a setting of intensity and focus, the distribution dispersion is related to the two independent actions of horizontal and vertical deflections. Consequently, the dispersion is modelled by assigning: (i) two inde-

llensitl 2

ax;

ol, y = o-x"

tg :~.

(3 )

The p a r a m e t e r o';, decreases according to the signal slope (e.g. rising edge of the fast transient) and is at a m a x i m u m , and equal to ~r~., for a D C signal: O.,v

(41

O'v .

x,/1 + tg2~

Also its c o m p o n e n t s in the reference system (C, x, y) are derived through simple geometrical considerations: oy- tg :~ a~.x - 1 + tg2:~ '

a~. ~r;,~,- 1 + tg2~"

(5 )

Once the dispersion has been evaluated, in order to draw the area (1. h) including the beam trace at each instant (spot), the dimensions 1 and h are assigned as: l=z'Ax,

where

Ax=max{~i~.,:c~.,.l.

h = z" Ay:

where

! . P t Ay = max {~.~., c~.,.~. ,.

16)

and z is the given confidence level [28]. The coordinates Xp and yp of the generic point P included in the b e a m trace are determined on the basis of their distances dx' and dy' from the axes x' and y': dx' = In,-'(Xp - Xc) + n~.-(yp - Yc)L, where n . , -

Fig. 4. Gaussian charge distribution related to the impact area of the electron beam on the diode target (~: saturation threshold ).

tg ~ v/1 + tg2:~

and

n,.-

d y ' = Ln~ • (xp - Xc) + n'y "(Yv - yc)t, wheren~=n~,

and

n~.=-nx.

1 ~ " x/1 + tg2~ (7)

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P. Arpaia et al.

For each generic point P of the beam trace, the charge intensity I is inversely proportional to the horizontal sweep speed and dependent on the combination of the two contributions along the x and y axes: L I .....

1

s ,~

[ exp

( d x '2 -

\2<,

dy'2)] + --

2<)J'

P'I

P'4

P4 (

"

p

p'

P]

. [0I

(8)

O~

O,

where L is the colour scale and s is a scaling factor equal to: s --

1

P~

(9)

O.~. mi n '

P'~

The saturation effect of the diode response is taken into account by forcing intensity values greater than a given threshold (~) to be equal to the threshold. Finally, in order to take into account the differences in target element charge capability, noise can be added to the digitized charge data.

4.1.2. Astigmatism effect model. From a physical point of view, the astigmatism effect involves a distortion of the geometric characteristics of the charge distribution stored in the diode target. This distortion has been taken into account by considering the undistorted distribution on an ideal plane, the distorted distribution on an actual plane and a geometric transformation from the ideal plane to the actual one. The transformation relates each point of the two planes and has been modelled by considering both the ideal and distorted distributions as each is subdivided into four sectors (see Fig. 5). Each sector is identified by the plan centre, by two symmetrical bisectors and by the part of the plane contour included in the two bisectors. In this way the displacement of each charge distribution point due to the astigmatism effect is related to: (i) the shift of the distorted plane centre, (ii) the rotation of the distorted plane bisectors and (iii) the deformation of the target contour lines. Therefore, knowledge of the ideal and distorted centres and contours of the diode target is required. The ideal centre and contour of the diode target are design parameters of the scan converter to be modelled and so they are assigned. Meanwhile, the geometrical characteristics of the actual diode

P'z Fig. 5. Astigmatism error model (IOPI = p).

target can be obtained by means of calibration techniques [24]. In order to simplify the analytical expression of the transformation, a polar representation has been chosen, so the target contour can be easily described by a simple relationship .['= f(p, O), where p is the distance between the current point (P) and the centre of the image (O) and 0 the angle between the segment IOPI and the bisector of the corresponding sector, as shown in the example of Fig. 5. This approach leads to the assignation in the model of: - the coordinates of the centre and of the contour of the diode target without distortion [O, Pl, P2, P3, P4]: the coordinates of the centre and of the contour of the diode target with distortion [O', P], P2, P;, P;]; a simple matrix-based polar coordinate transformation to pass from the generic point coordinates of the non-distorted target to the generic point coordinates of the distorted target.

4.2. Reading block and signal processing block In order to take into account the analog to digital conversion carried out after reading gun activities, an ADC model (Fig. 1) is provided [16]. Such a model presents a parallel structure based

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P. Arpaia et al.

>la'tanl IV3 V0:Vint

+

v6

U

>

V2

v~= k * v 1 vt(t) = vo(t-~)

vj = a * t a n h ( V l / b )

v 6= LSB * trunc(vffLSB

+ 0.5)

vs = d * [1 - c o s h ( v l / c ) ]

Fig. 6. Block diagram of the ADC error model. on functional elements, each one taking into account the effect of an ADC error source (Fig. 6): (i) the delay introduced by the ADC components (r), (ii) the amplitude compression (tanh function}, (iii) the distortion of the acquisition chain (cosh function), (iv) the ADC gain error (k) and (v) the ideal quantization effect. The signal processing block of the model includes the reference array in a matrix form containing the correcting values to be subtracted from the output matrix of the writing block. in this block, the same centroid algorithm used to identify the charge peak coordinate in a vertical line, described in Eq. ( 1 ), has been implemented to obtain the digitized version of the input signal from the output matrix of the writing block.

5. U s e r i n t e r f a c e o f t h e m o d e l

For easy utilization of the model, even by unskilled users, a Virtual Instrument (VI) using LabWindows T M was set up (Fig. 7). The developed VI is interfaced both to the proposed model and to an actual scan converter-based transient digi-

tizer. In the first case (Fig. 7at, the VI allows all the model parameters to be set directly via its panel. In the second case (Fig. 7b), the VI makes the remote control of the digitizer more accessible. In both cases, the VI also allows (i) on-line help for each working parameter and (ii) testing of digital signal processing techniques, applied to simulated or digitized data, in order to improve the digitizer's dynamic performance [3]. In Fig. 7a, a sine wave trace and the corresponding centroid waveform as they appear in the model output, and the corresponding set-up of the model parameters, can be observed. In the model VI the data acquisition process is defined by assigning the following parameters according to the actual digitizer (Tektronix SCD 5000) specifications: the diode target size in a range up to 1024 x 1024, the time window (defined by creating a correspondence between the time and the number of target matrix columns) from 5 ns up to 100 ms, the input range up to 5 V, the nominal bits (related to the diode target size} from 6 up to 11, the sampling frequency (up to 10 GHz) and all the parameters characteristic of the desired trigger event. Furthermore, the intrinsic differences in target element charge capa-

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Tektronix

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m Scan Converter

ma{~

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. ,

,.

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model

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!

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:~ ' ~~

-s.6~

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Fig. 7. Virtual instrument panels of: {a) the model, (b) the actual digitizer.

P. Arpaia et al.

I 11

bility and the transformation that models the astigmatism effect can be also finely tuned. In Fig. 7b the developed VI front panel for the remote control of the Tektronix SCD 5000 digitizer is shown. In this case, the SCD 5000 VI panel is characterized by a diode target size of 512 × 1024 and a nominal resolution of 11 bits. In particular, a sinewave of 2.5 Vrms and 20 M H z reported in the figure was obtained with: a time window of 1 las, input range 5 V, intensity 48.2%, focus 49.0% and a single-shot trigger. The output of the VI panel shows: (i) the charge data of the linear array and lii) the corresponding centroid results, as read by the instrument and represented in the same format as the model output.

6. Examples of model working conditions Several simulation and experimental tests were carried out in order to: (a) verify the model response to variation in different parameters, (b) validate the model and (c) set up a digital filter to enhance digitizer performance. (a) The model capability of effective representation of the signal trace on the target is highlighted in the sine wave of Fig. 8a [ 1.5 V-251 M H z stored in a 256 x 256 matrix, 5 ns time window): both the blooming effect near the crests and the decrease in width and intensity of the trace at the zero crossings are shown (intensity levels are shown through the grey scale). Furthermore, in the same figure, the effects on the trace of the electronic beam dynamic and its movement on the diode target call also be noted (i.e. the blooming effect corresponding to the trace asymmetry near the crests). The model response to the parameter variations can be evidenced by comparing Fig. 8a and Fig. 8b: (i) the expected "diffusion" of the trace due to an intensity increase in Fig. 8b has been fully compensated by the focusing attained through the decrease in ~rx and o-~; lii) the blooming effects and the variations in the trace width and intensity, due to the dynamic of the signal, have been slightly reduced by decreasing the parameter L. Finally, the same sine wave of Fig. 8a is reported in Fig. 8c with a noticeable distortion due to the astigmatism effect.

a)

b)

\

\

Fig. 8. Model output sine waves: (al trace with evident "blooming" effect: (b) "blooming" and variations in trace width and intensity reduced by means of parameters a,, o-~ and l= (c) the same trace as qa) but with astigmatism effect.

(b) The model was validated through a set of comparative tests on the SCD5000 digitizer aimed at experimentally tuning the model parameters (k, z, cL~, at., L, t)). In particular, given a setting of intensity, focus and acquisition time: (i) a first rough estimate of model parameters is obtained by comparing the model traces with those of the SCD5000, in the absence of vertical deflection (i.e. a DC signal); (ii) starting from the rough estimate, the comparative procedure is repeated in the presence of vertical deflection (i.e. a high-frequency sine wave), and the parameters are finely tuned by tracing the single beam spot in the most critical regions of the waveform (i.e. high-frequency sine

112

P. Arpaia et al.

wave crests and zero crossings); (iii) the final estimation result is evaluated by computing differences among simulated and actual centroids. The fine parameter tuning through the spot characteristic analysis is illustrated in the example of Fig. 9. The spot is included in a rectangle with dimensions 1= za'x, h = za~, in order to evidence the distribution dispersion. In particular, in Fig. 9 the spots: (a), (e) and (d) allow the zero and maximum derivative conditions, respectively, to be verified; (b) and (c) allow the accumulative effect of two adjacent spots to be studied. Finally, in Fig. 10 the results of the validation process are shown for a sine wave of 3.5 Vrms and 10 MHz acquired in a time window of 100 ns ],024 samples, with intensity = 24.2% and focus = 49.8% ( Fig. 10a). The corresponding main model parameters are: (Fig. 10b) k = 5 , z = 3 , a x = 4 , a~.=4, L = 9, 0 = 2 1 . In particular, there was a difference lower than 1 LSB between the signals obtained from the centroid application to the model output and the actual charge data distribution. (c) In order to reduce the distortion effects of the error sources, a digital filter was applied to the digitized charge distribution stored in the linear

Fig. 10. Validation process results: comparison of(a) instrument and (b) model outputs.

array [3]. As a first step, the jth column of the charge data matrix V(i, j) is transformed into the Walsh domain, by obtaining the corresponding ,]th column of the matrix Vw(n,j): Vw(n, j) = ~

~

V(i, j) WAL(n, i)

i=0

T

......

b

a

Fig. 9. Model parameter fine tuning through the analysis of beam spot characteristics in zero and m a x i m u m derivative conditions (a, e, d) and in adjacent positions (b, c). For case d the beam trace dimensions l and t7, according to Eqs. (6) are also given.

113

P. Arpaia eta/.

~1= 0 ..... N -

1,

(10)

where N is the element number in a vertical line and WALln, i) is the set of Walsh functions [29]. The distortion effects are reduced through a moving-window average algorithm applied to Vw(n,/t. This algoritlhm operates iteratively by averaging three columns from the current one and by treating the resulting column as the new current one. The final result is stored in a new matrix VFw. Then, by applying the Inverse Walsh Transform to each column of VFw, the matrix V' is obtained: X

.

~,J

~'%•

•m

a)

o" i " '~

~

m,m

,w ,it"" w

% %

•"

%

.%. ,,"

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L

V'(i, j)= ~ VFw(n,j) WAL(n, i), tl - - ( )

i = 0 ..... N - 1 .

°o

o." o,

O'

(11)

,

%

Hnally, application of the centroid algorithm to the columns of the filtered matrix V'(i, j) identifies the digitized input signal. Such a digital filter allows the trace area corresponding to (i) the crests to be more clearly defined, so the blooming can be reduced, and (ii) the zero crossings to be enhanced, so the insufficient writing speed efl'ects can be compensated for. In conclusion, the signal (Fig. llb) obtained by means of the centroid application to the filtered matrix is less distorted and more continuous than the signal obtained by means of the centroid application to the non-filtered matrix (iFig. 1 la).

-

m% •

,__.._,

--

2

Fig. 11. Signals obtained by means of centroid application t~_~ (a) non-filtered matrix and ib) filtered matrix.

evidencing peculiar errors [31] in order to compare their results with those provided by traditional tests and select the most effective: and (iv) the educational computer-aided illustration of new techniques related to high-speed conversion, in order to highlight in detail the scan working principle and in particular to show its error sources.

7. Conclusions In this paper a behavioural model for scan conversion-based transient digitizers has been presented. A virtual instrument panel has simplified the model parameter tuning in all the operating conditions, so the model behaviour was made as similar as possible to the actual digitizer behaviour. The model turns out to be useful in several fields: (i) scan converter design, in order to test new solutions for the diode target and to provide straightforward feedback to the designer; (ii) the analysis of the effects of the target image processing on the scan converter performance [30]; (iii) the development of new testing techniques capable of

References [ I ] R. Hayes, Scan conversion, Handshake" 12 (1987) 12. [2] T . R McComb, J. Kuffel and R. Malewski, Measuring characteristics of the fastest commercially-available digitizers. I E E E Trans. on Power Delivery 2 (1987} 6{:,1 670. [3] P. Arpaia, F. Cennamo, P. Dapontc and M. D'Apuzzo, Dynamic characterization of scan conversion based transient digitizers, I E E E Trans. +m In,strum. amt Meas. 44 ( 19951 643 646. [4] F. Cennamo, P. Daponte. M. D'Apuzzo and M. Sawtstano, Digitizing signal analyzer calibration. Proc, I M E K O X I I World Con~re,ss, Beijing, China, 1991, pp. 148 153. [5] F. Cennamo, P. Daponte and M, Savastano, l)ynamic

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