A fast 2-bit digitizer for radio astronomy

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38. NO. 6. DECEMBER 1989 1109

A Fast 2-Bit Digitizer for Radio Astronomy

Abstract-The design and performance details for a 2-bit digitizer operating at 250-MHz clock rate are presented. This digitizer is part of a new correlator system for Caltech’s Owens Valley Radio Obser- vatory (OVRO) 3-element millimeter-wave interferometer. The performance of the digitizer circuit is analyzed in terms of threshold errors, indecision, sampling aperture width, and timing errors. For an input bandwidth of 125 MHz, digitizer distortion actually improves the sensitivity of the interferometer by about 0.3 percent, but limits the dynamic range of the instrument to about 2 x lo3.

Si nels f r o m Si n a l s f r o m teQescope I teQescope 2

-ve lags

I. INTRODUCTION IGITAL signal processing techniques were first used D in radio astronomy in an autocorrelator system for

measuring power spectra [ 11. The techniques have since been extended to crosscorrelators for interferometry and most modem arrays now use digital systems (for example 123). Where the signals are Gaussian processes, as in radio astronomy, there is only a moderate sensitivity degradation even for very coarse quantization schemes; hence, 1- or 2-bit correlators are common.

We are building a digital crosscorrelator for the Owens Valley Radio Observatory (OVRO) millimeter-wave -interferometer [3]. This system can correlate signals in four independent frequency bands each up to 125 MHz wide. The correlator is a 2-bit spectral-line system [4] with sampling at the Nyquist rate, hence, the maximum clock rate is 250 MHz. The system has a serial architecture with the multiplier and accumulator sections operating at the sampling rate as shown in Fig. 1. This is a departure from the parallel processing approach used in many radio telescope systems (for example [5]) and has the advantage of simplicity.

The digitizer is one of the most critical elements in the correlator because its operation is not ideal and this affects the sensitivity of the instrument. Other parts of the correlator are less important in this respect because they are digital circuits where operation is perfect unless a device has failed. Digitizer output state errors are caused by im- perfect operation of either the sampler or quantizer sections of the digitizer. In this paper, we review the effects of these imperfections on the performance of the OVRO interferometer.

Manuscript received January 3, 1989; revised May 22, 1989. This work was supported by a grant from the IBM Corporation. The OVRO Milli- meter-Wave Interferometer is supported by the National Science Founda- tion under Grant AST 87-14405.

The authors are with the Owens Valley Radio Observatory, California Institute of Technology, Pasadena, CA 91 125.

IEEE Log Number 8930980.

c o r r e 1 a t o r outputs to computer

Fig. 1 . Architecture of the OVRO correlator

11. THE OVRO DIGITIZER The OVRO digitizer is a 3-threshold circuit with the

threshold detector outputs encoded into a 2-bit word, giving the transfer function shown in Fig. 2. This encoding was adopted for simplicity since it requires only an OR operation on the outputs of the upper and lower threshold detectors. The scheme is appropriate for the 2-bit correlator multiplication table described by Cooper [6] which results in a sensitivity of 0.88 relative to a perfect analog correlator.

The speed of the digitizer is modest in comparison to some of the results published in the literature (for example [7], [SI). Unfortunately these fast devices are not com- mercially available and as a result were unsuitable for the OVRO system. We, therefore, used a Plessey SP93803 [9] sampling comparator circuit which was the fastest bi- polar device readily available when the digitizer was de- signed. The other digitizer components are standard 11C or 1OOK ECL circuits [lo].

The digitizer circuit is shown in Fig. 3. Each sampling comparator output is clocked into a D-type flip-flop which holds the comparator output state for the duration of the clock period. The magnitude bit encoding is performed by a wired-OR connection at the flip-flop outputs. Each flip-flop drives a synchronous counter which gives an output frequency proportional to the rate of comparator “high” states, thus providing a threshold voltage monitor. In the OVRO digitizer the comparator threshold voltages are provided by a manually adjustable potential di- vider circuit and the thresholds are continuously monitored using the counter arrangement described above. Correc- tions for threshold voltage errors are applied at the correlator output. The threshold monitor circuits could also be used in a scheme where the thresholds are continuously adjusted.

0018-9456/89/1200-1109$01.00 0 1989 IEEE

1110 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38, NO. 6, DECEMBER 1989

o u t p u t s t a t e

i n p u t ALi tl t i zer

s i g n magnitude b i t blt

Fig. 2 . Transfer function for a 3-threshold digitizer with 2-bit output encoding.

p - driver

magnitude bit outputs

RF input

s i g n bit outputs

Clock

Clock __

SP9270 1 line receiver

Fig. 3. The OVRO digitizer.

111. DESIGN TOLERANCES AND PERFORMANCE DETAILS Digitization is a 2-stage operation involving sampling

and quantization and there are distortions associated with both of these processes. Sampler distortion involves errors in the timing of samples and nonzero sample aperture width while quantizer distortion is caused by quantization threshold errors and indecision near a threshold. These effects were considered by D’Addario et al. [ 111 for a 2-threshold digitizer and in the following sections we ex- tend the analysis to the 3-threshold digitizer used in the OVRO interferometer.

fects can be corrected if the threshold errors are measured. The performance of the system is then limited by temperature-induced variations between threshold mea- surements.

A useful estimate of the effects of offset variations can be obtained by considering an analog correlator (i.e., a simple voltage multiplier) with mean inputs equal to the maximum threshold variation, 6v,, in the digital system. The maximum offset variation at the output of the analog correlator is

6% = d 6 U J 2 (1) A. Threshold Errors

The effect of threshold errors on the sensitivity of a 2-bit correlator system was studied by Cooper 161, who showed that changes of up to about +20 percent in the magnitude comparator thresholds reduced the sensitivity of the instrument by less than 1 percent. Threshold errors

offset in the measured correlation function. These two ef-

where g is the gain of the correlator. Offset variations are important only if they are greater than the correlator output noise after integration. For a cross correlator with rectangular input passbands of width B and unity rms input voltages, the output noise is [4]

U , = ~ (2) g also change the correlator scale factor and introduce an

( 2 B 7 )

PADIN AND EWING: DIGITIZER FOR RADIO ASTRONOMY 1111

where T is the integration time. Thus the maximum usable integration time, T , , , ~ ~ , is

Tmax = 2B ( 6vo) *

( 3 ) 1 -- -

2B (6%) where 6v, and 6vo are norma!ized to the rms input voltage. Note that in this paper, thresholds and associated errors are always normalized to the rms input. Equation (3) gives a lower limit to T , ~ ~ because we have assumed that the thresholds vary so as to give the maximum offset effect. For the OVRO system, the temperature coefficient of the normalized digitizer thresholds is about IOp4 K-l and the temperature stability of the equipment is about + 2 K. As- suming an input bandwidth of 125 MHz, T,,, is then approximately 40 h which is adequate for most radio astronomy experiments. Phase switching in the OVRO interferometer reduces the offset effect by several orders of magnitude.

To estimate the size of correlator scale factor variations, we consider a magnitude comparator threshold variation to be equivalent to a change in the digitizer rms input. The fractional scale factor variation due to small magnitude threshold variations, & u , ~ and 6urlr in just one digitizer is

(4)

Assuming a threshold variation of 4 x as for the previous analysis, utU = - U , / = 0.9 and the worst-case situation with 6ut/ = -6vtu gives a scale factor variation of 4 X Thus for observations of a strong source, threshold variations could limit the signal-to-noise ratio at the correlator output to 3 X lo3. This in turn represents a worst-case limit to the dynamic range of a map produced by the interferometer. In this context, the dynamic range is the ratio of the peak source brightness to the rms noise in a region of the map which contains no sources. For an observation of a point source at the field center, the visibility is constant, and correlator scale factor variations on a timescale much less than the observation time are equivalent to adding noise uniformly over the visibility measurement plane. In the map, this gives a noise level equal to the product of the source brightness and the scale factor variation. Hence, the dynamic range limit in this case is equal to the reciprocal of the scale factor variation. For more complex sources, the dynamic range limit due to scale factor variations is less severe because the source visibility does not have its maximum value for the entire observation.

1 1 (U

+ m v tu2

+ 2 10 3 0

r\l Vto2 L

.! 0 0 * rl

W

tl2 ; ; v

01

Digitizer 1 output state

V 10 1 1 V t o l "tu 1

01 00 t l l

ct tc - d l l 0 1 u l

Fig. 4. Correlator multiplication table for a 3-threshold digitization scheme. The dashed lines are the boundaries of indecision regions.

does not lie in a well-defined state and the digitizer output may adopt either of the states separated by the threshold. In the following analysis, we assume that the two states have equal probability so that the effect of indecision is simply to increase the quantization noise. However, a real digitizer may behave in a more complicated way. If a comparator input overdrive is too small to cause the output to slew to the correct state the digitizer output may remain in the state of the preceeding sample. This will introduce correlation function dependent errors at the correlator output.

The correlator multiplication table for a 3-threshold digitization scheme with indecision as described above is shown in Fig. 4. The signal-to-noise ratio at the output of the correlator is given by [6]

C wij ~ p , j ( P ) ( 5 )

i , j R2 =

where wii is the multiplication table weight for the state i j , P, is the probability of occupation for the state i j , N is the number of samples in the integration period, and p is the correlation coefficient. For a continuous (unquan- tized) correlator, the equivalent expression is

R, = p N 1 1 2 . (6) Hence, the efficiency of the 2-bit correlator relative to an ideal analog correlator is

i P c w ; , P , ( P ) I i , j

.a B. Indecision

Indecision is a direct result of finite comparator gain and bandwidth. There is a range of input voltages, cen- tered on the comparator threshold, for which the output

This is shown in Fig. 5 for the multiplication table with n = 9, m = 3, and 1 = 0 (called the suppressed inner

1112 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38, NO. 6, DECEMBER 1989

I I I , , , , , ,

d=0.2

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 NORMALIZED THRESHOLD

Fig. 5. The effect of indecision on the correlator efficiency. The abscissa is the normalized magnitude threshold and d is the normalized indecision width. For these data U,,, = 0, U," = - U , , = 0.9, and the multiplication table has n = 9, m = 3, and I = 0. Results are shown only for non- overlapping indecision regions.

product table by Cooper [ 6 ] ) which is used in the OVRO correlator. Note that small indecision regions improve the correlator efficiency as if the correlator multiplication table were changed to more closely approximate the analog case. The increase in efficiency (assuming optimized thresholds) is about 3 percent. A similar effect is observed for the optimum multiplication table ( n = 9, m = 3, 1 = 1 ), but the improvement in efficiency is only about 2 percent.

For the OVRO digitizer, we investigated the indecision process using the arrangement of Fig. 6. The variable delay was adjusted to align a sample with a positive-going input signal zero crossing, and the required change in the sign comparator threshold voltage to give a stable, high output was measured. The threshold voltage change corresponds to the half-width of the indecision region if the comparator has a sample aperture width which is small compared with the time that the input signal spends in the indecision region. Thus at very low input frequencies, the measurement is dominated by indecision. At higher input frequencies aperture width effects dominate, resulting in an approximately linear increase in the threshold voltage change with increasing input frequency. This enables the aperture width and indecision effects to be roughly separated. For the OVRO digitizer, the width of the indecision region is about 10 mV which corresponds to d = 0.01 in the notation of Fig. 5.

Indecision changes not only the sensitivity of the correlator but also its scale factor. The scale factor due to indecision is a function of the correlation coefficient, and if a correction is not applied, this nonlinearity can limit the dynamic range of a map produced by the interferometer. The correlation coefficient dependent part of the scale factor is shown in Fig. 7, which was obtained by evalu- ating the numerator of (5), normalizing the results to the zero correlation coefficient case and then normalizing to the d = 0 case. For the OVRO digitizer, d = 0.01 which gives a maximum scale factor error of io-?

I OMHz r e f e r e n c e Clock

Fig. 6 . Test arrangement for investigating indecision and aperture width effects.

CORRELATION COEFFICIENT

Fig. 7. The correlation coefficient dependent part of the scale factor due to indecision. The normalized indecision width is d and for these data U,,, = 0, U , , = - U , , = 0.9, and the multiplication table has n = 9, m = 3, and 1 = 0.

C. Aperture Width The sample aperture width is one of the parameters that

determines the maximum operating frequency of the digitizer. If a threshold transition occurs during the aperture time, the digitizer output is uncertain and may fall in either of the states separated by the threshold as described in the analysis of indecision. Thus we can consider a finite aperture width as equivalent to indecision. For a given threshold, the equivalent indecision width is obtained by equating the probability of a transition during the aperture time with the probability that the digitizer input lies within the indecision region. For the sign comparator, the equivalent indecision width, normalized to the digitizer rms input, is given by [12]

= (2n) l12 ( 1 - ~ L [ o , 0, p a ( t a ) ] } , for ueq << 1

( 8 ) "tP,n

where L is the bivariate normal integral, pa is the auto- correlation function of the digitizer input, and t , is the aperture width. For a magnitude comparator, the corresponding expression is

for ueq << 1 (9 )


where U , is the normalized magnitude threshold. The effect of finite aperture width is obtained by performing the indecision analysis with du = d/ = veqmag and do = ueqsign in the table of Fig. 4. The results of this are shown in Fig. 8 for the scheme with I = 0 and U,, = - U , / = 0.9. Note that the sensitivity degradation which occurs for Bt, > 0.12 can be reduced by increasing the threshold voltage as Bt, and the equivalent indecision width increase (see Fig. 5).

For the OVRO digitizer, the aperture width is approximately 120 ps and the maximum input bandwidth is 125 MHz giving Bt, = 0.015 for which the sensitivity effect is about 0 .3 percent. Referring to Fig. 8, for a sensitivity degradation of 5 percent, Bt, = 0.38 which corresponds to an input bandwidth of 3.2 GHz. This represents an upper limit to the operating frequency of a digitizer using Plessey SP93808 devices.

D. Timing Errors Sample timing errors reduce the sensitivity of the inter-

ferometer because the relative delay between signals at the correlator inputs is not always zero. The sensitivity degradation due to an interdigitizer timing error, AT, is U21

D ( T ) = sinc (2BA7) (10) where sinc ( x ) = sin ( ~ x ) / a x , B is the digitizer input bandwidth and we have assumed that the three comparators in a digitizer operate at the same time. In the OVRO digitizer, the maximum variation in the sample clock timing (due to temperature and power supply variations) is about 100 ps and with an input bandwidth of 125 MHz, the corresponding sensitivity degradation is 0.1 percent.

The effect of timing skews between the three comparators in a digitizer is more complex. To understand this, consider a correlator in which one digitizer has comparator timing errors AT,, Are, and AT) . The correlator output, relative to the ideal case, is:

C(AT,, AT07 AT/) P l h r m

= 1 Z ( v ) d v D ( A 7 , ) + !j z ( v ) d v D ( A ~ , ) l)ll I h

P UII

where D ( A T ) is given by (10) and Z is the normal probability function. For the particular case of no sign comparator timing error, I AT, I = I AT/ 1 = AT and thresholds U,, = U , + AV,, and urt = - U , + Av, , , we have:

C = {''' Z(v) dv + 2 1 Z(v) dv D ( A T ) m

~ 1)1 U ,

+ (A% - A v r / ) [ 1 - D ( W ] Z ( V , > ,

for AV, << U , . ( 12) The first two terms indicate the sensitivity degradation due to the timing skews while the third term is a skew and

Z o 1 0.1 0.2 0.3 0.4

APERTURE WIDTH X BANDWIDTH

Fig. 8. The effect of aperture width on the correlator efficiency. For these data I)," = 0, U,,, = -U,, = 0.9, and the multiplication table has n = 9, rn = 3 , and 1 = 0.

threshold error dependent scale factor. For the OVRO digitizer, the maximum value of AT is 100 ps which corresponds to D = 0.999, giving a sensitivity degradation of 0.03 percent with U , = 0.9. The intercomparator timing skews are so small because all the comparators in a digitizer are on the same integrated circuit. The maximum difference in normalized threshold errors is approximately 0.01, hence, for U , = 0.9 the peak skew and threshold scale factor term is 3 x lop6. Note that any variation in the terms D and C due to timing and threshold variations will cause scale factor variations and these can limit the dynamic range of a map produced by the interferometer.

E. Extension to Higher Frequencies The maximum sample rate for the OVRO digitizer is

approximately 450 Msamples s- ' and this is limited by the speed of the ECL circuits which support the SP93808 comparator. The operating limit for the SP93808 itself is set primarily by sample time variations. For observations with low signal-to-noise ratio where the dynamic range of the map is not an important consideration, the digitizer operating frequency is limited by sensitivity degradation due to interdigitizer timing variations. Assuming a timing stability of 100 ps, a 5-percent sensitivity degradation corresponds to an input bandwidth of 875 MHz. Note that this is a more severe constraint than the 3.2-GHz bandwidth limit imposed by aperture width effects. A single SP93808 comparator circuit cannot digitize a signal of 875-MHz bandwidth because the time between samples is too small for the circuit to slew between logic states. However, a digitizer using several SP93808 circuits with a multiphase clock arrangement should achieve the performance predicted above.

For observations of strong radio sources, the dynamic range of the map is of paramount importance and in this regime correlator scale factor variations due to threshold voltage and interdigitizer timing variations limit the digitizer operating frequency. With the simple threshold gen- erator and clock distribution arrangement used in the

1114 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38, NO. 6. DECEMBER 1989

Fig. 9. Photograph of the OVRO digitizer. This unit contains two 2-bit digitizers each using half a Plessey SP93808 circuit. The black packages above the SP93808 are the D-type flip-flops which hold the comparator outputs and the white packages above these are the threshold monitor counters. The sign and magnitude bit outputs to the correlator are on the left and right sides of the box. Each 2-bit digitizer in this dual unit has 8 sign and 8 magnitude bit outputs (hence, 16 connectors on each side of the box). This allows for signal distribution in a correlator system for an array with up to 9 telescopes.

OVRO digitizer, the map dynamic range is limited to a few thousand for an input bandwidth of 125 MHz. For the same dynamic range, the bandwidth could be increased by perhaps a factor of 5 by improving the digitizer threshold control and reducing temperature variations which cause delay changes.

IV. CONSTRUCTION A surface-mount construction technique was used for

the digitizer primarily because many of the components were only available in surface-mount packages. The sub- strate is 10-ml thick RT/duroid 6010.5’ chosen because a 5 0 4 microstrip transmission line is only 10 ml wide and can easily be routed between the leads of a surface-mount circuit. The layout of a dual 2-bit digitizer is shown in Fig. 9. Note that the signal distribution circuits which feed the correlator are part of the digitizer.

‘RTlduroid 6010.5, Rogers Corp., Chandler, AZ 85226.

V. CONCLUSIONS We have described a 2-bit 250-MHz clock rate digitizer

which is part of a digital correlator for the OVRO millimeter-wave interferometer. The digitizer uses Plessey SP93808 comparators in a 3-threshold ‘‘flash converter” configuration.

Timing errors in the digitizer degrade the sensitivity of the correlator by about 0.1 percent, but we have found that indecision and aperture width effects improve the sensitivity by about 0.3 percent. This improvement in sensitivity occurs only for small aperture widths and indecision regions and is the result of indecision changing the correlator multiplication table. Threshold voltage and interdigitizer timing variations limit the dynamic range of a map produced by the interferometer to about 2 X lo3 which is adequate for millimeter-wave astronomy, but could be increased by improving the threshold control and reducing temperature-dependent timing variations.

For applications where dynamic range is not a serious


problem, the SP93808 comparator could be used to digitize signals with up to 875-MHz bandwidth if a 5-percent sensitivity degradation (due to timing errors) can be tol- erated.

ACKNOWLEDGMENT The authors would like to thank the Plessey Company

plc for providing a SP93808 device in advance of its com- mercial release.

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to radio astronomy,” Tech. Rep. 412, Res. Lab. Electronics, MIT, 1963.

[2] A. R. Thompson, B. G. Clark, C. M. Wade, and P. J. Napier, “The very large array,” Astrophys. J. Suppl.. vol. 44, pp. 151-167, 1980.

[3] C. R. Masson, G. L. Berge, M. J . Claussen, G. M. Heiligman, R. B. Leighton, K. Y. Lo, A. T. Moffett, T . G. Phillips, A. I. Sargent,

S. L. Scott, D. P. Woody, and A. Young, “The Caltech millimeter wave interferometer,” in Proc. I984 U.R.S.I. Int. Symp. Millimeter Submillimerer Wave Radio Astronomy, Granada, pp. 65-73, 1984. A. R. Thompson, J . M. Moran, and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy. A. Bos, “Functional design of a wideband digital spectrometer,” Tech. Rep. 179, Netherlands Foundation for Radio Astronomy, 1986. B. F. C. Cooper, “Correlators with two-bit quantisation,” Aust. J.

K. Poulton, J . J. Corcoran, and T. Hornak, “A I-GHz 6-bit ADC system,” IEEE J. Solid-state Circuits, vol. SC-22, pp. 962-970, 1987.

New York: Wiley, 1986.

Phys., vol. 23, pp. 521-527, 1970.

[8] H. KO and T . Van Duzer, “A new high-speed periodic-threshold comparator for use in a Josephson A/D converter,” IEEE J . Solid- Sfate Circuits, vol. SC-23, pp. 1017-1021, 1988.

[9] SP93808 Dara Sheet, The Plessey Company, plc., 1988. [IO] FIOOK ECL Data Book, Fairchild Semiconductor Corporation, 1986. [ l l ] L. D. D’Addario, A. R. Thompson, F. R. Schwab, and J. Granlund,

“Complex cross comelators with three-level quantization: Design tolerances,” Radio Sci., vol. 19, pp. 931-945, 1984.

(121 S. Padin and R. I . Davis, “A wideband correlator employing a single-bit digital by analogue multiplication scheme,” Radio Sci., vol. 21, pp. 437-466, 1986.

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A fast 2-bit digitizer for radio astronomy

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