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/7

7

Mean v____ Udotflow direction iku ZU u

Hot wire 3, / ,>at right angles

to pLane of other two wires. 4

Fig. 1. Model of hot-wire array.

Fig. 2. Schematic of analog computer signal processing circuit.

error due to uncertainty of the wire calibration constants, Kc andKa, is, therefore, reduced significantly.Such a procedure also minimizes the error in the final result, due

to linearization and differences in wire time constants. This is dueto the different stimuli. Typically, wires 1 and 2 would be operatedas linearized constant-temperature anemometers and wire 3 as aconstant-current unit (or resistance thermometer), in order toachieve the best possible velocity-to-temperature sensitivity. Sincethe hot-wire response is nonlinear to velocity and linear to temper-ature fluctuations, linearization of the two velocity wire outputswill result in a slightly distorted temperature signal. Conversely,for the temperature wire, the temperature response will be linearbut the velocity response will be nonlinear. Also, it has been shownby Kronauer [5] that, especially for short wires, fluid velocityfluctuations produce a slightly different wire time constant fromthat associated with temperature fluctuations. Although the methoddescribed cannot correct either deficiency, any errors present willbe negligible, because the primary signals representing each flowcomponent are corrected only by a small amount.The main limitation of the method is in flows where a multiwire

array would produce errors due to flow interference, or the size ofthe wire array would result in loss of spatial resolution.

REFERENCES[11 K. Bremhorst and K. J. Bullock, "Spectral measurements of tem-

perature and longitudinal velocity fluctuations in fully developedpipe flow," Int. J. Heat Mass Transfer, vol. 13, pp. 1313-1329, 1970.

12] , "Hot-wire anemometer measurements in flows where directionof mean velocity changes during a traverse," IEEE Trans. Instrum.Meas., vol. IM-18, pp. 163-166, Sept. 1969.

[31 S. Corrsin, "Extended applications of the hot-wire anemometer,"NACA TN 1864, 1949.

[4] D. S. Johnson, "Velocity and temperature fluctuation measure-ments in a turbulent boundary layer downstream of a stepwisediscontinuity in wall temperature," J. Appl. Mech., vol. 81, pp.325-336, 1959.

[51 R. E. Kronauer, "Survey of hot-wire theory and techniques,"

Harvard University, Cambridge, Mass., Pratt and Whitney Rep.137, 1953.

161 J. C. Wyngaard, "The effect of velocity sensitivity on temperaturestatistics in isotropic turbulence," J. Fluid Mech., vol. 48, pt. 4, pp.763-769, 1971.

A 2.5-ns Tim g Standard

H. M. CRONSON, SENIOR MEMBER, IEEE, ANDP. G. MITCHELL, MEMBER, IEEE

Abstract-The design, construction, and calibration of a passivetransmission-line network that provides 2 pulses separated by 2.5ns + 1 ps, when excited by a single pulse, is described. The timingstandard is useful for calibrating time window durations in time-domain measurement.

I. INTRODUCTION

Time-domain metrology characterizes a component by its tran-sient response to a subnanosecond baseband pulse [1], [2]. Thewaveforms of interest are acquired by a sampling oscilloscope with

Manuscript received May 28, 1973. This work was supported by theU. S. Army Metrology and Calibration Center, Army Missile Command,Redstone Arsenal, Alabama, under contract DAAHOl-71-C-1414.The authors are with the Sperry Research Center. 100 North Road,

Sudbury, Mass. 01776.

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, MARCH 1974

Open circuited stub fines-zo

~0zo zo

28(t)

T

I

Zo

1 z0 load

I

( a )

21

zo

( b)Fig. 1. Pulse delay circuits. (a) Open stub conflguration. (b) Loop

conflguration.

a computer-controlled closed-loop scan. The sampled time-domainpoints are then translated into the frequency domain and scatteringparameters computed. Frequency transformation is usually accom-plished with the fast Fourier transform (FFT) where discrete valuesare harmonically related to the reciprocal of the time window dura-tion. For example, measurements taken in a 2.5-ns window resultin frequencies which are integral multiples of 400 MHz. To avoidfrequency errors, the window duration must be accurately known.This paper describes the design, construction, and calibration of anetwork for establishing precisely the end points of a 2.5-ns window.

II. DESIGN

The timing standard was used in conjunction with a pulse gener-ator that provided an 8-V smoothed impulse with 60-ps halfwidthat a repetition rate of 80 kHz [3]. Using a variation of the open-stub technique [4], the standard provided a double-pulse outputfor a single-pulse input. The design principles can be understoodwith reference to the circuit shown in Fig. 1 (a). An incident pulseat the cross will be partially transmitted toward the load and alongthe open stubs with a transmission coefficient of 2. At a time T = 21/vlater, where 1 is the length of the stut) and v the velocity of propaga-tion, the pulses traveling along the stubs return to the cross wherethey are partially transmitted toward the load and generator. Theimpulse response of the network is given by

h(t) = 2[6(t) + a(t -T)]

which consists of the desired two impulses separated by a time T.The circuit diagram of the netw~ork actually built is shown in

Fig. 1(b) and contains several refinements. First, the two open-circuited stubs of length 1 are replaced by a continuous loop oflength 21 [5]. Thuis only one line need be cut precisely instead oftwo. Secondly, a 20-dB attenuator was added between the generatorand the cross. This reduces the magnitude of the reflection from thecross into the generator and prevents damage to the sampling diodes,if the signal from the pulse generator and time standard combinationwas fed directly into the sampling head. A photo of the standardwith the cover removed is shown in Fig. 2 (a), along with the oscillo-scope display of the two pulses in Fig. 2 (b).A crucial phase in developing the standard was to establish that

the time delay was as close to 2.5 ns as possible. Since frequenciescan readily be measured with much more precision than time inter-vals, we used continuous-wave (CW) techniques to calibrate thestandard. The measurement procedure consisted of cutting thelength of the timing line, 21, so that the observed nulls in the fre-

quency response of the fixture occurred at the desired predeterminedfrequencies. The null frequencies can be determined from the FFTof h(t), i.e.,

13[h (t)] = H () = [1 + exp (-jwT)].

We observe that H (co) = 0, whenwxT = (2n + 1) r for n = 0,1,2,* - .For T = 2.5 ns, the null frequencies are f = (2n + 1) X 200 MHz.

III. CALIBRATION

A block diagram of the experimental arrangement used for meas-uring the null is found in Fig. 3. After a few small reductions in linelength, the null, as observed on the oscilloscope, occurred at 200.0MHz. Repeated trials at this length gave frequencies differing byless than 0.1 MHz. Therefore, the estimated accuracy of the timingcalibration is 2.5 ns i I ps.Trimming the loop was facilitated by the special cross design

within the box with the four screws shown in Fig. 2(a). The boxhas a top and bottom half with right-angle grooves to accept 0.141-in diameter coaxial line. The outer conductors and dielectric of thelines are removed over a short distance in the vicinity of the junc-tion and the center conductors soldered together. Trimming isaccomplished by shortening both the inner and outer conductor ofone end of the loop. Temperature effects were calculated to con-tribute less than 0.11 ps/°C and, therefore, can be neglected.The timing standard can be constructed for any desired time

window. It is simple in design and inexpensive to construct. In con-junction with the pulse generator, it provides a more accurate cali-bration than is possible with commercially available marker gen-erators.1

REFERENCES[1] A. M. Nicolson et al,, "A plications of time-domain metrology to

the automation of broad-band microwave measurements," IEEETrans. Microwave Theory Tech., vol. MTT-20, pp. 3-9, Jan. 1972.

[2] H. M. Cronson and G. F. Ross, "Current status of time-domainmetrology in material and distributed network research,' IEEETrans. Instrum. Meas., vol. IM-21, pp. 495-500, Nov. 1972.

[3] H. M. Cronson, P. G. Mitchell, and J. L. Allen, "Time-domainmetrology study," U. S. Army Missile Command, Redstone Arsenal,Ala., Final Rep., Phase I, SRRC-CR-72-9, Aug. 1972.

[4] G. F. Ross, "The synthetic generation of phase-coherent microwavesignals for transient behavior measurements," IEEE Trans. Micro-wave Theory Tech., vol. MTT-13, pp. 704-706, Sept. 1965.

151 , "The generation of pulse-modulated signals at C band andbeyond," IEEE Trans. Microwave Theory Tech., vol. MTT-19, pp.96-99, Jan. 1971.

1 For example, the Model 901 Marker Generator manufactured byEH Research Laboratories, Inc., Oakland, Calif.

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SHORT PAPERS

(a)

( b)Fig. 2. Timing standard photographs. (a) Fixture with cover removed. (b) Oscilloscope display of timing pulses (vert.

scale 200 mV/div; hor. scale 500 ps/div).

Coaxial tees -'

Fig. 3. Experimental block diagram for calibrating the timing standard.

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