Instrumentation
MEASURING FAST OPTICAL SIGNALS! Amplifiers, Displays, and Transmission Lines F. E. Lytle Department of Chemistry Purdue University Lafayette, Ind. 4 7 9 0 7 This is t h e second of a two-part series designed t o examine t h e various experimental approaches used t o measure fast optical signals ( > l o 0 psec and < l o 0 nsec), and give a detailed discussion of individual components. A survey of available technology is accompanied by a critical evaluation of attendant drawbacks. T h e first p a r t of the series discussed detector characteristics and availability ( I ) ; this second part is concerned with t h e problems involved in transforming t h e detector current output into a usable displayed signal. Amplifiers and Displays
Pulse Amplifiers. All of the detectors discussed, except mechanical streak cameras, are photon-to-electron convertors. Monitoring fast optical signals can then be reduced to one of making high-speed current measurements. Unfortunately, performing this task a t low current levels is extremely difficult (2).T h e origin of t h e problem resides in the expression for t h e rms thermal noise current generated in t h e amplifier shunt resistance R. Its value can be determined by t h e relationship:
where ii and T have their common meaning, and L f is t h e equivalent noise bandwidth of t h e amplifier. This equation indicates t h a t low noise current is only attainable for large values of R On the other hand, t h e 3dB bandwidth of t h e amplifier is determined by:
where C is usually t h e stray s h u n t capacitance. This equation dictates a small value of R for making fast measurements. Thus, the noise a n d t h e bandwidth (risetime) are always traded against each other. By use of s h u n t techniques, a n order of magnitude guide for t h e rms current-risetime product is 1.4 X A-sec when t h e signal-to-noise ratio is unity (2).Thus, a risetime of 1 nsec (10-90%) yields a minimum detectable current of 1.4 FA. Naturally, a n improved risetime generates more noise, whereas a lower noise level degrades the risetime. A large variety of fast pulse amplifiers is available, and a few are shown in Table I. When choosing a n amplifier, one should be careful not to simply employ a unit designed for CW operation even when it satisfies t h e 7 , . - F A 3 d ~ = 0.35 relationship (2). Such devices often ring when subjected t o abrupt changes and “droop” over any level portion of t h e waveform. Pulse amplifiers are specifically designed to remain linear a t high frequencies and to introduce a constant phase delay for all frequencies. T h e smallest signal t h a t can be amplified with a unity signal-to-noise ratio is determined by t h e equivalent noise input, which, as an examination of Table I shows, follows t h e current-risetime guideline very well. T h e largest linear output varies from model t o model but normally falls between 1-10 V. When cascading several amplifiers to achieve higher gains, two consider-
ations have t o be made. First, t h e equivalent noise input to t h e initial stage will be amplified and added to t h a t for the second and subsequent stages. Thus, a n input signal-to-noise ratio of 1:l will undoubtedly get worse as the number of stages is increased. Second, t h e overall risetime of the combination can be calculated by t h e relationship:
where 7 2 , ~ 3 etc., , are the individual amplifier values. An interesting result of the propagation of risetimes is t h e observation that a n amplifier only three times faster than a n attached detector will introduce less than a 10% additional error in measuring t h e optical waveform. Thus, a 500-psec amplifier will not significantly distort the output of any of t h e photomultipliers listed in Table V in ref. I , and with t h e exception of t h e crossed-field devices, would only distort those in Table VI in ref. 1 by a maximum of 40%. One natural application of highspeed pulse amplifiers is t h e situation where the available light level is larger than the minimum detector limit given in Table X of ref. I , b u t t h e corresponding current output is not large enough to drive the chosen display. As an example, consider the single photon pulse output of a n EM1 98169B when it is used as a n input to t h e ORTEC time-to-amplitude convertor (TAC). Simply put, the peak current (2.1 mA computed by dividing t h e gain by the number of electrons per
ANALYTICAL CHEMISTRY, VOL. 4 6 . NO. 9, AUGUST 1974
817A
Table 1. Characteristics of Several Fast Pulse Amplifiers r,, nsec
Gain
Noise. limit, pV
Max output, V
Droop, %/psec
Manufacturer
Yt3
i/lOO ft,' MHz
174 58A
1500 1900
1TC 1TC
0.105 V 0.199 v
7 cw 19 T C
10 50
58C
1900 1900
1TC 2 sc
0.199 NCV 0.219 NCV
19 TC 1sc
50 50
3000 5000
2
sc 1c
0.336 NCV 0.412 NCV 0.475 ANCV 0.432 NCV 0.555 NCV0.880 NCV 0.945 ANCV
1 sc
150 200 200 200 400 500 500
223 212 213 215 214 217 21 8 219 Data f r o m Alpha.
5000 50130 7000 11Ol10 11000
I C 2 sc 2 c
1c
1c
7 c 7 c 7 sc
1c 1c 1c
'
Suitable connectors
-
BNC, TNC, SMA, GR BNC, MHV, TNC, GR, VHF, C, N, S M A BNC, TNC, VHF, GR, C, N, SMA C, N VHF, C, N, GR VHF, C, N, G R VHF, C, N , APC, GR C VHF, C VHF, C
', C
c3pper' TC, t i n n e d c o p p e r ' 3C silvered copper' CW copper-covered steel. c Outside cable diameter iri inches; V, Polyvinylchloride; NCV. nonbontamihating polyvinylchldrtde'; ANCV, NCV w i i h an'arrnor of 0.126 aluminuni wire. ,] N u m b e r of strands t o center C o n d u ~ t o r '. Data estimated from AniDhenol Catalogue W61. 2
a t different delayed times. After this operation t h e multiplexed ADC can examine their voltages at a relatively slow rate. An example is t h e LRS Model WD2000 (Table 111). T h e chief advantage of this approach is the ability to have variable and/or arbitrarily close sample spacing. Naturally, t h e chief disadvantage is t h e cost necessary to gather a large number of points. 'The convertor device operates on a completely different principle. A fast electron beam gun writes on a miniature array of silicon diodes. This array can then be interrogated at t h e user's leisure by use of a read gun. T h e result is an image reconstructed either as binary words or a T V picture. T h e convertor itself can capture and display sine waves as fast as 2.4 GHz ( 4 ) ;howevrr, the need for oscilloscope vertical and horizontal amplifiers reduces t h e small signal capability to 500 MHz. In general, there are several points
about transient waveform analyzers t h a t t h e potential user should keep in mind. First, unlike sampling oscilloscopes, t h e aperture time might not bear any relationship to t h e risetime of t h e device. Second, their sensitivity may be poor and may require some form of preamplification. Finally, and most important, t h e degree of signal shot noise should be estimated since i t cannot be averaged out by repetition. As an example, consider a 400-nm optical pulse yielding a 50-mV signal when followed by a n RCA C70045D photomultiplier ( T =~ 0.5 nsec), amplified by a Tektronix ';A19 plug-in ( T =~ 0.8 nsec), and displayed on a Tektronix R7912 transient recorder. By use of the overall detector sensitivity of 7.9 X l o 5 A/W, a corresponding optical power of 1.3 n W can be calculated. This corresponds to about two photons per risetime interval! Even if t h e signal were increased to 5 V, the number of photons per time interval would
still be only 200 with a corresponding shot noise level of about 7%.
Transmission Lines General Considerations (5-7). As the frequency of a n electrical signal traveling along a conductor is increased, the bulk o f t h e current being carried will be shifted to a small layer near the surface. This is called the skin effect and is due to inductance generated within the conductor. In a d dition, the reactance associated with any stray shunt capacitance will decrease with increasing frequency. As a result of these two problems, the propagation of nanosecond pulses over normal conductors becomes difficult. A transmission line consists of two parallel conductors so arranged t h a t t h e electromagnetic wave is situated between them. T h e current does not have to go below the skin to propagate freely, dramatically reducing the effect of self-inductance. In addition,
ANALYTICAL CHEMISTRY, VOL. 46. NO. 9 , AUGUST 1974
821 A
the shunt capacitance to ground can be controlled carefully by the nature of the dielectric material and the conductor spacing. Consequently, a pulse can be sustained in a transmission line with minimal distortion. Transmission lines can take several forms, the three most common being parallel wires (twisted pairs), a strip parallel to a ground plane (strip lines). or coaxial conductors. In each case, the impedance can be expressed as a pure resistance calculated by simple formulas (Figure 2). Although the exact magnitude is arbitrary, a detailed examination of the sources of distortion yield best values of 70 R for an air dielectric and 50 R for plastic dielectrics. The user should be reminded that such lines do not have a d c resistance t h a t is related in any way to their nominal impedance. In fact, the dc value should be as close to zero as possible, if signal distortion is to be minimized. All t h a t the rating implies is the Ohm's law relationship between the magnitude of the radio frequency voltage and the corresponding current. Table IV lists some of the more common cables. They are placed in an order determined by several major physical variables: voltage, number of shields, and jacket material. T h e RG58A/U is probably the most common type for general applications; the RGl74IU is useful where a small size is important. Risetimes and Delay Lines. For short distances (-1 f t ) the risetime of virtually any coaxial transmission line is insignificant compared to t h a t for most detector-amplifier combinations. However, because of the finite resistance of the conductor and highfrequency interactions with the dielectric, the risetime increases with the square of the length of the cable. T h e severity of this problem can be estimated from the 3dB frequency given in Table IV. Operationally, one should use F B ~to B calculate the risetime for 100 f t and then adjust the value for the actual length of cable employed. If extremely long runs are required for equipment interconnections, the fastest cable should be considered even if it is of a n undesirable diameter. As an example, a 100-ft length of 58A (0.199 in. diam) would have a risetime in the vicinity of 35 nsec, whereas the same run using 218 (0.88 in. diam) would only have a value of 0.7 nsec. Many applications exist where signals are to be stored or delayed for timing purposes. When delays of 20 nsec or less are required, simple cables will suffice, with the necessary length depending upon the speed of electromagnetic radiation through the dielectric. The ratio of this velocity to t h a t of light in a vacuum is given by l l h , where h is the square root of the di822A
Table V. Characteristics of Several 50-n Coaxial Connectors Fee. . ._
Type.
quency limit Voltage GHz' VSWR
Matin@
APC-7
.,.
12.4
1.15
S
SMA
375
1.8
1.15
T
GR 900
500
8.5
1.06
GR
874 BNC
500 500
8
1.1 1.3
S
10
TNC
500
10
1.3
T
c
1000
10
1.25
B
N
1500
11
1.25
T
TPS
1500
10
C
4000
2
1.3 1.25
B
"> B
B
APC, a recision connector. SMA SMB etc., subminiature: BNC, bayoneted qeal connector; fNC,threaded neal donnedtor; C,' constant; N. neal; and TPS.three pin series. a S, sexless; B, bayonet; T, threaded.
electric constant of the material ( l l h equals 0.66 for polyethylene and 0.71 for Teflon). Since light travels 30 cm in 1 nsec, the propagation distances will be 19.8 cm/nsec in polyethylene and 21.3 c m h s e c in Teflon. When the delay times get longer than 20 nsec and signal distortion is not desirable, commercial lines should be used. As examples, the Tektronix Model 7 M l l provides two fixed 75nsec delays each with a risetime of 173 psec; and the Ortec Model 425 provides delays up to 31 nsec in 1-nsec steps. Coaxial Connectors. Obviously, the object of a connector is to provide a flexible method for transferring a signal from one point t o another without the necessity of soldering. Table V lists the characteristics of several types and demonstrates t h a t as in coaxial cables, the major variabilities are voltage, size, and frequency response. One new important parameter has been added, the voltage standing wave ratio ( V S W R )(8).This is defined mathematically as V S W R = (Vo V r ) / Vo ( - V,), where Vo is the original voltage sent down the cable toward the connector, and V , is the voltage reflected back up the cable from the connector. In analogy with the refractive index, this value is a measure of the impedance mismatch between the cable and the connector. The closer to unity, the better the match and the smaller any reflection. If the equipment to be interconnected does not already come hardwired, one should first choose the coaxial cable since this may restrict the selection of connectors. Next in the decision should come the operating voltage, frequency response, and
+
ANALYTICAL CHEMISTRY, VOL. 46, NO. 9. AUGUST 1974
the VS WR. Finally, if a choice still exists, one might choose among sexless, bayonet, or threaded couplings. Although it is certainly possible to assemble your own coaxial connectors, our experience has indicated that somewhere around 10-100 MHz, the beginner's job may attenuate and/or distort fast signals. This is particularly true when newer crimped versions are used instead of the older clamped varieties. To avoid any potential problems, the novice might want to purchase preassembled cables available from several manufacturers. As examples, Tektronix sells BNC, N, GR, and SMA connectors attached to a variety of cables; Times Wire and Cable offers TNC-cable combinations with a n F j d R near 10 GHz. Adapters. Virtually any connector can be mated with another type by the use of adapters. The main disadvantage of their prolific usage is the introduction of additional reflective losses. In addition to the standard varieties, Amphenol makes SMA-to-stripline jacks that can be mounted directly onto printed circuit boards. The use of ordinary BNC tees should be avoided a t higher frequencies. Instead a 50-12 power divider, such as the GR 874-TPD, should be employed if the signal really is meant to be split, or a pick off such as the Tektronix 017-0061-00 if the second branch is to be a trigger source. Terminations and attenuators should have the requisite frequency characteristics. As examples, Tektronix offers a BNC 50-Cl feedthrough termination with a V S WR of 1.2 a t 500 MHz, whereas the same device in an SMA configuration has a V S W R of only 1.15 a t 18 GHz.
Grounding. A compete discussion of radio frequency grounding techniques is beyond the scope of this article. The reader is referred to Morrison’s monograph on the subject (9). However, it is imperative t h a t one piece of advice be given. When attempting to achieve interdevice grounding, the connecting wire should be constructed from a hollow wire braid threaded with a solid copper conductor. Every foot or so, the two should be brought into good electrical contact by soldering. This procedure assures both a dc and radio frequency ground by circumventing the skin effect. Alternate Approaches Throughout the above discussion of fast components, it was assumed that the signal was being examined directly. T o add some degree of perspective to this coverage, there are several methods involving indirect measurements. T h e two most common of these alternates are the single-photon and gated detector schemes for the nanosecond regime, and electric Kerr effect shutters and two-quantum techniques for the picosecond regime ( I O ) . In the single-photon method, a fast optical signal is reconstructed by measuring the time interval between the start of the experiment and the arrival of the radiation a t the detector. If the instrument is so designed that only one photon causes a cathode photoejection per experiment, the original intensity distribution is equivalent to a count vs. time interval plot ( 1 2 ) . There are essentially three advantages to this approach. First, the transit time spread of the photomultiplier determines the time uncertainty instead of the anode risetime. This generates a concomitant improvement in the time resolution by a factor of two to three. Second, the instrument is extremely sensitive since it is designed to operate via single photons. And finally, the data are automatically presented in a digital format facilitating any numerical treatment. Disadvantages are the relatively high cost (as compared to a sampling scope route) and the requirement t h a t the event has to be repeated a large number of times (2.5 x IO6 repetitions for a 500channel triangular pulse and a 1%precision). In a gated detector a grid is placed inside the tube close to the photocathode. The potential of this grid is ordinarily kept more negative than the cathode so that any ejected electrons are repelled back to the photoactive surface. Then a t some fixed time with respect to the start of the experiment, the tube is turned on by applying an attractive potential to the grid. The operative time of the detector is sim-
ply determined by how long the grid is held a t the “on” state. By slowly varying the delay between the start of the experiment and the start of the gating, the detector can be made to behave like a boxcar integrator. Two advantages of this approach make it quite attractive. First, the only fast circuitry involved is the pulse generator used to drive the gating grid; consequently, an ordinary picoammeter with a long time constant can be used to measure the anode output. And second, the average current limitations of the tube are hard to surpass since it is in an “off” state most of the time. Therefore, it is excellent for observing high repetition rate signals or short time segments of longlived phenomena. T h e chief disadvantage is relatively slow gating times (2-5 nsec) as compared to the risetimes found in Tables V and VI in ref. 1. Conclusions Once the detector has been chosen, the physical description of the experiment and the desired form of the output can be used to specify a signal processing system.
T i m e Scale. Virtually any type of amplifier-display combination can be used for times greater than 1 nsec. However, sampling techniques and repetitive signals (ignoring streak cameras) are required for the picosecond regime. The overall risetime of the system is determined by the sum of the squares of those for the components, including the interconnecting cables. Repetition R a t e . With repetitive signals any approach discussed can be used. On the other hand, single shots must be examined by transient waveform recorders. When performing such an experiment, the effect of inherent photon noise should be calculated, particularly if detecting the signal requires the full gain of a photomultiplier. Sensitivity. I t is best to obtain the requisite sensitivity directly via the detector. This is because the limitations given in Table X in ref. 1 cannot be beat by any amount of post amplification. If the sensitivity is satisfactory, but the detector signal is not large enough to drive the display device, go to a pulse amplifier to gain the needed improvement.
Figure 3. Measurement space for fast optical signals and suggested instrumental approaches Area inside any circle denotes specific type of signal; area outside has opposite connotation. Thus, space exterior to all three rings would represent intense, repeatable nanosecond event
ENSIT
slier/
Any D e t e c t o r / Sampling S c o p e
ANALYTICAL CHEMISTRY, VOL. 46, NO. 9, AUGUST 1974
823A
Hardcopy Output. Transient waveform recorders possess t h e most convenient output in t h e form of a n analog or digital image. Next down t h e line are sampling oscilloscopes and boxcar integrators, which provide analog output and can be readily interfaced t o a computer via a n external DAC and/or ADC. T h e least flexible approach is t h a t utilizing a traveling wave oscilloscope, since the user usually has to resort t o photography. Cost. Cost effectiveness decisions are possible in choosing a display system. As an example, t h e boxcar integrator should be used only by those possessing no electronic expertise or those having large sums of money. This is because a sampling oscilloscope can be made to behave like a boxcar integrator for a small investment. An opposite example exists with low repetition rate signals. If the event can a t all be repeated, a transient waveform recorder might be substituted for a sampling oscilloscope. T h e chief advantage of this arrangement is the ability to gather many data points per experiment, t h u s minimizing the overall time necessary to achieve a Although highly experigiven S/N. ment dependent, the costhime tradeoff probably exists around a 10-lo2 Hz repetition rate.
In Figure 3 t h e three key parameters, time, intensity, and repetition rate, are used to characterize the measurement space applicable t o fast optical signals. T h e suggested approaches are a balance between cost, ease of assembly, and t h e ability t o process the data. The time scale by itself is not a strong factor in determining the instrumental configuration. Its only real effect is t o eliminate t h e transient recorder on t h e basis of risetimes. Next, the signal intensity dictates t h e choice of detector. Photodiodes are chosen for strong signals because of wiring simplicity and minimal power supply requirements. Finally, t h e repetition rate combined with a subnanosecond time scale imposes the most severe restrictions on the experiment. For such signals with a high intensity, streak cameras are necessary, whereas those with a low intensity are the author’s idea of a losing proposition owing to inherent optical shot noise.
Acknowledgment T h e author is indebted to J. Amy, R. Santini, and T . McCain for discussion on experimental approaches in the gigahertz regime. Appreciation is also extended to A1 Kumble of Amphenol Corp. for his help in deci-
Polymer Molecular Weight Methods
phering the abbreviation for several of the coaxial connectors.
References (1) F. E. Lytle, Anal. Chem., 46 (6), 545A (1974).
(2) P. G. Cath and A. M. Peabody, ibid., 43 ( l l ) ,91A (1971). (3) H. V. Malmstadt e t al., “Electronic Measurements for Scientists,” p p 83146, Benjamin, Menlo Park, Calif., 1974. (4) R. Hayes e t al., Electronics, 46,97 (1973). ( 5 ) I. A. D. Lewis and F. H . Wellq,“Millimicrosecond Pulse Techniques, Pergamon, Elmsford, N.Y., 1959. (6) Jack Spergel, “Coaxial Cable and Connector Systems,” in “Handbook of Wiring, Cabling, and Interconnecting for Electronics,” Charles A. Harper, Ed., McGraw-Hill, New York, N.Y., 1972. ( 7 ) W. R. Blood, Jr., “ M E C L System Design Handbook,” Motorola, Inc., 1971. (8)Douglas Blakeslee, “ T h e Radio Amateur’s Handbook,” American Radio Relay League, Newington, Conn., 1972. (9) Ralph Morrison, “Grounding and Shielding Techniques in Instrumentation,” Wiley, New York, N.Y., 1967. (10) D. J . Bradley and G. H. New, Proc. I E E E , 62,313 (1974). ( 1 1) W. R. Ware, “Transient Luminescence Measurements,” in “Creation and Detection of the Excited State,” A. A. Lamola, Ed., pp 213-302, Marcel Dekker, New York, N.Y., 1971.
Research supported in part through funds provided by the National Science Foundation under Grant GP-2224448.
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