Advisory Panel Jonathan W Amy Jack W Frazer G Phillip Hicks
INSTRUMENTATION Donald R Johnson Charles E Klopfenstem Marvin Margoshes
Harry L Pardue Ralph E Thiers William F Ulrich
High-speed Current Measurements PIETER G. CATH ALAN M. PEABODY Keithley Instruments, Inc., 28775 Aurora Rd., Cleveland, Ohio 44139
Electrometers provide the means of detection and measurement of small electrical currents in many important instrumental methods utilized in chromatography, electrochemistry, and spectroscopy. A consideration of several approaches to high-speed current measurements can prove helpful in designing or selecting an optimum detector for a particular instrumental application. MEASUREMENT of small electrical currents has been the hasis for a number of instrumental methods used by the analyst. Ion chambers, high-impedance electrodes, many forms of chromatographic detectors, phototubes, and multipliers are commonly used transducers which require the measurement of small currents. Devices used for this measurement are often called electrometers. It is the purpose of this article to point out the trade offs that one makes to ohtain desired characteristics and to present in some detail the design techniques for a new type of electrometer which is optimized for measurements in the 1 Hz to 5 kHz region (lo-" to 113'~ A resolution).
THE
Current-Detection Limitations. I n any measurement, if source noise greatly exceeds that added by the instrumentation, optimization of instrumentation is unimportant. When source noise approaches the theoretical minimum, optimization of instrumentation characteristics becomes imperative. To determine the category into which his measurement falls, the researcher needs to he familiar with the characteristics which impose theoretical and p r a c t i h limitations on his measurement. Most researchers are familiar with the theoretical limitations present in voltage measurements. The noise increases with source resistance, and the familiar equation for the mean-square noise voltage is exz = 4 kTRAf
(1 ) where k is the Boltzmann constant, T is the absolute temperature of the source resistance, R, and ~f is the noise bandwidth ( d 2 times the 3 dB bandwidth for a single R C rolloff) _._,_ I n the case of current measurements, i t is more appropriate to con-
sider the noise current generated by the source and load resistances. The mean-square noise current generated hy a resistor is given hy Equation 2.
From this cquation, i t is immediately apparent that the measurement of a small current requires large values of R-i.e., high impedance levels. However, this presents difficulties for measurements requiring wide bandwidths because of the R C time constant associated with a highmegohm resistor and even a few picofarads of circuit capacitance. Figure 1shows a current source generating a voltage across a parallel RC. The frequency response of this current measurement is limited by the R C time constant. Figure 2 shows this response and the -3 d B point occurs a t a frequency
Low noise and high speed, therefore, are contradictory require-
,
Figure 1. In the shunt method, current is measured by the voltage drop across a resistor
Figure 2. The frequency response of the shunt method is limited by omnipresent shunt capacitance
ANALYTICAL CHEMISTRY, VOL. 43. NO. 11, SEPTEMBER 1971 (REPRINTED WITHOUT ADVERTISING]
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Instrumentation
Current-Feedback Technlqw The basic circuit configuration used in the currentfeedhack technique is shown in Figure 4. I n this configuration, the currentmeasuring resistor, R, is placed in the feedhack loop of an inverting amplifier with a gain of A.. The frequency response obtained with this circuit is identical to that shown in Figure 36. Fo again is the frequeney associated with the RC time constant
Figure 3. By tailoring
the frequency response of the amplifier (3.9). the frequency response of the shunt method can be extended (3b)
ments. T o optimize a current-measuring system, techniques must he used which obtain high speed using high-impedance devices. High.Speed
Methods
High speed can, of course, he obtained in a shunt-type measurement by using a low value for the shunt resistor, As pointed out above, such a small resistor value introduces excessive noise into the measurement. A second method to achieve handwidth is t o keep R large, to accept the frequency roll-off starting a t PO, and to change the frequency response of the voltage amplifier as shown in Figure 3a. The combined effects of the RC time constant followed by this amplifier are shown in Figure 3b, and i t is seen that the frequency response of the current measurement has been extended to PI. The frequency a t which the amplifier gain starts to increase must he exactly equal to the frequenry Fo determined by the RC time constant in order for this approach to result in a flat frequency response. Therefore, this method is useful only for applications where the shunt capacitance, C , is constant. Aside from this drawback, this is a legitimate approach being used in low-noise, high-speed current-measuring applications. I n addition t o current noise in the shunt and in the amplifier input stage, a major source of noise in this system arises from the voltage-noise generator associated with the input stage (reflected as current noise in the shunt resistor) caused by the
high-frequency peaking in the following stages of amplification. More will he said about this in the discussion on noise behavior. A third method used for speeding up a current measurement employs guarding techniques to eliminate the effects of capacitances. Unfortunately, only certain types of capacitances, such as cable capacitance, can he conveniently eliminated in this manner. Eliminating the effect of parasitic capacitances associated with the source itself becomes very cumbersome and may not he feasible in many instances. T h e major sources of noise in this system are identical to those mentioned in the second system. A fourth circuit configuration combines the capability of lownoise and high-speed performance with tolerance for varying input C and eliminates the need for a separate guard by making the ground plane an effective guard. This is the current-feedback technique. This technique gives a typical improvement of a factor of three over shunt techniques. Again, the major sources of noise are identical to those mentioned in the second system.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 11. SEPTEMBER 1971
The frequency response of the system is extended t o a frequency F , where
FI = A Z O
(5)
Note t h a t the frequency response is automatically flat without having to match break points. However, the total bandwidth of the system, FI, is still limited by the value of the shunt capacitance, C , across the input. This improved frequency response of the feedback technique avoids the use of low values for R which could generate excessive current noise. Refinements of the Feedback System. A major difficulty of the feedback system arises from shunt capacitance associated with the high-megohm resistor, R, in the feedback path. If the shunt capacitance across this resistor is CF, then the handwith, FP, of the system is determined by the time constant, RCa
A slight modification of the feedhack loop can correct this problem, as shown in Figure 5. If the time constant, RICI, is made equal to the time constant, RCs, it can be shown
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Figure 4. Basic circuit configuration for the feedback method
that the circuit within the dotted line behaves exactly as a resistance R. The matching of time constants in this case does not become a drawhack because the capacitances involved are all constant and not affected hy input capacitance.
Figure 5. Frequency compensation in the feedback method removes the effect of shunt capacitance across the high-impedance measuring resistor
Noire In Current Measurements
Noise forms a hasic limitation in any high-speed current-measuring system. The shunt system gives the simplest current measurement but does not give low-noise performance. A properly designed feedback system givcs superior noisebandwidth performance. Noise Behavior of the Shunt Syslem. High speed and low noise are contradictory requirements in any current measurement hecause some capacitance is always present. The theoretical performance limitation of the shunt system can he calcudoes not contribute noise to the lated as follows: measurement. The rms thermal noise current, i , , , Noise Behavior of the Feedback Sysgenerated by a resistance R is given tem. There are three sources of by noise in the feedback system that have to he looked a t closely. The first two, input-stage shot noise and current noise from the measuring reThe equivalent noise bandwidth, Af, sistor, are rather straightforward. of a parallel RC combination is Af The third, voltage noise from the in= 1/(4 R C ) and the signal bandput device of the amplifier, causes width (3 d B bandwidth) is Fo = some peculiar difficulties in the mea1 / ( 2 r R C ) . For practical purposes, surement. peak-to-peak noise is taken as five Any resistor connected to the intimes therms value. put injects white current noise The peak-to-peak noise current (Equation 7). I n the circuit of Figcan now he written as ure 4, the only resistor that is connected to the input is the feedback inpn = 2 x 10-9 F~ 4 .5 (8) resistor, R. As in the shunt system, R must he made large for lowest I n practice, a typical value for noise. Because this noise is white, shunt capacitance is 100 pF. With the total contribution can he calcuthis value, the following rule of lated by equating Af to the equivathumb is obtained: lent noise bandwidth of the system. The lowest ratio of detectable The second source of noise is the current divided by signal bandcurrent noise from the amplifier inwidth using shunt techniques is put. This component is essentially 2 x l W 4 A/Hz for a peak-tothe shot noise associated with the peak signal-to-noise ratio equal gate leakage current, io, of the input to 1. device. Its r m s value equals A corollary for this rule of thumb expresses the noise current in terms of obtainable rise time (10-90% rise Z=d/Zj (9) time t, = 2.2 R C ) . The lowest product of detectwheree is the electronic charge. able current and rise time using The contribution of this noise genshunt techniques is 7 X erator is also white. Not only do Asec. these two noise sources generate I n this derivation i t has been aswhite current noise, the noise in a sumed that the voltage amplifier ’
Figure 6. The voltage noise associated with the amplitier input device is an important source of noise in the high-speedfeedback system
given bandwidth is also independent of the input capacitance, C. The major source of noise in a feedback current measurement is the noise Contribution associated with the voltage noise of the input amplifier. The voltage noise can he represented by a voltage noise generator, en. a t the amplifier input as shown in Figure 6. This noise generator itself is assumed to be white. However, ita total noise contrihution to the current-measuring system is not white. Inspection of Figure 6 will reveal that a t low frequencies a large amount of feedback is applied around the voltage noise source, e.. However, the RC combination attenuates the high-frequency components of V,, so that no feedback is present a t high frequencies. Thus, the noise Contribution to the output voltage, V,.,, from the voltage noise source, en, is no longer independent of frequency. The noise is “colored” and increases in intensity for all frequencies higher than Fo. The resulting noise spectrum is shown in Figure 7b. The total system noise is related to the area under this curve. Because the logarithm of frequency ie plotted on the horieontal axis, the area under the curve a t higher frequencies represents a significantly larger amount of noise than a similar area a t low frequencies. For comparison, Figure 7a shows
ANALYTICAL CHEMISTRY, VOL. 43. NO. 11, SEPTEMBER 1971 IREPRINTED WiTHOUT ADVERTISING)
Instrumentation
T o obtain optimum wideband noise performance under these conditions, a filter with a single highfrequency roll-off-i.e., -6 dB/ octave-is not sufficient and -12 dB/octave is required. The effect of 3, -6 dB-filter is shown in Figure 7a, b. The filter is used to limit the system bandwidth to a frequency F1, smaller than F1. The effect of A this filter on the noise spectrum is shown in Figure 7 b . It can be seen that there are again high-frequency noise components above Fz,the useable bandwidth of the system. These can be eliminated by using a filter with a -12 dB/octave roll-off. The result of such a filter on noise performance is also shown in Figure 7b. The reason that a -12 dB-filter gives superior performance over a -6 dB-filter in this application arises from the unusual manner in which the noise is colored.‘ I n most other cases, the noise is reasonably white across the bandwidth of interNOISE est and a -12 dB-filter then gives INCREASED C,, SPECTRUM C only marginal improvement. (id*} One parameter affecting t’he noise behavior remains to be discussed. This is the effect of the input capacitance, C, on the voltage noise. An increase in t’he input capacitance will lower the frequency, F o , and also F1 since F , = AoFo. Figure 7 c shows how an increase in input capacitance changes the noise spectrum. Because total-system wideFigure 7. The bandwidth of the high-speed feedback system (a) can be limited by using a filter with either a -6 dB/octave or a -12 dB/octave roll-off. The effect band noise is related to t’he area unof the filter on the noise spectrum is shown in b. Effect of input capacitance on der the noise-spectrum curve, this noise is shown in c increase in input capacitance results in more wideband noise. For the same reason, increased At the high-frequency end, the noise also results from adding cathe frequency response of the curvoltage noise is liniitcd by the fre- pacitance across the feedback resisrent-measuring system. Figure 7a quency, F A , which is the high-fre- tor: R , which is often done to limit is iclcntical to Figure 3b. quency roll-off point of the opera- the signal bandwidth and is referred It is interesting a t this point to tional amplifier. I t should be noted comparc this noise spectrum with to as damping. For low-noise widethat even though the useful bandthc frequency rcsponse of the voltband performance, signal bandn.irlth of thc system extends only to width should be limited by use of a age aniplificr i n Figure 1 as shown F 1 , there are noise componcnts of in Figurc 3a. A vo!tagc noise source filter amplifier. higher frcquency present. TO oba t the input of tile amplifier nould Sarrowband signal-noise perfortain bcst xiclcbintl noise ~icrfor- mance, as when using the amplifier generate a noisc spectrum according ni:incc, thcse high-freqllency noisc to the tunplifier frcqucncy rcsponse in a lock-in system, is dependent componcnts have to be removed. only on the net system noise a t the as s1~on.n in Figurc 30. The noise This c:in he ncllie\d by atltling a apectriim of such a system, thcn, is chosen operating frequency and is low-pass filter scction following tlie independent of any bandwidth limitlentical to the noise spectrum of fcctll):ick input stage. If thc I)nndthc fccdback system ns givcn in Figiting in the input amplifier. ,4s can ure 7b. This illustrates the ~ c l l - \xws of this lo\v-l,ass filtcr is ti1Rdc be seen in Figure 7c, increased input :itljristnble, tliis filtcr cnn Pc’rve tlie k n o \ ~ nfact tli:it .signal-to-noise percapacitance incre,ases narrowband dual purpo.sc of rcinoving high-freformnncc of a nicasureincnt cannot noise if F , falls below the operating cliicncy noise :inti of limiting thc .sigbc improvctl by fectlI):ick tcclifrequency. 11ii1 hii(1ividtIi of tlic system. n i qucs.
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ANALYTICAL CHEMISTRY, VOL. 43, NO. 11, SEPTEMBER 1971 (REPRINTED WITHOUT ADVERTISING)
Instrumentation -
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incrcinlly :ivnilnblc currcnt amplificr ivill I)c drscri1)cd. This amplifier (Kcitlilcy AIodcl 427) is debigiictl to incorporate tlic principles dcbcrilml above. Figure 8 shows a hlocl; diagram of tliis high-spced c~irrcnt-mcnsuriii~ systcm. The input nmplificr is n wideband, highgain fcetllxwk systcm using a fieldcffcct transistor input. Tlie clioicc of input device is determined by the trade-off s involving the dcbired sensitivity, stability, and frequency response. Figure 9 shoms the frcqucncy and scnsitivity areas for which diffcrcnt input devices have proved optimum, taking into account that most of the dcvices are limitcd by the practical rule of thumb of lo-'* A/Hz. Electron counting is the exccption with a practical limit of 10-l' A/Hz. The input amplifier is followed by an adjustable low-pass filter having a -12 dB/octave roll-off and a voltage gain of lox. The voltage gain i n the low-pass filter avoids premature overloading in the input amplifier which can be seen as fol-
Event-Counting Techniques
h 11 cii t i rely tli ffercn t approach
t0
nicasurcmciit of ina all currents is I'owiblc with event-counting tccliiiiqucs. In thcse tecliniqucs, intliviclunl clcctrons are counted in a fashion similnr to the counting of rndintion quanta in. photon counting. Thcec tccliniqucs arc limited to measuring small currcnts in a i.ncuuin. T o IK dctcctnblc, electrons miist bc tlctcctcd nitli an elcctron multiplier or ~)lioto-multiplier. Very sinnll currents can be nicnsured, but circuit spccd limits the maximum tletcctnblc currcnt to thc range of to l O - I 3 A . Rcsolution in this technique is dctcrmincd by statisticnl conderntions, and the product of resolution and rise timc for this nietliod is 4 >< 10-lRAsec. tlic
High Performance Current Amplifier
As an cisample of n.1iat can be achieved with the feedback technique, the performance of a com-
9
R.
R
ADJUSTABLE LOW-PASS FILTER
1
0
*
Ir. *
Figure 8.
..-J
Block diagram of a high.speed current amplifier (Keithley Model 427)
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l
l
l
l
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lows. The maximum output mage Vout is 2 1 0 V. The maximum signal level a t the input of the lowpass filter is, therefore, +1 V. At this point in the circuit, wideband noise could still be present and exceed the 1-V signal level. The voltage gain of 10 in the filter allows the total pre-filter wideband noise to exceed the full-scale signal by a factor of 10 (20 d 3 ) . The frequency response of this filter is adjustable for variable damping control. T o complete the 427 Current Amplifier a current-suppression circuit is added and overload-sensing circuits monitor pre- and post-filter overloads. Xoise performance must be examined for two methods of measurement. First, dc techniques for real-time measurements with bandwidth equal to the current-amp ifier frequency response must be considered. Second, we must examine ac techniques (lock-in, Boxcar) where the current-amplifier frequency response must extend to the operating or center frequency while bandwidth is limited to a much lower value by the demodulator time constant. It should be noted that use of ac techniques is to be avoided if the prime noise contributors are white, that is, if they have a constant noise per unit bandwidth. First, by definition, white noise increases with bandwidth regardless of center frequency, even if that frequency is dc. Second, a current-amplifier-shunt or feedback-requires lower shunt resistors as operating frequency is raised and noise per unit bandwidth increases with operating frequency. Thus, translating the operating frequency from dc provides no reduction in noise and may actually increase it. The sensitivity and speed of the 427 Current Amplifier for either dc or ac measurements can be compared to the best performance obtainable with the shunt method. The best noise-rise time product that can be achieved for dc measurements with a 100-pF shunt capacitance in a shunt system is equal to 7 x Asec. The feedback amplifier achieves 2 X 10-15 Asec with a 100-pF input shunt capacitance, which is approximately a 10dB improvement. This 10-dB improvement over a theoretically per-
ANALYTICAL CHEMISTRY, VOL. 43, NO. 11, SEPTEMBER 1971 (REPRINTED WITHOUT ADVERTISING)
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Inmumentation
Figure 10. Plot Of noiseimprovement contours illustrating the improvement that can be obtained with the feedback method over the best that can be achieved with the shunt method at different OPerating frequencies
feet shunt system typically covers the span of bandwidths from 1 Hz to 3 kHz, with input shunt capacitance between 10 and loo0 pF. When used in ac narrowband systems, the degree of improvement depends on the amount of input capacitance and the operating frequency. The achievable improvement over the shunt method can be plotted in a graph similar to a set of noise contours. Figure 10shows the
measured improvement (negative dB) that can be obtained with the 427 amplifier at any given frequency and input capacitance cumpared to a shunt method using an ideal (noiseless) voltage amplifier. Acknowledgment
The contributions of G.Angeline, J. Maisel, and R. Babinec are gratefully acknowledged.
ANALYTICAL CHEMISTRY. VOL. 43. NO. 11,SEFTEMBER 1971
[REPRINTED WITHOUT ADVERTISING1
