1938
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
Sir: T h e comments from El-Hosseiny and Gilbert on my paper “Interferometric Concentration Determination of Dextran after Gel Chromatography” ( I ) are in some respects not correct. I a m compelled to correct some of their statements. (1) The signal reading is not calibrated against the anthrone method. T h e instrument, Multiref 901, is calibrated directly into RIU for full scale (e.g., I n = 100 X 50 X etc. for full scale). T h e conversion from chart reading to concentration is thus performed on the basis of a pre-known value of the specific refractive index increment of the solute. The analysis using the anthrone method was in ( I ) used as a measure of the accuracy of the interferometric method. (2) T h e method is, for certain, capable of determining the order of t h e retardation difference between the continuous flowing sample and reference solutions. T h e description of the interferometric method was mainly devoted t o the determination of small concentrations of solute (e.g., less than 700 ,ug/mL dextran) in column effluents, since this is an analysis of utmost interest. However, as readily seen from the presented theory of the instrumental principle ( I ) , higher concentrations of the solute can be determined also. T h e sinusoidal signal from the instrument will cause a cyclical pattern of t h e signal when the refractive index difference between the sample and reference cells exceeds the measuring range of the instrument (In 273 X lo4 on the Calibration range, see Equation 1 ( I ) ) . Thus, for two solutes with refractive indices producing a
-
retardation difference of la and Ip2,respectively, where A% = Ipl+ m X 360 degrees and I p l 5 66 degrees, the recorder pen will for solute 2 move u p and down to produce m fringes, read a “peak height” equivalent to that of solute 1, and finally produce a fall of the curve also consisting of m fringes before reaching the baseline. This type of signal has been presented earlier for a LC detector based upon the interferometric principle (2). It is thus obvious that the interpretation of the recorder signal is unambiguous and, furthermore, the order of the retardation difference is readily determined from the number of fringes produced by the recorder pen (provided that the response time of the system is sufficiently low). This approach is far more convenient than that suggested by El-Hosseiny and Gilbert, which includes the measurements of the retardation at two different wavelengths, which is so far not possible with t h e Multiref 901.
LITERATURE CITED (1) L. Hagel, Anal. Chem., 50, 569 (1978). (2) M. Bakken and V. I. Stenberg, J . Chromatogr. Sci., 9, 603 (1971).
Lars Hagel Pharmacia Fine Chemicals AB Box 175 S-751 04 Uppsala, Sweden
RECEIVED for review June 12,1978. Accepted August 7,1978.
AIDS FOR ANALYTICAL CHEMISTS Programmable-Gain or Auto-Gain Amplifier K. R. O’Keefe Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523
I t is frequently desirable in the chemical laboratory to provide variable gain output from instrumentation that has a large working range. Examples of such instrumentation include fluorometers, gas and liquid chromatographs, polarographs, pulse polarographs and related voltammetric instruments, and plasma emission spectrometers. The outputs from these instruments can vary by up to 5 orders of magnitude over their useful working range ( I ) . In many cabes, gain or attenuation controls are provided on the instrumentation and/or on associated readouts, such as strip-chart recorders; however, these manual controls are not generally useful for automatic data processing or data logging. Automatic gain control circuits have been described in the literature ( 2 ) ,b u t have often been complicated, expensive, and/or slow in addition to providing only attenuation of large signals. This report describes a fast, accurate, inexpensive programmable-gain amplifier that is useful with automatic data acquisition systems. This device has been used in our laboratories on a dc plasma emission spectrometer, a gas chromatograph, and a pulse polarograph with excellent results. Operation in either programmable-gain or autoranging mode is possible.
INSTRUMENTATIQN A schematic diagram of the basic programmable gain amplifier is shown in Figure 1. The operation of the amplifier can be best 0003-2700/78/0350-1938$01 O O / O
understood by considering the input-output characteristics of operational amplifier A1 (Model 3308/12C, Burr Brown Corporation, Tucson, Ariz.). The output voltage of this device, Vout, can be related to the inputs by the expression:
where A is the open loop gain of the amplifier, Vt and V are the input voltages at the noninverting and inverting inputs of the amplifier, respectively, and R L M is the common-mode rejection ratio of the amplifier (3). The input voltage, Vt,in the configuration shown is the input voltage to the programmable gain amplifier, and V is a voltage determined by the digital-to-analog converter (DAC) and amplifier (A2, Model 3308/12C, Burr Brown Corp.) in the feedback loop of A l . The output current, io, of the DAC used in this work (Model ICBBC, Date1 Systems, Canton, Mass.) is determined by the output voltage of A 1 which supplies the DAC reference current through R1 and by the scale factor inputs to the DAC (symbolized in Figure 1 by inputs of the form 2”) and can be represented by the relationship:
where N is the decimal representation of the scale factor input t o the DAC. The output voltage of A2, which is V of A l , is thus (with R2 = R l ) : V_ = N.Vo,,/256 (3) C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
1939
Table I. PROM Settings, Gain, and Voltage Ranges for t1.25 to ~10.00 V Output from Autoranging Amplifier PROM address
PROM contents
0
2
255 32 4
3
1
1
+15v
gain
input voltage range, V 1.2451 - 9.961 0.15625 - 1.23 0.01953 - 0.15625 0.00488 - 0.03906
1.0039 8
64 2 56
@
p-$j++
DAC IC3
-
MOST SIGNIFICANT W M K ) FROM COMPUTER
L A ~ ~ SIGNAL ~ s "FROM COMFUTER
--.DAD
-lSV
Figure 2. Control input schematic diagram
'Out
=
[
256.A 256 + A.NIvin
(4)
or, if A -lo6, which is true for the amplifiers used in this work, Vout
256 = --.vi, N
I
I
(5)
Thus, by putting the multiplying DAC in the feedback loop of AI, the circuit shown exploits the programmable less-than-one gain of the DAC to allow gains in the range of 1.0039 (N= 255) to 256 ( N = 1). If a multiplying DAC with a larger range of input scale factors is used, a larger gain is available. For example, a 10-bit DAC allows gains of 1.0010 to 1024 and a 16-bit DAC allows gains of 1.00002 to 65,636. The configuration of Figure 1 is used directly as a programmable gain amplifier with scale factor inputs selected either by means of switches or by the control element, which is usually a computer or microprocessor-based data acquisition system. The control configuration used is shown in Figure 2. In this circuit SW1 selects panel switch or computer gain setting by multiplexing the two sets of control lines to the DAC scale factor inputs through IC1 and IC2 (both SN74157). When the gain is controlled by the computer, an appropriate 8-bit output word is latched upon computer command into IC3 and IC4 (both SN74LS174) and this word controls the gain of the amplifier. Operation in the panel control mode allows setting the gain by manually setting panel switches (SW2-9). The amplifier can be used in an auto-gain configuration as well as in the programmable-gain configuration described above. The auto-gain configuration is shown in Figure 3. In this circuit, operational amplifiers A3 and A4 (Model 3308/12C, Burr Brown Corp.) are used as voltage comparators, comparing the output voltage from the auto-gain amplifier with reference voltages set by the potentiometers associated with the two amplifiers. Typical reference voltages are +10.00 V and +1.25 V, and the auto-gain circuit adjusts the programmable gain to keep the voltage output within this range. If, for example, the output of the programmable-gain amplifier goes above +10.00 V, the output of A3 changes from about +13.5 to about -13.5 turning Q1 (2N3393) off. Q1 acts as a level converter that converts the comparator output to a TTL compatible signal. The output of Q1 is inverted and gated to the up/down counter, U / D l , by means of a gating circuit described by Defreese, U'oodruff, and Malmstadt ( 4 ) that is intended to ensure that the counter is not triggered spuriously. The high logic level produced when Q1 turns off is inverted and is clocked into FF1 a t the next high-to-low transition of the 100-kHz clock input. The low logic datum at D is toggled onto
Figure 3. Schematic diagram of control for autogain mode of operation
the Q output of FF1 on the subsequent low-to-high transition of the clock. The 100-pf capacitor connected to the preset input of FF1 then begins to discharge through the 100-Qresistor and, after about 20 ns, the Q output of FF1 is reset to a high logic level. This 20-ns low logic level pulse appears at the "count down" input of U/D1. The output of the counter thus decreases by 1 selecting a new programmable read-only memory (PROM 1)address whose contents are output. These contents are the input to the gain select of the DAC of the programmable-gain amplifier and are available for display or input to a computer so the gain of the amplifier can be determined. For example, if the gain of the amplifier is 64 as the voltage output approaches +10.00 V, corresponding to an input voltage of 0.15625 V, the PROM contents at the address selected by U / D l would be 4 (N= 4) as can be verified by inspection of Equation 5. When the voltage increases above +10.00 V, the PROM address decreases by 1 as described above and the contents of the new address are output to the gain control inputs of the DAC. To reduce the output to 1.25 V, the contents of this new location should be 32 ( N = 32). This value of N reduces the gain of the amplifier to 8, and hence reduces the output voltage to f1.25 V for an input voltage of 0.15625 V. The circuit operates similarly if the output voltage decreases below $1.25 V. Table I shows the contents of PROM locations and voltage range available for the conditions selected. Note that for this configuration a 2-bit up-down counter and a 4 X 8 PROM is adequate. Tighter voltage limits or higher maximum gain requires a longer counter and a larger PROM.
PERFORMANCE O F T H E CIRCUIT Performance characteristics of t h e programmable-gain amplifier t h a t affect its utility for instrumental applications include input-output linearity, gain predictability, and response time. These characteristics were evaluated for the system described here and were found to be generally as
1940
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
Table 11. Linearity of the Programmable-Gain Amplifier of Figure 1 input voltage, V
output voltage, V
predicted output voltage, Vu
Table 111. Gain Predictability of the Programmable-Gain Amplifier of Figure 1
1/N error, %
N = 255 10.000
8.820 7.890 7.132 5.998 4.27 3 3.322 2.711 1.999 1.421 0.727 0.488 0.246 0.136
9.949 8.858 7.953 7.215 6.084 4.400 3.447 2.853 2.121 1.618 1.358 1.088 0.510 0.051
9.997 8.841 7.930 7.187 6.076 4.386 3.454 2.855 2.158 1.591 0.911 0.677 0.440 0.332
-0.5 t0.2 t 0.3 t 0.4 t 0.1 t0.3 -0.2 -0.1
1.7 t1.7 t 33.7 $. 37.8 t 13.7 -551.0 -
N == 8 0.2500 0.2000 0.1500 0.1250 0.1000 0.0750 0.0500 0.0300 0.0200 0.0100
8.200 6.647 5.033 4.211 3.422 2.611 1.823 1.177 0.864 0.471
8.222 6.621 5.021 4.221 3.420 2.620 1.820 1.180 .860 ,540
-0.3 t 0.4 t0.2 -0.2 tO.l
-0.3 t 0.2 -0.3 t0.5 -14.6
Predicted from regression expression Vmt = 0.9797Vh 0.199 V for N = 255 and Vat = 32.OlVh t 0.219 V for N = 8. a
t
expected, based upon t h e specifications of t h e devices used in t h e actual circuit. T h e linearity of the programmable-gain amplifier of Figure 1 was measured a t several different values of N and was generally excellent for output voltages greater than about 1 V. Typical results for two values of N are presented in Table 11. T h e values of gain from the regression expressions from Table I agree well with the theoretical values of 1.003 and 32.000 (errors-2.4 and +0.03%, respectively, for hi = 255 and N = 8). T o achieve low offset voltages, amplifier A1 must be very carefully adjusted for zero offset voltage. Alternatively, an offset circuit can be added t o the output of A2 of Figure 1. I t is important to keep t h e voltage output of A2 positive at all times as a negative excursion will cause the circuit to become unstable and latch-up. I t is also important to work in t h e range of output voltages from +1.5 to +10.00 V. This is largely due to the DAC specifications which ensure good linearity for input reference currents of only 0.4 to 4.2 mA ( 5 ) . Within these limitations, a linearity of about k0.370 can be achieved. Gain predictability was evaluated by measuring the gain of t h e circuit of Figure 1 as a function of input scale factor N.These results are summarized in Table 111. The regression equation relating voltage gain to input scale factor is very close
V-t, Vu 1.414 1.974 2.280 2.911 3.207 4.044 5.433 6.550 8.230
N 255 127
11.11
23
111
87 79 63 47 39 31
(X
100)
0.392 0.787 0.901 1.149 1.266 1.587 2.128 2.564 3.226 4.348
predicted Vat, Vb 0.969 1.983 2.27 5 2.912 3.212 4.036 5.424 6.543 8.242 11.121
error, 70 t31..5 -- 0.5 t 0.2 0
-0.2 t 0.2 t 0.2 t 0.1 -0.1 -0.1
Input voltage, 1.000 V. Based upon regression expression V, = [256.6/N] Vi, - 0.037 V. to the predicted expression (Equation 5). T h e gain factor differs from the predicted value by about 0.2% and the offset (-37 mV) is well within t h e range expected from t h e specifications of the devices used. Response time of the programmable-gain amplifier was determined in both the programmed and auto-gain modes of operation. T h e 3-db point of the circuit of Figure 1 was determined by increasing the frequency of a 1.00-V peakto-peak input sine wave until t h e output voltage dropped to 2.86 V peak-to-peak with N = 63. T h e 3-db point was estimated to be 215 kHz. This value varies by about f 2 0 % as t h e gain is varied over the range 1 t o 100. T h e settling time was estimated by observing the output waveform (V,,J on an oscilloscoDe when a 1-to 2-V sauare wave with a rise time of about 20;s was VI". T h e settiing time was observed to be about 3 ps. About the same settling time was observed when t h e input voltage was fixed a t 1 V and the gain was stepped from 2.02 t o 2.95 by changing N from 127 t o 87. This is expected since the DAC exhibits faster response than the OA's used in this work. The circuit response of the auto-gain circuit is identical to that of the programmable gain circuit when the gain does not change. When the input voltage goes outside the preset limits of the auto-gain amplifier, the circuit output requires about 15 ps to settle t o its new value. Again, this is partially determined by the slew rate of the OA's used in this work, although there is a n additional fixed 5-10 ps delay due to the clocked nature of the auto-gain circuit. T h e circuit described thus has excellent characteristics in terms of response speed, linearity, gain predictability, and range. Any of these characteristics can be extended by selection of different components, e.g., faster OA's, a higher resolution DAC, etc. LITERATURE CITED H. H. Willard, L. L. Merritt, Jr., and J. A. Dean, "Instrumental Methods of Analysis," 5th ed., D. Van Nostrand and Co., New York, N.Y., 1974. S.R. Pareies, Anal. Chem.. 46, 464 (1974). , J. G. G-aeme, G. E. Tobey, and L. P. Huelsman, "Operational Amplifiers," McGraw-Hili Book Co., New York, N.Y., 1971. (4) James D. Detreese, Teny A. Woodruff, and H. V. Malmstadt, Anal. Chsm., 46, 1471 (1974). (5) Data Sheet DlCAJl 0702, Date1 Systems, Inc., Canton, Mass., 1977. ~
RECEIVED for review April 10, 1978. Accepted July 11, 1978.
