Datasheet AD538 (Analog Devices) - 9

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AD538 THEORY OF OPERATION RE-EXAMINATION OF MULTIPLIER/DIVIDER ACCURACY
Traditionally, the accuracy (actually the errors) of analog total error calculations for both grades over the 100:1 input multipliers and dividers has been specified in terms of percent range are illustrated in Table 4. This error specification format of full scale. Thus specified, a 1% multiplier error with a 10 V is a familiar one to designers and users of digital voltmeters full-scale output would mean a worst-case error of +100 mV at where error is specified as a percent of reading ± a certain any level within its designated output range. While this type of number of digits on the meter readout. error specification is easy to test evaluate, and interpret, it can For operation as a multiplier or divider over a wider dynamic leave the user guessing as to how useful the multiplier actually range (>100:1), the AD538 has a more detailed error specification is at low output levels, those approaching the specified error that is the sum of three components: a percent of reading term, limit (in this case) 100 mV. an output offset term, and an input offset term for the VY/VX log The error sources of the AD538 do not follow the percent of ratio section. A sample application of this specification, taken full-scale approach to specification, thus it more optimally from Table 4, for the AD538AD with VY = 1 V, VZ = 100 mV fits the needs of the very wide dynamic range applications and VX = 10 mV would yield a maximum error of ±2.0% of for which it is best suited. Rather than as a percent of full reading ±500 μV ± (1 V + 100 mV)/10 mV × 250 μV or ±2.0% scale, the AD538’s error as a multiplier or divider for a 100:1 of reading ±500 μV ± 27.5 mV. This example illustrates that (100 mV to 10 V) input range is specified as the sum of two with very low level inputs the AD538’s incremental gain (VY + error components: a percent of reading (ideal output) term VZ)/VX has increased to make the input offset contribution to plus a fixed output offset. Following this format, the AD538AD, error substantial. operating as a multiplier or divider with inputs down to 100 mV, has a maximum error of ±1% of reading ±500 μV. Some sample
Table 4. Sample Error Calculation Chart (Worst Case) Total Error VY VZ VX Ideal % of Reading Total Error Summation as a Input Input Input Output Total Offset Error Error Term Summation % of the Ideal (V) (V) (V) (V) Term (mV) (mV) (mV) Output
100:1 INPUT 10 10 10 10 0.5 (AD) 100 (AD) 100.5 (AD) 1.0 (AD) RANGE 0.25 (BD) 50 (BD) 50.25 (BD) 0.5 (BD) Total Error = ±% rdg 10 0.1 0.1 10 0.5 (AD) 100 (AD) 100.5 (AD) 1.0 (AD) ±Output VOS 0.25 (BD) 50 (BD) 50.25 (BD) 0.5 (BD) 1 1 1 1 0.5 (AD) 10 ) (AD 10.5 (AD) 1.05 (AD) 0.25 (BD) 5 (BD) 5.25 (BD) 0.5 (BD) 0.1 0.1 0.1 0.1 0.5 (AD) 1 (AD) 1.5 (AD) 1.5 (AD) 0.25 (BD) 0.5 (BD) 0.75 (BD) 0.75 (BD) WIDE 1 0.10 0.01 10 28 (AD) 200 (AD) 228 (AD) 2.28 (AD) DYNAMIC 16.75 (BD) 100 (BD) 116.75 (BD) 1.17 (BD) RANGE Total Error = 10 0.05 2 0.25 1.76 (AD) 5 (AD) 6.76 (AD) 2.7 (AD) ±% rdg ± Output V 1 (BD) 2.5 (BD) 3.5 (BD) 1.4 (BD) OS ± Input VOS × (VY + VZ)/VX 5 0.01 0.01 5 125.75 (AD) 100 (AD) 225.75 (AD) 4.52 (AD) 75.4 (BD) 50 (BD) 125.4 (BD) 2.51 (BD) 10 0.01 0.1 1 25.53 (AD) 20 (AD) 45.53 (AD) 4.55 (AD) 15.27 (BD) 10 (BD) 25.27 (BD) 2.53 (BD) Rev. E | Page 9 of 16 Document Outline Features Applications Functional Block Diagram General Description Revision History Specifications Absolute Maximum Ratings ESD Caution Pin Configuration and Function Descriptions Typical Performance Characteristics Theory of Operation Re-Examination of Multiplier/Divider Accuracy Functional Description Stability Precautions Using The Voltage References One-Quadrant Multiplication/Division Two-Quadrant Division Log Ratio Operation Analog Computation Of Powers And Roots Square Root Operation Applications Information Transducer Linearization ARC-Tangent Approximation Outline Dimensions Ordering Guide