21 pages
English
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# the statistical average of many conversions Stated dif ferently it is the voltage input at which the uncertainty of the conversion is

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21 pages
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the statistical average of many conversions. Stated dif- ferently, it is the voltage input at which the uncertainty of the conversion is 50%. Code Width The distance (voltage differential) between two transition points is called the “Code Width.” Ideally the ig M INTRODUCTION This application note is intended for PIC16C7X users with some degree of familiarity with analog system design. The various sections discuss the following topics: • Commonly used A/D terminology • How to configure and use the PIC16C71 A/D • Various ways to generate external reference voltage (VREF) • Configuring the RA3:RA0 pins COMMONLY USED A/D TERMINOLOGY The Ideal Transfer Function In an A/D converter, an analog voltage is mapped into an N-bit digital value. This mapping function is defined as the transfer function. An ideal transfer is one in which there are no errors or non-linearity. It describes the “ideal” or intended behavior of the A/D. Figure 1 shows the ideal transfer function for the PIC16C7X A/D. FIGURE 1: PIC16C7X IDEAL TRANSFER FUNCTION Authors: Sumit Mitra, Stan D'Souza, and Russ Cooper Microchip Technology Inc. FFh FEh D ig ita l c od e o u tp ut Code Width (CW) 04h Using the Analog-to-D Ó 1997 Microchip Technology Inc.

• input voltage

• no then

• select bank0

• conversion

• code width

• result depends

• absolute error

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##### Approximation error

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Ó  1997 Microcih peThconolygI .Dnc05S0E-46gepa 1
04h03h02h01h00h
FIGURE 2: ALTERNATE TRANSFERFUNCTIONFFhFEh
Code Width(CW)04h03h02h01h00h
Authors:Sumit Mitra, Stan DSouza, andRuss CooperMicrochip Technology Inc.INTRODUCTIONThis application note is intended for PIC16C7X users withsome degree of familiarity with analog system design.Thevarious sections discuss the following topics:• Commonly used A/D terminology• How to conﬁgure and use the PIC16C71 A/D• Various ways to generate external referencevoltage (VREF)• Conﬁguring the RA3:RA0 pinsCOMMONLY USED A/DTERMINOLOGYThe Ideal Transfer FunctionIn an A/D converter, an analog voltage is mapped intoan N-bit digital value. This mapping function is deﬁnedas the transfer function. An ideal transfer is one in whichthere are no errors or non-linearity. It describes the“ideal” or intended behavior of the A/D. Figure 1 showsthe ideal transfer function for the PIC16C7X A/D.FIGURE 1: PIC16C7X IDEAL TRANSFERFUNCTIONFFhFEh
Note that the digital output value is 00h for the analoginput voltage range of 0 to 1LSb. In some converters,the ﬁrst transition point is at 0.5LSb and not at 1LSb asshown in Figure 2. Either way, by knowing the transferfunction the user can appropriately interpret the data.Transition PointThe analog input voltage at which the digital outputswitches from one code to the next is called the “Tran-sition Point.” The transition point is typically not a singlethreshold, but rather a small region of uncertainty(Figure 3). The transition point is therefore deﬁned asthe statistical average of many conversions. Stated dif-ferently, it is the voltage input at which the uncertaintyof the conversion is 50%.Code WidthThe distance (voltage differential) between twotransition points is called the “Code Width.” Ideally theCode Width should be 1LSb (Figure 1).
MAN546Using the Analog-to-Digital (A/D) Converter
A N    5    4   6
Center of Code WidthThe midpoint between two transition points is called theCenter of Code Width” (Figure 3).FIGURE 3: TRANSITION POINTS7Codeunder6 test100%5 0% Center of4 50% code width3Low side2 transition1Transition0 pointsDifferential Non-Linearity (DNL)It is the deviation in code-width from 1LSb (Figure 4).The difference is calculated for each and everytransition. The largest difference is reported as DNL.It is important to note that the DNL is measured afterthe transfer function is normalized to match offset errorand gain error.Note that the DNL cannot be any less than -1LSb. In theother direction, DNL can be >1LSb.FIGURE 4: DIFFERENTIAL NON-LINEARITY
7DNL = 1/4 LSb654Ideal trna n(fsofrerfunctioDNL = +3/4 LSb reference only)3Actual transfer2 function10DNL = -1/4LSb to +3/4LSb
DS00546E-page 2
Absolute ErrorThe maximum deviation between any transition pointfrom the corresponding ideal transfer function isdeﬁned as the absolute error.This is how it is measuredand reported in the PIC16C7X (Figure 5). The notabledifference between absolute error and integral non-lin-earity (INL) is that the measured data is not normalizedfor full scale and offset errors in absolute error.Absolute Error is probably the ﬁrst parameter the userwill review to evaluate an A/D. Sometimes absoluteerror is reported as the sum of offset, full-scale andintegral non-linearity errors.Total Unadjusted ErrorTotal Unadjusted Error is the same as absolute error.Again, sometimes it is reported as the sum of offset,full-scale and integral non-linearity errors.No Missing CodeNo missing code implies that as the analog input volt-age is gradually increased from zero to full scale (orvice versa), all digital codes are produced. Statedotherwise, changing analog input voltage from onequantum of the analog range to the next adjacent rangewill not produce a change in the digital output by morethan one code count.MonotonicMonotonicity guarantees that an increase (or decrease)in the analog input value will result in an equal orgreater digital code (or less). Monotonicity does notguarantee that there are no missing codes. However, itis an important criterion for feedback control systems.Non-monotonicity may cause oscillations in such sys-tems.The ﬁrst derivative of a monotonic function always hasthe same sign.FIGURE 5: ABSOLUTE ERROR
76Error = 3/4LSb5Actual transferfunctio4nIfduenaclt itornansfer3Error = 1/4LSb2Error = 1/4LSb10Absolute Error = +3/4LSb
Ó 1997 Microchip Technology Inc.
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