AN546 Converter Datasheet pdf - Digital Converter. Equivalent, Catalog

AN546

Using the Analog-to-Digital (A/D) Converter

Authors:

Sumit Mitra,

Stan D’Souza, and

Russ Cooper

Microchip Technology Inc.

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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

FFh

FEh

Note that the digital output value is 00h for the analog

input voltage range of 0 to 1LSb. In some converters,

the ﬁrst transition point is at 0.5LSb and not at 1LSb as

shown in Figure 2. Either way, by knowing the transfer

function the user can appropriately interpret the data.

Transition Point

The analog input voltage at which the digital output

switches from one code to the next is called the “Tran-

sition Point.” The transition point is typically not a single

threshold, but rather a small region of uncertainty

(Figure 3). The transition point is therefore deﬁned as

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

Code Width should be 1LSb (Figure 1).

FIGURE 2: ALTERNATE TRANSFER

FUNCTION

FFh

FEh

Code Width

(CW)

04h

03h

02h

01h

00h

Analog input

voltage

04h

03h

02h

01h

00h

Analog input

voltage

DS00546E-page 1

AN546

Center of Code Width

The midpoint between two transition points is called the

“Center of Code Width” (Figure 3).

FIGURE 3: TRANSITION POINTS

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Code

under

test

100%

50%

Center of

code width

Low side

transition

Transition

points

Differential Non-Linearity (DNL)

It is the deviation in code-width from 1LSb (Figure 4).

The difference is calculated for each and every

transition. The largest difference is reported as DNL.

It is important to note that the DNL is measured after

the transfer function is normalized to match offset error

and gain error.

Note that the DNL cannot be any less than -1LSb. In the

other direction, DNL can be >1LSb.

FIGURE 4: DIFFERENTIAL NON-LINEARITY

DNL = 1/4 LSb

DNL = +3/4 LSb

Ideal transfer

function (for

reference only)

Actual transfer

function

DNL = -1/4LSb to +3/4LSb

Absolute Error

The maximum deviation between any transition point

from the corresponding ideal transfer function is

deﬁned as the absolute error. This is how it is measured

and reported in the PIC16C7X (Figure 5). The notable

difference between absolute error and integral non-lin-

earity (INL) is that the measured data is not normalized

for full scale and offset errors in absolute error.

Absolute Error is probably the ﬁrst parameter the user

will review to evaluate an A/D. Sometimes absolute

error is reported as the sum of offset, full-scale and

integral non-linearity errors.

Total Unadjusted Error

Total 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 Code

No missing code implies that as the analog input volt-

age is gradually increased from zero to full scale (or

vice versa), all digital codes are produced. Stated

otherwise, changing analog input voltage from one

quantum of the analog range to the next adjacent range

will not produce a change in the digital output by more

than one code count.

Monotonic

Monotonicity guarantees that an increase (or decrease)

in the analog input value will result in an equal or

greater digital code (or less). Monotonicity does not

guarantee that there are no missing codes. However, it

is an important criterion for feedback control systems.

Non-monotonicity may cause oscillations in such sys-

tems.

The ﬁrst derivative of a monotonic function always has

the same sign.

FIGURE 5: ABSOLUTE ERROR

Error = 3/4LSb

Actual transfer

function

Ideal transfer

function

Error = 1/4LSb

Absolute Error = +3/4LSb

DS00546E-page 2

Ratiometric Conversion

Ratiometric Conversion is the A/D conversion process

in which the binary result is a ratio of the supply voltage

or reference voltage, the latter being equal to full-scale

value by default. The PIC16C7X is a ratiometric A/D

converter where the result depends on VDD or VREF.

In some A/Ds, an absolute reference is provided result-

ing in “absolute conversion”.

Sample and Hold

In sample and hold type A/D converters, the analog

input has a switch (typically a FET switch in CMOS)

which is opened for a short duration to capture the

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voltage onto

typically started

after

on-chip capacitor.

the sampling switch

is closed.

Track and Hold

Track and Hold is basically the same as sample and

hold, except the sampling switch is typically left on.

Therefore the voltage on the on-chip holding capacitor

“tracks” the analog input voltage. To begin a conversion,

the sampling switch is closed.

The PIC16C7X A/D falls in this category.

Sampling Time

Sampling Time is the time required to charge the

on-chip holding capacitor to the same value as is on the

analog input pin. The sampling time depends on the

magnitude of the holding capacitor and the source

impedance of the analog voltage input.

Offset Error (or Zero Error)

Offset Error is the difference between the ﬁrst actual

(measured) transition point and the ﬁrst ideal transition

point as shown in Figure 6. It can be corrected (by the

user) by subtracting the offset error from each conver-

sion result.

FIGURE 6: OFFSET ERROR

5 Actual transfer

function

Ideal transfer

function

Offset error

AN546

Full Scale Error (or Gain Error)

Full Scale Error is the difference between the ideal full

scale and the actual (measured) full scale range

(Figure 7). It is also called gain error, because the error

changes the slope of the ideal transfer function creating

a gain factor. It can be corrected (by the user) by multi-

plying each conversion result by the inverse of the gain.

FIGURE 7: FULL SCALE ERROR

FFh

FEh

FDh

FCh

03h

02h

01h

00h

Actual transfer

function

Ideal

transfer

function

Actual full-scale range

Ideal full-scale range

Integral Non-Linearity (INL), or Relative Error

The deviation of a transition point from its

corresponding point on the ideal transfer curve is called

“Integral Non-Linearity” (Figure 8). The maximum dif-

ference is reported as the INL of the converter.

It is important to note that Full Scale Error and the

Offset Error are normalized to match end transition

points before measuring the INL.

FIGURE 8: INTEGRAL NON-LINEARITY

Deviation = +3/4LSb

Actual transfer

function

Ideal transfer

function

Deviation

2 = +1/4LSb

Deviation

1 = -11/4LSb

INL in this example is -1/4LSb to +3/4LSb

DS00546E-page 3

Digital Converter. AN546 Datasheet

AN546 Converter. Datasheet pdf. Equivalent