MPXM2102AS datasheet(496/670 Pages) MOTOROLA

496 / 670 page

AN1556

3–350

Motorola Sensor Device Data

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Summarizing (through Step 4), the calculations are based

on a minimum desired resolution. The resolution requirement

determines the number of steps or “pieces” into which the

signal must be broken. This number of steps or “pieces”

multiplied by the number of millivolts per step equals a

minimum voltage range which is defined as the Minimum

Required Span. Finally to ensure that this Minimum Required

Span is achieved over the entire distribution of sensor spans,

the gain is calculated using the worst case smallest sensor

span.

Note: The gain also will have variation due to resistor

tolerances in the amplifier circuit. To ensure that the system

variation due to resistor tolerances is negligible when

compared to other sources of variation, the system should be

designed using resistors with tolerances of 1% or better.

5. Calculate the worst case Maximum Span. The Maximum

Span is the largest possible span and is calculated using

the maximum full–scale sensor voltage span, MaxFSS,

and the Gain. The worst case maximum full–scale sensor

span occurs at the coldest temperature, MinTemp. After

calculating the Maximum Span, the remaining dynamic

range within the A/D’s window or saturation levels of the

amplifier is the smallest number of “bits” (most limiting

case) available for headroom.

Maximum Span =

[Gain]

• [MaxFSS] • [1 + TCVFSS • (MinTemp – 25)]

The term [1 + TCVFSS • (MinTemp – 25)] is the temperature

effect on the span.

The Maximum Span calculated from the above equation is

depicted in Figure 4.

6. Calculate the Calculated Headroom. The Calculated

Headroom is a subset of the general term “headroom”

because it reserves “bits” in the A/D’s dynamic range only

for the sources of variation from the sensor’s zero–pres-

sure offset voltage. Headroom, in general, is reserved for

all sources of variation: system components, resistor

tolerances (if significant), and the sensor. However, the

largest part of the “headroom” must be reserved for the

device–to–device variations and temperature effects on

the sensor’s zero–pressure offset voltage. Therefore, the

sources of variation from the other system components

are subtracted immediately from the headroom so that

the focus can be on the sensor–related variations (refer

to Figure 5 and the following equation for the Calculated

Headroom). For these design examples, the supply is a

single, regulated 5 V

± 5% supply (the regulator’s

tolerance is referred to as Vtol). An assumption for a

typical rail–to–rail op–amp’s saturation levels (referred to

as Vlo and Vhi) is 0.2 V above the low supply rail (ground)

and 0.2 V below the high supply rail (5 V). Additionally,

the worst case (smallest) supply voltage is 5 V – 5% or

4.75 V.

Calculated Headroom

+ 5

· (1– Vtol

100

)– 2

· Vlo – Maximum Span

The preceding equation assumes that the difference

between Vhi and the high supply rail (or high reference of an

A/D) is equal to the difference between Vlo and the low supply

rail (or low reference of an A/D); thus the term (2

• Vlo).

VS’s NOMINAL VALUE

(NOT INCLUDING Vtol)

VS (INCLUDING Vtol) AND

A/D HIGH REFERENCE

HIGH SAT. LEVEL

OF AMPLIFIER

FULL–SCALE

OUTPUT VOLTAGE

ZERO PRESSURE

OFFSET VOLTAGE

LOW SAT. LEVEL

OF AMPLIFIER

GROUND AND A/D

LOW REFERENCE

MAXIMUM

SPAN

CALCULATED

HEADROOM

AMPLIFIER’S

DYNAMIC

RANGE

Figure 5. From Ground to VS, a Section of Voltage Is

Reserved for Each Source of Variation

Step 6 is considered a pivotal step because it transitions the

methodology’s calculations from the performance require-

ments to the headroom requirements. Up to Step 6, the

methodology considered only the span of the sensor to

guarantee a minimum resolution despite device–to–device

variation, component tolerances, and temperature effects.

Upon calculating the Calculated Headroom, the remaining

steps of the methodology that are detailed below consider the

offset variations (due to device–to–device and temperature).

These offset variations are added together to comprise what

is defined as the Required Headroom which is the required

number of “bits” in the A/D’s dynamic range needed to

accommodate the offset variations. This Required Headroom

is then compared to the Calculated Headroom (from the

preceding calculation) to determine if the Calculated Head-

room is sufficient to allow for the offset variations (i.e., the

Calculated Headroom must be greater than or equal to the

Required Headroom). In the case that the Calculated Head-

room is not sufficiently large, relaxing the resolution require-

ment or reducing, if possible, the variation of either offset,

span, component tolerances, or a combination of all three is

required.

7. Calculate the maximum offset drift due to temperature

fluctuations (defined as the Maximum Temperature Effect

on Offset). A conservative approach to this calculation is

to determine the maximum total voltage change of offset

over the application’s entire operating temperature range.

This maximum change of offset is the product of the Gain,

TCVoff, and the application’s entire operating temperature

range (from Maxtemp to MinTemp). Since the tempera-

ture coefficient of offset can be positive or negative, the

offset may increase or decrease with increasing tempera-

ture and, likewise, for decreasing temperature. Though

this step only considers the maximum magnitude of the

change in offset due to temperature, a segment in the

Required Headroom is reserved for both possibilities of a

positive or negative temperature coefficient of offset (see

Figure 6). The sign (positive or negative) of the total offset

change due to temperature is also considered in upcom-

ing steps.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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