Electronic Instrumentation - Resistive sensors€¦ · Electronic Instrumentation Resistivesensors RomanoGiannetti Univ.PontiﬁciaComillas— ICAI RomanoGiannetti ElectronicInstrumentation

Electronic InstrumentationResistive sensors

Romano Giannetti

Univ. Pontificia Comillas — ICAI

Romano Giannetti Electronic Instrumentation Univ. Pontificia Comillas — ICAI 1 / 22

Outline1 Introducción2 Resistive sensors: big variations.3 ∆R conditioning4 Linearization methods

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Resistive sensors

Electricsensor

Digital done!

Analog

passive

resistive smallvariations

bigvariations

reactive

activecurrent

voltage


Small or big variations?

R(x

) =f(x

)Ravg

measurement range ∆x

output

rang

e∆R

x

R(x) The sensor is called a smallvariations sensor if:

∆RRavg

1

and a big variation otherwise.

∆R/Ravg type0.01 small variations0.3 big variations0.12 ?

In the last case, it’s a greyarea. . .


∆ R sensors: linearity

x

R(x)

S1S2S3S4

The sensor is linear when thesensitivity is constant. So:

S1 is not linear;S2 is not linear;S3 is linear;S4 is . . . ?

Typically, ∆R sensors are notlinear; the exception arepotentiometric (electro-mechanic)sensors.


∆R: basic conditioning

In a descriptive way, the conditioning of a resistive sensor, bigvariations, is simple:

I0 R(x)

V1(x) = I0R(x)

E0

Vo(x) = I0R(x) + E0

Sensitivityadjustment

Zeroadjustment


∆R: basic conditioning 2Often the current through the sensor is limited, so it is impossible todo the sensitivity adjustment in one step:

I0 R(x)E0

A vo

supply block

conditioning proper

Clearly, the adder and the amplifier can be swapped.


Implementation

If the sensor is floating:

supply zero sens.

−

+

R(x)

R0

E0

R−

+

R

R

EZ

R1−

+

R2

vo

vo = R2

R1

(−E0

R0R(x) + EZ

)


Important details!

When designing the circuits, keep in mind the following details:If the sensor is not floating, you have to change the supply stage(there are several possible configurations, look around).Always check that the operational amplifiers do not saturate ateach stage!Yes, you can compact this into a two op-amp’s circuit (even withjust one, sometime) but be careful: early optimization is evil!

You can use the (several) degrees of freedom to optimize your designtoward various target (low error, low consumption, and so on).


linearization: the problem

x

R(x)

S1S2S3S4

Unfortunately, ∆R sensors areoften non-linear.Non-linear output in aninstrument is better avoided, forseveral reasons, but basically:

Reading the value on anon-linear scale is difficultand error-prone;when in a control loop, thelocal gain depend on thevalue, which can be anightmare for stability.


linearization: the objective

x

R(x)

Sensor’s calibration curve

x

vo(x)

Output’s calibration curve


Linearization methods

Basically, we will study three methods for linearizing a sensor (or aninstrument):Method #0 : pass. The lazy engineer’s one.Method #1 : invent something special. The smart engineer’s one.Method #2 : do that exactly. The rich (and with a lot of time

available) engineer’s one.


How-to linearize: method #0

R lin

x

R(x)

Sensor’s calibration curve

εnl

Let’s look at it. . .1 . . . well, it’s not so

non-linear, no?2 So we will ignore the

non-linearity and designeverything as if the sensorwere linear.

3 Then, we will compute thedifference between our(invented) sensor and thereal one as a linearity error.



(Yes, I know. Method #1 later...)

R(x) = fnl(x)

RM

xM x

R(x)

Sensor’s calibration curve Let’s look at it. . .1 We measure a value forR(x) = RM through a linearconditioning system.

2 With a µC, we will computexM = f−1

fl (RN).3 Finally, you can recreate the

output with a DAC ordirectly use it.This is almost exact (withsufficient bits) but expensive.



Method #1 for linearizing is based on the specific characteristics ofthe sensor; the basic concept is to design a conditioning circuitad-hoc for it.

we can find a physical circuit that cancels out the non linearity(for example: a logarithmic amplifier can linearize a sensor withan exponential calibration curve);we can modify the sensor by adding components that (totally orpartially) compensate the non-linearity;and so on; the key is the inventiveness of the designer.


Linear conductance sensorsSome resistive sensor has a calibration curve where its conductance islinear with the measured quantity.If the sensor has a calibration curve like:

R(x) = k

x

I can supply it with constant V andconvert the resulting I in voltage:

vx = −E0R0

R(x) = −E0R0

kx

−

+

R0

R(x)

E0

vx

. . . and then continue with the normal zero and sensitivityadjustment.


Almost linear conductance sensors

x

R(x

)

k/x

k/xα

xα/k

Sometimes is worth mixing twomethods. For example, in this casethe sensor is (green)

R(x) = k

xα, α = 0.7

You can apply method #1 as if itwere of the 1/x kind and obtain amuch less non-linear curve (red).

Then you can apply method #0 or #2 with better results overall.


Parallel resistor, concept

−10 0 10 200

5

10

15

20

x

R(x

)

If you have a sensor thathas high sensitivity, andis wildly nonlinear

you can trade part of yoursensitivity with linearity by usinga parallel fixed resistor.

This is commonly used withNTC thermistors.


NTC sensors

NTC (Negative Temperature Coefficient) are probably the mostcommon used resistive temperature sensors.

−10 0 10 20

5

10

15

20

T (C)

R(x

)(kΩ)

β = 5000 Kβ = 2000 K -t° -t°

The calibration curve is anArrhenius function:

R(T ) = R0eβT

− βT0 , T in K

where β is the “sensitivity” (sic)of the NTC — in the range of1000K–5000K.


Parallel resistor, intervalsHow do we find a value for Rp?

x1 x2 x30

2

4

6

8

10R(x)

Rp

∆1

∆3

R(x

)

R(x)//Rp


Intervals

The idea is choosing Rp so that the two intervals ∆1 and ∆2 areequals, as if the calibration curve were lineal.

∆1 = ∆2 ⇒ R(x1)//Rp −R(x2)//Rp = R(x2)//Rp −R(x3)//Rp

Solving for Rp leads to:

Rp =R(x2)

(R(x1) +R(x3)

)− 2R(x1)R(x3)

R(x1)−R(x3)− 2R(x2)

Obviously, you have to check that the value for Rp is reasonable:positive (!) and not too small — otherwise the sensitivity will droptoo much.


Parallel resistor, tangent

x1 x2 x30

2

4

6

8

10R(x)

Rp

R(x

)

R(x)//Rp

If the range of interest is a smallportion around x2, we can findthe value of Rp giving themaximum linearity with:

∂2R(x)//Rp

∂x2

∣∣∣∣∣x=x2

= 0

which is still an equation withjust Rp as unknown.

For NTC (where x is T ), we can find1 Rp = β − 2T2

β + 2T2R(T2).

1Not easily. . .


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Electronic Instrumentation - Resistive sensors€¦ · Electronic Instrumentation Resistivesensors RomanoGiannetti Univ.PontiﬁciaComillas— ICAI RomanoGiannetti ElectronicInstrumentation