A Simple Microcontroller Based Digitizer for

Differential Inductive Sensors

Nandagopal Ramadoss, Student Member, IEEE and Boby George, Member, IEEE

Department of Electrical Engineering, Indian Institute of technology Madras, India. e-mail : boby@ee.iitm.ac.in

Abstract—This paper presents a simple digitizer suitable for

differential variable inductive/reluctance sensors. The proposed

scheme uses two digital I/O pins, a counter and a comparator of a

microcontroller and obtains a digital output directly proportional

to the measurand which is sensed using a differential variable

inductive/reluctance sensor possessing either a linear or an

inverse transfer characteristic. The scheme uses a ratio-metric

approach in the computation and hence the output is less

sensitive to variation in the parameters such as excitation voltage,

reference voltage, offset of the comparator, etc. A prototype of

the proposed system has been built and tested using standard

variable inductors that emulated a differential inductive sensor

following an inverse characteristic. The output recorded was

linear across the full range and worst-case error noted was less

than 0.3 %. For the prototype developed, the time taken to

complete a measurement was 200 s. The prototype digitizer has

been interfaced with a commercially available LVDT and tested.

The worst-case error observed in this test was 0.77%. Also, the

same digitizer has been employed to get a digital readout from a

differential variable reluctance based displacement sensor. The

worst-case error was less than 0.83%. The test results establish

the efficacy of, the simple and cost effective, scheme developed.

Keywords—Differential inductive sensor; Digitizer;

microcontroller interface; linearization; timer-counter; DVRT;

LVDT

I. INTRODUCTION

Inductive sensors are widely used in various industrial applications for sensing the displacement [1], proximity [2], pressure [3], position [4], etc. There are inductive/variable reluctance/eddy current based sensors that use a single coil [1], [3] for sensing. There are also differential inductive sensors with two coils where the inductances change in a push-pull/differential manner, with respect to the measurand [2], [4], [5]. Sensors with multiple coils/loops [6] are also in use. Some of the inductive sensors possess a linear relationship between the quantity being measured [4] and the inductance, for a limited range, while inductive/reluctance sensors that possess an inverse characteristic [7], [8] are also available in the market. Differential variable reluctance/inductive sensors with linear characteristic can be represented as in (1) and that with inverse characteristic [8] can be represented as in (2). In (1) and (2) k indicates the transformation constant of the sensor while x is the measurand. L0 is the nominal value of the inductance at x = 0.

kxLL 101 and kxLL 102 (1)

kx

LL

1

01 and

kx

LL

1

02 (2)

Conventional methods of measurement of inductance of sensors rely on, tedious, bridge balancing. Later, with the help of electronic systems, the inductance measurement became less cumbersome. The quazi-balanced [9] and modified Maxwell-Wien bridge [10] schemes are examples of such improvements. The wide spread use of digital systems for storage and processing enforced the conventional measurement circuits to employ an Analog to Digital Converter (ADC) to enable the transfer of data to the digital systems. A DSP [6] based scheme reported for differential variable reluctance transducers is such an example. This type of requirement lead to the development of signal conditioning units that provide direct digital output proportional to the measurand, e. g., the inductance-to-digital converter based on dual-slope principle, presented in [8], which is well suitable for low speed applications. Direct interface circuits (direct microcontroller to sensor) suitable for resistive and capacitive sensors have been reported [11]. These circuits make use of the change in R-C time constant of R-C series circuit, i.e., when one of the elements changes (either R or C) with respect to the measurand while the other element is kept constant. A time period which is a function of the time constant of the circuit is measured using a counter module in the microcontroller [11]. A similar approach can be used for measurement of inductance. The principle behind measurement of the time constant of an R-L circuit has been presented in [12] while a basic idea of a microcontroller interface for measurement of an unknown inductance, in terms of a reference inductor, has been reported in [13]. Among the methods listed above, the DSP [6] and dual-slope [8] based schemes can be used to obtain a direct digital output from a differential reluctance/inductive sensor but they are complex and expensive.

A new simple direct interface scheme, suitable for obtaining a digital output proportional to the quantity being sensed by a differential inductive/reluctance based sensor is presented in this paper. The scheme is suitable for differential type inductive sensors following either linear, as in (1), or inverse, as in (2), characteristic. It employs a ratio-metric approach [8], hence the effect of variation in various circuit parameters in the final output is negligible. The operation of the scheme, details of the prototype developed and test results after interfacing it with an LVDT and a Differential Variable Reluctance Transducer (DVRT) are presented in the sections below.

This full text paper was peer-reviewed at the direction of IEEE Instrumentation and Measurement Society prior to the acceptance and publication.

978-1-4799-6144-6/15/$31.00 ©2015 IEEE

Fig. 1. Schematic of the proposed microcontroller based digitizer for

differential inductive sensor.

Fig. 2. Timing diagram of the proposed microcontroller based

digitizer suitable for differential inductive sensor.

II. MICROCONTROLLER BASED DIGITIZER FOR DIFFERENTIAL

INDUCTIVE SENSOR

The proposed digitizer for differential inductive sensors

uses two digital input/output pins DIO-1 and DIO-2 of a

microcontroller (C) along with its built-in counter and

comparator. A block diagram representation of the scheme is

shown in Fig. 1. The inductors L1 and L2 that follow (1) or (2)

are respectively connected to the pins DIO-1 and DIO-2 of the

C. The common ends of the L1 and L2 are connected to a

fixed resistor RS. Voltage vo across this resistor is given to the

comparator OC of the C. vo is given to the inverting terminal

of OC while its other terminal is connected to fixed voltage

Vref. Transition (high to low) in the output voltage vc of OC

triggers an interrupt that stop the counter of the C. Diodes D1

and D2 connected across L1 and L2, respectively, serve as

freewheeling diodes. They will be in the reverse biased

condition (OFF), during the measurement activity on the

corresponding inductor and will not affect the normal

operation. The measurement starts when there is an active low

trigger signal at DIO-3. The counter output, after the

measurement process (discussed below) is send to display

using a digital port.

A. A C Based Digitizer for the Inductive Sensor

The measurement starts as soon as the DIO-3 of the C gets

a high to low transition as indicated in the timing diagram in

Fig. 2. The moment DIO-3 goes low, the C sets DIO-1 to logic

high (VCC) and DIO-2 to high impedance (HZ) state. At the

same instant the counter of the C also starts. In this

condition, the voltage VCC at DIO-1 is available across the series

combination of L1 and RS. There will be a current iL1, given by

(3), flowing through the inductor L1.

1111

1LRt

E

CCL

EeR

Vi

(3)

In (3), 111 PLSE RRRR , where RL1 is the resistance of

the coil that forms L1 and RP1 is the output resistance of the

digital pin DIO-1. This current flows through the RS and hence

the corresponding voltage vo(L1) across it can be represented

as in (4).

111)(1

1

LRt

E

CCSo

EeR

VRLv

(4)

The vo(L1) increases in an exponential fashion as in Fig. 2 and

in (4), with an initial value of zero and final value as VCC. The

output of OC will be high until vo(L1) reaches Vref. When

vo(L1) crosses Vref, the comparator output vc will change from

high to low and stop the counter as illustrated in Fig. 2.

Let us consider that the time taken for vo(L1) to change

from 0 to Vref is T1. Then, the time T1 can be represented as in

(5). The output of the counter for this duration is noted as N1.

SCC

ErefSCC

E RV

RVRV

R

LT

1

1

11 ln (5)

As mentioned above, the change in the state of the OC (from

high to low) stops the counter. It also instructs the C to set

DIO-1 to logic low, while keeping DIO-2 in HZ. In this

condition, the current through RS and vo will come back to zero

as in Fig. 2.

The next step is to measure a time/count as a function of

the inductance L2. In order to do this, the C will set the DIO-2

to logic high (VCC) and DIO-1 to high impedance (HZ) and start

the counter. Now, there will be a current flow through L2 and

RS and there will be a voltage vo(L2) across RS as indicated in

Fig. 2, and expressed in (6).

Fig. 3. Flowchart of the sequence of operations during a measurement

cycle.

221)(2

2LRt

E

CCSo

EeR

VRLv

(6)

In equation (6), 222 PLSE RRRR , where RL2 is the coil

resistance of inductor L2 and RP2 is the output resistance of the

pin DIO-2. As in the case of vo(L1), the voltage vo(L2) will also

increase with time and reach Vref, say at time T2, as illustrated

in Fig. 2. At this instant, vc will change from high to low, and

generate an interrupt to stop the counter and set DIO-2 to low

and keep DIO-1 in HZ. This will bring the vo(L2) to zero. The

time T2 can be expressed as in (7). The corresponding output

from the counter is noted as N2 as illustrated in Fig. 2.

SCC

ErefSCC

E RV

RVRV

R

LT

2

2

22 ln (7)

Now, if we consider that RE1 = RE2 and perform a ratio-

metric operation as in (8), we can observe that the outcome is

independent of VCC, Vref, RS and RE. The resistances of the

coils of differential inductive sensors usually have very small

mismatch , similarly, the output resistances of the digital pins

(DIO-1 and DIO-2) employed are also considered to have very

small mismatch (less than 0.5 ). If there is a small mismatch

in the resistance values of the coils, it can be corrected by

introducing an additional resistance in the lowest resistance

path.

21

21

21

21

21

21

LL

LL

NN

NN

TT

TT

(8)

If we substitute for L1 and L2 in (8) as given in (1), the linear

characteristic, we get the measurand kx as

21

21

NN

NNkx

. (9)

The expression (9) for output will remain same even if we use

the inductive sensor that follows the inverse characteristic as

in (2). Thus, the digital ratio-metric output, of the counter

outputs N1 and N2, is directly proportional to the measurand.

Details of the prototype developed and test results are given in

the section below.

III. EXPERIMENTAL SETUP AND RESULTS

A prototype of the proposed scheme has been realized

using off-the-shelf items to evaluate the practicability of the

digitizer for differential inductive sensor. The entire prototype

system was built using a single microcontroller and a few

additional components. The microcontroller employed was IC

ATSAM3x8E [14] from ATMEL Corporation. The

Timer/Counter module of the microcontroller was used to

implement the counters that count and provide N1 and N2. This

counter module can measure time with a resolution of 23.8 ns.

The comparator was realized using a high speed comparator

IC LM311P [15]. This generates the interrupt to stop the

counter, whenever vo crosses Vref. The microcontroller DIO’s

are used for realizing start trigger input, counter interrupt input

(vC) and excitation outputs (DIO-1 and DIO-2). To achieve

precise execution control and timing; PORT - D (<D1:2> and

<D9:10>) and Timer/Counter-1 module was used to

implement the measurement scheme as they are not

multiplexed with any other functionality.

The value of resistor RS used was 150 Ω; this was fixed as

a better tradeoff between time constant of the R-L circuit and

output current sourcing capacity (< 25 mA) of the digital I/O

pin of the microcontroller. The non-inverting input of the

comparator OC was connected to a reference voltage

Vref = 1.65 V. This reference value was finalized based on the

SPICE simulation studies conducted to understand the best

value of Vref to obtain the best change in voltage of vo to noise

ratio for a range of values of inductances (10 mH to 60 mH)

used to test the prototype in the first stage of testing. The

inverting input of the OC was connected to the voltage vo

across RS. The output of OC was connected to the interrupt

input pin of the microcontroller. The freewheeling diodes D1

and D2 were implemented using IN4148. A suitable program

as per the flow chart given in Fig. 3. was developed and

loaded into the microcontroller using Ardunio IDE with DUE

hardware. Outputs of the counters were transferred and

displayed in a computer through serial communication.

In order to test the prototype developed, two standard

variable inductors, manufactured by General Radio Company,

Massachusetts, were used whose values can be set as per (1)

or (2) to emulate the differential inductive sensor. The variable

inductors were realized using two mutually coupled inductors

having self-inductance value of 19.90 mH. The effective

inductance of each unit can be varied from 6.00 mH to

50.00 mH by varying the mutual coupling between the

inductors. To emulate the differential sensor as in (2), the

above-mentioned standard inductors were set initially at

12 mH. This was taken as the nominal inductance L0. Then,

the required inductance values, as per (2), for every step of

increase in kx equal to 0.05 were computed. The standard

inductors were set to those values computed and

corresponding N1 and N2 values were recorded. The

measurement was repeated for 10 times for every set of kx and

the average value was displayed in the computer. To complete

one cycle of measurement the developed system took less than

Fig. 4. A photograph of the experimental set-up. The microcontroller and

a small PCB with the comparator IC and terminals to connect the

inductors and probes are visible. The standard inductor boxes used, for the initial tests, and oscilloscope that indicate the important waveforms

are also visible in the picture.

Fig. 5. Snap-shot of the waveforms observed in an oscilloscope during the

experiment.

Fig. 6. The counts N1 and N2 noted from the microcontroller

corresponding to the values of L1 and L2 [set as per equation (2)]. L0

was set as 12 mH, in this experimental study. The value of kx computed using N1 and N2 as per (9) and the error in each

measurement are indicated.

Fig. 7. Experimental set-up developed to test the microcontroller based

interface with a commercially available LVDT.

200 s.

A photograph of the experimental set-up is given in Fig. 4.

The important waveforms from the prototype were observed

in a mixed signal oscilloscope MSO6034A from Agilent

Technologies. A snap-shot of the waveforms recorded is

shown in Fig. 5. The time durations T1 and T2 were measured

in the oscilloscope and count values N1 and N2 from the

microcontroller were compared. These values were found to

be matched with the theoretical values computed using SPICE

tools. Fig. 6 shows a plot of values N1 and N2 measured using

the counter of the microcontroller when L1 and L2 were varied

as per (2), i.e., inverse characteristic. It also shows the ratio-

metric output computed, as per (9), using the counter outputs

and the error in each reading. The worst-case error in the

output for the range tested was found to be less than 0.3 %.

The sources of the error include mismatch between RL1 and

RL2, RP1 and RP2 [11], noise, etc. The results show that the

proposed scheme is a promising, simple and low cost, method

for obtaining a direct digital output from the differential

reluctance/inductive sensors.

A. Testing with an LVDT

In order to assess the performance of the scheme in

practical applications, a few more tests were conducted. In one

of the tests, the prototype measurement unit developed was

interfaced with a commercially available a.c. type LVDT

(range of 0-25 mm), manufactured by Spranktronics,

Bangalore and experiments were conducted. A photograph of

the experimental set-up is shown in Fig. 7. The two secondary

coils of the LVDT were connected to the measurement unit as

illustrated (L1 and L2) in Fig. 1. The primary of the LVDT was

not used. Resistance RL1 of the coil with inductance L1 was

68.8 , while that of L2 was RL2 = 68.5 . In the test set-up,

the plunger rod of the LVDT was connected to a precision

displacement unit based on a screw gauge arrangement which

has a resolution of 10 m. The inductance values (L1 and L2)

of the secondary coils were measured using the prototype unit

developed, for a range of displacement of 15 mm in every

steps of 1 mm. Value of kx was then calculated as in (9) and

the displacement measured was computed. The counter

outputs N1 and N2, measured output x (displacement),

percentage error observed in each measurement are plotted

and given in Fig. 8. The results show that the proposed simple

Fig. 10. Output and error characteristic of the proposed interface circuit

obtained when interfaced with a DVRT.

Fig. 8. Output obtained from the tests conducted after interfacing the

prototype with the LVDT. Counts N1 and N2, measured displacement,

and the error in each point are shown.

Fig. 9. Experimental set-up to test the microcontroller based interface

with a differential variable reluctance displacement transducer that

follows an inverse transfer characteristic between measurand and change in inductance. A simplified equivalent circuit of the DVRT is

also shown (inset).

microcontroller based scheme is useful to realize a direct

digitizer for LVDT, which are widely used in the industry.

B. Tests with a Differential Variable Reluctance Trsnducer

(DVRT)

Later, the prototype digitizer was interfaced with a DVRT

and employed it for displacement measurement. For this, a

basic DVRT has been built in the laboratory using two

inductors wound using 27 AWG enameled copper wire on a

suitable former. Number of turns in each coil was 645. The

length of the coil was 35 mm while its inner and outer

diameters were 9 and 14.44 mm, respectively. The magnetic

plunger used was the same employed in the displacement

transducer of inductive valve lift transducer (model no: AVL

426) from AVL List GmbH. It has a diameter of 2 mm. The

inductances of the coils without the core were L1 = 1.101mH

and L2 = 1.097mH. The mismatch between the resistance of

the coils was (RL1-RL2 =) 0.1 . As in the case of the LVDT

mentioned above, the plunger rod was attached to the screw

gauge based displacement unit. A snapshot of the

experimental set-up is given in Fig. 9. The readings (L1 and L2

in terms of N1 and N2) were taken for a displacement of 10

mm for each step of 1 mm. As this is a DVRT, the L1 and L2

(and hence N1 and N2) were not linear, instead it followed an

inverse characteristic as in (2). Values of kx and the

displacement x were computed using the N1 and N2 in each

step as in (9). The values of N1 and N2, along with measured

displacement and the associated error noted are provided in

the graphs given in Fig. 10. As in the case of LVDT, the

results from DVRT reiterate the practicality of the proposed

digitizer.

C. Other Tests

Other than the above discussed tests, we also verified the

effect of mismatch in the resistance of the digital output pins

of the microcontroller employed. In order to do this, we first

measured the output resistance offered by the digital pins of

the microcontroller employed in the prototype. The average

value of the resistance measured for 20 different output pins

was 44.49 . The maximum deviation of resistance noted

between the pins was less than 0.15 . Then, we performed a

SPICE simulation study to compute the effect of such a

mismatch in the final output. In the simulation, the resistance

representing the output resistance of the digital pin was varied

from 45 to 45.5 in steps of 0.05 , emulating a maximum

of about 1% variation in resistance. Error computed for the

maximum deviation noted (for the largest resistance condition)

was less than 0.125%. Similarly, the measurement system was

subjected change in temperature. For this test, the LVDT that

was connected to the measurement was set to a fixed position

and the measurement unit was exposed to an elevated

temperature using a hot air gun. During the test, the

temperature surrounding the measurement unit was sensed

using an LM35 temperature sensor and recorded the

temperature and output from the LVDT (measured using the

prototype microcontroller interface). Worst case error

observed for an increase of 20 oC (increased from 25 to 45

oC)

was 0.8%.

IV. CONCLUSIONS

A simple microcontroller based digitizer that provides a

linear output for differential variable reluctance/inductive

sensor possessing either a linear or an inverse characteristic

has been developed and the technical details are presented in

this paper. The presented scheme uses the digital input/output

pins, comparator and counter of a microcontroller system, to

realize the digitizer. It does not require an ADC hence a basic

microcontroller with sufficiently high clock frequency will be

enough to realize the proposed scheme. A prototype of the

scheme has been developed and tested using standard

inductance boxes, emulating the differential sensor with

inverse characteristic. The output from the prototype unit was

linear for the entire range tested, with a worst-case error less

than 0.3 %. The developed digitizer is useful for differential

variable reluctance transducers for displacement measurement

[6], [16], inductive differential pressure transducers [8], etc.

As the measurement unit is very compact, it can be easily

integrated within the sensor housing itself. The measurement

system developed has also been employed to obtain a digital

output from a commercially available LVDT and a DVRT.

The test results using these sensors show the practical use of

the proposed scheme.

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