CAPACITANCE LEVEL MEASUREMENT

BASIC MEASURING PRINCIPLEA capacitor is formed when a level sensing electrode isinstalled in a vessel. The metal rod of the electrode actsas one plate of the capacitor and the tank wall (orreference electrode in a non-metallic vessel) acts as theother plate. As level rises, the air or gas normallysurrounding the electrode is displaced by materialhaving a different dielectric constant. A change in thevalue of the capacitor takes place because the dielectricbetween the plates has changed. RF (radio frequency)capacitance instruments detect this change and convertit into a relay actuation or a proportional output signal.The capacitance relationship is illustrated with thefollowing equation:

C = 0.225 K ( A )D

where:C = Capacitance in picoFaradsK = Dielectric constant of materialA = Area of plates in square inchesD = Distance between the plates in inches

VESSEL WALL

ELECTRODE

D

METAL SHELL

MEASURED MATERIAL

SENSOR INSULATION

METAL ELECTRODE

EARTH GROUND

The dielectric constant is a numerical value on a scaleof 1 to 100 which relates to the ability of the dielectric(material between the plates) to store an electrostaticcharge. The dielectric constant of a material isdetermined in an actual test cell. Values for manymaterials are published by the National Institute ofStandards and Technology.In actual practice, capacitance change is produced indifferent ways depending on the material beingmeasured and the level electrode selection. However,the basic principle always applies. If a higher dielectricmaterial replaces a lower one, the total capacitanceoutput of the system will increase. If the electrode ismade larger (effectively increasing the surface area) thecapacitance output increases; if the distance between

measuring electrode and reference decreases, then thecapacitance output decreases.Level measurement can be organized into three basiccategories: the measurement of non-conductivematerials, conductive materials and proximity ornon-contacting measurement. While the followingexplanations oversimplify the measurement, theyprovide the basics that must be used to properly specifya capacitance measurement system.� Non-Conductive Materials—As previously stated,

capacitance changes as material comes between theplates of the capacitor. For example, suppose thesensor and the metal wall are measuring theincreasing level of a non-conductive hydrocarbon.Figure 1 depicts a typical system.

While the actual capacitive equation is very complex, itcan be approximated for the above example as follows:

C =0.225 (Kair x Aair)

+0.225 (Kmaterial x Amaterial )

Dair Dmaterial

Since the electrode and tank wall are fixed in place, thedistance between them will not vary. Similarly, thedielectric of air and of the measured material remainconstant (air is 1 and the hydrocarbon is 10).Consequently, the capacitance output of the systemexample can be reduced to this very basic equation:

C = (1 x Aair) + (10 x Amaterial )

As this equation demonstrates, the more material in thetank, the higher the capacitance output will be. Thecapacitance is directly proportional to the level of themeasured material.� Conductive Materials—The same logic for non-

conductive materials applies for conductivematerials, except that conductive material acts as theground plate of the capacitor, rather than the tank

Figure 1- Capacitive Measurement In Non-Conductive Media

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wall. This changes the distance aspect of theequation, whereby the output would becomparatively higher than for a non-conductivematerial. However, it still remains fixed; therefore, aslevel rises on the vertically mounted sensor, theoutput increases proportionally.NOTE: A material is considered conductive when it has aconductivity value of greater than 10 microSiemens/cm.

WARNINGA non-insulated level sensingelectrode must NOT come in contactwith conductive material, in whichcase the sensor will act like a switch.

� Proximity (non-contacting) Measurements—Thelevel sensing electrode is normally a flat platemounted parallel to the surface of the material. Thematerial, if conductive, acts as the ground plate ofthe capacitor. As level rises to the sensor plate, theeffective distance between plates is decreased, thuscausing an increase in capacitance. In non-conductive materials, the vessel acts as the groundplate and the mass of material between the plates isthe variable. In the measurement of non-conductiveand conductive materials, the area changes and thedistance is fixed. Proximity level measurement isexactly the opposite in that the area is fixed, butdistance varies.Proximity level measurement does not produce alinear output and can only be used when the levelvaries by several inches.

Some typical level sensor installations for measuringconductive and non-conductive materials and forproximity level measurement are shown inFigures 2 and 3.

APPLICATIONSApplications for RF point level controls and analogtransmitters/controllers are widespread. Granularapplications range from light powders to heavyaggregates. Applications in liquids, slurries and pastesare commonplace. Capacitance level can also be usedto detect the interface between two immisciblematerials.Selecting the proper level sensing electrode andinstalling it in the proper location are important factorsthat contribute to the success of any application. Athorough understanding of these factors is required.• Electrode Selection—The electrode is the primary

measuring element and must be capable ofproducing sufficient capacitance change as itbecomes submerged in the measured material.Several electrode types are offered, each havingspecific design characteristics. Capacitance (per footof submersion) vs. dielectric constant curves arepublished for each type as installed in various sizevessels. For non-conductive materials, these curvesare non-linear. Figure 4 shows a typical set ofcurves. As the size of the tank gets smaller, thecapacitance per foot of submersion increases. Aconductive material essentially makes the tank bethe size of the electrode insulation. Note: Continuous level transmitter applications require aminimum span of 10.0 pF and a maximum span of 10,000 pF.

In this case, the saturation capacitance is used.Table A lists basic capacitance values for differentelectrodes and tank sizes.

CAPACITANCE LEVEL PROBESELECTION GUIDE The simplest applications are clean, non-coatingconductive liquids (such as many water-based liquids)in metallic tanks. An insulated probe must be used, andthe fluid is grounded to the probe through the tank. Thecapacitance change per foot = the saturationcapacitance.Clean, non-coating conductive liquids (such as manywater-based liquids) in non-metallic tanks require theuse of a concentric probe. The capacitance change perfoot = the saturation capacitance. See application note“RF Level Measurement in Lined Vessels withGrounded Shell” for details on lined or coated metallictank applications. Clean, non-coating non-conductiveliquids (such as many hydrocarbons ) in non-metallictanks require the use of a concentric probe. TheFigure 2

Figure 3

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GENERAL PURPOSE PROBE - TFE INSULATED

70

60

50

40

30

20

10

10 20 30 40 50 60 70 80DIELECTRIC CONSTANT

CA

PA

CIT

AN

CE

PE

R F

OO

T (

pF)

capacitance change per foot depends upon thedielectric constant of the material.Clean, non-coating non-conductive liquids (such asmany hydrocarbons ) in metallic tanks require specialconsideration. A bare (un-insulated) probe can be used,but one must insure that the probe does not come incontact with any conductive liquid that may contaminatethe non-conductive liquid (such as water in oil). If thisoccurs, the output will be driven to full scale, regardlessof the actual level in the tank. Note that an insulatedprobe can also be used. The probe’s metal fitting mustbe grounded to the metal tank wall, and the distancefrom the tank wall to the probe must be constant alongthe entire length of the probe, to provide a linearchange in analog output per change in fluid height. Ifthis is not the case (i.e. the tank is “irregular” in shape),or if the tank is greater than 15 ft in diameter, aconcentric probe should be used. The capacitancechange per foot depends upon the dielectric constant ofthe material, as well as the tank diameter (tankdiameter does NOT effect the concentric probe).After making a preliminary probe selection based uponthe above considerations, it is important to insure thatthe capacitance of the probe selected meets thefollowing limitations: the capacitance at zero level in thetank is less than 500 pFd, and the maximumcapacitance at full span level is more than 10 pFd butless than 10,000 pFd. Also, the zero to span ratio mustnot exceed 10 to 1. That is, if the zero pf value is 200,the span must be at least 20 pf.

THIS IS CALCULATED AS FOLLOWS:For the LV5100 probe, TFE insulated, in a 24" tank,with a dielectric = 2 (air has a much lower dielectric, sothis calculation is very conservative), the pFd per foot is6 pFd. The maximum length of this probe is 12 ft, sothat the maximum probe capacitance in the open air is= (6 x 12) + (42 pFd - gland capacitance) = 114 pFd,which is less than 500 pFd. Note that no probe hasgreater than 50 pFd gland capacitance.

Helpful Hint500 pFd can only be exceeded with anLV5300 probe of greater than 25 ft length, orgreater than 9 ft length in the LV5102 PVDFinsulated heavy duty probe, or greater than91⁄2 ft length in the polyethylene insulatedheavy duty probe.

For the LV5100 probe, TFE insulated, in a 24" tank,with a dielectric = 2 (this is a typical value forhydrocarbons) the pFd per foot is 6 pFd. The maximumlength of this probe is 12 ft, so that the maximum spancapacitance is = (6 x 12) + (0 pFd - gland capacitanceis not added to the span) = 72 pFd, which is greaterthan 10 pFd and less than 10,000 pFd. Note that if theprobe were only 1 ft long, that the maximum spancapacitance would be only 6 pFd, which is less than therequired 10 pFd.

Helpful Hints• 10,000 pFd can only be exceeded with an

LV5300 probe of greater than 39 ft length, orgreater than 10 ft length in the LV5202 orLV5212 PVDF insulated enhancedperformance probe with a conductive liquid.

• To have less than 10 pFd span, one musthave a span of less than 1 ft fornon-conductive liquid with dielectric lessthan 20 and in a tank greater than1" diameter.

• Note that the “Saturation Capacitance”values should be used when the liquid isconductive (i.e. above 20 microsiemens/cm),such as water-based fluids that are notultra-pure or distilled or deionized.

Field Calibration Required:Capacitive level transmitters must always be calibratedfor zero and span in the field. The concentric probe canbe tested in a bucket or small tank of the liquid to bemeasured; all other probes must be calibrated after finalinstallation by changing the material level and adjustingthe zero and span pots.Unlined Plastic Tanks:Due to the low gains in large tanks, concentric probesare recommended for unlined plastic tanks to minimizethis effect and to provide a ground reference.Large Diameter Metal Tanks for Low DielectricFluids (such as Hydrocarbons)Due to the low gains in large tanks, concentric probesare recommended for metal tanks greater than 20 footdiameter used to measure low dielectric fluids (such ashydrocarbons). Also, if concentric probe is impractical,mount closer to tank wall if possible.• Electrode Location—Mounting positions should be

carefully considered. They must be clear of the inflowof material as impingement during a filling cycle cancause serious fluctuations in the capacitancegenerated. Side mounted electrodes with point levelcontrols are typically mounted at a downward angleto allow the measured material to drain or fall fromthe electrode surface. Electrodes mounted in nozzles should contain ametal “sheath” extending a few inches past thenozzle length. The sheath renders that part of the

Figure 4

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electrode insensitive to capacitance change, andtherefore, ignores the material which may build up in the nozzle.

NOTE: In addition to the electrode selection and location factors,there are other considerations which can have a significant impact onthe measurement. See “Special Considerations” below.

ELECTRODE

EQUIVALENTCIRCUITS

1. Temperature—The dielectric constant of somematerials varies with temperature which affectsthe capacitance measured by the electrode.Generally, materials with a higher dielectricconstant are less affected by temperaturevariation. The temperature effect is usually givenin the tables of dielectric constants.

WARNINGThe effect of changing temperature and changingdielectric can not be quantified; if temperature ordielectric constant change, it is recommendedthat the level transmitter be calibrated at eachtemperature and dielectric constant value toquantify the effect of the changes.

2. Moisture Content—The dielectric constant ofgranular materials changes with changingmoisture content. This variation can causesignificant measurement errors, so eachapplication must be carefully examined. Accuracyrequirements determine the amount of moisturechange that is tolerable.

WARNINGThe effect of changing moisture content can notbe quantified; if moisture content changes, it isrecommended that the level transmitter becalibrated at each moisture level value toquantify the effect of the changes. In addition,the LV5000 series level transmitter should NOTbe used with hygroscopic materials (i.e. thosematerials that absorb moisture from theatmosphere).

3. Static Change—Air-conveyed, non-conductivegranular materials such as nylon pellets build up astatic charge on the electrode which can damagethe electronic components in the measuringinstruments.

WARNINGThe LV5000 series level transmitter shouldNOT be used with materials that could build upstatic charges.

4. Composition—The dielectric constant of themeasured material must remain constantthroughout its volume. Mixing materials withdifferent dielectric constants in varying ratios willchange the overall dielectric constant and theresultant capacitance generated. Solutions havinga high dielectric constant are less affected due tothe saturation capacitance of the electrodesystem. See capacitance vs. dielectric constantcurve in Figure 4.

WARNINGThe LV5000 series level transmitter should NOTbe used with materials of varying compositions.

5. Conductivity—Large variations in the conductivityof the measured material can introducemeasurement error. The proper electrodeselection can minimize this effect. A thick wallelectrode insulation is recommended in this case.

WARNINGThe effect of changing conductivity can not bequantified; if conductivity changes, it isrecommended that the level transmitter becalibrated at each conductivity value to quantifythe effect of the changes.

6. Material Buildup—The most devastating effect onthe accuracy of RF capacitive measurements iscaused by the buildup of conductive material onthe electrode surface. Non-conductive buildup isnot as serious since it only represents a small partof the total capacitance. Latex, carbon black, andfine metal powders are examples of materials thatproduce conductive coatings.

Special Considerations

WARNINGVertically mounted electrodes must be clearof agitators and other obstructions and farenough from the vessel wall to prevent“bridging” of material between the electrodeand the vessel wall.

CONTINUOUS LEVEL MEASUREMENTVarious methods are used to minimize the coatingerror. These include proper electrode selection, higherfrequency measurements, phase shifting andconductive component subtraction circuits.Coating error is illustrated by the diagram shown inFigure 5. The submerged portion of the electrodegenerates nearly a pure capacitive susceptance. Sincethe electrode is insulated, a conductive component isvirtually non-existent. However, the upper section of theelectrode, coated with conductive material, generates

an error signal consisting of a capacitive susceptanceand a conductive component. The result is anadmittance component which is 45° out of phase withthe main level signal. A study of transmission linetheory is required to prove this phenomenon. Anequivalent circuit for the coated section is shown as aladder network producing the phase shifted error signal.

Figure 5

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Table A—Capacitance Values (pF per foot) Conductive

Non-Conductive Materials/Tank Diameter MaterialDielectric = 2 Dielectric = 20 Dielectric = 80 (Saturation

Type of Sensor 1" 24" 96" 1" 24" 96" 1" 24" 96" Capacitance)General Purpose (LV5000 Series):TFE Teflon® Insulated 15 pF 4 pF 2 pF 63 pF 39 pF 34 pF 73 pF 62 pF 58 pF 76 pFPolyethylene Insulated 16 pF 6 pF 3 pF 123 pF 57 pF 46 pF 167 pF 120 pF 117 pF 189 pFPVDF Insulated 18 pF 7 pF 4 pF 178 pF 68 pF 50 pF 280 pF 169 pF 142 pF 350 pFHeavy Duty (LV5100 Series):TFE Insulated 35 pF 6 pF 4 pF 74 pF 44 pF 36 pF 78 pF 66 pF 62 pF 79 pFPolyethylene Insulated 48 pF 5 pF 3 pF 172 pF 66 pF 52 pF 190 pF 131 pF 116 pF 198 pFPVDF Insulated 52 pF 8 pF 5 pF 282 pF 78 pF 58 pF 340 pF 190 pF 158 pF 365 pFEnhanced Performance (LV5200 Series):PFA Teflon® Insulated 23 pF 5 pF 3 pF 147 pF 160 pF 48 pF 187 pF 128 pF 114 pF 207 pFPolyethylene Insulated 22 pF 8 pF 5 pF 260 pF 78 pF 58 pF 410 pF 210 pF 165 pF 518 pFPVDF Insulated 25 pF 10 pF 8 pF 330 pF 80 pF 60 pF 640 pF 260 pF 205 pF 950 pFFlexible Cable (LV5300 Series):PFA Teflon® Insulated 14 pF 5 pF 3 pF 50 pF 34 pF 30 pF 57 pF 49 pF 30 pF 58 pFPolyethylene Insulated 17 pF 5 pF 3 pF 103 pF 52 pF 43 pF 132 pF 101 pF 91 pF 146 pFPVDF Insulated 18 pF 5 pF 3 pF 154 pF 62 pF 48 pF 222 pF 145 pF 128 pF 254 pFConcentric (LV 5500 Series)Teflon® 25 67 75 76Polyethylene 25 142 175 189Kynar 35 220 305 350

45°

METHOD A

METHOD B

e

c

ERRORSIGNAL

SUSCEPTANCE

LEVELSIGNAL

CONDUCTANCE

ec

Admittance Vector DiagramFigure 6

One means of cancelling the error signal is to measurethe conductive component (c) shown in Figure 6,Method A. Since the 45° relationship exists, thecapacitive error component (e) is the same magnitudeand can be subtracted from the total output signal,thereby effectively canceling the error signal.Another cancellation method is to introduce a 45° phaseshift to the entire measurement as shown in Figure 7,Method B. This automatically cancels the coating errorportion because the conductance component (c) stillhas the same magnitude as the error component (e),resulting in the appropriate level signal. Instrumentswhich incorporate these techniques are known as“admittance” types.The coating error can also be reduced by increasing thecapacitive susceptance. This is accomplished byincreasing the frequency of measurement and/ordecreasing the electrode insulation wall thickness.It should be noted that any of these techniques cannotperfectly cancel the coating effect, but each tends toreduce the error.

WARNINGFor all of the preceding reasons, RFcontinuous level instrumentation is notused in inventory control applications.

These are process control devices which require carefulevaluation of the listed considerations to providesatisfactory results.

Reproduced with the permission of Great Lakes Instruments.

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