20321 - PubAg - USDA
354
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
Flow-Through Coaxial Sample Holder Design for Dielectric Properties Measurements from 1 to 350 MHz Kurt C. Lawrence, Member, IEEE, Stuart 0. Nelson, Fellow, IEEE, and Philip G. Bartley, Jr., Student Member, IEEE
Abstract—A system for measuring the dielectric properties of cereal grains from 1 to 350 MHz with a coaxial sample holder is presented. A signal-flow graph model was used to determine the permittivity of several polar alcohols from the full two-port Sparameter measurements. At the lowest frequencies 1-25 MHz where the phase measurements are less accurate, a lumpedparameter model was used to predict the dielectric loss factor values. The system was calibrated with measurements on air and decanol and verified with measurements on octanol, hexanol, and pentanol. The standard error for the polar alcohols used for verification was 2.3% for the dielectric constant and 7.6% for the dielectric loss factor. Although measurements were taken on static samples, the sample holder is designed to accommodate flowing grain. Index Terms— Coaxial line, dielectric properties, particulate material, permittivity measurement, signal flow graph. I.
INTRODUCTION
OMMERCIAL radio-frequency (RF) and microwave C grain moisture measuring instruments have been in use for many years. RF moisture meters are commonly used with static samples to measure the moisture content of cereal grains. Interest in microwave aquametry, the measurement of moisture content in liquids, semi-solids, and solids by microwave techniques, has also flourished in recent years with much of the current microwave moisture content research focusing on density-independent, on-line moisture monitoring techniques [II, [2]. The dielectric properties of wheat are dependent on frequency, moisture content, temperature, and density [3], [4]. Measuring the moisture content of flowing grain is usually difficult and expensive because the variations in the bulk density as the grain flows through a sensor cause errors in moisture prediction. The reason density affects moisture content measurements (and why most moisture meters need information on the weight of the sample) is evident from the definition of wet-basis moisture content M, in percent
M = 100 (:)(1) \mT
Manuscript received August 15, 1997; revised November 19, 1998. The authors are with the Russell Research Center, Agricultural Research Service, U.S. Department of Agriculture, Athens, GA 30604 USA. (Mention of company or trade name is for purpose of description only and does not imply endorsement by the U.S. Department of Agriculture. Publisher Item Identifier S 0018-9456(98)09787-3.
where m is the mass of water and MT is the total mass of the material. Dividing both numerator and denominator by the sample volume v yields
M = 100 (m/v '\p)
(2)
where p is the sample bulk density. Thus, moisture content is the mass of water per unit volume divided by the density. Knowing the sample weight and volume reduces the prediction of moisture content to an estimation of the mass of water within a sample. Since the dielectric constant of free water is much larger than that of the grain dry matter, it is relatively easy to sense the mass of water within a grain sample. The dielectric properties of interest are defined as the relative complex permittivity, C = - j€", where C' is the dielectric constant and c" is the dielectric loss factor. For an on-line moisture meter to be accurate, either a measure of density must be obtained, or a system that senses moisture content, independent of density, must be developed. Density-independent microwave moisture techniques are available [1], [5]—[7], but their costs are too high for many applications. Thus, a moisture meter, operating at lower frequencies where component costs are less, that is density-independent, and suitable for flowing grain, would be desirable. A broadband coaxial cell was developed for dielectric properties measurements over a frequency range from 1 to 3 GHz [8]. Several calibration techniques were needed to cover the entire frequency range. The transition sections of the coaxial cell were isolated from the sample section, but the cell was designed for static measurements and was not suitable for flowing materials. A flowing grain moisture meter based on the output of an LM555 integrated-circuit timer/oscillator, where the oscillator frequency was a function of the capacitance of a test cell filled with grain, has also been developed [9]. Measurements on flowing grain provided an average standard error of 0.62% moisture content for five different grains. In other studies with a sample holder suitable for flowing grain, wheat moisture content was also sensed, independent of bulk density, from measurements of complex impedance at 1 and 10 MHz [10]. The system utilized a shielded parallel-plate sample holder to measure moisture content of static samples with a standard error of 0.5% moisture content for samples with moistures ranging from 11 to 22% and with densities ranging from 0.65 to 0.85 g/cm 3 . It appeared that errors might
0018-9456/98$10.00 © 1998 IEEE
LAWRENCE et al.: FLOW-THROUGH COAXIAL SAMPLE HOLDER DESIGN
355
Type N connector semirigid coaxial line
II
Brass Strap
A
Teflon fitting Di Sul
Fig. 1. Symmetrical two-port coaxial sample holder for dielectric properties measurements on flowing grain. Dimensions in centimeters.
be reduced if measurements at frequencies around 100 MHz were included. Complex impedance measurements from 1 to 110 MHz with essentially the same shielded parallel-plate sample holder as described in [10] were used to obtain the moisture content of static wheat samples of varying densities and moisture contents [11]. Multivariate analysis of the data was used to determine optimum measurement frequencies. From these analyses, frequencies of about 2, 25, and 80 MHz were used to provide a calibration for moisture content Al as follows:
Teflon / Support Brass , Dielectric / Spacer
Semirigid Coaxial Line
[(Cm - Cn)
1M=29.6+0[(Gm ] 2.3 1(CmCa)1 1(CmCa)1 —19.81 [(Gm Ga)]24 —18.23 [(Cm - Ga)]83 (3) where Cm and Ca are the capacitances of the sample holder filled and empty, respectively, Gm and Ga are the conductances of the sample holder filled and empty, respectively, and the numeric subscripts refer to measurement frequencies. With (3), the standard error of the validation data set was 0.35% moisture content with a -0.08% bias. This technique showed promise as a new, inexpensive method for sensing moisture content that was applicable to flowing grain. However, because measurements of capacitance and conductance were used in (3), it is dependent on the exact experimental setup. If a similar analysis were performed with permittivity measurements, the technique would then be independent of sample geometry and universally applicable to dielectric properties measurement systems. Furthermore, since the shielded parallel-plate sample holder is not ideally suited for measurements at frequencies as high as 100 MHz and grain is often transferred in circular ducts, a coaxial sample holder might be better suited. Therefore, a coaxial flow-through sample holder was constructed for measuring the permittivity of cereal grains from 1 to 350 MHz. The sample holder design, model development, calibration, and verification are presented in this article.
Brass Strap Fig. 2. Enlarged view of the transition section of the coaxial line.
II.
SAMPLE HOLDER DESIGN
The coaxial electrode geometry was also selected for its broadband characteristics and because its dimensions were large enough to accommodate cerealgrains. The sample holder was designed to operate in the TEM mode with a characteristic impedance of 50 Q when empty, and the inside diameter of the outer conductor was selected as 7.62 cm (3 in). One disadvantage of the coaxial sample holder though, involves the transition from the coaxial line of the measuring instrument to the larger dimensions of the sample holder. In a coaxial sample holder with the grain flowing along the axis between the electrodes, the transition is not isolated. This makes modeling the sample holder much more difficult. To completely model the sample holder, both reflection and transmission measurements were needed, so a two-port sample holder was designed and is shown in Fig. 1. An enlarged view of the transition is shown in Fig. 2. The measuring section of the sample holder consists of a 7.62-cm (3-in) ID aluminum tubing outer electrode and a 3.30-cm (1.30-in) OD aluminum inner electrode, both 15.24 cm (6 in) in length. Teflon fittings,
356
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
Semi- Transition Measuring Section Transition Semirigid I Section I Section rigid Section I I Section T1 I 'r2 I 1+ 1', 1, 1-17, I 13 1
IBM compatible PC was used for instrument control, data storage, and data processing. ifi.
Ir, T
1'
I
MODEL DEVELOPMENT
-r,
r, r3
-r, Ir, 11r, 12 1
1173 1,
I
Fig. 3. Signal-flow graph of the coaxial sample holder. The semirigid Section contains the connector, adapter, and semirigid coaxial line with the 90° bend. The transition section is modeled with a generic, two-port symmetric S-parameter network. The sample Section 15 the main permittivity measuring section.
A. Signal-Flow-Graph Model The electric field E(d) of an electromagnetic wave propagating through a material can be defined in complex notation as E(d) = E(0)e--, d
(4)
where E(0) is the amplitude of the electric field at the reference plane, d is the distance from the reference plane, = a + j13 is the complex propagation constant of the material, ot is the attenuation constant, and /3 is the phase constant. The sample holder was designed with axial symmetry which was confirmed by measurements (Su m Sm, S21m S 12m) . It can be modeled with a signal flow graph consisting of a series of cascaded two-port networks as shown in Fig. 3 [12]—[14]. The semirigid section represents the phase delay associated with the connector, adapter, and the length of semirigid coaxial line. Preliminary measurements on just this section indicated that it is lossless with no reflection, so the transmission coefficient can be written as
which isolate each end of the sample holder, were machined with the same ID as the outer electrode, Each Teflon fitting also supports the inner electrode by a 7,62-mm (0,30-in) long Teflon diagonal support that has a 6,35-mm (0,25-in) diameter hole drilled in the center to accommodate the semirigid coaxial line (6,35-mm OD). A hole was drilled in the sidewall of each Teflon fitting to allow the semirigid coaxial line to exit the sample holder. Type N connectors were attached to the outer end of each semirigid coaxial line. The 90° bends in the semirigid lines have a radius of 1.91-cm (0.75-in). At the other end of the semirigid line, the inner conductor extends beyond the outer conductor and fits into a hole drilled in the (5) end of the aluminum inner electrode. Set screws in each end of the inner electrode were used to clamp the coaxial line center where w is the angular frequency (27rf), p. is the relative perconductor and insure good electrical contact. The aluminum meability of the material (p. = 1 for nonmagnetic materials), inner electrode and the Outer conductor of the semirigid line l is the permittivity of the surrounding medium, d 1 is the are separated by a 3.18-mm (0.125-in) thick insulating Teflon combined lengths of the various components of the semirigid disk with the same diameter as the inner electrode. section, and c is the speed of light. To make electrical contact between the outer electrode of the The transition section represents the transition from the semirigid line and the aluminum tubing, a 5.08-mm (0.20-in) semirigid coaxial line to the larger dimensions of the sample wide brass strap was soldered to an 11.7-mm (0.46-in) OD measuring section. As mentioned, the transition section is brass bushing of 3.18-mm (0.125-in) thickness. The bushing 'not isolated from the unknown sample material, so it was was tightly fitted onto the end of the semirigid coaxial line first modeled as a general two-port network with unknown such that the end of its outer conductor was flush with the reflection coefficient F 2 and transmission coefficient T2 . The surface of the brass strap. The brass strap extended to the sample section model consists of a reflection (F 3 ) from the outer diameter of the aluminum tubing and electrical contact dielectric interface, and a transmission coefficient (T3 ) which was maintained by clamping the strap between the end of the represents the wave propagating through the dielectric material tubing and the lip of the Teflon fitting. The strap was positioned [15] with below the Teflon diagonal support for protection from flowing grain, and the brass bushing was fitted into a recess bored in the Teflon diagonal support. A Teflon cap, which fit over the —-1 (6) end of the Teflon fitting, provided a bottom for the sample + 1 holder to contain the samples when the sample holder was V3 oriented vertically for the measurements. The total volume of T3 (7) the sample holder was 1076 cm3. Full two-port scattering parameter measurements where d3 is the length of the sample section, and 63 is the (Su m , S 12m, S21m, S22m) from 1 to 350 MHz were collected permittivity of the sample. with a Hewlett Packard HP8753C Network Analyzer. Type Each two-port network in Fig. 3 can be cascaded so that the N-to-APC-7 adapters were connected to each end of the model can be reduced to a single two-port network consisting sample holder coaxial lines to facilitate connection to the of only four elements [14]. Then by measuring a material net-work analyzer. The reference planes were the APC-7 end of known permittivity, the unknowns in the model can be of each adapter. A full two-port calibration was performed determined by iterative techniques until the errors in the with a short, open, load, and thru connection (SOLT). An simplified two-port network are minimized. =
E
_j/di/'c
LAWRENCE
et al.:
FLOW-THROUGH COAXIAL SAMPLE HOLDER DESIGN
TABLE I DEBYE STATIC AND HIGH-FREQUENCY DIELECTRIC CONSTANT
VALUES AND RELAXATION FREQUENCY VALUES FOR THE POLAR ALCOHOLS USED FOR CALIBRATION AND VERIFiCATION
f0 (MH.z) Temp. °C Source Decanql 7.98 2.9 80 21.5 Baker-Jarvis [17] Octanol 9.6 3.3 129 25 Bottreau etal. [19] Hexanol 12.9 3.3 152 20 Buckley and Maryoti [18] Pentanol 15.66 3.3 190 20 Clarke [16]
Semi- Transition Measuring Section Transition Semirigid I Section I I Section I rigid Section Section TI I 14 I+Y2 1, I 1+ I' T3 1-I', I T3 1+Y2 T4 i T
Alcohol e, e,,,
Analysis, model characterization, and verification were performed with the sample holder empty and filled with the four polar alcohols, pentanol, hexanol, octanol, and decanol, which have known dielectric properties [ 16 ] — [ 1 9] . Permittivity values were calculated from the Debye equations [ 20 ] . Table I lists the static and high-frequency dielectric constants, the relaxation frequency, and the measurement temperatures for the polar alcohols used in this work. Prior to installing the semirigid section in the sample holder, the end of the semirigid line was shorted and the length of the semirigid line d1 was determined from timedomain measurements. Physical measurements were used for the length of the sample section d3 . Initial values of 19.8 and 15.24 cm were used for d 1 and d 3 , respectively. As a first approach, the dimensions of d 1 and d3 and known dielectric properties values were used in the model, shown in Fig. 3, to calculate the S-parameters of the transition section (I' 2 and T2 ). By assuming all model dimensions and permittivity values are exact, all errors associated with the model were forced into the transition section. Examination of the transition S-parameters, when the sample holder was empty, indicated that r 2 was nearly zero and 7'7 was almost one for all frequencies. However, when the sample holder was filled with an alcohol, the results varied significantly with frequency and were quite unpredictable. Thus, the transition section had both a permittivity-dependent and permittivityindependent affect. This resulted from not being able to isolate the transition from the sample material, 'which is common with static sample holders [8]. Attempts were made to model the transition as a step discontinuity [21]. A lumped capacitive element [12] replaced r 2 and T2 as the transition section, but this too produced unsatisfactory errors. After numerous unsuccessful attempts to model the transition with other lumped elements or empirical equations, this technique was abandoned. The next approach involved comparison of the total model S-parameters to the measured values. First the empty sample holder was evaluated. Assuming a perfect transition (i.e., 172 = 0 and T2 = 1), the total phase shift of S21m was compared to the phase shift predicted by the model at several frequencies. From this comparison, it was observed that the measured phase shift was always larger than the model phase shift, so the model needed an additional length of 9.1 cm to compensate for this difference. This additional length was attributed to the brass straps located at the transitions, which connected the outer conductor of the semirigid line to the outer conductor of the sample measuring section. The additional length was then incorporated in T2 of the transition sections.
357
1
k k frH- F3H2
14
1 +'(2
1, I-I', T3 1+
r, 1, 1+Y, T. T
Fig. 4. Modified signal-flow graph where the transition section has been replaced with two transmission networks and a lumped admittance network.
This explained why the transition could not be modeled with lumped elements alone. As before, analysis with the polar alcohols indicated the transition must be divided such that a portion is affected by the permittivity of the sample material and a portion is independent of sample material. Furthermore, the model also needed a network to provide a small attenuation and reflection in the transition section which was accomplished by a lumped admittance network. Thus, the transition section of the signal-flow graph (Fig. 3) was replaced with two transmission networks and a lumped element network as shown in Fig. 4, where T4 and 2' have the same general form as T1 and T3 , but with different lengths d4 and d5 , respectively, and = Y+2 (8) where Y is the normalized admittance of the lumped element. Since T5 represents the phase delay through the sample material associated with the transition, it must be preceded by a network that provides for a reflection from a dielectric interface, which is the same as (6) and is shown in Fig. 5 as r'3 . However, both T5 and T3 are influenced by the same permittivity, so the original dielectric interface network between them can be removed (1' 3 = 0). This allows us to simplify the signal-flow graph to that shown in Fig. 6, where Tf is a combination of T1 and T4 , and T is the combination of T3 and T5 with T' =e—j// (9) T __jw/d/c (10) where d'1 = d1 + d 4 and d'3 = d3 + d5 . To determine the optimum lengths of d'1 and d, an iterative program was written which minimized the model error of the total 521 when the sample holder was empty and filled with decanol. Once the final values of d'1 = 22.94 cm and d'3 = 17.94 cm were obtained the calibration was complete and another iterative program was used to determine the permittivity values from the cascaded flow graph (Fig. 6). The solution for the flow graph is [14] S11 S22 = X 11 + -
S21S12 -
T(1 +
Y2X22 Y2)X21
1—Y2X22
(11) ( 12)
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
358
Semi- Transition rigid I Section Section I T4 i+y, i+r'; T,
Measuring Section
1+l 3 T3 1-l'
f-i', f-I',
'2
Ti T4
i+', i-i'; T5
1-I',
Transition Section
Semi-
I rigid
Section
I 'I', i-r3 i+Y2
*. k k
'F, 1+1' I
i
'r5 i+r i+;
Fig. 5. Signal-flow graph with an additional network I"3 to account for the reflection from the dielectric interface prior to T.
For a parallel-circuit, lumped-parameter model, the measured conductance is given by
Semi- Transition Measuring Section Transition SemiSection rigid rigid Section Section Section I l+Y I 1+I' T 1-I 1+Y1 I T I
I
UYZ'.
Gm = Gsr + C 5 + C f
F'
r, }r , b2I i+y2 i-r, T; i+r, 1+Y2 T YIJ1' -
where Car is the conductance of the semirigid lines, Gs is the conductance of the sample, and C 1 is the conductance associated with the fringing fields. Substituting the general relation C = wC0 c" for Gsr and C 5 , where C. is the capacitance with vacuum (air) as a dielectric, into (14) yields
I I
I
Fig. 6 Final signal-flow graph model where the transmission networks T1 and T4 have been combined as T1' and networks T3 and T5 have been combined as T.
where T 2 (1 + Y)2W11 Xii= T Y2 + 1— T(1 + Y2)W21 = 1 =
11
(14)
Gm = W(Cosr4eflon + CO5 e'5') + C1 . (15)
For Teflon, the loss factor in this frequency range is about 0.0004. Solving (15) for e' yields If = -0.0004 ( osr ) . (16) The ratio ( Cosr /C0s ) 2.6 1 so (16) may be approximated as ii m f
Y2 W21
2irfCO5
+1-
and
(17)
If the sample holder is empty (€' = 0, Cm = Gair = measured conductance of the empty sample holder), (17) reduces to C 1 =G air and one obtains
'r'I1 r2 r'3,J. / 'r'2\ .13 ) TX? 13IL 13 VV25 F2T'2 = 1 - 33 = 1_33
TX? I
if nT - Gair
The permittivity was determined when the magnitude of the error vector between the model and measured S21 values was minimized over all frequencies (E IS21m - S21I).
2rfC0
18
IV. ERROR ANALYSIS AND RESULTS
B. Lumped-Parameter Model Because the frequency range of the measurements extended down to 1 MHz where the wavelength is 300 m, reflection and transmission phase-angle measurements were less sensitive in this region and gave large worst-case measurement errors (see Section IV). Even though the phase insensitivity produced large worst-case measurement errors at the lower frequencies, only the dielectric loss factor measurements did not agree well with the calibration standards. Therefore, a lumped-parameter model was used for the dielectric loss factor measurements from 1 to 25 MHz. From the four measured S-parameters, one can calculate the reflection coefficient Fm as if the sample holder were terminated with an open circuit, where
Fm= Sum + S12m521m 1 - S22,. The conductance Gm can then be calculated from Fm.
(13)
To evaluate the accuracy of the system, an uncertainty analysis was performed. Possible sources of errors include instrument errors, errors associated with the permittivity values of the alcohols used as standards, and model errors. After a full two-port calibration (SOLT), typical instrument uncertainties for the HP8753C are 50 dB directivity D, 40 dB source match M5 and load match ML, ±0.05 dB frequency response TR, ±0.03 dB transmission frequency response TT, and 100 dB crosstalk C. The accuracies of the measurements are given as [22] Su l AS21
D+TRS ll +M5 S 1
(19)
C + TT S21 + M8 S11 S21 + ML S22 S21 .
( 20)
The phase uncertainty is given as (AS,, \ A® 11 = sin 1 (21) Sil
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
Flow-Through Coaxial Sample Holder Design for Dielectric Properties Measurements from 1 to 350 MHz Kurt C. Lawrence, Member, IEEE, Stuart 0. Nelson, Fellow, IEEE, and Philip G. Bartley, Jr., Student Member, IEEE
Abstract—A system for measuring the dielectric properties of cereal grains from 1 to 350 MHz with a coaxial sample holder is presented. A signal-flow graph model was used to determine the permittivity of several polar alcohols from the full two-port Sparameter measurements. At the lowest frequencies 1-25 MHz where the phase measurements are less accurate, a lumpedparameter model was used to predict the dielectric loss factor values. The system was calibrated with measurements on air and decanol and verified with measurements on octanol, hexanol, and pentanol. The standard error for the polar alcohols used for verification was 2.3% for the dielectric constant and 7.6% for the dielectric loss factor. Although measurements were taken on static samples, the sample holder is designed to accommodate flowing grain. Index Terms— Coaxial line, dielectric properties, particulate material, permittivity measurement, signal flow graph. I.
INTRODUCTION
OMMERCIAL radio-frequency (RF) and microwave C grain moisture measuring instruments have been in use for many years. RF moisture meters are commonly used with static samples to measure the moisture content of cereal grains. Interest in microwave aquametry, the measurement of moisture content in liquids, semi-solids, and solids by microwave techniques, has also flourished in recent years with much of the current microwave moisture content research focusing on density-independent, on-line moisture monitoring techniques [II, [2]. The dielectric properties of wheat are dependent on frequency, moisture content, temperature, and density [3], [4]. Measuring the moisture content of flowing grain is usually difficult and expensive because the variations in the bulk density as the grain flows through a sensor cause errors in moisture prediction. The reason density affects moisture content measurements (and why most moisture meters need information on the weight of the sample) is evident from the definition of wet-basis moisture content M, in percent
M = 100 (:)(1) \mT
Manuscript received August 15, 1997; revised November 19, 1998. The authors are with the Russell Research Center, Agricultural Research Service, U.S. Department of Agriculture, Athens, GA 30604 USA. (Mention of company or trade name is for purpose of description only and does not imply endorsement by the U.S. Department of Agriculture. Publisher Item Identifier S 0018-9456(98)09787-3.
where m is the mass of water and MT is the total mass of the material. Dividing both numerator and denominator by the sample volume v yields
M = 100 (m/v '\p)
(2)
where p is the sample bulk density. Thus, moisture content is the mass of water per unit volume divided by the density. Knowing the sample weight and volume reduces the prediction of moisture content to an estimation of the mass of water within a sample. Since the dielectric constant of free water is much larger than that of the grain dry matter, it is relatively easy to sense the mass of water within a grain sample. The dielectric properties of interest are defined as the relative complex permittivity, C = - j€", where C' is the dielectric constant and c" is the dielectric loss factor. For an on-line moisture meter to be accurate, either a measure of density must be obtained, or a system that senses moisture content, independent of density, must be developed. Density-independent microwave moisture techniques are available [1], [5]—[7], but their costs are too high for many applications. Thus, a moisture meter, operating at lower frequencies where component costs are less, that is density-independent, and suitable for flowing grain, would be desirable. A broadband coaxial cell was developed for dielectric properties measurements over a frequency range from 1 to 3 GHz [8]. Several calibration techniques were needed to cover the entire frequency range. The transition sections of the coaxial cell were isolated from the sample section, but the cell was designed for static measurements and was not suitable for flowing materials. A flowing grain moisture meter based on the output of an LM555 integrated-circuit timer/oscillator, where the oscillator frequency was a function of the capacitance of a test cell filled with grain, has also been developed [9]. Measurements on flowing grain provided an average standard error of 0.62% moisture content for five different grains. In other studies with a sample holder suitable for flowing grain, wheat moisture content was also sensed, independent of bulk density, from measurements of complex impedance at 1 and 10 MHz [10]. The system utilized a shielded parallel-plate sample holder to measure moisture content of static samples with a standard error of 0.5% moisture content for samples with moistures ranging from 11 to 22% and with densities ranging from 0.65 to 0.85 g/cm 3 . It appeared that errors might
0018-9456/98$10.00 © 1998 IEEE
LAWRENCE et al.: FLOW-THROUGH COAXIAL SAMPLE HOLDER DESIGN
355
Type N connector semirigid coaxial line
II
Brass Strap
A
Teflon fitting Di Sul
Fig. 1. Symmetrical two-port coaxial sample holder for dielectric properties measurements on flowing grain. Dimensions in centimeters.
be reduced if measurements at frequencies around 100 MHz were included. Complex impedance measurements from 1 to 110 MHz with essentially the same shielded parallel-plate sample holder as described in [10] were used to obtain the moisture content of static wheat samples of varying densities and moisture contents [11]. Multivariate analysis of the data was used to determine optimum measurement frequencies. From these analyses, frequencies of about 2, 25, and 80 MHz were used to provide a calibration for moisture content Al as follows:
Teflon / Support Brass , Dielectric / Spacer
Semirigid Coaxial Line
[(Cm - Cn)
1M=29.6+0[(Gm ] 2.3 1(CmCa)1 1(CmCa)1 —19.81 [(Gm Ga)]24 —18.23 [(Cm - Ga)]83 (3) where Cm and Ca are the capacitances of the sample holder filled and empty, respectively, Gm and Ga are the conductances of the sample holder filled and empty, respectively, and the numeric subscripts refer to measurement frequencies. With (3), the standard error of the validation data set was 0.35% moisture content with a -0.08% bias. This technique showed promise as a new, inexpensive method for sensing moisture content that was applicable to flowing grain. However, because measurements of capacitance and conductance were used in (3), it is dependent on the exact experimental setup. If a similar analysis were performed with permittivity measurements, the technique would then be independent of sample geometry and universally applicable to dielectric properties measurement systems. Furthermore, since the shielded parallel-plate sample holder is not ideally suited for measurements at frequencies as high as 100 MHz and grain is often transferred in circular ducts, a coaxial sample holder might be better suited. Therefore, a coaxial flow-through sample holder was constructed for measuring the permittivity of cereal grains from 1 to 350 MHz. The sample holder design, model development, calibration, and verification are presented in this article.
Brass Strap Fig. 2. Enlarged view of the transition section of the coaxial line.
II.
SAMPLE HOLDER DESIGN
The coaxial electrode geometry was also selected for its broadband characteristics and because its dimensions were large enough to accommodate cerealgrains. The sample holder was designed to operate in the TEM mode with a characteristic impedance of 50 Q when empty, and the inside diameter of the outer conductor was selected as 7.62 cm (3 in). One disadvantage of the coaxial sample holder though, involves the transition from the coaxial line of the measuring instrument to the larger dimensions of the sample holder. In a coaxial sample holder with the grain flowing along the axis between the electrodes, the transition is not isolated. This makes modeling the sample holder much more difficult. To completely model the sample holder, both reflection and transmission measurements were needed, so a two-port sample holder was designed and is shown in Fig. 1. An enlarged view of the transition is shown in Fig. 2. The measuring section of the sample holder consists of a 7.62-cm (3-in) ID aluminum tubing outer electrode and a 3.30-cm (1.30-in) OD aluminum inner electrode, both 15.24 cm (6 in) in length. Teflon fittings,
356
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
Semi- Transition Measuring Section Transition Semirigid I Section I Section rigid Section I I Section T1 I 'r2 I 1+ 1', 1, 1-17, I 13 1
IBM compatible PC was used for instrument control, data storage, and data processing. ifi.
Ir, T
1'
I
MODEL DEVELOPMENT
-r,
r, r3
-r, Ir, 11r, 12 1
1173 1,
I
Fig. 3. Signal-flow graph of the coaxial sample holder. The semirigid Section contains the connector, adapter, and semirigid coaxial line with the 90° bend. The transition section is modeled with a generic, two-port symmetric S-parameter network. The sample Section 15 the main permittivity measuring section.
A. Signal-Flow-Graph Model The electric field E(d) of an electromagnetic wave propagating through a material can be defined in complex notation as E(d) = E(0)e--, d
(4)
where E(0) is the amplitude of the electric field at the reference plane, d is the distance from the reference plane, = a + j13 is the complex propagation constant of the material, ot is the attenuation constant, and /3 is the phase constant. The sample holder was designed with axial symmetry which was confirmed by measurements (Su m Sm, S21m S 12m) . It can be modeled with a signal flow graph consisting of a series of cascaded two-port networks as shown in Fig. 3 [12]—[14]. The semirigid section represents the phase delay associated with the connector, adapter, and the length of semirigid coaxial line. Preliminary measurements on just this section indicated that it is lossless with no reflection, so the transmission coefficient can be written as
which isolate each end of the sample holder, were machined with the same ID as the outer electrode, Each Teflon fitting also supports the inner electrode by a 7,62-mm (0,30-in) long Teflon diagonal support that has a 6,35-mm (0,25-in) diameter hole drilled in the center to accommodate the semirigid coaxial line (6,35-mm OD). A hole was drilled in the sidewall of each Teflon fitting to allow the semirigid coaxial line to exit the sample holder. Type N connectors were attached to the outer end of each semirigid coaxial line. The 90° bends in the semirigid lines have a radius of 1.91-cm (0.75-in). At the other end of the semirigid line, the inner conductor extends beyond the outer conductor and fits into a hole drilled in the (5) end of the aluminum inner electrode. Set screws in each end of the inner electrode were used to clamp the coaxial line center where w is the angular frequency (27rf), p. is the relative perconductor and insure good electrical contact. The aluminum meability of the material (p. = 1 for nonmagnetic materials), inner electrode and the Outer conductor of the semirigid line l is the permittivity of the surrounding medium, d 1 is the are separated by a 3.18-mm (0.125-in) thick insulating Teflon combined lengths of the various components of the semirigid disk with the same diameter as the inner electrode. section, and c is the speed of light. To make electrical contact between the outer electrode of the The transition section represents the transition from the semirigid line and the aluminum tubing, a 5.08-mm (0.20-in) semirigid coaxial line to the larger dimensions of the sample wide brass strap was soldered to an 11.7-mm (0.46-in) OD measuring section. As mentioned, the transition section is brass bushing of 3.18-mm (0.125-in) thickness. The bushing 'not isolated from the unknown sample material, so it was was tightly fitted onto the end of the semirigid coaxial line first modeled as a general two-port network with unknown such that the end of its outer conductor was flush with the reflection coefficient F 2 and transmission coefficient T2 . The surface of the brass strap. The brass strap extended to the sample section model consists of a reflection (F 3 ) from the outer diameter of the aluminum tubing and electrical contact dielectric interface, and a transmission coefficient (T3 ) which was maintained by clamping the strap between the end of the represents the wave propagating through the dielectric material tubing and the lip of the Teflon fitting. The strap was positioned [15] with below the Teflon diagonal support for protection from flowing grain, and the brass bushing was fitted into a recess bored in the Teflon diagonal support. A Teflon cap, which fit over the —-1 (6) end of the Teflon fitting, provided a bottom for the sample + 1 holder to contain the samples when the sample holder was V3 oriented vertically for the measurements. The total volume of T3 (7) the sample holder was 1076 cm3. Full two-port scattering parameter measurements where d3 is the length of the sample section, and 63 is the (Su m , S 12m, S21m, S22m) from 1 to 350 MHz were collected permittivity of the sample. with a Hewlett Packard HP8753C Network Analyzer. Type Each two-port network in Fig. 3 can be cascaded so that the N-to-APC-7 adapters were connected to each end of the model can be reduced to a single two-port network consisting sample holder coaxial lines to facilitate connection to the of only four elements [14]. Then by measuring a material net-work analyzer. The reference planes were the APC-7 end of known permittivity, the unknowns in the model can be of each adapter. A full two-port calibration was performed determined by iterative techniques until the errors in the with a short, open, load, and thru connection (SOLT). An simplified two-port network are minimized. =
E
_j/di/'c
LAWRENCE
et al.:
FLOW-THROUGH COAXIAL SAMPLE HOLDER DESIGN
TABLE I DEBYE STATIC AND HIGH-FREQUENCY DIELECTRIC CONSTANT
VALUES AND RELAXATION FREQUENCY VALUES FOR THE POLAR ALCOHOLS USED FOR CALIBRATION AND VERIFiCATION
f0 (MH.z) Temp. °C Source Decanql 7.98 2.9 80 21.5 Baker-Jarvis [17] Octanol 9.6 3.3 129 25 Bottreau etal. [19] Hexanol 12.9 3.3 152 20 Buckley and Maryoti [18] Pentanol 15.66 3.3 190 20 Clarke [16]
Semi- Transition Measuring Section Transition Semirigid I Section I I Section I rigid Section Section TI I 14 I+Y2 1, I 1+ I' T3 1-I', I T3 1+Y2 T4 i T
Alcohol e, e,,,
Analysis, model characterization, and verification were performed with the sample holder empty and filled with the four polar alcohols, pentanol, hexanol, octanol, and decanol, which have known dielectric properties [ 16 ] — [ 1 9] . Permittivity values were calculated from the Debye equations [ 20 ] . Table I lists the static and high-frequency dielectric constants, the relaxation frequency, and the measurement temperatures for the polar alcohols used in this work. Prior to installing the semirigid section in the sample holder, the end of the semirigid line was shorted and the length of the semirigid line d1 was determined from timedomain measurements. Physical measurements were used for the length of the sample section d3 . Initial values of 19.8 and 15.24 cm were used for d 1 and d 3 , respectively. As a first approach, the dimensions of d 1 and d3 and known dielectric properties values were used in the model, shown in Fig. 3, to calculate the S-parameters of the transition section (I' 2 and T2 ). By assuming all model dimensions and permittivity values are exact, all errors associated with the model were forced into the transition section. Examination of the transition S-parameters, when the sample holder was empty, indicated that r 2 was nearly zero and 7'7 was almost one for all frequencies. However, when the sample holder was filled with an alcohol, the results varied significantly with frequency and were quite unpredictable. Thus, the transition section had both a permittivity-dependent and permittivityindependent affect. This resulted from not being able to isolate the transition from the sample material, 'which is common with static sample holders [8]. Attempts were made to model the transition as a step discontinuity [21]. A lumped capacitive element [12] replaced r 2 and T2 as the transition section, but this too produced unsatisfactory errors. After numerous unsuccessful attempts to model the transition with other lumped elements or empirical equations, this technique was abandoned. The next approach involved comparison of the total model S-parameters to the measured values. First the empty sample holder was evaluated. Assuming a perfect transition (i.e., 172 = 0 and T2 = 1), the total phase shift of S21m was compared to the phase shift predicted by the model at several frequencies. From this comparison, it was observed that the measured phase shift was always larger than the model phase shift, so the model needed an additional length of 9.1 cm to compensate for this difference. This additional length was attributed to the brass straps located at the transitions, which connected the outer conductor of the semirigid line to the outer conductor of the sample measuring section. The additional length was then incorporated in T2 of the transition sections.
357
1
k k frH- F3H2
14
1 +'(2
1, I-I', T3 1+
r, 1, 1+Y, T. T
Fig. 4. Modified signal-flow graph where the transition section has been replaced with two transmission networks and a lumped admittance network.
This explained why the transition could not be modeled with lumped elements alone. As before, analysis with the polar alcohols indicated the transition must be divided such that a portion is affected by the permittivity of the sample material and a portion is independent of sample material. Furthermore, the model also needed a network to provide a small attenuation and reflection in the transition section which was accomplished by a lumped admittance network. Thus, the transition section of the signal-flow graph (Fig. 3) was replaced with two transmission networks and a lumped element network as shown in Fig. 4, where T4 and 2' have the same general form as T1 and T3 , but with different lengths d4 and d5 , respectively, and = Y+2 (8) where Y is the normalized admittance of the lumped element. Since T5 represents the phase delay through the sample material associated with the transition, it must be preceded by a network that provides for a reflection from a dielectric interface, which is the same as (6) and is shown in Fig. 5 as r'3 . However, both T5 and T3 are influenced by the same permittivity, so the original dielectric interface network between them can be removed (1' 3 = 0). This allows us to simplify the signal-flow graph to that shown in Fig. 6, where Tf is a combination of T1 and T4 , and T is the combination of T3 and T5 with T' =e—j// (9) T __jw/d/c (10) where d'1 = d1 + d 4 and d'3 = d3 + d5 . To determine the optimum lengths of d'1 and d, an iterative program was written which minimized the model error of the total 521 when the sample holder was empty and filled with decanol. Once the final values of d'1 = 22.94 cm and d'3 = 17.94 cm were obtained the calibration was complete and another iterative program was used to determine the permittivity values from the cascaded flow graph (Fig. 6). The solution for the flow graph is [14] S11 S22 = X 11 + -
S21S12 -
T(1 +
Y2X22 Y2)X21
1—Y2X22
(11) ( 12)
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1998
358
Semi- Transition rigid I Section Section I T4 i+y, i+r'; T,
Measuring Section
1+l 3 T3 1-l'
f-i', f-I',
'2
Ti T4
i+', i-i'; T5
1-I',
Transition Section
Semi-
I rigid
Section
I 'I', i-r3 i+Y2
*. k k
'F, 1+1' I
i
'r5 i+r i+;
Fig. 5. Signal-flow graph with an additional network I"3 to account for the reflection from the dielectric interface prior to T.
For a parallel-circuit, lumped-parameter model, the measured conductance is given by
Semi- Transition Measuring Section Transition SemiSection rigid rigid Section Section Section I l+Y I 1+I' T 1-I 1+Y1 I T I
I
UYZ'.
Gm = Gsr + C 5 + C f
F'
r, }r , b2I i+y2 i-r, T; i+r, 1+Y2 T YIJ1' -
where Car is the conductance of the semirigid lines, Gs is the conductance of the sample, and C 1 is the conductance associated with the fringing fields. Substituting the general relation C = wC0 c" for Gsr and C 5 , where C. is the capacitance with vacuum (air) as a dielectric, into (14) yields
I I
I
Fig. 6 Final signal-flow graph model where the transmission networks T1 and T4 have been combined as T1' and networks T3 and T5 have been combined as T.
where T 2 (1 + Y)2W11 Xii= T Y2 + 1— T(1 + Y2)W21 = 1 =
11
(14)
Gm = W(Cosr4eflon + CO5 e'5') + C1 . (15)
For Teflon, the loss factor in this frequency range is about 0.0004. Solving (15) for e' yields If = -0.0004 ( osr ) . (16) The ratio ( Cosr /C0s ) 2.6 1 so (16) may be approximated as ii m f
Y2 W21
2irfCO5
+1-
and
(17)
If the sample holder is empty (€' = 0, Cm = Gair = measured conductance of the empty sample holder), (17) reduces to C 1 =G air and one obtains
'r'I1 r2 r'3,J. / 'r'2\ .13 ) TX? 13IL 13 VV25 F2T'2 = 1 - 33 = 1_33
TX? I
if nT - Gair
The permittivity was determined when the magnitude of the error vector between the model and measured S21 values was minimized over all frequencies (E IS21m - S21I).
2rfC0
18
IV. ERROR ANALYSIS AND RESULTS
B. Lumped-Parameter Model Because the frequency range of the measurements extended down to 1 MHz where the wavelength is 300 m, reflection and transmission phase-angle measurements were less sensitive in this region and gave large worst-case measurement errors (see Section IV). Even though the phase insensitivity produced large worst-case measurement errors at the lower frequencies, only the dielectric loss factor measurements did not agree well with the calibration standards. Therefore, a lumped-parameter model was used for the dielectric loss factor measurements from 1 to 25 MHz. From the four measured S-parameters, one can calculate the reflection coefficient Fm as if the sample holder were terminated with an open circuit, where
Fm= Sum + S12m521m 1 - S22,. The conductance Gm can then be calculated from Fm.
(13)
To evaluate the accuracy of the system, an uncertainty analysis was performed. Possible sources of errors include instrument errors, errors associated with the permittivity values of the alcohols used as standards, and model errors. After a full two-port calibration (SOLT), typical instrument uncertainties for the HP8753C are 50 dB directivity D, 40 dB source match M5 and load match ML, ±0.05 dB frequency response TR, ±0.03 dB transmission frequency response TT, and 100 dB crosstalk C. The accuracies of the measurements are given as [22] Su l AS21
D+TRS ll +M5 S 1
(19)
C + TT S21 + M8 S11 S21 + ML S22 S21 .
( 20)
The phase uncertainty is given as (AS,, \ A® 11 = sin 1 (21) Sil
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