A Microwave Sensor for Evaluation of Plastic Wall Thickness

Non destructive measurement of the thickness and monitoring its variation of lossy dielectric slab products is of great interest in many facets of industry. Methods are based on measurements of transmitted and/or reflected electromagnetic power from a dielectric material under test by an incident electromagnetic wave. The recorded amplitude and phase of the transmitted or reflected wave is analyzed and processed to create appropriate correlations with physical and/or dimensional variations of a material. Many techniques (transmission/reflection line, free space, open ended coaxial or waveguide probe) have been developed to measure these properties such as techniques in time domain or frequency domain with one port or two ports, etc. Every technique is limited to specific frequencies, materials and applications [1–3]. However, in some industrial processes used materials have a low permittivity or high loss; opposite wall is not metal–backed and only one side of materials is accessible. Reflectivity signal from the opposite wall is low, these methods unsuitable in industry. Resonant measurements are the most accurate. To reduce the sensor size, it is appropriate to use the resonance properties of microstrip antennas [4]. The lightweight construction and the suitability for integration with MICs (Microwave Integrated Circuits) are two more of their numerous advantages. Microstrip printed antenna technology is suitable for low cost manufacturing. This is important, since MICs are much easier to handle and less expensive than the alternative waveguides. Suitability of microstrip antennas for low–frequency applications have been demonstrated in [5]. Although microstrip antennas are widely used, there is a little research on the design of near–field microstrip antennas for evaluation of plastic wall thickness and monitoring its variation for industrial applications.


Introduction
Non destructive measurement of the thickness and monitoring its variation of lossy dielectric slab products is of great interest in many facets of industry. Methods are based on measurements of transmitted and/or reflected electromagnetic power from a dielectric material under test by an incident electromagnetic wave. The recorded amplitude and phase of the transmitted or reflected wave is analyzed and processed to create appropriate correlations with physical and/or dimensional variations of a material.
Many techniques (transmission/reflection line, free space, open ended coaxial or waveguide probe) have been developed to measure these properties such as techniques in time domain or frequency domain with one port or two ports, etc. Every technique is limited to specific frequencies, materials and applications [1][2][3]. However, in some industrial processes used materials have a low permittivity or high loss; opposite wall is not metal-backed and only one side of materials is accessible. Reflectivity signal from the opposite wall is low, these methods unsuitable in industry. Resonant measurements are the most accurate. To reduce the sensor size, it is appropriate to use the resonance properties of microstrip antennas [4]. The lightweight construction and the suitability for integration with MICs (Microwave Integrated Circuits) are two more of their numerous advantages. Microstrip printed antenna technology is suitable for low cost manufacturing. This is important, since MICs are much easier to handle and less expensive than the alternative waveguides.
Suitability of microstrip antennas for low-frequency applications have been demonstrated in [5]. Although microstrip antennas are widely used, there is a little research on the design of near-field microstrip antennas for evaluation of plastic wall thickness and monitoring its variation for industrial applications.

Theory
The relative complex permittivity of an isotropic material is dependent on several variables, such as frequency, temperature, density, and moisture content. From a view of slab thickness measurement, these variables must be fixed or appropriate correlations must be established. The loss factor, is often used to study the structure and composition of materials. The depth of penetration d of microwaves into a dielectric is a function of the total dielectric loss tangent and the vacuum wavelength 0 where ' r  is the real part of dielectric permittivity r  ,  tan is the total dielectric loss tangent, Microwave has been low dept of penetration inside Carbon Fibre Reinforced Plastics (CFRP) and results from measurement can be ambiguous to interpret. Lower frequency wave penetrates deeper (Fig. 1). However, the size of the antenna increases and the resolution degrades rapidly. Problem can be solved using a substrate integrated waveguide antennas or low-frequency microstrip antennas [5]. The substrate material (filler) is selected with the nearest dielectric permittivity as the measurement slab. The fillers can significantly reduce the frequency of operation and keeping the small size of antennas, reducing reflection from a measurement wall, increases the penetration depth, maintains the resolution, and increasing the detection sensitivity and measurement accuracy. Polarizability of microwave signals enables the study of fiber bundle orientation or misalignment during manufacturing and provides information about cut or broken fiber bundles. To eliminate the influence of anisotropy for wall thickness measurement should be used microwaves of circular polarization.
Assuming a perpendicular plane wave traveling through a layer of low-lossmaterial ( " thickness h , the real and imaginary components of the relative complex permittivity are determined as follows [2]: where Eq. (2) shows that phases information is necessary to determine the sample thickness h , when is known the numerical value   . At a given frequency, sample thickness should fall within the following interval [3] where m is an integer to be determined. In any industrial process control, the phase ambiguity problem has to be solved in a way that can be easily automated.
If a dielectric slab thickness , the integer m can be determined as well as Nicholson-Ross-Weir conversion technique by analysis of group delay. Delay through the material is a function of the material total length and can be used to resolve this ambiguity. Measurements at two different frequencies can also be used to solve the phase ambiguity problem [2,3].
For one side thickness measurement, wave reflected from the opposite side must pass the same distance as the incident wave. If the incident wave propagation vector is perpendicular to the dielectric surface, the penetration depth should be at least twice higher. In this case, better suited the patch antenna [4]. The fields at the end of the patch can be split into tangential and normal components with respect to the ground plane. Normal field components create only near field. Their contribution to the far field in broadside direction cancels each other. The tangential field components, which are in phase, combine to give the maximum radiated field normal to the surface of the patch, create far field and penetrate into a dielectric deeper. Normal and tangential fields are complementary for sensor applications and allow measurement from low to highest thickness.

Sensor design
To measure the thickness and properties of the low permittivity or high loss composites, when only one side of materials is accessible, most suitable are microstrip antennas. They are narrowband antennas compared to conventional microwave antennas, since the radiation is a consequence of a resonance [4]. For resonant measurement antenna (sensor), a special feeding technique (proximity coupling) was used. This antenna uses electric and magnetic coupling, in which no physical connection is made between the feed line and the dipole [7]. Proximity coupled microwave thickness sensor antenna have many advantages over end fed and coaxial fed antenna. Some advantages include: no galvanic contact between feed line and radiating element, low permittivity patch substrate with a large thickness, no drilling required, less spurious radiation, better resonance sensitivity.
The antenna (Fig. 2) consists of two stacked substrates 3, 4 with a ground plane 5 underneath and two collinear microstriplines 1, 2 at different levels. The feed line 2 is located between the two substrates and overlaps the dipole 1, located on top of the substrate 3. The theory behind proximity feed patches is quite complex and only design guidelines will be presented [7].
ANTENNA MAGUS ® -antenna design software could easily calculate specifications (geometric dimensions, effective dielectric permittivity, return loss and attenuation). Final corrections are then made for coupling from numerical evaluation with CST MICROWAVE STUDIO ® (CST MWS). Tune the length variable of the patch antenna in the model such that the tuned patch radiates at the desired frequency. Tune the patch overlaps distance in the model such that the patch will give maximum parallel resonant quality. Geometric dimensions and parameters of the experimental proximityfed antenna are given in Table 1. The antenna radiation characteristic at centre frequency is shown in Fig. 3. The approach here is based on the idea that for sensing applications exploited resonance properties of this antenna.
An equivalent circuit of the antenna shown in [7]. The coupling capacitance between the feed line and the patch is a distributed element, which with feed line and equivalent shunt capacitance and inductance of patch forms transmission line resonator (TLR) circuit. Input impedances of low-loss transmission line resonators are generally expressed in terms of transcendental functions, so it is difficult to quantify analytically. CST MWS allows to evaluate impedance and admittance of TLR in broad frequency range. Fig. 4 shows the field distributions at feed line (the TLR surface) as some resonant states of n = 1, 2, 5 for comparison.
A change in the permittivity of the patch environment causes a change in its capacitance and hence a shift of the resonator frequency. This circumstance allows to evaluate the thickness of the high loss composites via recording of resonant frequency or phase deviation. The input impedance and admittance of TLR circuit in frequency range 2 to 5 GHz are shown in Fig. 5. As we can see in Fig 5 in frequency range 2 to 5 GHz gets tree shunt (a) and two series (b) resonance. Maximum shunt non-loaded resonance quality is 1150 at 2,863 GHz. Additional investigation showed that the lowest shunt resonance occurs at 0.92365 GHz. At this frequency, real part of impedance Z = 7100 Ohms and non-loaded resonance quality are 1050. For sensing applications, due to high quality most suitable shunts resonance of TLR. In order to increase patch tangential electric field component influence, TLR shunt resonance operating frequency area must be close as possible to antenna center frequency.

Sensor substrate materials
The most critical parameter for patch antennas is the dielectric permittivity, which must be controlled to within +/-0,2 % to achieve a resonant frequency accuracy of +/-0.1 %. [8]. The top substrate must be made with a lower permittivity to produce loosely bound fringing fields, yielding better radiation and increases the sensitivity. For a foam substrate, there is no surface-wave excitation losses and higher efficiency are obtained by making the substrate thicker. A higher value of permittivity of bottom substrate causes tightly coupled field, that don't produce spurious radiation. After analysis, the most appropriate materials for top and bottom substrate of proposed microwave sensor are presented in the Table 2 and 3. ROHACELL ® 31 HF at Evonik Industries AG is a 100 % closed-cell rigid foam plastic based on PMI (Polymethacrylimid) with a fine cell, excellent bonding properties, extremely low dielectric permittivity and particularly favorable transmission properties in the highfrequency region. Owing to its excellent creep compression resistance (dimensional change under the influence of pressure and temperature), ROHACELL® 31 HF is ideally suited for microwave sensors in industry and allows measurements under hostile environments and relative high temperatures. Rogers RT/duroid® 5870 and 5880 high-frequency laminates at Rogers Corporation are PTFE composites reinforced with glass micro fibers. They have the lowest dielectric permittivity and loss of any reinforced PTFE material, are isotropic, have uniform electric properties over frequency, extremely low water absorption characteristics and resistant to all solvents and reagents normally used in etching printed circuits or plating edges. Parameter stability in broad temperature range makes them well suitable for microwave sensor.

Sensor numerical evaluation
The CST MICROWAVE STUDIO ® evaluation model of plastic slab thickness measurement is shown in Fig. 6. Measured variable depends mainly on slab materials, thickness, operating frequency and on the distance between the sample and the sensor (gap size). Dielectric properties over a temperature range of common plastics for numerical evaluation can find in [9]. To simplify the measurement at first there were only flat polypropylene plates with thickness d between 1 mm and 10 mm used. Sensor shunt resonant frequency was measured for various thickness and gap sizes h at several frequency ranges. The best orthogonal behaviour was located in a frequency range of 2,8 GHz to 2,9 GHz when the opposite wall is free. The dielectric loading of sensor affects both its resonant frequency and impedance (Fig. 7).  As the dielectric thickness of the substrate increases from 1 to 4 mm, the antenna shunt resonant frequency decreases from 2,849 to 2,833 GHz, which increases the real part of impedance Z from 1050 to 1375 Ohms. For thickness from 4 to 10 mm frequencies decrease more slowly to 2,823 GHz and Z decreases to 1065 Ohms. The following results focus on a measurement frequency of 2,8 GHz to 2,9 GHz, where the best results were achieved (Fig. 8 a). Similar measurements were also performed at frequencies of 4,5 to 4,7 GHz (Fig. 8 b).
As shown in Fig. 8 resonant frequency deviation of the polypropylene slab thickness variation is greater at lower operating frequency area. At higher frequencies, the deviation is smaller. This confirms, that to increase the sensors sensitive need to select operating area closer to the center frequency of the antenna. Real impedance and resonant frequency are almost independent of boundary conditions on the other side of the plastic wall (Fig. 8, a)  During the measurement at manufacturing process is difficult to ensure a fixed minimal gap between the antenna and the measured object. To examine the accuracy of method, it is necessary to evaluate the influence of the gap to resonant frequency change. The influence of the gap size to resonant frequency is shown in Fig. 9 Fig. 9. Resonance frequency deviation versus of the gap size h variation Products of plastics are formed at higher than ambient temperatures, in addition the product temperature is changing during the technological process and is needed to evaluate the temperature effect to the resonant frequency drift. There is a need to control polypropylene product manufacturing process at the temperature of (40…60) °C. Fig. 10 shows the resonance frequency drift due to temperature effect.
For the formation of products from plastics uses various fillings, which changes the dielectric properties. Fillers for microwave incur additional losses, which reduce the resonance curve parameters and reduce the potential to measure the thickness of plastic in this way. Fig. 11 Fig. 11. The antenna impedance changes versus of the loss tangent As shown in Fig. 11, the losses have a greater impact on  tan closer to 1. When  tan <0,1 (curves 3, 2, 1) loaded resonance quality Q varies in range from 235 to 980.
Phase detector circuit would achieve highest sensor sensitivity. For a constant frequency measurement, the phase shift as a function of the coupled with composite thickness permittivity change and can be approximated by [10] 2 2 where Q is the loaded resonance quality, and r   is absolute changes of the detected permittivity. A sensor phase sensitivity can be defined as Sensitivity factor is in range 185 to 770, depending of loss. So the phase detector allows the design sensitive slab thickness sensors for high lossy composite if the absolute changes of the thickness (and permittivity also) are small.

Conclusions
A proximity-fed patch antenna sensor for evaluation is used. The main element of the sensor is electromagnetic coupled patch -feed transmission line resonator, which allows to evaluate the thickness of the high loss composites via recording of resonant frequency or phase deviation. For sensing applications, due to high resonance quality (up to 1150 at 2,863 GHz), most suitable shunt (parallel) resonance of TLR. When composite  tan <0,1 and wall thickness is 10 mm, loaded resonance quality varies in range from 235 to 980. Phase detector circuit would achieve highest sensor sensitivity. Sensor phase sensitivity factor is in range from 185 to 770, depending of loss. Method is suited when the fixed air gap up to 1 mm between the wall and sensors occurs, and total loss tangent of dielectric is up to 0,1. With this method was evaluated polypropylene wall thickness measurement from 1 to 10 mm. Showed good spatial resolution, penetration depth and detection sensitivity.