GB2471024A - Determining dielectric properties of a material - Google Patents

Abstract

A device which measures the dielectric properties of a material by applying a bias voltage across the cell; the material being held in a cell. The cell may be elongate in structure and tapered to either end. A bias voltage may be applied t the cell by a bias line, operatively connected to the cell. The device may have a three layer structure, the cell being sandwiched between a resonant patch and a ground plane. The cell may be fabricated using a standard photolithography process and held to the ground plane and resonator using a thin layer of polyimide, the ground plane and resonator being rubbed in anti-parallel in the transverse direction. The material may be a liquid crystal.

Description

I

Devices and Techniques for Broadband and Single Frequency Measurement of Dielectric Properties of Liquid Crystals and Anisotropic Materials

Background to the Invention

The interest in reconfigurable microwave devices has led to the development of various voltage tuneable materials. Liquid crystal (LC) is a very promising tuneable material as its dielectric properties can be controlled under an external bias field with virtually no power consumption. Several LC based microwave devices have been reported in the literature, such as tuneable microstrip antennas, variable delay lines, phase shifters and steerable reflect arrays.

A number of factors influence the choice of LC best suited to a particular microwave application. The main aspects are the temperature range, dielectric anisotropy, viscosity and tuning voltage. Microwave devices are particularly sensitive to changes in the dielectric constant as it directly affects their frequency of operation. Therefore, characterization of the dielectric properties of the LC is essential and can be achieved by either resonant or broadband methods. S... * S

* ** The resonant technique is highly sensitive and offers precise characterization of *.: : the dielectric permittivity. For example, a cavity perturbation method has been *..

used to characterize nematic LC at 9 and 35 GHz. The measurements were performed for rectangular waveguide resonators with two insertion holes for LC filled tubes. Alignment of the LC molecules was achieved in two orthogonal directions using a magnetic field. However, the use of holes for the insertion of LC into the resonator, affects the distribution of the electric and magnetic field in the cavity. Furthermore, the use of the magnetic field to align the LC is impractical due to problems with size and power consumption.

Although the resonance method offers high sensitivity, it has the disadvantage of being applicable to individual (spot) frequencies. The method is used to characterize nematic LCs at 9 GHz and 35 GHz to a good accuracy. On the other hand, the broadband method is normally a preferred choice whenever the LC characterization over a wide and continuous range of frequencies is required. A broadband coaxial line method is known to measure the properties of the nematic LC from 360 MHz to 23 GHz with a reasonable accuracy and a broadband W-band measurements of nematic LCs has been proposed using the rectangular waveguide. Moreover it is known to perform measurements using crossed magnetic field in order to align the molecules of the the nematic LC in two predefined directions. However, for LC-based practical devices, the application of the magnetic field is not suitable for the alignment of the LC due to problems of power consumption, size, and field distribution of the device producing the

magnetic field.

In addition, demand for high density millimetre wave circuits poses stringent criteria on performance, integration and cost of microwave devices. Coplaner waveguides (CPW) and finite ground coplanar waveguide (FGCPW) have traditionally been very well suited for the excitation of millimetre wave devices due to their planar structure and ease of fabrication. On the other hand, historically, the most commonly used transmission line in RF circuits is microstrip * : * line, however other types of transmission lines are also used. The balanced : **** stripline is one such example. *0Ss *

The use of monolithic microwave integrated circuits (MMIC5) in the 1 970s and **** *..: 25 the prospect of performing on-wafer measurements by the use of CPW probes * : have been a major driving force in the integration of CPW with microstrip lines.

Recently the requirement for the integration of CPW or FGCPW with various transmission lines at millimitre-waves imposed the need for suitable transitions which have to be low-loss, low-cost and easy to fabricate. Furthermore, the transition needs to provide minimal reflections and radiation. Houdart (IEEE MTT-S Int.Microwave Symp.Digest, (1979), 116-8) describes various transitions from CPW to microstrip, coax and slotted lines, together with achievable losses.

Further, a transition from CPW to microstrip line with the bottom conductor partially removed has been presented, whilst various transitions from conductor backed CPW to microstrip line have been disclosed.

Even though the CPW or FGCPW to the microstrip line transitions are important and well established, in certain RF system-on-chip applications, a low-loss low-radiation transition is required to comiect the CPW or FGCPW to the microstrip line with a finite ground plane. When the width of the ground plane is the same as the strip line the resulting structure is, in effect, a balanced strip line.

In this description, commercially available software, ADS 2006 is used for the design and optimisation and cascade microtech MI 50 probe station is used in the measurements.

Summary of the Invention

According to the invention there is provided a device to measure the dielectric *...

*: properties of a material, inparticular liquid crystals, the device comprising, * * : ** a cell to hold material, S.. * S..

a means to apply a bias-voltage across the cell, processing means receiving data from the cell, processing said data and outputting the results of the processing to * . . 25 output means. The device allows more rapid and accurate characterization of the electric properties of the material under analysis.

Preferably the cell is elongate in structure and further preferably is tapered to either end to give low reflectivity and wideband transitions.

Optionally the bias-voltage is provided by a bias line, operatively connected to the cell.

Advantageously, the device has a 3-layer structure, the cell to hold the material being sandwiched between a resonant patch and a ground plane.

The cell is conveniently fabricated using a standard photolithography process and held to the ground plane and resonator by means of a thin layer of polyimide, the ground player and resonator being rubbed in anti-paradol fashion in the transverse direction. This gives the material, particularly liquid crystals a preferred orientation in the absence of an applied voltage.

Brief Description of the Drawings

The invention will now be described with reference to the accompanying drawings for which show two embodiments of a device for measuring the electric properties of a material. In the drawings: Figure 1 is an illustration of a first embodiment of a device, *I..

figure 2 shows measured return loss of the LC cell with bias voltages between 0 and 11 V, * ** b * * * figure 3 shows measured (a) and simulated (b) performance of the resonator when * LC Pool is replaced by a dielectric, figure 4 shows extracted dielectric constant for different voltages,

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*SS*S* * * figures 5a and Sb are respectively a perspective view and a side view of a proposed measurement structure, figures 6a and 6b show measured and simulated performance of two back-to-back tapers for (a) Si 1 and (b) S21, figure 7 shows measure magnitude and phase of LC cell for (a) OV and (b) liv, figure 8 shows extracted Eeff for different voltages from OV (as bottom most line) and iiv (as upper most line), figure 9 shows extract eft at 40 GHz, at room temperature against applied slow varying AC voltage, figures 1 Oa and lOb show a perspective and top view respectively of a transition, figure 11 shows S 11 parameter of two transitions in Figure 10 connected back-to-back, with A being a simulation and B a measurement (A & B), figure 12 shows S2 1 parameter of two transitions in Figure 10 connected back-to-back, with (A) being a simulation and (B) a measurement, figure 13 shows the Si 1 of transition in Figure 10 extracted by (A) simulation and (B) by measurement, * * **S.

figure 14 shows the S21 of transition in Figure 10 extracted by (A) simulation and .: :* (B) by measurement, S. figure 15 shows wrapped phase of S 11 a transition in Figure 10 extracted by (A) simulation and (B) measurement and figure 16 shows unwrapped phase of S21 by transition in Figure 10 extracted by (A) simulation and (B) by measurement.

Detailed Description of the Invention

A first embodiment of a cell used to measure the dielectric constant of an LC is shown in Figure 1. As is evident in the figure, the proposed LC cell is a two-layer structure, with an LC layer formed under a resonant patch. The two layers are identical and have a thickness of h=lOljim with a relative dielectric constant of Cr=3.66. The bottom layer is used merely as a boundary for the LC pool. In this way, the LC layer is effectively sandwiched between the resonator and the ground plane. A resonator is electro-magnetically excited using microstrip lines in order to match the impedence of the co-planer waveguides (CPW) probes. The advantage of this configuration lies in the fact that a probe station may be conveniently used to obtain S parameters. An advantage of this method is that the LC molecules can be aligned by direct application of an electric field. This is achieved by application of a low frequency AC voltage signal which induces switch of the LC. Precise values of the anisotropic dielectric constant can be determined.

The length of the resonator shown in Figure 1 corresponds to LXg/2=l.96mm at 40GHz, and its width is Wz=1.l3mm. A high impedance line connected to the middle (although frequency ranges of 10-60 GHz can be used with suitably sized resonators) of the resonator is used to bias the LC cell using a slowly varying AC voltage. * . * I.. * I..

The LC cell is fabricated using a standard photo-lithography process on commercially available Rogers Duroid substrates. A thin layer of polyimide is * : * * then applied to the ground plate and resonator substrate, which are in turn rubbed in an anti-parallel fashion, in the transverse direction. Rubbing results in a preferred LC orientation in the absence of an applied voltage.

EXPERIMENTAL RESULTS

An LC as described above is filled with the LC mixture E7. Measurements of scattering parameters were made using an Anritsu Lightning 3739D vector network analyzer connected to a Cascade Microtech Ml 50 Probe station.

A low frequency AC signal was applied via the high impedance line shown in Figure 1. The signal amplitude was varied from OV to liv in I V steps. The measured Si 1 parameters for different applied voltages are shown in Figure 2. A clear shift in the resonance frequency is observed in the measured responses, indicating that increasing the voltage gradually switches the LC molecules. The 0 V state corresponds to the LC being un-switched, whilst the 11V state is assumed to be the fully switched state. In the un-switched state the LC is aligned in the transverse direction. Hence, the effective dielectric constant at OV is referred to as eftJ.. . At I1V the LC molecules are fully aligned with the external electric field and the effective relative dielectric constant is 8eff,1. The values Of Ceff between OV and liv are extracted using the following equation: Eeff (i) * S a...

Here ?g represents the wavelength at resonance and is determined by the length of the resonator, while X represents the free space wavelength at resonance.

However, the measured values only allow for the extraction of effective dielectric * permittivity of the LC. In order to evaluate the two permittivities, the structure :: is modelled by the Method of Moments (MoM) using the commercial package ADS Momentum simulation software. The accuracy of this method is firstly S * confirmed by comparing the simulated and experimental results for Figure 1 when the LC layer is replaced with a dielectric with h=lOlpm and cr3.66. Figure 3 depicts this comparison. As is evident from the figure, good agreement between the measured and simulated responses is achieved. The set of relative dielectric constants is now produced by changing the relative dielectric permittivity of the substrate under the resonant patch that represents the LC layer.

The relative dielectric permittivity of the LC extracted in this way, from the non-switched state (OV) to the fully switched state (11 V) is shown in Figure 4. The relative dielectric anisotropy is defined as: s= ei2) From the data in Figure 4, .L=2*75 and E12.98, giving a dielectric anisotropy of L\0.23. The extracted C1,Er11OfE7 are in close agreement with recorded values.

The LC cell used for the dielectric characterization consists of a balanced stripline where a pool of LC is sandwiched between the two strips of the line. Unlike the previous methods where the LC is magnetically biased, one of the novel features of the present broadband characterization is the direct application of electric field to the LC through the two strips using a low voltage source. This feature allows determination of the voltage value required for complete switch of the LC from one dielectric constant to the next in specific directions. Furthermore, in this method, the voltage dependence of the rotation of LC molecules can be quantified. These data are important in designing LC based reconfigurable RF devices. Also, in this paper, a new special transition from the balanced stripline to the finite ground coplanar waveguide (FGCPW) is reported. This transition ** facilitates the probe-station measurement and eases the application of external

electric field to the LC under test. * **

A further embodiment of a device to measure the properties of liquid crystals, which device is particularly applicable for use with nematic LCs is disclosed in Figures 5a and Sb. A nematic LC is characterized by an orientational far-order of **I.

: * its rigid molecules, represented by the director, n. This orientational order of the LC molecules gives rise to different dielectric macroscopic properties of the nematic LC with respect to the direction of the applied electric or magnetic field.

This gives rise to two dielectric permittivities. When the applied field is parallel to i, Cjf is for the direction parallel and is for the direction normal to the applied field, However, LC devices are normally preconditioned by surface treatments so that in the absence of the electric or magnetic field the director, i, is along the direction preferred by the device preparation and in this case c11 is for this direction. The preferred direction is normally achieved by rubbing the surfaces in contact with the LC, but other techniques are also in use. When the electric or magnetic field is applied, the director, , aligns itself to a direction which minimizes the LC free energy. This direction is not necessarily the direction of the field. However, when the electric or magnetic field is sufficiently large, the director switches fully to the direction of the field and hence c11 is essentially for this direction whereas, c is essentially for the preferred (rubbed) direction. This case is known as a fully switched LC. Using the values of and the permittivity tensor of the LC can be setup.

The LC cell used for the dielectric characterization consists of a balanced stripline where a pool of LC is sandwiched between the two strips of the line. Unlike prior art methods in which an LC is magnetically biased, the present broadband characterization utilises the direct application of an electric field to the LC through the two strips using a low voltage source. This allows determination of the voltage value required for complete switch of the LC from one dielectric constant to the next in specific directions. Furthermore, in this method, the * : : ::* voltage dependents of the rotation of LC molecules can be quantified. Such data is important in designing LC-based reconfigurable RF devices. Furthermore a * new transition from the balance stripline to the finite ground co-planar waveguide (FGCPW) facilitates the pro-station measurement and eases the application of

external electric field to an LC under test. **S* *S..

* Based on the knowledge of operational behaviour of of nematic LCs under the * electric field, a cell for the measurement of the dielectric constant of nematic LCs at mm-wave frequencies is set up. As shown in Fig. 5, the LC cell is terminated into two tapers providing low reflections and very wideband transitions to FGCPW as well as offering DC connectivity from the CPW to the cell.

Therefore, a probe-station can be conveniently used to obtain the overall scattering parameters.

As can be seen in Fig. 5, the measurement structure consists of three layers, where each layer is specified by its thickness and dielectric constant. The thicknesses lot and dielectric constants of the layers are h1-381um, Cr19.8, h2Lum, Er23.66 and h3=381pm, &r33.27. The LC pooi formed between the two strips of the balanced stripline has an effective length of LL1 350im.

The two terminal transitions at the ends of the LC cell have equal lengths measuring LT=2000Rm. They are designed with a view to obtain ?g/2 at 30GHz.

Figure 6 shows the theoretical and experimental performances of the two tapers in back-to-back configuration, which are in good agreement. As will be shown later, extraction of the dielectric properties of an LC requires determination of the S-parameters of each of the two identical tapers first. These are achieved by utilizing a method which assumes a single mode propagation regime as described in Cosu (IEEE Microwave and Wires components letters, Volume 13 (2), 60-62, (February 2003)).

Having obtained the S-parameters of the tapers, the extraction of the effective dielectric constants of a nematic LC filling the cell under no bias voltage and *::: under a bias voltage fully switching the LC is achieved through the use of the following matrix expression: * [Tmeas11Ttap]. [Ttransl [TLc] [Tinvtrans][Tinvtap] (1) where [Tmeas] represents the overall 25 measured transmission matrix of the structure in Figure 5. In the cascaded transmission matrix (1), ETtapi is for the tapers (which are experimentally obtained), [Ttrans] is due to the possible discontinuity between the LC pool and the taper (party known), and [TLC] is for the LC pool. Matrices [Tinvtrans] and [Tinvtap] represent matrices [Ttrans] and [Ttap], but for the reverse direction. The transmission matrix of the LC pooi is given by: 1-L 1 le & 0 [TCJ1 L (a) L o Where (aeff4jj3eff represents the complex propagation constant in the LC region.

By solving (1), I3eff and hence the effective dielectric constant, in \ \2..

fffccO\ (.) 21TJ Of the LC for different bias voltages can be calculated. In (3), X0 represents the free space wavelength.

EXPERIMENTAL RESULTS

The experimental results for the second embodiment are as follows. The LC cell together with the terminal tapers, Figure 5 proposed for the measurement of the dielectric constant of LCs is fabricated using a standard photolithography process.

The fabrication is performed on standard, commercially available Roger Duroid substrates. The top and bottom layer surfaces of the cell are covered with a thin layer of polyimide in order to obtain a smooth surface and a protection against copper. These surfaces are treated with a rubbing cloth to allow anchoring of the LC molecules in the transverse direction in the absence of any external electric field. Using a combination of the capillary action and injection, the LC cell is filled up with a LC mixture. The sample is probed using Cascade Microtech M150 probe station and the measurements of the scattering parameters are performed with Anritsu Lightning 3739 D vector network analyzer.

* S. 5.5 * . * A slow varying ac signal is then applied to the LC cell through a wideband bias-tee, at room temperature. The amplitude of the ac voltage is varied from 0 V to * 25 11 V and the scattering parameters of the overall structure, Figure 5 are measured.

Figure 7 shows the results of the amplitude and phase of S21 for two different *..S voltages. The extract Ceff, using equations (1), (2) and (3), is shown in Figure 8 for voltages0V, I V,2V, 3V,4V, 5V,6V, 7V,9Vand liv.

Figures 7 and 8 indicate that as the voltage increases, the LC gradually switches on. The 0 V state is assumed to correspond to the LC cell being non-switched, while the 11 V state corresponds to the LC cell being ftiiiy switched. The measurements of 8eff between these two states correspond to the transient states between non-switched and fully switched states. Figure 9 shows the measurements of Ceff at 40 GHz, room temperature against the applied voltage. If we define the measurement of Ceff at 0 V as Ceff1, and the measurement of Ceff at 11 V to as Ceff11, the dielectric anisotropy is defined as: ff -eff ffj From the data in Figure 5, LCefO.273 for the LC under test.

From our observation of the results of the extraction of the dielectric constant of two known materials (air and another dielectric) using the tecimique given above, the extracted effected dielectric constants of the LC under test have acceptable accuracy to be used as the actual dielectric constants of the LC material the measured band of the frequency. However, more accurate results can be obtained by formulating an analytical expression for Ceff of the balanced stripline and hence extracting more accurate values for 8r of the LC under-test. *..S * * **.. *

* .* S.. * . * S. * . S *.

In the description below is described a taper from a FGCPW to the balanced *...

stripline. The transition is wide-band and is designed to operate within the frequency range DC to 65 0Hz.

The physical appearance of the proposed transition is shown in Figure As can be seen from this figure, the proposed transition is triple layered, where the thicknesses and dielectric constants of the dielectric layers are h1 381tm, Er19.8, h2254j.im, cr2254im, h3=381im.

C r33.27. The FGCPW is designed to have 50�= characteristic impedance, while the width of the finite ground has chosen to be less than ? /2. This design condition ensures that parallel plate higher order modes and transverse resonance modes do not occur. In this design, G515tm, S=85j.m and W=200m, while the length of the FGCPW section is L1=l000pin. The transition from the FGCPW ground plane to the ground of the balance stripline, which is inverted in this transition, is achieved by the use of two via interconnects, each with a diameter of d=1501.xm. The length of the via interconnects is equal to the thickness of the middle layer, i.e. 254.xm. The length of the tapered section is LT=2OOOum and is designed so that its length at 300Hz is approximately equal to Xg 12. The taper is used as a matching circuit and its presence is necessary in order to keep reflections at a minimum. The width of the balanced stripline is W5-J000pm and the support for the vias is L2z=290pm.

EXPERIMENTAL RESULTS

The proposed transition is first designed through available closed-form mathematical expressions and then its performance (its reflection and insertion * losses) is verified and slightly optimized using the commercial software, ADS. In the design and measurement, always two back-to-back transitions are used in *..

order to avoid simulation and measurement problems associated with the asymmetry of the structure. **S* *

****s* The back-to-back transitions for the experimental work are fabricated using a standard photolithography process. The fabrication process is performed on the standard, commercially available Roger Duroid substrates, while the via interconnects are made by the use of conductive epoxy. The measurements of the scattering parameters are performed with the Anritsu Lightning 3739 D Vector network analyzer, while Cascade Microtech Ml 50 is used in the measurements.

The CPW probes used in the measurements have a pitch size of 250 tm.

As with the simulation, due to the asymmetrical geometry of the proposed transition, direct measurements of its S-parameters are not possible using the probe station. However, under the assumption of a single mode propagation regime and matched conditions for the balanced stripline, the S-parameters of the transition are extracted using a method similar to the one in Cosu. Originally, this method is developed for the extraction of the S-parameters of both the active section and the input and output CPW tapers of the Mach-Zehnder modulator, In order to apply the S-parameters extraction procedure, two structures with identical input and output transitions with the balanced microstrip line between them are needed. In this work, one of the structures consists of two directly connected back to back transitions, while the second structure comprises the two transitions connected through a 1mm long balanced stripline. The measured and simulated S-parameters of the two back to back connected transitions are shown in Figures 12 and 13. These figures show a good agreement between the measurement and simulation.

The extraction procedure is then applied to both the measured and simulated *....: results and the extracted insertion and transmission losses of one of the transitions * * : are displayed in Figures 13-16. For this transition SI 11<-lO dB, generally. *S.

* Figures 13-16 show a good agreement between the measured and simulated results over DC to 65 GHz range. For the important parameter 1S211, the *...

maximum disagreement is 0.7 dB at 58 GHz. This can be attributed to the fabrication process, especially the use of conductive epoxy for producing the vias.

The maximum measured and simulated insertin losses of the transition are about 2.1 dB. It is found that part of the insertion losses is due to some surface wave radiation. -15

It will of course be understood that the invention is not limited to the specific details described herein, which are given by way of example only, and that various modifications and alterations are possible within the scope of the invention. * S *S.. *

S..... * * * *. * . . S... * *S.

S **S.

S S...

*SSS.. S *

Claims (7)

1. CLAIMSI. A device to measure the dielectric properties of a material, the device comprising, a cell to hold material, a means to apply a bias-voltage across the cell, processing means receiving data from the cell, processing said data and outputting the results of the processing to output means.
2. 2. A device according to Claim 1, wherein the cell is elongate in structure.
3. 3. A device according to Claim 2, wherein the cell is tapered to either end.
4. 4. A device according to any preceding claim, wherein the bias-voltage is provided 1y a bias line, operatively connected to the cell.
5. 5. A device according to any preceding claim the device has a 3-layer structure, the cell to hold the material being sandwiched between a S...resonant patch and a ground plane.S **S. * .*
6. 6. A device according to any preceding claim, wherein the cell is fabricated : .. 25 using a standard photolithography process and held to the ground plane * and resonator by means of a thin layer of polyimide, the ground plane and resonator being rubbed in anti-parallel fashion in the transverse direction. S...

   S
7. 7. A device substantially as herein described with reference to and as illustrated by the accompanying drawings.