Determining dielectric properties of nematic liquid crystals at microwave frequencies using inverted microstrip lines

Figures & data

Table 1. Power consumption of active arrays using different phase shift technologies.

Technology	Array size	Power consumption (W)	Applications
Silicon based [21]	$8\times 8$	20	MMIC antenna arrays
Silicon based [21]	$16\times 16$	65	MMIC antenna arrays
MLC based [22]	$8\times 8$	5.5	ALCAN’s smart antenna
MLC based [22]	$16\times 16$	15	ALCAN’s smart antenna

Table 2. The common measurement techniques to characterise LCs.

Method	LC	Freq. (GHz)	${\epsilon }_{r\mathrm{\perp }}$	${\epsilon }_{r\parallel }$	$\mathrm{\Delta }{\epsilon }_r$	Error (%)
Split-cylinder resonator [31]	QYPD-036	5	2.28	3.08	0.80	6.5
Circular patch resonator [32]	BL006	5	2.69	3.12	0.43	1.5
Patch resonator [33]	E7	40	2.74	3.16	0.42	2
Coaxial transmission line [34]	K15	5	2.60	2.77	0.17	20
Planar transmission line [35]	E7	60	3.105	3.457	0.35	NA
Microstrip line [36]	E63	60	2.78	3.37	0.59	3
Metamaterial absorber [37]	E7	90-120	2.61	3.03	0.42	1

Figure 1. The chemical structure of the LC monomer, QYPD-036.

Table 3. The comparison of the recently available NLCs and the classical display mixtures E7 (Merck) for display and photonic applications.

LC	$n_e$	$n_o$	$\mathrm{\Delta }n$	${\epsilon }_{r,\mathrm{\perp }}$	${\epsilon }_{r,\parallel }$	$\mathrm{\Delta }{\epsilon }_r$	Clearing point $T_c$
			@589 nm			@1 KHz	(°C)
E7(Merck)	1.739	1.523	0.216	5.2	19.6	14.4	58
QYPD-036	1.770	1.521	0.251	5.6	19	13.4	95
JC-M-LC-E7	1.741	1.517	0.224	5.3	16.7	11.4	58

Figure 2. (Colour online) Design 1 of an NLC-based IMSL: on Substrate 1, the inverted microstrip line and the CPW for measurement are on two sides of the board, and they are connected through a via. Substrate 2 is to provide a cavity in the middle board to contain the NLC mixture, and the bottom board is working as a metallic ground plane.

Figure 3. (Colour online) The inverted microwstrip line, NLC in the cavity and the electric fields of the waves propagating through.

Figure 4. (Colour online) The detailed dimensions of the IMSL designs: case 1 refers to the vias used in Design 1, and case 2 refers to the coupling mechanism employed in Design 2.

Table 4. The dimensions of the two IMSL designs in millimetres.

Parameter	Design 1	Design 2
$L_1$	30	30
$W_1$	20	22
$L_2$	20	20
$W_2$	10	12
$W_3$	8.985	8.9
$W_4$	1.03	1.4
$w$	0.2	2
$D_{in}$	1	1
$D_{out}$	2	2
$d_{in}$	0.25	—
$d_{out}$	0.45	2
g	0.5	1.4

Figure 5. Cross section of the inverted microstrip line structure under two scenarios: (a) the empty cavity and (b) the cavity was filled with LCs.

Table 5. The factor to calculate the effective length of IMSLs under the two scenarios.

Scenario	Design	Factor for effective length (F)
Air	Design 1	2.00
	Design 2	2.62
LC	Design 1	2.07
	Design 2	2.64

Figure 6. (Colour online) Fabrication process of the IMSL device based on Design 1: (a) top view of Substrate 1, (b) bottom view of Substrate 1, (c) the top surface of the board of ground plane was spin-coated with a thin layer of PI and (d) the bias voltage being applied on an IMSL device based on Design 1.

Figure 7. (Colour online) Fabrication process of the IMSL devices based on Design 2: (a) top view of Substrate 1, (b) bottom view of Substrate 1, (c) the top surface of the board of ground plane was spin-coated with a thin layer of PI and (d) a completed IMSL device based on Design 2.

Table 6. The dielectric properties of the JC-M-LC-E7 LC determined based on the measurements of the IMSL devices.

Design	Condition	f (GHz)	${\epsilon }_{r,LC}$	$f_3$ (GHz)	$f_4$ (GHz)	$tan\delta$
Design 1	Unbiased	4.32	2.18	4.656	4.842	0.039
	Biased	4.06	2.62	4.463	4.518	0.012
Design 2	Unbiased	4.25	2.17	4.654	4.861	0.044
	Biased	3.92	2.82	4.327	4.389	0.014

Table 7. The dielectric properties of the QYPD-036 LC determined based on the measurements of the IMSL devices.

Design	Condition	f (GHz)	${\epsilon }_{r,LC}$	$f_3$ (GHz)	$f_4$ (GHz)	$tan\delta$
Design 1	Unbiased	4.27	2.26	4.136	4.514	0.068
	Biased	3.92	2.86	4.023	4.084	0.015
Design 2	Unbiased	4.17	2.24	4.178	4.476	0.069
	Biased	3.81	2.95	3.958	4.024	0.017

Figure 8. (Colour online) The comparison of scattering parameter of the empty IMSL device (Design 1, air in the cavity) between simulation and measurement.

Figure 9. (Colour online) Simulated and measured scattering parameters of the IMSL device (Design 1) with JC-M-LC-E7 being filled in the cavity, under 0 and 20 V ($V_{pp}$) bias voltage applied, respectively.

Figure 10. (Colour online) The comparison of scattering parameter of the empty IMSL device (Design 2, air in the cavity) between simulation and measurement.

Figure 11. (Colour online) Simulated and measured scattering parameters of IMSL device (Design 2) with JC-M-LC-E7 LC being filled in the cavity, under 0 and 32 V ($V_{pp}$) bias voltage applied, respectively.

Figure 12. (Colour online) Fabricated NLC-based IMSL devices: (a) the three devices based on Design 1 and (b) the two devices based on Design 2.

Figure 13. (Colour online) The difference between the measured and simulated results of resonant frequency for the empty DUTs (the Design 1 of IMSL, air in the cavity).

Figure 14. (Colour online) The difference between the measured and simulated results of resonant frequency for the empty DUTs (the Design 2 of IMSL, air in the cavity).

Table 8. The uncertainty analysis based on the IMSL devices of Design 1.

Device	Resonant freq. (GHz)	$\mathrm{\Delta }f$, Freq. dev. (GHz)	${\epsilon }_r$	$\mathrm{\Delta }{\epsilon }_r$
Simulated	5.90	0.00	1.00	0.00
DUT 1	6.10	0.20	0.88	0.12
DUT 2	5.80	0.10	1.07	0.07
DUT 3	5.98	0.08	0.96	0.04

Table 9. The uncertainty analysis based on the IMSL devices of Design 2.

Device	Resonant freq. (GHz)	$\mathrm{\Delta }f$, freq. dev. (GHz)	${\epsilon }_r$	$\mathrm{\Delta }{\epsilon }_r$
Simulated	5.40	0.00	1.00	0.00
DUT 1	5.57	0.17	0.86	0.14
DUT 2	5.31	0.09	1.08	0.08

Anokiwaves Inc. Introduction to all silicon millimeter-wave 5G arrays. Microwave Journal; 2019 [cited 2020 June 5]. Available from: https://www.microwavejournal.com/articles/31937-introduction-to-all-silicon-millimeter-wave-5g-arrays

 Google Scholar

ALCAN Systems, Dehghani MR. ALCAN’s smart antenna’s 5G opportunities and solutions. 2019 [cited 2020 June 5]. Available from: https://www.alcansystems.com/alcans-smart-antennas-5g-opportunities-and-solutions/

 Google Scholar

Sánchez JR, Nova V, Bachiller C. Characterization of nematic liquid crystal at microwave frequencies using split-cylinder resonator method. IEEE Trans Microw Theory Tech. 2019;67(7):2812–2820.

 Web of Science ®Google Scholar

Schaub DE, Oliver DR. A circular patch resonator for the measurement of microwave permittivity of nematic liquid crystal. IEEE Trans Microw Theory Tech. 2011;59(7):1855–1862.

 Web of Science ®Google Scholar

Yazdanpanahi M, Bulja S, Mirshekar-Syahkal D, et al. Measurement of dielectric constants of nematic liquid crystals at mm-wave frequencies using patch resonator. IEEE Trans Instrum Meas. 2010;59(12):3079–3085.

 Web of Science ®Google Scholar

Mueller S, Penirschke A, Dam C, et al. Broad-band microwave characterization of ilquid crystals using a temperature-controlled coaxial transmission line. IEEE Trans Microw Theory Tech. 2005;53(6):1937–1945.

 Web of Science ®Google Scholar

Bulja S, Mirshekar-Syahkal D, James R, et al. Planar transmission line method for measurement of dielectric constants of liquid crystals in 60 GHz band. In: Proceedings of the 2009 Asia Pacific Microwave Conference; 2009 Dec 7–10. Singapore: IEEE; 2009. p. 341–344.

 Google Scholar

Bulja S, Mirshekar-Syahkal D, James R, et al. Measurement of dielectric properties of nematic liquid crystals at millimeter wavelength. IEEE Trans Microw Theory Tech. 2010;58(12):3493–3501.

 Web of Science ®Google Scholar

Lu HB, Jing SC, Xia TY, et al. Measurement of LC dielectric constant at lower terahertz region based on metamaterial absorber. IEICE Electron Express. 2017;14(12):2017046.

 Web of Science ®Google Scholar