Dielectric Characterization of PCB Laminate Materials Using Improved Capacitive Coupled Ring Resonators ^†

Abstract

An improved ring resonator structure consisting of a capacitive coupling fixture is presented. Dielectric characterization is carried out using a fitting method that allows for comparison between measured and simulated results by setting a coupling level of about −4 dB and an unloaded quality factor of about 54. The key factor in this approach is the coupled energy, which permits measurements to be made well above the noise threshold. Furthermore, when applied within a frequency range, the dielectric dispersion can be studied as well. As proof-of-concept fixtures, five structures for the L-band at resonance frequencies of 1 GHz, 1.25 GHz, 1.5 GHz, 1.75 GHz, and 2 GHz are designed, manufactured, and measured. The method applied in this study provides good results as verified by error calculations.

1. Introduction

Dielectric characterization of materials has played an important role in the field of the radio frequency (RF) application design. It is well known that different microwave circuit and antenna approaches require knowledge of the dielectric properties of the materials used for design and implementation. In other fields, such as agriculture and medicine, dielectric measurements have been used to determine physical relationships in order to characterize products [1] and human tissues [2].

Planar structures are widely used as circuit elements in RF components due to their ease of fabrication and the simplicity of determining their electric characteristics in their transmission structures, for instance, the impedance. The most common planar transmission structures are stripline, microstrip, slotline, coplanar waveguide, coplanar strips, inverted microstrip, suspended microstrip, microstrip with overlay, strip dielectric waveguide, and inverted strip dielectric waveguide [3]. In all of the above cases, these planar structures are mechanically supported/wrapped by a dielectric laminate material characterized by a determined complex permittivity (lossy), which is frequency dependent, i.e., dispersion is present [4].

Thanks to its ease of acquisition, FR-4 is one of the most widely used dielectric laminate materials. It is especially popular with students and young researchers for proof-of-concept approaches and elementary experiments, as well as in countries with emerging economies. This material is composed by glass fibers, which offer reinforced mechanical support. Therefore, FR-4 laminates become anisotropic, which determines the dielectric behavior of the material as a function of the frequency and the direction of the established electric field [5].

One technique used to determine the dielectric properties and dispersion that occur in planar structures utilizes large ring resonators fed by transmission probes through coupling gaps which do not significantly perturb the field of the ring resonator [6]. To determine the dispersion effect and avoid the impact of mutual inductance, [6] recommended a large ring resonator greater than 5$\lambda$. In addition, transmission $\mathit{Q}$ measurements are made by varying the coupling gap distance. Although the length restriction is provided here with the aim of studying the dispersion effect, there exist other proposals of compact ring-resonators sensors for specific applications, such as the one reported in [7].

When the ring resonator has been measured, analyses supported by the well-known theory are performed to determine and characterize the relative permittivity, loss tangent, conductor losses, dielectric losses, and even the radiation losses of microstrip or stripline structures. A comparison of different theoretical models was reported in [8], supported by experimental research which established important observations and recommendations to take into account when considering the application of these methods.

Dielectric characterization procedures using ring-resonator methods have been utilized as part of different research fields, such as dielectric RF sensors [9,10] and the design and implementation of wearable antennas in the textile industry [11,12].

In this paper, ew present a microstrip ring-resonator structure excited by an improved capacitive coupler fed by micro-stripline probes for dielectric characterization of PCB laminates. Section 2 shows the design considerations for the measuring structure. The characterization procedure of the FR-4 PCB laminate in the L Band is described in Section 3, the results are detailed in Section 4, and Section 5 provides our conclusions.

2. Dielectric Characterization Measuring Setup

Figure 1 shows the proposed measuring setup for dielectric characterization of planar laminates used with microstrip technology. The structure consists of transmission line probes, capacitive coupling structures, and the ring resonator. The mean radius r is designed for the fundamental resonance provided by n = 1 (TM₁₁₀ mode) in (1):

$$2\mathsf{\pi }\mathit{r}=\mathit{n}{\lambda }_g,$$

(1)

where ${\lambda }_g$ is the guided wavelength in the medium. As seen in (1), the operation frequency at the fundamental resonance is reduced by increasing the ring radius r.

Capacitive coupling is achieved through concentric ring segments at the end of the microstrip transmission line probes. The aim of this structure is to increase the coupling energy in the ring resonator, thereby allowing a better determination of the measured quality factor of the resonator (unloaded Q ≈ 54) by ensuring a coupling level of about −4 dB, i.e., a much better coupling level than that of −60 to −40 dB recommended in [5]. This capacitive structure holds a constant coupling gap from the outer radius of the ring resonator, which should be as small as possible while taking into account any subsequent manufacturing limitations.

The length of the concentric ring segments is determined by the aperture angle $\mathsf{\theta }$. In order to design an adequate aperture angle, the coupling quantity of the capacitive structure is analyzed by simulating the ${\mathit{S}}_{21}$ parameter at a resonance frequency. Figure 2 shows the variation in the magnitude of the ${\mathit{S}}_{21}$ parameter at a resonance frequency of the TM₁₁₀ mode versus the aperture angle $\mathsf{\theta }$ of the capacitive coupling structure. The slope of the curve in Figure 2 is analyzed, establishing a convergence at $\mathsf{\theta }$ = ${30}^{\mathrm{o}}$. Beyond this point, variations in the magnitude of the ${\mathit{S}}_{21}$ parameter are negligible.

3. L-Band Dielectric Characterization of an FR-4 Laminate

Due to the high coupled energy realized by the capacitive structure in the measuring setup, the dielectric characterization procedure can be achieved by measuring the ${\mathit{S}}_{21}$ parameter at a given resonance frequency and then fitting this measured result to those obtained by three-dimensional electromagnetic simulations. Thus, the matching procedure varies ${\mathsf{ϵ}}_{\mathrm{r}}$ and tan($\mathsf{\delta }$), which, under tolerance considerations, provide the dielectric parameters.

For this experimentation, an FR-4 laminate with h = 1.5 mm, t = 17 $\mathsf{\mu }$m, estimated dielectric relative permittivity ${\mathsf{ϵ}}_{\mathrm{r}}$ = 4.3, and estimated loss tangent tan($\mathsf{\delta }$) = 0.025 was used as the device under test. Five circular one-wavelength ring resonators (Wa = 2.77 mm) with capacitive coupling were implemented for the L-band at the resonant frequencies 1 GHz, 1.25 GHz, 1.5 GHz, 1.75 GHz, and 2 GHz, with respective mean radii of 26.48 mm, 21.18 mm, 17.65 mm, 15.13 mm, and 13.24 mm. The length of the rings was designed utilizing the estimated dielectric values. The transmission lines probes were 50-Ω-microstrip lines (W_50 = 2.77 mm) fed by coaxial lines through SMA connectors attached to the laminate. The coupling gap, as mentioned above, was s = 0.3 mm to allow fabrications. Figure 3 shows a photograph of the five manufactured structures.

4. Results and Discussion

Figure 4 shows the measured and simulated ${\mathit{S}}_{21}$ parameter results after the fitting procedure. The structures were simulated using finite-element simulations with CST Studio Suite, while measurements were realized using a vector network analyzer. The fitting procedure focused on the resonance frequency by varying the permittivity value ${\mathsf{ϵ}}_{\mathrm{r}}$ and on the coupling level by varying tan $\mathsf{\delta }$. It can be seen that the resonance frequency in all fixtures is shifted down. This reveals that the real permittivity value ${\mathsf{ϵ}}_{\mathrm{r}}$ is larger than the estimated one of 4.3. In addition, the dielectric losses determine the coupling level, on the one hand due to the conductance effect of the resulting equivalent circuit derived from the transmission line model analysis of the closed-loop ring resonator and on the other due to the capacitive effect of the coupling gap [13]. In the same way, the obtained bandwidth is determined by dielectric losses through the relationship of the former using the unloaded quality factor provided in (2) [14]:

$$|S_{21}|=20lo{g}_{10}\left(1+\frac{Q_L}{Q_U}\right)$$

(2)

The differences between the measured and simulated results of the bandwidth are, in our understanding, twofold: first, due to the natural anisotropy of the FR-4 substrate, and second due to dispersion.

Table 1. Dielectric characteristic values of the resonators.

Parameter	Structure “A” Designed Resonance Frequency at 1 GHz	Structure “B” Designed Resonance Frequency at 1.25 GHz	Structure “C” Designed Resonance Frequency at 1.5 GHz	Structure “D” Designed Resonance Frequency at 1.75 GHz	Structure “E” Designed Resonance Frequency at 2 GHz
${\mathsf{ϵ}}_{\mathrm{r}}$	4.3975	4.4673	4.4601	4.4606	4.4140
tan($\mathsf{\delta }$)	0.0139	0.0216	0.0174	0.0180	0.0208

summarizes the adjusted dielectric values.

Table 2. Error calculation of the ${\mathit{S}}_{21}$ parameter, resonance frequency (${\mathit{f}}_{\mathrm{r}}$), loaded Q, and unloaded Q for the five ring resonator structures.

Structure	Designed Resonance Frequency [GHz]	Parameter	Measured	Simulated	Absolute Error
A	1	${\mathit{S}}_{21}$ [dB]	−3.9679	−4.0805	0.1129
		${\mathit{f}}_{\mathrm{r}}$ [GHz]	0.9810	0.9804	0.0006
		Loaded Q	20.4918	17.7305	2.7613
		Unloaded Q	55.8807	47.2986	8.5821
B	1.25	${\mathit{S}}_{21}$ [dB]	−4.0239	−3.9204	0.1035
		${\mathit{f}}_{\mathrm{r}}$ [GHz]	1.2300	1.2346	0.0046
		Loaded Q	20.6186	13.5685	7.0500
		Unloaded Q	55.6091	37.3548	18.2544
C	1.5	${\mathit{S}}_{21}$ [dB]	−3.9519	−3.9535	0.0016
		${\mathit{f}}_{\mathrm{r}}$ [GHz]	1.4760	1.4760	0.0000
		Loaded Q	20.4918	16.4474	4.0444
		Unloaded Q	56.0592	44.9805	11.0787
D	1.75	${\mathit{S}}_{21}$ [dB]	−3.9608	−3.9807	0.0199
		${\mathit{f}}_{\mathrm{r}}$ [GHz]	1.7220	1.7218	0.0002
		Loaded Q	19.4175	14.5773	4.8402
		Unloaded Q	53.0259	39.6510	13.3749
E	2	${\mathit{S}}_{21}$ [dB]	−4.0899	−4.1222	0.0323
		${\mathit{f}}_{\mathrm{r}}$ [GHz]	1.9740	1.9739	0.0001
		Loaded Q	19.1939	14.3885	4.8054
		Unloaded Q	51.1101	38.0792	13.0309

outlines the error calculations for the ${\mathit{S}}_{21}$ parameter, resonance frequency, and quality factors obtained after fitting the five structures. All of the results show small absolute errors; thus, the aim of the work is completed.

5. Conclusions

An improved structure for the determination of dielectric characteristics in planar laminates has been presented in concept as a fitting method using adjusted simulated parameters and with five proof-of-concept structures. The laminate is of an FR-4 type of material, which has been dielectric characterized within the L band at frequencies of about 1 GHz, 1.25 GHz, 1.5 GHz, 1.75 GHz, and 2 GHz. The structure shows a ring resonator for the fundamental resonance, i.e., the length of the ring is one wavelength. A capacitive coupling structure for the ring resonators is the key approach of this work. Compared with other implementations, where coupling levels of about −45 to −28 dB on an FR-4 substrate [5], −15 to −10 dB on a TLY5 substrate [15], and −15 dB on textile materials [11] have been reported, the coupling level of about −4 dB for the structures presented here allows for the establishment of a reliable fitting method to determine the relative permittivity and dielectric losses. Error calculations between the simulated and measured results of coupling level, resonance frequency, and quality factors confirm the good performance of the proposed method.

In consequence, the method we have proposed in this paper can be widely used in the dielectric characterization of planar laminates. The functionality of this method expands the knowledge around determining the dispersion behavior of substrates.