Mm-wave characterisation of printed circuit boards Dmitry Zelenchuk 1, Vincent Fusco 1, George Goussetis 1, Antonio Mendez 2, David Linton 1 ECIT Research Institute: Queens University of Belfast, UK 1 University of Granada, Spain 2 Introduction Millimeter wave technology paves the way to next generation wireless applications, e.g. high-bandwidth LAN at 60 GHz [1]. There is a growing demand for using inexpensive printed circuit board substrates (PCBs) for mm-wave devices. The knowledge of the electromagnetic PCB substrate parameters is vital for accurate design, especially in the mmwave range where dimensions based on electrical characteristic such as substrate permittivity are tolerance critical. Today, most substrate PCB manufacturers specify the dielectric parameters of their substrate materials at 10 GHz. Consequently in realized designs at mmwavelengths, frequency shifts attributed to permittivity deviation commonly occur. A comprehensive review of the techniques for dielectric characterization has been made in [2] and it has been concluded that waveguide cavity resonant methods remain the most accurate in terms of permittivity and loss tangent determination. Ideally, a metallic waveguide cavity filled entirely with a dielectric would provide a fully screened test environment with near homogeneous field distribution and excellent loss tangent resolution potential. In order to synthesize such an environment for a PCB material, we propose the use of substrate integrated waveguide (SIW) resonators. SIW is a fully screened transmission line, which is compatible with standard PCB processing techniques [3]. Electric field distributions in SIW are very close to those in metallic waveguides and there is a straightforward relation between the transmission lines. As a consequence, the field is uniform in the vertical direction for substrates thinner than a half of guided wavelength. The latter is a unique feature of SIW resonators in comparison with other planar resonators, and thus it allows direct measurement of the absolute value of relative permittivity as well as straightforward calculation of metal loss ensuring accurate characterization of loss tangent. Theory A substrate integrated waveguide rectangular cavity is shown in Fig. 1. It has been shown in [4] that both propagation and attenuation constants of a SIW waveguide are equivalent to the quantities of a rectangular waveguide with effective width a eff, 1.08 0.1 The substrate permittivity ε r and the loss tangent tan δ can be obtained from measured unloaded resonant frequency and quality factor of a rectangular SIW cavity:, 2 tan 1 1 (1)
The quality factor for the metal loss for the TE 1n0 mode of a rectangular cavity with different metals at the top, bottom and sidewalls can be extended from classical formula given in [5] as follows: 2 2 2 (2) where, h is the substrate thickness, and 120 Ohm,, and are the surface resistances of the sidewall, top and bottom metallization, respectively. The radiation losses can be neglected subject to the sufficient via density (s < 2d)[6]. Sample design We now study PTFE-based Taclamplus substrate whose specified permittivity is and loss tangent is 0.0008 at 50GHz [7]. The thickness of the substrate was 0.1mm. The top metalized layer is made of 18µm thick copper with electrical conductivity 5.8e+7 S/m. The bottom ground plane is made of 3mm thick 63-37 brass with conductivity 1.6e+7 S/m. (a) (b) Fig. 1. (a) - layout of a rectangular substrate integrated waveguide resonator fed with GSGprobes through u-shaped aperture, (b) - equivalent circuits of a single-port resonator: second Foster s form. The design of a practical SIW cavity requires an appropriate feeding mechanism. In this paper we propose the use of small U-shaped aperture for probing, as shown in Fig. 1a. The aperture is fed by a standard GSG probe thus removing any uncertainty with respect to the reference plane [8]. The probe acts as a current source feeding the resonator through inductive coupling. The U-shaped slot acts as a short current probe and placed close to the magnetic field maximum to ensure effective coupling. The resonator is represented as a series RLC circuit at the equivalent circuit in Fig. 1b. This is the second Foster s form in [8]. As discussed in [8] for the second Foster s form the relationship between loaded and unloaded resonant frequencies reads as 1 2 1 (3) 2 where is the coupling susceptance, the external quality factor, the unloaded quality factor, the coupling coefficient. Since the coupling is inductive 0 and hence.
The parameters f L, Q e, b e, and Q 0 can be retrieved from the measurements. In this paper Matlab Q0REFL and Q0TRAN programs from [9] have been used for this purpose. The unloaded frequency was extracted from measured parameters with the aid of (3). Three different sets of 13 resonator geometries prepared for the experiment with all of them having two additional replicas, see Fig. 2. Each of 13 resonators in all sets has cavity dimensions a = 2.25mm, 2.35mm + n*0.2mm, n=0,1, 11 and b = 2.8mm, designed to resonate at the TE 120 mode at a certain frequency within the 60-110GHz frequency range. The resonators with equal a are gathered in the rows of nine samples on the test board, see Fig. 2a. The first and second sets were designed for one-port measurements and have different via dimensions and apertures. For all resonators the excitation point is placed at y f = 0.46a. The third set was designed for two-port weakly excited resonators measurements, in which case the loaded resonant frequency is expected to be very close to the unloaded one. Most of the geometry parameters for the resonators of the third set are retained from the first set except for two apertures shifted to yield weak coupling, see inset in Fig. 2a. The parameters common for all sets of the apertures are w u = w d = 0.1mm, w c = 0.07mm, w s = 0.08mm, D p = 0.25mm. The parameters that differ between the sets are gathered in Table I. Table I. Parameters of the measurement sets Set,mm,mm,mm Ports #1 0.2 0.34 0.08 1 0.46 0.2-0.5 #2 0.25 0.4 0.115 1 0.46 0.5-1 #3 0.2 0.34 0.08 2 0.29 0.03-0.06 (a) (b) Fig. 2. (a) -photograph of the test samples; columns 1,4,7 set 1, columns 2,5,8 set 3, columns 3,6,9 set 2, (b)-microphotograph of probed one-port resonator. Experimental results The structures were measured using a Cascade millimeter-wave probe station with 50 ohm ground-signal-ground (GSG) probes. The pitch of the probes is 150 µm. The probes before each measurement were calibrated using an automated LLRM-procedure at the probe station and the calibration error was below 0.1 db for a frequency band of 2GHz in the vicinity of the resonance of each sample. This error level is acceptable as the mentioned Matlab
programs apply curve-fitting algorithms and are capable of retrieving necessary characteristics from noisy data [9]. A microphotograph of the probed samples from the first set is shown in Fig. 2b. 2.09 2.09 2.07 2.07 2.04 2.02 2.05 2.05 2 (a) (b) (c) Fig. 3. Measured permittivity :(a) set 1, (b) set 2, (c) set 3. The unloaded resonant frequency is extracted from the measurement and averaged over sample replicas. The unloaded resonant frequency for each measured sample has been used in the expression for the relative permittivity (1) and the resultant data in all the diagrams is plotted against the nominal natural resonant frequency. As expected due to manufacturing tolerances there is spread of the measured permittivities, which are shown with error bars in Fig. 3. Since the measured permittivity values do not vary significantly with frequency within the measured range, the values have been averaged in order to obtain a single value for Taclamplus permittivity at mm-waves. Table II contains the data obtained. For single-port experimental tests both the average value and the error are very similar. For the two-port measurements, made on set 3, the error is about 2 to 3 times higher in comparison to single port. Table II. Comparison of measured permittivity and loss tangent to the one specified by manufacturer. Set Meas. Spec Error, % Spec Meas., smooth Error, % Meas., rough Error, % 1 24 0.84 0.8 1.12 40 0.734 8 2 2.073 1.29 0.8 1.12 40 0.738 8 3 2.0533 2.23 0.8 1.07 34 0.684 14 Extracted from the measurements unloaded quality factor was substituted into (1) along with the calculated with (2) and the loss tangent was calculated. This calculation takes into account that two different metals copper and brass are used to form the top and bottom of the cavity, and the side wall posts metallization is copper. The calculation has been performed both for smooth and rough metallization, with roughness height of 0.7µm. The extracted data were averaged over frequency and the mean values of all the test sets are shown Table II. The error has been reduced from 34-40% for smooth metal to 8-14% when the roughness is taken into account, which presents a significant improvement. The latter result is rather promising for mm-wave PCB characterisation.
Conclusion Mm-wave dielectric characterization of printed circuit board materials using a new substrate integrated waveguide resonator technique has been demonstrated in the paper. A comprehensive set of test samples was designed and measured over the 60 to 110 GHz frequency range. The method is robust with respect to the aperture dimension deviations, making the method less sensitive to etching tolerances hence more readily extendable to deployment at higher frequencies. The retrieved substrate permittivity and loss tangent are in a good agreement with the known nominal values specified by manufacturers. References [1] Y. P. Zhang and D. Liu, Antenna-on-Chip and Antenna-in-Package Solutions to Highly Integrated Millimeter-Wave Devices for Wireless Communications, IEEE Transactions on Antennas and Propagation, vol. 57, no. 10, pp. 2830-2841, Oct. 2009. [2] J. Sheen, Comparisons of microwave dielectric property measurements by transmission/reflection techniques and resonance techniques, Measurement Science and Technology, vol. 20, no. 4, p. 042001, Apr. 2009. [3] D. Deslandes and K. Wu, Integrated microstrip and rectangular waveguide in planar form, IEEE Microwave and Wireless Components Letters, vol. 11, no. 2, pp. 68 70, 2001. [4] F. Xu and K. Wu, Guided-wave and leakage characteristics of substrate integrated waveguide, IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 1, pp. 66-73, Jan. 2005. [5] D. M. Pozar, Microwave Engineering, 2nd ed. John Wiley & Sons, 1997. [6] M. Bozzi, M. Pasian, L. Perregrini, and K. Wu, On the losses in substrate-integrated waveguides and cavities, International Journal of Microwave and Wireless Technologies, vol. 1, no. 05, p. 395, Sep. 2009. [7] TacLamPLUS RF & Microwave Laminate. [Online]. Available: http://www.taconicadd.com/pdf/taclamplus.pdf. [8] A. J. Canos, J. M. Catala-Civera, F. L. Penaranda-Foix, and E. Reyes-Davo, A novel technique for deembedding the unloaded resonance frequency from measurements of microwave cavities, IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 8, pp. 3407-3416, Aug. 2006. [9] D. Kajfez, Q Factor Measurements Using MATLAB. Norwood, MA 02062: Artech House, 2011, p. 189.