Estimation of Noise Suppression in MSL with Co-Zr-Nb films Considering Impedance Matching

Abstract

Sheet- and film-type soft magnetic materials have been widely used to suppress unexpected noise in mobile and wearable devices using ferromagnetic resonance (FMR) losses [1][2]. The designs of these magnetic noise suppressors are mainly based on large-scale electromagnetic field simulations and "trial and error" experiences. In previous studies, the effect of the complex permeability of the magnetic sheet and film on circuit parameters of transmission lines was investigated by a simple magnetic circuit analysis using only the cross-sectional size and material parameters [3]. However, the effect on the reflection and the transmission coefficients have not been estimated quantitatively and the design guideline of the noise suppressor has not been clarified.In this paper, the estimation method of the reflection and the transmission coefficients of a transmission line with a noise suppressor is investigated including the effect of the complex permeability. A 95 μm-width microstrip line (MSL) with a Co-Zr-Nb film is discussed as a test bench. The electrical equivalent circuit parameters of the MSL with Co-Zr-Nb film were calculated by the magnetic circuit analysis and the characteristic impedance was estimated. The thickness of the Co-Zr-Nb film was determined considering impedance matching below 1 GHz range, where it was assumed that a signal frequency range, and the conductive noise suppression by the Co-Zr-Nb film at 3 GHz was estimated.Figure 1 illustrates the magnetic circuit in the cross-sectional view of the MSL with the Co-Zr-Nb film. The MSL was fabricated on low-temperature co-fired ceramic (LTCC) substrate with the thickness h=100 µm and the relative permittivity of 9.8. The width, thickness and length of the signal line are ws=95 μm, ts=3 μm, and 10 mm, respectively. The Co-Zr-Nb film was fabricated using radio frequency (RF) sputtering and deposited on a SiO2 substrate. The film thickness t was obtained by the magnetic circuit analysis and the electromagnetic simulation so that the characteristic impedance of the MSL with and without the film have a same value. The electrical equivalent circuit of the MSL with the Co-Zr-Nb film was obtained to calculate the characteristic impedance. The circuit consists of series impedance Z = R + jωL = (Rm+Re+Rs) + jωLm and parallel conductance Y = jωC, where Rm and Lm were calculated by the magnetic circuit analysis considering the effect of the complex permeability of the Co-Zr-Nb film. Rs and Re were the resistance of the signal line including the skin effect and the increase of resistance due to the eddy current loss generated in the film [3], respectively. C = 2 pF calculated by experimental value at 0.1 GHz [4].Figure 2(a) shows the estimated characteristic impedance Z0 = (Z/Y)0.5 with t = 0.1-1 μm. Below 1 GHz, the impedance is roughly constant and the estimated impedance of the MSL with 1-μm-thick film is almost the same as the measured value of MSL without the film. Therefore, t = 1 μm was used to calculate the reflection and the transmission coefficient.Figure 2(b) and (c) shows the reflection coefficient |S11|, transmission coefficient |S21|, and the noise suppression Ploss/Pin = 1-(|s21|2 +|s11|2) of the MSL with 1-μm-thick film obtained by the electrical equivalent circuit analysis. In the case with the film, |S11| and |S21| were almost the same as the measured value within about 8 dB and 0.1 dB below 5 GHz, respectively. |S11| increased up to 8 dB below 1 GHz but the value kept less than -25 dB. On the other hand, |S21| decreased as the frequency increased because of the combination of FMR and Joule losses in each film at 3 GHz. Ploss/Pin is maximized at 3 GHz.In summary, the reflection and the transmission coefficients of a transmission line with a noise suppressor were quantitatively estimated including the effect of the complex permeability using the magnetic circuit analysis using the cross-sectional size and material parameters. The thickness of the Co-Zr-Nb film was determined considering characteristic impedance matching. As a result, the reflection coefficient was lower than -25 dB below 1 GHz, and the conductive noise suppression was obtained at 3 GHz. Those results give a way to clarify the design guideline of the noise suppressors. This work was supported in part by JSPS KAKENHI Grant Number 20K04497. Part of this work was carried out under the Cooperative Research Project Program of the Research Institute of Electrical Communication, Tohoku University. **