# Smooth Bend Structures Using Hybrid Compensation for Common-Mode Noise Reduction
###### Abstract  
The proposed smooth bend structure was implemented with a 150-degree bend to reduce the asymmetrical part of the differential bend and thus prevent mode conversion loss and common-mode noise. The smooth bend structure maintained the differential signal integrity. In addition, we proposed several hybrid compensation methods to enhance common-mode noise suppression and concluded that a smooth bend using the \"L-C-L\" compensation method offered the best performance. The frequency-domain analysis, from direct current (DC) to 6 GHz, was suppressed below 17.3 dB for the differential to common-mode conversion loss (Scd21) and maintained a differential insertion loss (Sdd21) above 2.18 dB. Furthermore, the 150-degree bend, using the \"L-C-L\" compensation method, reduced common-mode noise by 48.9% compared with a 150-degree bend structure in the time-domain analysis. The significant advantage of the proposed structure is that it can be easily fabricated using the printed circuit board (PCB) manufacturing process, reducing costs. The measurement results of the proposed design showed good consistency with the simulations. The proposed hybrid compensation structure successfully reduced the undesirable effects caused by asymmetry; as a result, mode conversion suppression was improved, and common-mode noise was reduced. b +
Footnote †: journal: Applied  
in voltage and current between ports. We can obtain the value of the compensation capacitor from this previous work [5]. A patch is added to the inner trace of the differential transmission lines to implement the compensation capacitor on the PCB. The patch on the inner trace increases the capacitive characteristics. This is called compensation capacitance. The capacitance value can be calculated using the parallel-plate capacitance formula shown in Equation (1):  
\[C_{\text{capacitance}}=\varepsilon\cdot\bigg{(}\frac{A}{d}\bigg{)}. \tag{1}\]  
The second method is compensating inductance [7]. This adds a short-coupled line to the inner trace of differential transmission lines to increase the inductive characteristics of the PCB. It uses this duality to derive the formula for compensating inductance. The compensation capacitance and inductance both achieve high common-mode noise immunity. The authors of [6] described a tightly coupled microstrip structure. The design concept that they presented in [6] demonstrated the impact on different values of even-mode impedance. A well-known formula shows that the coupling coefficient relates to the impedance under odd and even modes. The coupling coefficient, C, can be shown as:  
\[C=\frac{Z_{0c}-Z_{0c}}{Z_{0c}+Z_{0c}}. \tag{2}\]  
This involves the coupling between differential transmission lines, based on odd- and even-mode impedance. The method of setting both of these impedances was also discussed in [6]. The odd-mode impedance should be set at 50 Ohms to maintain differential signal transmission integrity. In other words, it is crucial to maintain the differential insertion loss, to improve performance by reducing mode conversion. Higher impedance increases the coupling between the inner and outer traces on differential transmission lines for even-mode impedance. As mentioned earlier, differential transmission lines lead to better signal transmission performance, which means decreased-field coupling if the traces have higher impedance. However, concerning the PCB itself, two points need to be discussed; one is insertion loss and the other concerns fabrication. Transmission loss will increase under higher even-mode impedance when the structure of the tightly coupled microstrip is applied. The loss per unit length on the signal can be analyzed and presented as a table. Our proposed solution is to use the structure of the tightly coupled microstrip on the low-loss PCB substrate. Higher even-mode impedance improves the differential signal transmission performance concerning the fabrication issue. However, higher even-mode impedance is challenging because the line width is thinner and the space needs to be closer.