tailieunhanh - Advanced Microwave Circuits and Systems Part 10

Tham khảo tài liệu 'advanced microwave circuits and systems part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling of Spiral Inductors 309 each segment. In this experiment coupling coefficient k23 is larger than the others because L2 and L3 are arranged parallelly. Coupling coefficient k14 is almost zero because L1 and L4 are arranged orthogonally. knm model is obtained from average coupling coefficient because ideal coupling coefficient is independent of frequency. Parameter extraction of 3-port symmetric inductor The 5-port modeling has been presented in Sect. and in this subsection calculation and parameter extraction of a 3-port inductor . a 2-port inducotor with a center tap shown in Fig. 18 are presented as a simple example. Note that the center tap is chosen as port 3 in Fig. 18. port3 Center-tap Fig. 18. A symmetric inductor with a center-tap. vlịl 1 v3o 1 3 v2 2 r z1 iz2 z M12 z V -12 yc 1. b Fig. 19. An equivalent circuit of 3-port inductors a whole b core part. 310 Advanced Microwave Circuits and Systems Fig. 19 a shows an equivalent circuit of 3-port inductors and Fig. 19 b shows core part of the equivalent circuit. In this case Zcore can be defined by the following equation. Z_ core Z1 jw M21 jw M12 Z2 54 Each element of the matrix Zcore expresses self and mutual components directly. Y11 Y12 Y13 Ymeas Y21 Y22 Y23 55 ự31 Y32 Y33 According to Eq. 28 Ysubn can be calculated by the following equations. Ysub1 Y11 Y12 Y13 56 Ysub2 Y21 Y22 Y23 57 Ysub3 Y31 Y32 Y33 58 The self and mutual inductances in Zcore can be derived from Yc as follows. Yc Ymeas Ysub 59 where Zcore Z1 j v M21 jư M12 Z2 BYc A 1 Y12 Y13 Y21 Y12 1 Y21 Y23 1 i Y21 Y23 Y12Y23 Y13Y21 Y13Y23 Y21 Y12 Y12 Y13 A Bt 0 1 0 1 60 61 62 63 64 65 1 1 0 0 1 0 0 0 1 0 Here a -type equivalent circuit shown in Fig. 20 is utilized for the parameter extraction. Each parameter in Fig. 20 . Z1 Z2 M12 Ysub1 Ysub2 Ysub3 can be calculated by Eqs. 56 57 58 60 62 . To demomstrate this method left-right asymmetry is evaluated for symmetric and asymmetric inductors as shown in Fig. 21. As I .