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Advanced Microwave Circuits and Systems Part 9

Tham khảo tài liệu 'advanced microwave circuits and systems part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 274 Advanced Microwave Circuits and Systems peak magnetic 2 ị-Ll R2 3.8 V2C E . V C peak electric 2 3.9 Eloss in one oscillation cycle 2 r V2 1 R a 2 L Rs oL R R 3.10 Where R represents the series resistance of the inductor C represents the total parasitic capacitance including that of the inductor and substrate Rs represents the substrate resistivity and Vo denotes the peak voltage at the inductor port. The inductor Q-factor can be obtained as shown in equation 3.11 by substituting equations 3.8 to 3.10 into 3.7. Q -R 1In 1 - C o2LC R Rs L R 2 1 r L L 3.11 The Q-factor in the equation 3.11 is expressed as a product of three factors where the first factor is called the ideal Q factor the second factor is called the substrate loss factor and the third factor is called the self-resonance factor. The inductance L is defined as L ọ I here Ọ is the magnetic flux crossing the inductor coil and I is the current flowing through the coil. The multi-layered coil inductor produces a large inductance L as an entire inductor because the multi-layered coil shows mutual inductance due to mutual electromagnetic induction between the multiple coils connected in series and thus increase the magnetic flux crossing the inductor coil. For this reason according to the multi-layered coil inductor the total length of conductive wire necessary for achieving a given inductance L tends to be short. The shorter the total length of the conductive wire for constituting the multi-layered coil inductor the smaller the resistance R in the multi-layered coil inductor tends to be. As can be seen in the above-mentioned first factor achieving a predetermined inductance L at a small resistance R contributes to an increase in the Q-factor. The inductor coils have to be constructed with good conductivity. The width and height of the coil traces have to be designed carefully to ensure low RF resistance at operating frequencies. The second factor in equation 3.11 suggests that a substrate having high .