Advanced electricity Code:6722

Md Kausher ahmed Instructor Electrical department

Lesson declared Coefficient of coupling

Learning outcomes After finish this lesson student will be to # Define co-efficient coupling. #Explain co-efficient of coupling.

Coefficient of coupling The coupling coefficient of resonators is a dimensionless value that characterizes interaction of two resonators. Coupling coefficients are used in resonator filter theory. Resonators may be both electromagnetic and acoustic.

Coupling coefficients together with resonant frequencies and external quality factors of resonators are the generalized parameters of filters. In order to adjust the frequency response of the filter it is sufficient to optimize only these generalized parameters.

Coupling coefficient considered as a positive constant Earlier well-known definitions of the coupling coefficient of resonators are given in monograph by G. Mathieu et al. Note that these definitions are approximate because they were formulated in the assumption that the coupling between resonators is sufficiently small. The coupling coefficient k for the case of two equal resonators is defined by formula.

k=|fo−fe|/f0, (1) where fe, fo are the frequencies of even and odd coupled oscillation of unloaded pair of the resonators and f0=fefo−−−−√. It is obvious that the coupling coefficient defined by formula (2) is a positive constant that characterizes interaction of resonators at the resonant frequency f0.

In case when an appropriate equivalent network having an impedance or admittance inverter loaded at both ports with resonant one-port networks may be matched with the pair of coupled resonators with equal resonant frequencies, the coupling coefficient k is defined by the formula.

k=K12x1x2−−−−√ (2) for series-type resonators and by the formula k=J12b1b2−−−−√ (3) for parallel-type resonators. Here K12, J12 are impedance-inverter and admittance-inverter parameters, x1, x2 are

reactance slope parameters of the first and the second resonant series-type networks at resonant frequency f0, and b1, b2 are the susceptance slope parameters of the first and the second resonant parallel-type networks. When the resonators are resonant LC-circuits the coupling coefficient in accordance with (2) and (3) takes the value kL=LmL1L2−−−−√

Fig: co efficient of coupling

Feedback # What is co efficient of coupling? # Draw the figure of co-efficient of coupling.

Thanks everybody