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For the internal resonators:

From Eqs. 4 and 8, it is possible to obtain Eq. 9:

From Eqs. 9 and 7, the coupling coefficient, ki, i + 1, can be found in Eq. 10:

Finally, by rearranging Eq. 10, length L can be calculated from Eq. 11:

For the first and the last resonators, Eqs. 12-15 provide important insights:

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