Closed-Form Expressions for the Design of Ladder-Type FBAR Filters

Procedure for the Design of Ladder Baw Filters Taking Electrodes Into Account

“…The supposition of infinitely thin electrodes makes the design of filters and the modelling of resonators easier [3,8]. However, in practice, the electrodes must be taken into account.…”

“…As explained in the introduction, a systematic methodology for the design of ladder BAW filters is presented in [3]. This is based on a collection of closed-form expressions that make it possible, without any optimization work, to relate the number of resonators N and the characteristics of series (f s a , C s 0 ) and shunt (f p a , C p 0 ) resonators with the desired filter specifications: Bandwidth, out-of-band rejection, and frequency allocation of the upper and lower transmission zeroes.…”

“…The limitation of this design methodology is that infinitely thin electrodes are assumed. In order to take the thickness of the electrodes into account the coupling coefficient of the piezoelectric material k 2 t must be replaced by the effective coupling coefficient k 2 eff in the closedform expressions presented in [3]. The drawback is that k 2 t only depends on the piezoelectric properties and can be obtained from (1), but k 2 ef f is not, a priori, known since it depends not only on the piezoelectric properties but also on the properties of the electrodes and the electrode-to-piezoelectric thickness ratio [9].…”

“…There are several BAW filter configurations, of which the laddertype is the most straightforward to implement [1][2][3][4][5]. Although there have been ladder filters since the thirties, the microwave community seems to mostly apply empirical design rules.…”

“…Although there have been ladder filters since the thirties, the microwave community seems to mostly apply empirical design rules. The paper presented in [3] is one of the few that has described a systematic methodology for the design of this type of filters. However, this systematic methodology, based on a collection of closed-form expressions, is only an early estimation since infinitely thin electrodes are assumed.…”