A generalized lumped element modeling for electrically and magnetically dual-tunable coupled microstrip filters is established through the introduction of the coupling factor which stands for coupling between magnetoelectric layered structure and the input/output microstrip. Then, the lumped element modeling for an existing filter is established and used to predict the electric and magnetic tunability of the filter that manifests as a shift in pass-band. The results have a good consistency with the experimental data and the electromagnetic simulation results in quality and quantity. Then the effects of applied electric field, microstrip's size, substrate's size, and the ferrite-piezoelectric layered structure's size on the filter performance are analyzed by the lumped element modeling. The predicted results show that the performance of the filter can be effectively improved through the increase of microstrip's length and the structure's thickness in a certain range, or the decrease of structure's width and length and the distance between the microstrip and the structure appropriately.

A lumped-equivalent circuit model of a novel magnetoelectric tunable bandpass filter, which is realized in the form of multi-stage cascading between a plurality of magnetoelectric laminates, is established in this paper for convenient analysis. The multi-stage cascaded filter is degraded to the coupling microstrip filter with only one magnetoelectric laminate and then compared with the existing experiment results. The comparison reveals that the insertion loss curves predicted by the degraded circuit model are in good agreement with the experiment results and the predicted results of the electromagnetic field simulation, thus the validity of the model is verified. The model is then degraded to the two-stage cascaded magnetoelectric filter with two magnetoelectric laminates. It is revealed that if the applied external bias magnetic or electric fields on the two magnetoelectric laminates are identical, then the passband of the filter will drift under the changed external field; that is to say, the filter has the characteristics of external magnetic field tunability and electric field tunability. If the applied external bias magnetic or electric fields on two magnetoelectric laminates are different, then the passband will disappear so that the switching characteristic is achieved. When the same magnetic fields are applied to the laminates, the passband bandwidth of the two-stage cascaded magnetoelectric filter with two magnetoelectric laminates becomes nearly doubled in comparison with the passband filter which contains only one magnetoelectric laminate. The bandpass effect is also improved obviously. This research will provide a theoretical basis for the design, preparation, and application of a new high performance magnetoelectric tunable microwave device.

A magnetoelectric tunable microwave filter is proposed, which has multi-passband at corresponding frequencies when different magnetic fields are applied on multi-magnetoelectric laminates. A generalized lumped equivalent circuit model for the filter is established to predict the transmission characteristics. For existing experimental results of the microstrip filter with one magnetoelectric laminate put on the coupling microstrip lines, therefore the lumped circuit model is degraded. And the validity of the model is confirmed from the result that the predictions of the model are in good agreement with the results obtained by the electromagnetic simulation software and experimental results. Then, the performance of the multi-passband microwave filter with a plurality of magnetoelectric laminates is studied by the lumped equivalent circuit. It is found that any single band of multi-passband can be tunable through controlling the applied field on a block of magnetoelectric laminate, which can improve the practicability and flexibility of the bandpass filter. Moreover, when the same field is applied on the magnetoelectric laminates, the multi-passband will be combined into a single passband. The combined single passband has significantly larger bandwidth than the corresponding bandwidth of the filter, which has a single laminate with the same applied field, which can improve the bandpass effect obviously.

According to the microwave transmission principle and the mechanism of ferromagnetic resonance (FMR), a generalized lumped element modeling for magnetoelectric tunable resonators based on the inverse magnetoelectric effect is established taking the impact of equivalent factors of piezoelectric layer into consideration. The lumped element modeling is used to analyze the electrically and magnetically dual-tunable FMR frequency drift of the magnetoelectric tunable resonator; the prediction results have a good agreement with the experimental results and the electromagnetic simulation results in quality and quantity. On this basis, this lumped element modeling is used to predict the effect of the applied electric field, the microstrip's width, the substrate's thickness, and the size of ferrite-piezoelectric layered structure on the ferromagnetic resonance. The results show that with the increase of applied electric field, the values of equivalent resistance R, inductor L, and turns ratio n increase slightly, while the value of C decreases slightly, the FMR frequency fr positively shifts; with the increase of the microstrip's width and substrate's thickness, the values of equivalent resistance R, inductor L, and turns ratio n decrease, while the value of C increases, the FMR bandwidth becomes narrower, and the ferromagnetic resonance attenuation becomes stronger at the same time. When the applied electric field is determined, with the increase of the length or thickness of layered structure, the FMR frequency shifts forward, the FMR peak point decreases first and then increases; with the width of layered structure increases, the FMR frequency of the resonator shifts backward, the FMR peak point decreases first and then increases.

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