MEMS filter with voltage tunable center frequency and bandwith
A filter and substrate voltage technology, applied in power oscillators, waveguide devices, circuits, etc., can solve problems such as insufficient frequency bandwidth tunability
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Embodiment 1
[0072] The following section shows, by way of example, a specific implementation of the filter tuning method. Assume:
[0073] Δf=(V p -V s )×10 5 (14)
[0074] It follows that a voltage difference of 50V is required to tune the center frequency to 5MHz. For this embodiment, the following values are assumed for the equivalent RLC model of the series resonator:
[0075] C x =6.6087×10 -17 V p 2 F(15)
[0076] L x = 4.6799 × 10 - 4 V p 2 H - - - ( 16 )
[0077] R x = 332.6365 V p 2 ...
Embodiment 2
[0090] A filter with a first notch at 900MHz and a notch-to-notch bandwidth of 10MHz is obtained.
[0091] How to use 2
[0092] For both series and parallel resonators, the required pole-zero separation is 5MHz for both. Use the following formula:
[0093]
[0094] For series and parallel resonators, V p 12.9023V and 12.9184V respectively.
[0095] To adjust the first notch frequency to 900MHz, (V p -V s ) = 27.4V. According to the shunt V obtained above p , the substrate bias of the shunt resonator is (12.9184-27.4) V=-14.4816V. Quadrature frequency tuning is not required for the series resonator since it is already at the correct frequency, 905MHz.
[0096] Figure 9 Shows that for the same ladder filter, only the structural bias V of the series and shunt resonators is corrected p and substrate bias V s , as calculated above. Larger bandwidths have only minor pass-band ripple degradation. Figure 9 , curve 160 is the calculated transfer equation for shunt re...
Embodiment 3
[0099] A ladder filter consisting of one parallel resonator and two series resonators is fabricated in SOI process and characterized. The resonator is a 310 μm (and 300 μm) x 100 μm x 3.1 μm released bar topped with 20 nm hafnium dioxide as a dielectric transduction layer. at V p = 5V, resulting in a passband 170 whose f c =817.2MHz, the bandwidth is 0.6MHz, the insertion loss (IL) is 3.2dB, such as Figure 10A shown. by placing V sub =15V applied to all resonators in the trapezoid, we can Figure 10B The center frequency of the filter is tuned from 817MHz to 809MHz without affecting IL (3.5dB) and form factor (1.3) as shown in the middle passband 172. Figure 10C Passband 174 is shown with its bandwidth tuned from 0.6MHz to 2.8MHz, while the center frequency remains unchanged at 817.2MHz. However, the passband ripple increases from 0.4dB to 1.8dB. finally, Figure 10D The mid passband 176 shows a combination of bandwidth and center frequency tuning. to get f c =810....
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