Semi-lumped designs Figure 10a. A semi-lumped design using disc flexural resonators and λ/2 coupling wires Figure 10b. Equivalent circuit of the semi-lumped circuit above Frequencies of the order of megahertz (MHz) are above the usual range for mechan

Semi-lumped designs


Figure 10a. A semi-lumped design using disc flexural resonators and λ/2 coupling wires


Figure 10b. Equivalent circuit of the semi-lumped circuit above
Frequencies of the order of megahertz (MHz) are above the usual range for mechanical filters. The components start to become very small, or alternatively the components are large compared to the signal wavelength. The lumped element model described above starts to break down and the components must be considered as distributed elements. The frequency at which the transition from lumped to distributed models takes place is much lower for mechanical filters than it is for their electrical counterparts. This is because mechanical vibrations travel at the speed of sound for the material the component is composed of. For solid components, this is many times (x15 for nickel-iron) the speed of sound in air (343 m/s) but still considerably less than the speed of electromagnetic waves (approx. 3x108 m/s in vacuum). Consequently, mechanical wavelengths are much shorter than electrical wavelengths for the same frequency. Advantage can be taken of these effects by deliberately designing components to be distributed elements, and the components and techniques used in electrical distributed element filters can be brought to bear. The equivalents of stubs and impedance transformers are both achievable. Designs which use a mixture of lumped and distributed elements are referred to as semi-lumped.[43]
An example of such a design is shown in figure 10a. The resonators are disc flexural resonators similar to those shown in figure 6, except that these are energised from an edge, leading to vibration in the fundamental flexural mode with a node in the centre, whereas the top diagram design is energised in the centre leading to vibration in the second flexural mode at resonance. The resonators are mechanically attached to the housing by pivots at right angles to the coupling wires. The pivots are to ensure free turning of the resonator and minimise losses. The resonators are treated as lumped elements; however, the coupling wires are made exactly one half-wavelength (λ/2) long and are equivalent to a λ/2 open circuit stub in the electrical equivalent circuit. For a narrow-band filter, a stub of this sort has the approximate equivalent circuit of a parallel shunt tuned circuit as shown in figure 10b. Consequently, the connecting wires are being used in this design to add additional resonators into the circuit and will have a better response than one with just the lumped resonators and short couplings.[43] For even higher frequencies, microelectromechanical techniques can be used as described below.
[Semi-lumped designs


Figure 10a. A semi-lumped design using disc flexural resonators and λ/2 coupling wires


Figure 10b. Equivalent circuit of the semi-lumped circuit above
Frequencies of the order of megahertz (MHz) are above the usual range for mechanical filters. The components start to become very small, or alternatively the components are large compared to the signal wavelength. The lumped element model described above starts to break down and the components must be considered as distributed elements. The frequency at which the transition from lumped to distributed models takes place is much lower for mechanical filters than it is for their electrical counterparts. This is because mechanical vibrations travel at the speed of sound for the material the component is composed of. For solid components, this is many times (x15 for nickel-iron) the speed of sound in air (343 m/s) but still considerably less than the speed of electromagnetic waves (approx. 3x108 m/s in vacuum). Consequently, mechanical wavelengths are much shorter than electrical wavelengths for the same frequency. Advantage can be taken of these effects by deliberately designing components to be distributed elements, and the components and techniques used in electrical distributed element filters can be brought to bear. The equivalents of stubs and impedance transformers are both achievable. Designs which use a mixture of lumped and distributed elements are referred to as semi-lumped.[43]
An example of such a design is shown in figure 10a. The resonators are disc flexural resonators similar to those shown in figure 6, except that these are energised from an edge, leading to vibration in the fundamental flexural mode with a node in the centre, whereas the top diagram design is energised in the centre leading to vibration in the second flexural mode at resonance. The resonators are mechanically attached to the housing by pivots at right angles to the coupling wires. The pivots are to ensure free turning of the resonator and minimise losses. The resonators are treated as lumped elements; however, the coupling wires are made exactly one half-wavelength (λ/2) long and are equivalent to a λ/2 open circuit stub in the electrical equivalent circuit. For a narrow-band filter, a stub of this sort has the approximate equivalent circuit of a parallel shunt tuned circuit as shown in figure 10b. Consequently, the connecting wires are being used in this design to add additional resonators into the circuit and will have a better response than one with just the lumped resonators and short couplings.[43] For even higher frequencies, microelectromechanical techniques can be used as described below.
[edit]Bridging wires






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