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22 January 2007 Concepts for micropneumatic and microhydraulic logic gates
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Previously, we proposed novel microvalve structures, amenable to bulk micromachining, which effected fully complementary behavior in the switching of pneumatic (compressible gas) signals from a high pressure state to a low state, and vice versa. Using our quantitative relations for the flow of compressible gases in microvalves, we described mathematically the steady-state behavior of these micro-pneumatic logic gates, and derived the transfer characteristic for switching between pneumatic states. In this work, we extend the steady-state description to encompass a mathematical treatment of the transient response of micro-pneumatic logic gates. By analogy to MOSFET scaling in integrated circuits, we also apply the full transient model to scaled versions of a micro-pneumatic ring oscillator, in order to illustrate the performance which these devices may afford. As with MOSFETs (which rely on the compressibility of the electron gas), the ultimate speed of these devices is limited by the velocity of sound of the compressible gas. Finally, we present structures which can be used to realize micro-hydraulic logic. In micro-hydraulic logic, because the working fluid is now incompressible, the physical structure must have an alternate means to achieve capacitance, or storage of mass. Such a means is embodied in a variable-volume component attached to each node in the logic circuit.
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Albert K. Henning "Concepts for micropneumatic and microhydraulic logic gates", Proc. SPIE 6465, Microfluidics, BioMEMS, and Medical Microsystems V, 64650T (22 January 2007);

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