*henning@aquarianmicro.com; phone 1 650 380-5309; http://www.aquarianmicro.com Concepts for Micro-Pneumatic and Micro-Hydraulic Logic Gates Albert K. Henning* Aquarian Microsystems, 199 Heather Lane, Palo Alto, CA USA 94303 ABSTRACT 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. Keywords: MEMS, microvalve, microfluidics, mass flow control, compact gas flow model, micropneumatic logic, microhydraulic logic LIST OF VARIABLES & m Mass flow (usually in sccm, normalized to 273 K and 1 atm) P c Control pressure P i Inlet pressure P o Outlet pressure P t Threshold pressure γ Ratio of specific heats, c p /c v α = +       + − γ γ γ γ 2 1 1 1 δ = + − 4 1 1 γ γ γ ( )( ) R Gas constant in p = ρRT (8314 m 2 /K-sec 2 divided by molecular weight) E Young’s modulus for the membrane material A s , B s Deflection coefficients for the membrane, related to membrane stroke D Microvalve inlet diameter h Microvalve membrane thickness a Microvalve membrane length (of one side) W Microvalve seat perimeter length (usually 4*D) z Microvalve membrane-to-inlet gap z 0 Microvalve membrane-to-inlet gap at zero stroke s Microvalve membrane stroke