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In this paper, we present integrated disk-in-cage poppet valves with tuned spring stiffness for gas flow control of a microgas analyzer. The valves require zero power and close at preset offset pressures (0-35 psig) to switch from gas sample loading onto a preconcentrator to concentrated constituent sample injection into a microgas chromatograph. Air flow rates of 4.5 mL/min at pressures of - 2.5--5 psig (vacuum sample loading) were measured. Hydrogen leak rates of 0.1 muL/s (0.006 mL/min) were measured with valves closed at 15 psig. Analytical and numerical modeling was used to guide design of valve spring constants (ranging from 10 to 1500 N/m) that control the valve open position, flow rate, and closing pressure. The parameter design space is limited to a range of seat overlap, valve size, and spring stiffness that will allow adequate flow rate, sealing, and closing at predictable pressures. A linear curve defining closing pressure as a function of spring constant, valve gap, valve size, and seat overlap fit measured closing pressure data and can be used to predict closing pressure for future designs.