lec15_inv_gate - 6.012 Electronic Devices and Circuits Fall...

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6.012 - Electronic Devices and Circuits - Fall 2003 ********** Inverter Switching Transient Analysis + V Pull Up Pull Down + v OUT + v IN - - Stage Load q N ( v OUT ) (a) + V DD + V DD i SL ( v OUT ) [ = n i IN (v OUT )] + - + - v OUT Pull Up Stage Load i PU ( v IN, v OUT) i PD = 0 i IN ( v IN ) q N ( v OUT ) i CH Pull down off V LO Æ V HI v IN = V LO i SL ( v OUT ) [ = n i IN ( v OUT )] + - + - v OUT Pull Up Pull Down Stage Load i PU ( v IN, v OUT) i PD ( v IN, v OUT ) i IN ( v IN ) q N ( v OUT ) i DCH V HI Æ V LO v IN = V HI (b) (c) The generic inverter stage (a) with the non-linear charge store shown explicitly. The charging cycle (b), and the discharging cycle (c). The charge store will in general be a non-linear function of the output voltage; so too are the currents. Thus the differential equations we must solve are Charging: dq N (v OUT )/dt = i CH (v OUT ), and Discharging: dq N (v OUT )/dt = i DCH (v OUT ).
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These are in general very complicated and difficult to solve by any means. If, however, the charge store can be modeled as a linear capacitor, C L (i.e., q N C L v OUT ), as illustrated below, then we can write, Charging: dv OUT /dt = i CH (v OUT )/C L and Discharging: dv OUT /dt = i DCH (v OUT )/C L These are now differential equations for v
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