6.012 - Microelectronic Devices and Circuits – Fall 2009 ********** Inverter Switching Transient Analysis +-vIN+-PullUpPullDownStage Load+ VqN(vOUT) vOUT(a) iSL(vOUT) [ = n iIN(vOUT)]+-+-vOUTPullUpStage Load+ VDDiPU(vIN, vOUT)iPD = 0iIN(vIN)qN(vOUT)iCHPull down offVLO ! VHIvIN = VLOiSL(vOUT) [ = n iIN(vOUT)] +-+-vOUTPullUpPullDownStage Load+ VDDiPU(vIN, vOUT)iPD(vIN, vOUT)iIN(vIN)qN(vOUT)iDCHVHI ! VLOvIN = VHI(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: dqN(vOUT)/dt = iCH(vOUT), and Discharging: dqN(vOUT)/dt = iDCH(vOUT).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, CL (i.e., qN ≈ CLvOUT), as illustrated below, then we can write, Charging: dvOUT/dt = iCH(vOUT)/CL and Discharging: dvOUT/dt = iDCH(vOUT)/CL These are now differential equations for vOUT(t) that we should at least be able to solve numerically, if we can not do so analytically. They also show us the value of knowing the size and shape of iCH and iDCH. (See Figure 6.14 in the course text, and thediscussion accompanying it, for more on this topic). +-+-vOUT+ VVT, KiDCH = iPD - iPUvIN = VHI iPDCLVHI !VLO+-vIN = VLO+-vOUT+ ViCH = iPUOFFCLVLO !VHIPullUpiPU(vIN, vOUT)PullUpiPU(vIN, vOUT)(a) (b) Charging (a) and discharging (b) cycles with a linear load capacitor and zerostatic load current. Note that for MOS inverters the static current into the stage load, iSL(vOUT), is zero. Finally, if the charge store can be modeled as a linear capacitor and the charging and discharging currents can also be approximated as being constant, then τLO→HI ≈ CL(VHI - VLO)/ICH, and τHI→LO ≈ CL(VHI - VLO)/IDCH We will find that we can use such an approximation to advantage when we areanalyzing CMOS inverters.MIT OpenCourseWarehttp://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Fall 2009 For information about citing these materials or our Terms of Use, visit:
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