MIT6_012F09_lec16_scaling

# MIT6_012F09_lec16_scaling - 1 6.012 Microelectronic Devices...

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1 6.012 - Microelectronic Devices and Circuits, Fall 2009 - 10/5/09 posting CMOS Gate Delays, Power, and Scaling GATE DELAYS In the last lecture (Lec. 15) we calculated the gate de- lay for a symmetrical CMOS inverter with V Tn = |V Tp | V T , C o * xn = C o * xp C o * x , and K n = K p , in which both the n- and p-channel devices were mini- mum gate length devices, i.e., L n = L p = L min . The p- channel device was made twice as wide as the n-channel device to get the desired K equality, because we assumed µ e = 2 µ h . We found that the gate delay was given by: 4 C L V DD τ GD K n (V DD - V T ) 2 Replacing C L and K n , to write this in terms of the device dimensions, we found after a bit of simple algebra: 12 n 2 V DD τ GD µ e L m in (V DD - V T ) 2 POWER There is zero static power in CMOS so the only con- tribution is the dynamic power P ave = C L V D 2 D f where f is the operating frequency and C L is the loading capacitance. This load will be the average fan-out, n, times the input capacitance of a similar CMOS gate, plus any parasitic interconnect capacitance: C L = n C o * x (L min W n + L min W p ) + C parasitic

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2 = 3 n C o * x L min W n + C parasitic Neglecting C parasitic , we can write P ave = 3 n C o * x L min W n V D 2 D f MAXIMUM POWER The maximum power dissipation will occur when the gate is operated at its maximum frequency (bit rate), which is in turn proportional to 1/ τ GD . Thus we can say 2 1 P ave max 3 n C o * x L min W n V D D τ GD 1 W n = 4 L min µ e C o * x V DD (V DD - V T ) 2
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MIT6_012F09_lec16_scaling - 1 6.012 Microelectronic Devices...

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