lecture6 - EECS 312 1 Lecture 6: CMOS Inverter, cont. EECS...

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Unformatted text preview: EECS 312 1 Lecture 6: CMOS Inverter, cont. EECS 312 Reading: 3.3.2, 5.4.1, 5.4.2 5.5.1, 5.5.2 EECS 312 2 Lecture Outline Delay analysis Equivalent resistance of devices More details on capacitance calculations Some CMOS inverter delay properties/studies EECS 312 3 Delay analysis EECS 312 4 Delay Analysis Integrate the charging current provided by the MOSFET to the load Current is highly non-linear with terminal voltages (C L has only minor dependency on voltage, which we neglect) We must use simplifications/approximations 1. Look at the driving transistor as a resistor 2. Look at the driving transistor as a constant current source ( ) ( ) dv v i v C t v v L p = 2 1 EECS 312 5 CMOS Delay: Resistive Model V DD V out V in = V DD R eq C L t pHL = f(R eq .C L ) = 0.69 R eq C L t V out V DD R eq C L 1 0.5 ln(2) 0.36 What is R eq ? EECS 312 6 Effective on-resistance of a MOSFET I D V DS V GS = V DD V DD /2 V DD R R mid Key: assumes saturation regime throughout! Valid in modern devices This I dsat definition is different than ours ( ) = + = 2 with 9 7 1 4 3 ) 1 ( 2 / 1 2 ' ' ' 2 / ' Dsat Dsat th dd dsat dd dsat dd V V dsat dd eq V V V V L W k I V I V dV V I V V R dd dd R eq EECS 312 7 Rabaeys definition The curve flattens at V dd > 1V Velocity saturation occurs, current increases for larger E-fields are fairly small Key R eq trends: R eq is inversely proportional to W/L R eq is relatively insensitive to V dd b/c as V dd , I d but voltage swing also 0.5 1 1.5 2 2.5 1 2 3 4 5 6 7 x 10 5 V DD (V) R eq (Ohm) EECS 312 8 CMOS Delay: Current Source Model V DD V in = V DD I av V out C L Let i(v) and C L (v) be a constant with respect to voltage = 2 1 v v av L p dv I C t Voltage swing across C L is from V dd to V dd /2 (50% delay) ( ) av dd L av dd dd L p I V C I V V C t 2 2 / = = EECS 312 9 CMOS Delay: Current Source Model V DD V in = V DD I av V out C L Question: What is I av ? Answer: Look at I-V curves I d is nearly I dsat through voltage swing I av ~ I dsat I d V ds EECS 312 10 Our Default Approach C L V dd I dsat C L V dd R eq = ( ) dsat dd dsat L dd L eq I V a I aC V C R 725 . 2 69 . = = a accounts for non-ideality of MOSFET as current source (a ~ 0.9 for 50% delay) Looking at the system in both ways a simple expression can be found for R eq dsat dd eq I V R 8 . = EECS 312 11 Equivalent Resistance for Rise/Fall Delays 50% delay is not the only important metric We need to linearize the device over a different voltage range to capture R eq for 10-90% rise/fall delay Current source assumption becomes less valid Resulting resistance for 10-90%: dsat dd I V R 55 ....
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lecture6 - EECS 312 1 Lecture 6: CMOS Inverter, cont. EECS...

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