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formulas_midterm1 - γ of the PMOS are negative = ≥ D t...

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Formula Sheet – Midterm 1 Spring Semester 2009 Professor E. Rosenbaum Professor N. Shanbhag Large-signal model parameters are underlined. These semi-empirical fitting parameters are technology-dependent and are provided to the circuit designer. Diode ( ) 1 = T D V V s e I I , where mV 25 = = q T k V B T BJT (npn, forward-active bias, i.e., I B > 0 and V CE > V CE,sat ) T BE T BE V V s A CE V V s C e I V V e I I + = 1 , where mV 25 = = q T k V B T E C I I = α 1 1 + = + = β β α β β B A CE B C I V V I I BJT Small-signal Model r π g m v be r o + v be - C E B i b = β i b This model is valid at low and moderate frequencies, and for v be < V T /10 = 5 mV. Small-signal model parameters are given by: T C m V I g = C A o I V r = m g r β π =
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MOSFET (long channel model equations) Define V ov = V GS – V t , where V t is the threshold voltage. NMOS ( ) F F SB t t V V V φ φ γ 2 2 0 + + = 0 , = D t GS I V V ( ) = < > 2 , & 2 ' DS DS t GS D ov DS t GS V V V V k L W I V V V V ( ) ( ) DS t GS D ov DS t GS V V V k L W I V V V V + = > λ 1 2 , & 2 ' PMOS ( ) | 2 | | 2 | 0 F F BS t t V V V φ φ γ + + = (Note: V
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Unformatted text preview: γ of the PMOS are negative #) , = ≥ D t GS I V V ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⋅ − ⋅ ⋅ = > < 2 , & 2 ' DS DS t GS D ov DS t GS V V V V k L W I V V V V ( ) ( ) DS t GS D ov DS t GS V V V k L W I V V V V ⋅ − ⋅ − ⋅ ⋅ = ≤ < 1 2 , & 2 ' (Note: λ is negative) MOSFET Small-signal Model g m v gs r o g mb v bs + v gs--v bs + S D B G This model is valid at low and intermediate frequencies, and for ( ) ov gs V v ⋅ ≤ 2 . . Small-signal model parameters are given by: D ov ov D m I L W k V L W k V I g ⋅ ⋅ ′ ⋅ ≅ ⋅ ⋅ ′ ≅ ⋅ = 2 | | | | 2 D o I r ⋅ = | | 1 χ ⋅ = m mb g g , where | | | 2 | 2 | | SB F V + ⋅ =...
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