NMOS and T-model: + VGD - D ID + IG VDS G VGS S Characteristics in Active Region : πΌπ· = + - - 1 π ππ·π µπ πππ₯ (ππΊπ − ππ‘ )2 (1 + ) 2 πΏ ππ΄ πΌπΊ = 0, ππ΄ ππ΄′ πΏ ππ = = πΌπ· πΌπ· π ππ = ∞, ππΊπ − ππ‘ = πππ , ππ = ππ·π ≥ πππ , 2πΌπ· π = µπ πππ₯ (ππΊπ − ππ‘ ) πππ£ πΏ ππ = √2πΌπ· µπ πππ₯ π/πΏ πππ₯ πππ₯ = , π‘ππ₯ ππ = π πΏ π πΏ +π π RC CS with Source Resistance: ππ πΊπ = 1 + (ππ + πππ )π π R1 RB ππ = πΊπ π£π = πΊπ π£π RE MOS Resistances as seen from pins: π 1 = ππ + (1 + ππ ′ππ )(π πΈ //(ππ + π π΅ )) ′ ππ = RD R1 + π 2 = D ro gmvgs R2 R3 CG: π΄ππ = 1 + (ππ + πππ )ππ cgd R2 In tr i n s ic G a i n a n d T r a n s i ti o n F r e qu e n c y : π΄0 = 2ππ΄ , πππ£ ππ = 2π(πππ +πππ ) Body Effect in MOSFETS: G vgs gmbvbs gmvgs ro S πππ = π = π(ππ π ) ππ π 2 = π 1 = ππ + [1 + (ππ + πππ )ππ ]π π - IC IB CD (Source Follower): + VCE - VDD + VBE gmvbe =βie ib B + vbe ro - - π 3 ≅ ππ + (π½ + 1) α re= g m ie E B vbe Rout vo RS 1 , π ππ’π‘ = π π //π π ππ + πππ ππ ππ ππ = ≅ 1 + (ππ + πππ )ππ ππ + πππ π π = π΄π£π π΄π£ = π΄π£π C + π π ππ π π ≅ π π +π π 1 + (ππ + πππ )π π gmvbe rπ Emitter degeneration : ππ ππ,πππ = 1 + ππ π πΈ ro πΊπππ = −ππ,πππ π ππ’π‘ E B Forward Active Region: π£πΆπΈ ππΆ = πΌπ π π£π΅πΈ/ππ (1 + ), ππ΅ = ππΆ /π½ ππ΄ πΌπΆ , ππ ππ = ππ΄ , πΌπΆ π΄0 = π ππ π€ππ‘β ππππ‘π‘ππ ππππ’ππππ ππ = High Frequency Model: ππ π πΈ ππ + π πΆ + π πΈ π 3 ≅ ππ + (π½ + 1)π πΈ π€βππ ππ = ∞ - ππ = ππ + π π΅ π½+1 π π (π½ + 1) π 3 = (π½ + 1) (ππ + π πΈ ) ππ + π πΆ + π πΈ C + VBC π πΆ ππ ππ ππ + NPN, Hybrid-Π and T Model : πΌπ ππ π = 0 → πππ = 0 RO (ππ + π π΅ ) π€βππ ππ = ∞ (π½ + 1) πΌπ π πΆ = 0 → π 2 ≅ 1 π π· π 2 ≅ + ππ + πππ 1 + (ππ + πππ )ππ π’π π’ππππ¦ 0.1 < π < 0.3 vi (ππ + π πΆ )(ππ + π π΅ ) (π½ + 1)ππ πΌπ π π΅ = 0 → π 2 ≅ ππ + ππ + π π· π 2 = 1 + (ππ + πππ )ππ D + π 2 ≅ RS ππ 1 1 π + π΅ ππ π½ (ππ + π πΆ )(ππ + π π΅ ) (π½ + 1)ππ + ππ + π π΅ + π πΆ S ππ 2π(ππ +πµ ) BJT Resistances as seen from pins: π πΏ π΄π = π΄ππ π πΏ + π π High Frequency Model: ro gmvbe Transition Frequency: CB: π΄ππ = 1 + ππ ππ πππ₯ = 3.9 × π0 , vgs cgs cπ - π0 = 8.854 × 10−12 πΉ/π G rπ E RL vout AVovi πππ’π‘ = π΄π ππ = π΄ππ ππ C - + vi cµ B+ + vbe + 1 gm - rb B Ro ro + vgs - ππ 1 ππ π π β« ππ + πππ ππ + πππ gmvgs ig=0 - + π΄π£ ≅ ππ΄ ππ π½ ππ C + vbe gmvbe rπ E Vsig B RE RE C + vb Rin gm,eff vb Rout - Wilson Current Mirror: ro π π = π½ππ (π΅π½π) 2 OCTC method: π π ≅ ππ3 ππ3 ππ2 (πππ) ππ» = ∑ π π πΆπ → ππ» ≅ Widlar Current Mirror: πΌπππ πΌπ π πΈ = ππ ππ πΌπ π ππ = π πΏ ′ + πΊπ π π ππ π πΏ ′ + π π ππ + vi −π π· π₯ππ ( ) 2π ππ ππ π΅π½π: π΄ππ = R1 vx −π πΆ π₯π πΆ ( ) 2π πΈπΈ π πΆ cx v1 π ππ ) 2ππ3 π΄π = π π (1 + π ππΏ π π ) (1 + π ) ππ3 ππ π π (1 + ↓ v1 c1 (πππ) π₯π πΆ 2 π₯πΌπ 2 πππ = ππ √( ) + ( ) (π΅π½π) π πΆ πΌπ π΄π ≅ v2 (1-V2/V1)cx c2 (1-V1/V2)cx ππ π π ππ3 πππ π βͺ 1 + π ππΏ π π ππ Low Frequency Response: ππ,1 = Diff. Amp. Input Offset Current: π₯π½ πΌππ = πΌπ΅ ( ) π½ (Ci’s are bypass/coupling capacitances) look like MOS high freq model: MOS: Rsig π ∏ (1 + ) π€π§,π πβππ ππ» (π ) = ππ ππππ€π π ∏ (1 + ) π€π,π rπ ππΏ = max(ππ,π ) cµ rx Vsig Usually bypass capacitance pole is 10 times larger than others cπ BJT: ππΏ = ππ,1 + ππ,2 + ππ,3 ↓ πΌπ ππ,1 βͺ ππ,π & ππ,1 βͺ ππ§,π ππ₯: ππ,3 = 0.8ππΏ & ππ,1 = ππ,2 = 0.1ππΏ cµ Rsig’ ππ,1 ππ π‘βπ ππππππππ‘ ππππ πππ ππ» = ππ,1 Two port parameters: 1 ππ§,π 2 Vsig’ cπ π πΌ [ 1] = π [ 1] π2 πΌ2 π = π −1 π πΌ [ 1] = π» [ 1 ] πΌ2 π2 πΊ = π» −1 Transfer Function of a Two Stage Amplifier ππ πΊπ1 (πΊπ2 − π πΆπ )π 1 π 2 = πππ 1 + π [πΆ1 π 1 + πΆ2 π 2 + πΆπ (πΊπ2 π 1 π 2 + π 1 + π 2 )] + π 2 [πΆ1 πΆ2 + πΆπ (πΆ1 + πΆ2 )]π 1 π 2 Approximated Locations of Poles when a Dominant Pole Exists π′π1 ≅ 1 π π πΆπ BJT high freq model can be simplified to High Frequency Response: ππ,π 1 + π π ππ πΆππ π (1 + ) (… ) ππ,1 Active Loaded: c2 2 ππ» 2 π΄ππ (π ) = π΄ππ (0) v2 c1 πππ£ π₯π π· 2 πππ£ π₯(π ⁄πΏ) πππ = √( ) +( ) + (π₯ππ‘ )2 2 π π· 2 π ⁄πΏ −2∑ 2 Resistively loaded: Miller Method: Diff. Amp. Input Offset Voltage: 1 π π + π π ππ ππ 1 + ππ π π ( ) ππ + π πΏ Diff. Amp. π£π₯ = π 1 + ππ π 1 π 2 + π 2 ππ₯ −1 πππ: π΄ππ = 2ππ3 π ππ −ππ4 π΅π½π: π΄ππ = π½3 π πΈπΈ =∑ π ππ ≅ R2 ππ» = π ππ πΆππ + π ππ πΆππ + π πΏ ′πΆπΏ load transistor): 1 g mv i - -Active load (Q3 diode connected, Q4 πππ π π πΏ ′ = π πΏ //ππ ix −π π· π₯π π· = ( ) 2π ππ π π· ππ π΄ππ = CS with source resistance: ππ πΊπ ≅ & π π ≅ ππ (1 + ππ π π ) 1 + ππ π π ππ» = π ππ πΆππ + π ππ πΆππ + π πΏ πΆπΏ -Resistive load, differential output: ππ ππ ππ ππ + ππ₯ +π π ππ π π ππ ′ = ππ //(ππ₯ +π π ππ ) 1 2πππ» For CS: Differential Amplifier CM Gain: πππ: π΄ππ ππ ππ ′ = 1 πΊπ2 π 2 πΆπ π 1 π′π2 ≅ πΊπ2 πΆπ πΆ1 πΆ2 +πΆπ (πΆ1 +πΆ2 )