03_Lecutre - Lecture 3 EE114 Lecture 3 Common Source...

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Lecture 3 EE114 R. Dutton, B. Murmann 1 EE114 Lecture 3 Common Source Amplifier Small-Signal Model R. Dutton, B. Murmann Stanford University R. Dutton, B. Murmann 2 Let's Build Our First Amplifier One way to amplify Convert input voltage to current using v oltage c ontrolled c urrent s ource (VCCS=“trans-conductance”) Convert back to voltage using a resistor (R) "Voltage gain" = Δ V out / Δ V in Product of the V-I and I-V conversion factors EE114 VCCS R ! V in ! V out ! I
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Lecture 3 EE114 R. Dutton, B. Murmann 3 Common Source Amplifier MOS device acts as VCCS EE114 I d V i V o V DD ( ) 2 2 1 t i ox D V V L W C I ! = μ ( ) R V V L W C V V t i ox DD o ! " " = 2 2 1 μ T R. Dutton, B. Murmann 4 Biasing Need some sort of "battery" that brings input voltage into useful operating region Define V OV =V I -V t , "quiescent point gate overdrive" – V OV =V GS -V t with no input signal applied EE114 I D + ! I d V O + ! V o V DD ! V i V I "Bias" "Signal" V I Δ V o Δ V i V O V OV V o
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Lecture 3 EE114 R. Dutton, B. Murmann 5 Relationship Between Incremental Voltages What is Δ V o as a function of Δ V i ? EE114 ( ) ( ) [ ] [ ] ! " # $ % & + ( ( ) = + ( ) = ) + ( ) = ( + ) = + OV i i OV D i i OV ox OV i OV ox o i OV ox DD o O V V V R V I V V V R L W C V V V R L W C V R V V L W C V V V 2 1 2 2 2 1 2 1 2 1 2 2 2 2 μ μ μ As expected, this is a nonlinear relationship Nobody likes nonlinear equations; we need a simpler model Fortunately, a (1 st order) linear approximation to the above expression is sufficient for 90% of all analog circuit analysis Note: V gs =V i =(V I + Δ V i ) R. Dutton, B. Murmann 6 Small Signal Approximation (1) Assuming Δ V i << 2V OV , we have EE114 !
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