ho6.l03_cs_small_signal

ho6.l03_cs_small_signal - 1 Lecture 3 Common Source...

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Unformatted text preview: 1 Lecture 3 Common Source Amplifier Small-Signal Model R. Dutton, B. Murmann R. Dutton, B. Murmann 1 EE114 (HO #6) Stanford University Let's Build Our First Amplifier • One way to amplify – Convert input voltage to current using voltage controlled current source (VCCS) – 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 R. Dutton, B. Murmann 2 EE114 (HO #6) 2 Common Source Amplifier • MOS device acts as VCCS T R. Dutton, B. Murmann 3 EE114 (HO #6) ( ) 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 Biasing • Need some sort of "battery" that brings input voltage into useful operating region • Define V OV =V -V , "quiescent point gate overdrive" OV I t – V OV =V GS-V t with no input signal applied Δ V o Δ V i V O V o R. Dutton, B. Murmann 4 EE114 (HO #6) "Bias" "Signal" V I i V OV 3 Relationship Between Incremental Voltages • What is Δ V o as a function of Δ V i ? ( ) ⋅ Δ + − = Δ + i OV ox DD o O R V V L W C V V V 2 1 2 μ Note: V gs =V i =(V I + Δ V i ) ( ) [ ] [ ] ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + Δ ⋅ ⋅ − = Δ + Δ ⋅ − = − Δ + ⋅ − = Δ OV i i OV D i i OV ox OV i OV ox o V V V R V I V V V R L W C V V V R L W C V L 2 1 2 2 2 1 2 1 2 2 2 2 μ μ R. Dutton, B. Murmann 5 EE114 (HO #6) • 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 Small Signal Approximation (1) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + Δ ⋅ ⋅ − = Δ OV i i OV D o V V V R V I V 2 1 2 • Assuming Δ V i << 2V OV , we have i...
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ho6.l03_cs_small_signal - 1 Lecture 3 Common Source...

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