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Lecture II

Lecture II. Lecture II: • Linear circuit theory review • Amplifier basics • MOS small signal model. R 2. R 4. I s. R 1. V s. R 3. Nodal analysis. Nodal analysis provides a systematic and reliable method to calculate all voltages and currents in a linear circuit. Nodal analysis.

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Lecture II

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  1. Lecture II Lecture II: • Linear circuit theory review • Amplifier basics • MOS small signal model A. Rivetti – INFN Sezione di Torino

  2. R2 R4 Is R1 Vs R3 Nodal analysis Nodal analysis provides a systematic and reliable method to calculate all voltages and currents in a linear circuit A. Rivetti – INFN Sezione di Torino Nodal analysis

  3. v1 v2 Is R1 Vs R3 Writing nodal equations R2 R4 A. Rivetti – INFN Sezione di Torino Nodal analysis

  4. R2 R4 v1 v2 Is R1 Vs R3 Writing the circuit matrix A. Rivetti – INFN Sezione di Torino Nodal analysis

  5. Solving the circuit matrix A. Rivetti – INFN Sezione di Torino Nodal analysis

  6. Vs R2 Is R1 R4 R3 Another example A. Rivetti – INFN Sezione di Torino Nodal analysis

  7. Lecture II Lecture II: • Linear circuit theory review • Amplifier basics • MOS small signal model A. Rivetti – INFN Sezione di Torino

  8. Amplifier characteristic • The input-output characteristic of an amplifier is usually a non-linear • function • Over some interval of the input signal, this function can be • approximated by a polynomial: • For narrow range of the input signal, we may write: • The above expression does not obey the superposition principle A. Rivetti – INFN Sezione di Torino Amplifier basics

  9. Small signal model • If a0 does not depend on the signal, we can write: • This is an expression that obeys the superposition principle • The small signal model takes into account only variations of signals within a circuit • The small signal equivalent circuit can be studied with the methods of linear circuit analysis A. Rivetti – INFN Sezione di Torino Amplifier basics

  10. Rs Vout Vi(t) Ri Vs(t) Voltage amplifier • AV = Vout/Vi • Input impedance high (ideally infinite) • Output impedance small (ideally zero) A. Rivetti – INFN Sezione di Torino Amplifier basics

  11. RS RO Vi(t) RI Vout AVVi RL Vs(t) VA small signal model • Note: impedances may also be complex A. Rivetti – INFN Sezione di Torino Amplifier basics

  12. Current amplifier Iout Rs Ii(t) Ri Is(t) • AV = Iout/Ii • Input impedance small (ideally zero) • Output impedance high (ideally infinite) A. Rivetti – INFN Sezione di Torino Amplifier basics

  13. Rs Ro Ii(t) Ri Iout(t) RL Is(t) Is(t) CA small signal model • Note: impedances may also be complex A. Rivetti – INFN Sezione di Torino Amplifier basics

  14. Rs Iout Vi(t) Ri Vs(t) Transconductance amplifier • AV = Iout/Vi • Input impedance high (ideally infinite) • Output impedance high (ideally infinite) • Important: the gain is not a number A. Rivetti – INFN Sezione di Torino Amplifier basics

  15. RS Ro Is(t) RL Vi(t) RI Iout(t) Vs(t) TCA small signal model • Note: impedances may also be complex A. Rivetti – INFN Sezione di Torino Amplifier basics

  16. Vout Rs Is(t) Ii(t) Ri Transimpedance amplifier • AV = Vout/Ii • Input impedance small (ideally zero) • Output impedance small (ideally zero) • Note: Gain is not a number A. Rivetti – INFN Sezione di Torino Amplifier basics

  17. Rs Ii(t) Ri Is(t) RO Vout AVVi RL TA small signal model • Note: impedances may also be complex A. Rivetti – INFN Sezione di Torino Amplifier basics

  18. Lecture II Lecture II: • Linear circuit theory review • Amplifier basics • MOS small signal model A. Rivetti – INFN Sezione di Torino

  19. Vs(t) gmVs Vs(t) DIDS W mn COX W mn (VGS – VTH) gm = = = COX 2 IDS DVGS L L Simplified small signal DC model The MOS transistor in saturation can be seen as a voltage controlled current source RS A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  20. Vdrain Vgate Vs Practical example What is the equivalent small signal model of this? W=100 mm L=10 mm mnCOX=190 mA/V2 VTH=0.6 V Vdrain=2.5 V Vgate=1.25 V A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  21. Gm simulation(1) 356.7 current (mA) 355.7 0 1 2 time (mS) Vs=1mV pk-pk A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  22. Gm simulation (2) 660 current (mA) 355 0 1 2 time (mS) Vs=250mV pk-pk A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  23. Vdrain r0 Vgate Vs Output impedance A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  24. ro Vs(t) gmVs Vs(t) DIDS W mn COX W mn (VGS – VTH) gm = = = COX 2 IDS DVGS L L 1 ro = lIDS Including the output impedance The MOS transistor in saturation can be seen as a voltage controlled current source with finite output impedance RS A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  25. Vs(t) DIDS DVTH W mn COX (VGS – VTH) gmb = = = DVBS L DVSB g gm 2fF+ VSB Bulk transconductance For a more accurate model, the bulk effect must also be taken into account RS ro gmbvbs Vs(t) gmVs A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  26. Vs(t) Small signal DC model The saturated MOS transistor is a voltage controlled current source with finite output impedance RS ro Vs(t) gmVs gmbvbs gm models the gate transconductance gmb models the bulk transconductance (the bulk effect) A. Rivetti – INFN Sezione di Torino MOS small signal DC model

  27. DIDS W mn gm = = COX 2 IDS DVGS L 1 ro = lIDS Some numbers… IDS = 100mA, W/L=50, mnCOX=190mA/V2 l=0.01V-1 gm = 1mS ro = 1MW A. Rivetti – INFN Sezione di Torino MOS small signal DC model

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