Lecture 16: Small Signal Amplifiers

1. Lecture 16:Small Signal Amplifiers Prof. Niknejad

2. Lecture Outline • Review: Small Signal Analysis • Two Port Circuits • Voltage Amplifiers • Current Amplifiers • Transconductance Amps • Transresistance Amps • Example: MOS Amp Again! University of California, Berkeley

3. Small Signal Analysis • Step 1: Find DC operating point. Calculate (estimate) the DC voltages and currents (ignore small signals sources) • Substitute the small-signal model of the MOSFET/BJT/Diode and the small-signal models of the other circuit elements. • Solve for desired parameters (gain, input impedance, …) University of California, Berkeley

4. Supply “Rail” A Simple Circuit: An MOS Amplifier Input signal Output signal University of California, Berkeley

5. VGS,BIAS was found in Lecture 15 Small-Signal Analysis Step 1. Find DC Bias – ignore small-signal source IGS,Q University of California, Berkeley

6. Small-Signal Modeling What are the small-signal models of the DC supplies? Shorts! University of California, Berkeley

7. Small-Signal Models of Ideal Supplies Small-signal model: short open University of California, Berkeley

8. Small-Signal Circuit for Amplifier University of California, Berkeley

9. Low-Frequency Voltage Gain Consider first   0 case … capacitors are open-circuits Design Variable Transconductance Design Variables University of California, Berkeley

10. Voltage Gain (Cont.) Substitute transconductance: Output resistance: typical value n= 0.05 V-1 Voltage gain: University of California, Berkeley

11. Input and Output Waveforms Output small-signal voltage amplitude: 14 x 25 mV = 350 Input small-signal voltage amplitude: 25 mV University of California, Berkeley

12. What Limits the Output Amplitude? 1. vOUT(t) reaches VSUP or 0… or 2. MOSFET leaves constant-current region and enters triode region University of California, Berkeley

13. Maximum Output Amplitude vout(t)= -2.18 V cos(t)  vs(t) = 152 mV cos(t) How accurate is the small-signal (linear) model? Significant error in neglecting third term in expansion of iD= iD(vGS) University of California, Berkeley

14. Generalized Amplifier Active Device University of California, Berkeley

15. Amplifier Terminology • Sources: Signal, its source resistance, and bias voltage or current • Load: Use resistor in Chap. 8, but could be a general impedance • Port: A pair of terminals across which a voltage and an associated current are defined • Source, Load: “one port” • Amplifier: “two port” University of California, Berkeley

16. One-Port Models (EECS 40) • A terminal pair across which a voltage and associated current are defined Circuit Block University of California, Berkeley

17. Small-Signal Two-Port Models • We assume that input port is linear and that the amplifier is unilateral: • Output depends on input but input is independent of output. • Output port : depends linearly on the current and voltage at the input and output ports • Unilateral assumption is good as long as “overlap” capacitance is small (MOS) University of California, Berkeley

18. Math 54 Perspective Can write linear system of equations for either ioutor vout in terms of two of iin, vin, iout, or vout: possibilities are What is physical meaning of 1? of 6? University of California, Berkeley

19. EE Perspective • Four amplifier types: determined by the output signal and the input signal … both of which we select (usually obvious) • Voltage Amp (VV) • Current Amp (II) • Transconductance Amp (VI) • Transresistance Amp (IV) • We need methods to find the 6  parameters for the four models and equivalent circuits for unilateral two ports University of California, Berkeley

20. Two-Port Small-Signal Amplifiers Voltage Amplifier Current Amplifier University of California, Berkeley

21. Two-Port Small-Signal Amplifiers Transconductance Amplifier Transresistance Amplifier University of California, Berkeley

22. Input Resistance Rin Looks like a Thevenin resistance measurement, but note that the output port has the load resistance attached University of California, Berkeley

23. Output Resistance Rout Looks like a Thevenin resistance measurement, but note that the input port has the source resistance attached University of California, Berkeley

24. Finding the Voltage Gain Av Key idea: the output port is open-circuited and the source resistance is shorted University of California, Berkeley

25. Finding the Current Gain Ai Key idea: the output port is shorted and the source resistance is removed University of California, Berkeley

26. Finding the Transresistance Rm University of California, Berkeley

27. Finding the Transconductance Gm University of California, Berkeley

28. Common-Source Amplifier (again) How to isolate DC level? University of California, Berkeley

29. DC Bias 5 V Neglect all AC signals 2.5 V Choose IBIAS, W/L University of California, Berkeley

30. Load-Line Analysis to find Q Q University of California, Berkeley

31. Small-Signal Analysis University of California, Berkeley

32. Two-Port Parameters: Generic Transconductance Amp Find Rin, Rout, Gm University of California, Berkeley

33. Two-Port CS Model Reattach source and load one-ports: University of California, Berkeley