Lecture 16: Small Signal Amplifiers

Transcription

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!

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, )

4 A Simple Circuit: An MOS Amplifier Input signal RD VDD Supply Rail v o v s I DS vgs = VGS + vs V GS Output signal

5 Small-Signal Analysis Step 1. Find DC Bias ignore small-signal source I GS,Q V GS,BIAS was found in Lecture 15

6 Small-Signal Modeling What are the small-signal models of the DC supplies? Shorts!

7 Small-Signal Models of Ideal Supplies Small-signal model: isupply gsupply = = v supply r supply = 0 short g supply isupply = = v supply 0 r supply = open

8 Small-Signal Circuit for Amplifier

9 Low-Frequency Voltage Gain Consider first ω 0 case capacitors are open-circuits Transconductance v = gv R r ( ) out m s D o A = g R r ( ) v m D o Design Variable W 2I gm = µ ncox ( VGS VT) = L V V GS DSAT, T Design Variables

10 Voltage Gain (Cont.) Substitute transconductance: A 2I = R r ( ) DSAT, v D o VGS VT g R m D Output resistance: typical value λ n = 0.05 V -1 r o 1 1 = = kω= 200kΩ λni D, SAT Voltage gain: A v 20.1 = ( ) =

11 Input and Output Waveforms Output small-signal voltage amplitude: 14 x 25 mv = 350 Input small-signal voltage amplitude: 25 mv

12 What Limits the Output Amplitude? 1. v OUT (t) reaches V SUP or 0 or 2. MOSFET leaves constant-current region and enters triode region VDS VDS, SAT = VGS VTn = 0.31V v, = VDSSAT, = 0.32 V omin amp = V = 2.18V

13 Maximum Output Amplitude v out (t)= V cos(ωt) v s (t) = 152 mv cos(ωt) How accurate is the small-signal (linear) model? vs V V = 0.32 GS Tn Significant error in neglecting third term in expansion of i D = i D (v GS )

14 Generalized Amplifier R S V DD v = V + v v S BIAS s s V BIAS I DD il = IDD id i D = f( v ) in v o R L v in i s I BIAS V SS Active Device

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

16 One-Port Models (EECS 40) A terminal pair across which a voltage and associated current are defined + v ab i ab Circuit Block i ab i ab + R thev + v ab v thev v ab R thev i thev

17 Small-Signal Two-Port Models + i in i out + v in v out 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)

18 Math 54 Perspective Can write linear system of equations for either i out or v out in terms of two of i in, v in, i out, or v out : possibilities are i = α v + α v out 1 in 2 out i = α i + α v out 3 in 4 out v = α v + α i out 5 in 6 out v = α i + α i out 7 in 8 out What is physical meaning of α 1? of α 6?

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 α parameters for the four models and equivalent circuits for unilateral two ports

20 Two-Port Small-Signal Amplifiers R s R out v s + v in R in Av v in R L Voltage Amplifier i in is Rs Rin Ai i in Rout RL Current Amplifier

21 Two-Port Small-Signal Amplifiers R s v s + v in R in G v m in Rout RL Transconductance Amplifier i in R out is Rs Rin Ri m in R L Transresistance Amplifier

22 Input Resistance R in Looks like a Thevenin resistance measurement, but note that the output port has the load resistance attached R in = v i t t R R S L removed, attached

23 Output Resistance R out Looks like a Thevenin resistance measurement, but note that the input port has the source resistance attached R out = v i t t R R L S removed, attached

24 Finding the Voltage Gain A v Key idea: the output port is open-circuited and the source resistance is shorted

25 Finding the Current Gain A i Key idea: the output port is shorted and the source resistance is removed

26 Finding the Transresistance R m

27 Finding the Transconductance G m

28 Common-Source Amplifier (again) How to isolate DC level?

29 DC Bias 5 V Neglect all AC signals 2.5 V Choose I BIAS, W/L

30 Load-Line Analysis to find Q I R D = V DD V R D out I D = 5V 10k Q 1 slope = 10k I D = 0V 10k

31 Small-Signal Analysis R in =

32 Two-Port Parameters: Find R in, R out, G m Generic Transconductance Amp R s v s + v in R in G v m in Rout RL R in = G m = g R = r R m out o D

33 Two-Port CS Model Reattach source and load one-ports: