EE105 - Fall 2006 Microelectronic Devices and Circuits

Transcription

1 EE105 - Fall 2006 Microelectronic Devices and Circuits Prof. Jan M. Rabaey (jan@eecs) Lecture 11: Voltage and Current Sources Administrativia Lab 3 this week Please make sure to work through the pre-lab Lab reports are PERSONAL Copying of someone else s report is NOT condoned. Discussion sessions this week MOS small signal Voltage and current sources Midterm 1 graded by Thursday Discussion of problem challenges and main deficiencies 2 1

2 Overview Last lecture Small signal model (continued) This lecture Some words about SPICE Voltage and current sources Moving to Amplifiers 3 Some words about SPICE Modified Nodal Analysis DC Analysis and Convergence Transient analysis Integration rules Non-linear equations 4 2

3 Moving to Circuits So-far: Common-source amplifier Next: Voltage and Current Sources Some more two-port elements made out of MOS transistors (so far only current and voltage sources) Deriving large and small signal models On to Four Port Elements From Here 5 Voltage References (Book 9.4) Generating a voltage: use a current source to set V GS 6 3

4 i Modeling the Voltage Source Find i OUT versus v OUT MOSFET is off or saturated? Why? OUT i OUT W = id, SAT I REF = μncox λ ) 2L 2 ( vgs VTn ) (1 nvds I REF v OUT Typical operating point: i OUT = 0 A 7 Small-Signal Source Resistance R S di = dv OUT OUT I OUT = 0 1 = v i t t Equivalent Circuit: R S i OUT V S - v OUT - 8 4

5 Creating a Current Source

6 Equivalent Circuit for I-Source Find the DC current for gray circle equivalent circuit I OUT ncox W = μ ( V ) 2 REF VTn 2 L Substitute for V REF 2 11 Small-Signal Resistance of I-Source 12 6

7 Current Sinks and Sources Sink: output current goes to ground Source: output current comes from voltage supply 13 Current Mirrors Idea: we only need one reference current to set up all the current sources and sinks needed for a multistage amplifier. 14 7

8 Application of Current Mirrors: Digital-to-Analog Converter V DD R L R REF v OUT D 0 D 1 D 2 D 4 i Do i D1 i D2 i D3 M REF M 0 M 1 M 2 M 3 Digital input: word D 0 D 1 D 2 D 3 voltages are either V DD or 0 V. Transistors M 0, M 1, M 2, M 3 have binary-weighted (W/L) ratios 15 Example Input word D 0 D 1 D 2 D 3 = 0101 I REF = 100 μa (W/L) REF = (W/L) 0 (W/L) 1 = 2(W/L) 0 (W/L) 2 = 2(W/L) 1 (W/L) 3 = 2(W/L) 2 Output voltage is v OUT = V DD R L (i D0 i D2 ) = V DD R L (I REF 4 I REF ) Sources of error: fab imprecision, channel-length modulation, 16 8

9 Moving to Amplifiers Amplifier Terminology Sources: Signal, its source resistance, and bias voltage or current Load: Use resistor/current source or in Chap. 8, but could be a general impedance Port: A pair of terminals across which a voltage and current are defined Source, Load: one port Amplifier: two port 17 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 R thev i ab v ab v thev v ab R thev i thev 18 9

10 Two-Port Models (Amplifiers) i in i out v in Circuit Block v out 19 Generalized Amplifier R S V DD v = V v v S BIAS s s V BIAS I DD il = I DD id i D = f( v ) in v o R L v in i s I BIAS V SS Active Device 20 10

11 (Small-Signal) Two-Port Models v in i in i out v out General case: four variables, v in, i in, v out, i out : Two independent, two dependent Four choices (Math 54): i in = f(v in, v out ), i out = f(v in, v out ) v in = f(i in, v out ), i out = f(i in, v out ) i in = f(v in, i out ), v out = f(v in, i out ) v in = f(i in, i out ), v out = f(i in, i out ) 21 Small-Signal Two-Port Models v in i in i out 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) 22 11

12 A Mathematical 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? 23 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) Need methods to find the 6 α parameters for the four models and equivalent circuits for unilateral two ports 24 12

13 Two-Port Small-Signal Amplifiers R s R out v s v in R in A v v in R L Voltage Amplifier i in is Rs Rin Ai i in Rout RL Current Amplifier 25 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 26 13

14 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 RSremoved, RLattached 27 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 RLremoved, RSattached 28 14

15 Finding the Voltage Gain A v Key idea: the output port is open-circuited and the source resistance is shorted 29 Finding the Current Gain A i Key idea: the output port is shorted and the source resistance is removed i A = i out iin R, R = 0 S L 30 15

16 Finding the Transresistance R m 31 Finding the Transconductance G m 32 16

17 Common-Source Amplifier (again) How to isolate DC level? 33 DC Bias 5 V Neglect all AC signals 2.5 V Choose I BIAS, W/L 34 17

18 Load-Line Analysis to find Q I RD V = DD V R D out 5V I D = 10k Q 1 slope = 10k 0V I D = 10k 35 Small-Signal Analysis R in = 36 18

19 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 37 Two-Port CS Model Reattach source and load one-ports: 38 19