2. Introduction to MOS Amplifiers: Transfer Function Biasing & Small-Signal-Model Concepts

Transcription

1 2. Introduction to MOS Amplifiers: Transfer Function Biasing & Small-Signal-Model Concepts Reading: Sedra & Smith Sec. 5.4 (S&S 5 th Ed: Sec. 4.4) ECE 102, Fall 2011, F. Najmabadi

2 NMOS Transfer Function (1) Transfer Function: Relation between output and input voltages. v i = NMOS i-v Characterisitics : KVL : V = R i + v S i = f ( v GS, v S ) * To find the transfer function, we start with v GS = 0 and increase v GS

3 NMOS Transfer Function (2) NMOS i-v Characterisitics : i = f ( v GS, v S ) KVL : V = R i + v S For v GS < V t, NMOS is in cutoff: i = 0 v = V R i = V S As we increase v GS passing V t, NMOS will come out of cut-off: i increases leading to a decrease in v S (due to KVL) v GS i v S

4 NMOS Transfer Function (2) To the right of point A, v GS >V t, and NMOS is ON. Just to the right of point A: o V ov = v GS V t is small. o v S is close to V because transfer function cannot have a discontinuity. o Thus, v S > V ov = v GS V t and NMOS is in saturation. i v S W 2 = 0.5µ ncox VOV L = V 0.5µ nc ox W L V 2 OV R V 2 OV

5 NMOS Transfer Function (3) As v GS increase: o V ov = v GS V t becomes larger; o v S becomes smaller. o At point B, v S = V ov = v GS V t To the right of point B, v S < V ov = v GS V t and NMOS enters triode. Point B is called the Edge of Saturation Exercise: Use NMOS i-v characteristics (and KVL), find V GS B and V S B

6 Graphical analysis of NMOS Transfer Function (1) NMOS i-v characteristics i = f ( vgs, vs ) is a surface * Plot for V t,n = 1 V and µ n C ox (W/L) = 2.0 ma/v 2

7 Graphical analysis of NMOS Transfer Function (1) Looking at surface with v GS axis pointing out of the paper Note: surface is truncated (i.e., v GS < 5 V)

8 Graphical analysis of NMOS Transfer Function (3) v i = NMOS i-v Characterisitics : KVL : V = R i + v S i = f ( v GS, v S ) KVL equation is a plane in this space. Intersection of KVL plane with the iv characteristic surface is a line. NMOS operating point is on this line (depending on the value of v GS.) If we look from the top (i axis out of the paper), we can see the transfer function.

9 Graphical analysis of NMOS Transfer Function (4) Looking at surface with v GS axis pointing out of the paper

10 Graphical analysis of NMOS Transfer Function (5) v S = 0 NMOS i-v Characterisitics : KVL : V = R i + v S i = f ( v GS, v S ) The Load Line is the relationship between i and v S imposed by the circuit (outside of NMOS). i = 0

11 Graphical analysis of NMOS Transfer Function (6) C B A Every point on the load line corresponds to a specific v GS value. As v GS increases, NMOS moves up the load line.

12 Foundation of Transistor Amplifiers A voltage amplifier requires v o /v i = const. o Transfer function has to be linear (but NMOS transfer function is NOT). Let us consider the response if NMOS remain in saturation at all times: o v GS should be a combination of constant value and a time-varying signal.

13 The response to a combination of V GS and v gs (signal) can be found from the transfer function Response to the signal appears to be linear!

14 Although the overall response is non-linear, the transfer function for the signal only is linear! v ds Constant: Bias Signal and response v GS = V GS + v gs v S = V S + v ds v gs i = I S + i d Non-linear relationship among these parameters Linear relationship among these parameters

15 An Analogy (1) Response h b Added Weight (signal) Boat H b = H B Pool H B H b Bias Bias + signal Total Height, H b = Bias (H B ) + response to signal (h b ) Complicated correlation between total height, H b, and weight of the boat. Simple correlation between h b and added weight

16 An Analogy (2) h b Added Weight (signal) H B H b Bias: H B Bias + Signal: H b Signal & response to signal: h b Bias: V GS, V S, I Bias + Signal: v GS, v S, i Signal & response: v gs, v ds, i d Non-linear correlations among Bias + Signal: v GS, v S, i Simple (and linear) correlation between signal and response to the signal: v gs, v ds, i d

17 Important Points! Signal: We want the response of the circuit to this input. Bias: State of the system when there is no signal (current and voltages in all elements). o Bias is constant in time (may vary extremely slowly compared to signal) o Purpose of the bias is to ensure that MOS is in saturation at all times. Response of the circuit and elements within to the signal is different that the response of the circuit and its elements to Bias (or to Bias + signal): o ifferent transfer function for the circuit o ifferent iv characteristics for the elements, i.e. relationships among v gs, v ds, i d is different than relationships among v GS, v S, i.

18 Limitations and Constraints Floating Boat analogy Boat should float at all times! o Sufficient water in the pool Transistor MOS should be in saturation at all times! o Bias point in Saturation* V GS > V tn V S > V GS - V tn o Cannot put too much weight (depends on the depth of the water!) o Signal amplitude cannot become too large (depends on Bias point!)** v GS = V GS + v gs > V tn v S = V S + v ds > V GS + v gs - V tn *Equations are for NMOS! ** Obviously, the second set is more restrictive

19 Issues in developing a MOS amplifier: 1. How to establish a Bias point (bias is the state of the system when there is no signal). o Stable and robust bias point should be resilient to variations in µ n C ox (W/L),V t, due to temperature and/or manufacturing variability. 2. Find the iv characteristics of the elements for the signal (which can be different than their characteristics equation for bias). o This will lead to different circuit configurations for bias versus signal 3. Compute circuit response to the signal o Focus on fundamental MOS amplifier configurations