2. Introduction to MOS Amplifiers: Concepts and MOS Small-Signal-Model

Transcription

1 2. Introduction to MOS mpliiers: Concepts and MOS Small-Signal-Model Sedra & Smith Sec. 5.4 & 5.6 S&S 5 th Ed: Sec. 4.4 & 4.6 ECE 102, Fall 2012, F. Najmabadi

2 NMOS Transer Function 1 Transer Function: elation between output and input oltages. i Circuit Equations: o NMOS i characteristics: i, o KL: o i F. Najmabadi, ECE102, Fall /26

3 NMOS Transer Function 2 1 For < t, NMOS is in cuto: i 0 & i 2 Just to the right o point : o O t is small, so i is small. o i is close to o Thus, > O and NMOS is in saturation. F. Najmabadi, ECE102, Fall /26

4 NMOS Transer Function 2 4 To the right o point B, < O t and NMOS enters triode. Point B is called the Edge o Saturation 3 s increases: o O t and i become larger; o i becomes smaller. o t point B, O F. Najmabadi, ECE102, Fall /26

5 NMOS Transer Function 2 1 For < t, NMOS is in cuto: i 0 & i 4 To the right o point B, < O t and NMOS enters triode. Point B is called the Edge o Saturation 2 Just to the right o point : o O t is small, so i is small. o i is close to o Thus, > O and NMOS is in saturation. 3 s increases: o O t and i become larger; o i becomes smaller. o t point B, O F. Najmabadi, ECE102, Fall /26

6 Graphical analysis o NMOS Transer Function 1 i NMOS i- Characterisitics : KL : i i, KL equation is a plane in this space. Intersection o KL plane with the i characteristics surace is a line. NMOS operating point is on this line depending on the alue o. I we look rom the bottom i axis out o the paper, we can see the transer unction. F. Najmabadi, ECE102, Fall /26

7 Graphical analysis o NMOS Transer Function 6 Looking parallel to axis Eery point on the load line corresponds to a speciic alue. Looking rom the bottom s increases, NMOS moes up the load line. F. Najmabadi, ECE102, Fall /26

8 Foundation o Transistor mpliiers 1 oltage ampliier requires o / i const. 2 examples below MOS transer unction is NOT linear o / i can be negatie minus sign represents a 180 o phase shit In saturation, howeer, transer unction looks linear but shited F. Najmabadi, ECE102, Fall /26

9 Foundation o Transistor mpliiers 2 In saturation, transer unction appear to be linear pproximate the transer unction with a tangent line at point Q with a slope o G: G ds G gs linear relationship or ds and gs F. Najmabadi, ECE102, Fall /26

10 Foundation o Transistor mpliiers 3 Let us consider the response i NMOS remains in saturation at all times and is a combination o a constant alue and a signal gs. gs F. Najmabadi, ECE102, Fall /26

11 The response to a combination o gs can be ound rom the transer unction F. Najmabadi, ECE102, Fall /26

12 esponse to the signal appears to be linear esponse o is also made o a constant part and a signal response part ds. Constant part o the response,, is ONLY related to, the constant part o the input Q point on the transer unction o preious slide. o i.e., i gs 0, then ds 0 The shape o the time arying portion o the response ds is similar to gs. o i.e., ds is proportional to the input signal, gs F. Najmabadi, ECE102, Fall /26

13 lthough the oerall response is non-linear, the transer unction or the signal is linear! Constant: Bias Signal and response ds gs ds i I i d gs Non-linear relationship among these parameters pproximately Linear relationship among these parameters F. Najmabadi, ECE102, Fall /26

14 Important Points and einitions! Signal: We want the response o the circuit to this input. Bias: State o the system when there is no signal. o Bias is constant in time may ary extremely slowly compared to signal o Purpose o the bias is to ensure that MOS is in saturation at all times. esponse o the circuit and its elements to the signal is dierent than its response to the Bias or to Bias signal: o Signal i characteristics o elements are dierent, i.e. relationships among gs, ds, i d is dierent rom relationships among,, i. o Signal transer unction o the circuit is dierent rom the transer unction or total input Bias signal. F. Najmabadi, ECE102, Fall /26

15 Issues in deeloping a MOS ampliier: 1. Find the i characteristics o the elements or the signal which can be dierent than their characteristics equation or bias. o This will lead to dierent circuit conigurations or bias ersus signal 2. Compute circuit response to the signal o Focus on undamental MOS ampliier conigurations 3. How to establish a Bias point bias is the state o the system when there is no signal. o o Stable and robust bias point should be resilient to ariations in µ n C ox W/L, t, due to temperature and/or manuacturing ariability. Bias point details impact small signal response e.g., gain o the ampliier. F. Najmabadi, ECE102, Fall /26

16 Signal Circuit 1 We will ind signal i characteristics o arious elements. 2 In order to use circuit theory tools, we will use the signal i characteristics o arious elements to assign a circuit symbol. e.g., o o We will see that the diode signal i characteristics is linear so or signals, diode can be modeled as a circuit theory resistor. In this manner, we will arrie at a signal circuit.

17 Bias and Signal Circuits Bias & Signal Bias Signal only Bias Signal - Bias? MOS... : : i, I, i i r, r gs,... MOS... : :, I,, I, MOS... : : r gs, i, r ds, i d, F. Najmabadi, ECE102, Fall /26

18 Finding signal circuit elements -- esistor esistor oltage Current i Equation Bias Signal: i i Bias: I I Signal: r i r i I?? r i I i I r i r resistor remains as a resistor in the signal circuit. F. Najmabadi, ECE102, Fall /26

19 Finding signal circuit elements IS & ICS Independent oltage source oltage Current i Equation Bias Signal: IS i IS IS const Bias: IS I IS IS const Signal: is IS IS i is i IS I IS?? is IS IS 0 is 0, i is 0 Similarly: n independent oltage source becomes a short circuit! n independent current source becomes an open circuit! F. Najmabadi, ECE102, Fall /26 Exercise: Show that dependent sources remain as dependent sources

20 Summary o signal circuit elements esistors& capacitors: o Capacitor act as open circuit in the bias circuit. The Same Independent oltage source e.g., : Eectiely grounded Independent current source: Eectiely open circuit o Careul about current mirrors as they are NOT ideal current sources early eect and/or channel-length modulation was ignored! ependent sources: Non-linear Elements: o iodes & transistors? The Same ierent! F. Najmabadi, ECE102, Fall /26

21 Formal deriation o small signal model F. Najmabadi, ECE102, Fall / ! a a >> a << Small signal means: a a a g i 1 Signal Bias or element i, : i Bias or element I, : I Signal or element i a, a : i a g a a a a i... 2!... 2! Taylor Series Expansion a a I I i i 1

22 Small signal model s i characteristics Small signal model is equialent to approximating the non-liner i characteristics cure by a line tangent to the i cure at the bias point i d r d d nt I F. Najmabadi, ECE102, Fall /26

23 eriation o MOS small signal model 1 MOS i equations: i, i G 0 Signal Bias or MOS i,, : i,, i G 0 Bias or MOS I,, : I,, I G 0 Signal or MOS i d, gs, ds : i d g gs, ds, i g 0 I i d i, Taylor Series Expansion in 2 ariables,,,... I, gs, ds i d, gs, ds F. Najmabadi, ECE102, Fall /26

24 eriation o MOS small signal model 2 F. Najmabadi, ECE102, Fall /26 ds gs d i,,, t ox n L W C i λ µ m O t t ox n t ox n g I L W C L W C ,, λ µ λ µ o t ox n t ox n r I I L W C L W C , 2, λ λ λ λ λ µ λ µ λ 0 g o ds gs m d i r g i

25 MOS small signal circuit model Input open circuit i 0 and i g g d m gs r ds o Statement o KCL Two elements in parallel g m I ro gmro >> 1 λ I λ O O O F. Najmabadi, ECE102, Fall /26

26 PMOS small signal model is identical to NMOS PMOS* NMOS PMOS small-signal circuit model is identical to NMOS o We will use NMOS circuit model or both! o For both NMOS and PMOS, while i 0 and I 0, signal quantities: i d, gs, and ds, can be negatie! F. Najmabadi, ECE102, Fall /26