1. 10/11/2004EE 42 fall 2004 lecture 181 Lecture #18 Summary of ideal devices, amplifier examples Reminder: MIDTERM coming up one week from today (Monday October 18 th ) This week: Review and examples

2. 10/11/2004EE 42 fall 2004 lecture 182 Midterm Monday, October 18, In class One page, one side of notes

3. 10/11/2004EE 42 fall 2004 lecture 183 Topics Today: Summary of ideal circuits Amplifier examples –Comparator –Op-Amp

4. 10/11/2004EE 42 fall 2004 lecture 184 Ideal devices Wire: Current in =current out No voltage differences Resistor

5. 10/11/2004EE 42 fall 2004 lecture 185 Ideal devices 2 Inductor: Ideal diode: Reversed bias  no current, open circuit Forward bias  no voltage drop, just like a wire

6. 10/11/2004EE 42 fall 2004 lecture 186 Ideal devices 3 Transformer +V1-+V1- +V2-+V2- N 1 and N 2 are the number of turns of wire

7. 10/11/2004EE 42 fall 2004 lecture 187 Ideal devices 4 ~ Voltage source: Voltage given, current can be anything Note: the voltage could be given as A function of time Current source Current given, voltage can be anything Note: the current could be given as A function of time

8. 10/11/2004EE 42 fall 2004 lecture 188 Ideal devices 5 ~ Dependent Voltage source: Voltage given as a multiple of another Voltage or a current, current can be anything Dependent Current source Current given as a multiple of a different current or voltage, voltage can be anything +V1-+V1- +V2-+V2- +V1-+V1-

9. 10/11/2004EE 42 fall 2004 lecture 189 NPN transistor The Base-Collector junction must be reverse biased. The model of the diode can be ideal, or better with a 0.7 volt turn on Beta could be anywhere from 40 to 400 E mitter B ase C ollector

10. 10/11/2004EE 42 fall 2004 lecture 1810 NMOS transistor If V GS is higher than the threshold V TH, then the switch is closed. S ource G ate D rain D G S The resistance from the source to the drain depends on the how much greater than threshold V GS is, and how wide the transistor is.

11. 10/11/2004EE 42 fall 2004 lecture 1811 PMOS transistor If V GS is lower than the threshold V TH, then the switch is closed. S ource G ate D rain S G D The resistance from the source to the drain depends on the how much below threshold (more negative) V GS is.

12. 10/11/2004EE 42 fall 2004 lecture 1812 Amplifier +  V0V0 +  V IN V 0 =AV IN But V 0 cannot rise above some physical voltage related to the positive power supply V CC (“ upper rail”) V 0 < V +RAIL And V 0 cannot go below most negative power supply, V EE i.e., limited by lower “rail” V 0 > V -RAIL

13. 10/11/2004EE 42 fall 2004 lecture 1813 Amplifier +  V0V0 +  V IN V 0 =AV IN Output is referenced to “signal ground” V 0 cannot rise above some physical voltage related to the positive power supply V CC (“ upper rail”) V 0 < V +RAIL V 0 cannot go below most negative power supply, V EE i.e., limited by lower “rail” V 0 > V -RAIL V +rail

14. 10/11/2004EE 42 fall 2004 lecture 1814 OP-AMPS AND COMPARATORS A very high-gain differential amplifier can function either in extremely linear fashion as an operational amplifier (by using negative feedback) or as a very nonlinear device – a comparator. Let’s see how! +  +  V0V0 AV 1 +  V1V1 RiRi Circuit Model in linear region +  A V+V+ VV V0V0 Differential Amplifier “Differential”  V 0 depends only on difference (V +  V - ) “Very high gain”  But if A ~, is the output infinite? The output cannot be larger than the supply voltages. It will limit or “clip” if we attempt to go too far. We call the limits of the output the “rails”.

15. 10/11/2004EE 42 fall 2004 lecture 1815 WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER ? +  V0V0 +  V IN Circuit model gives the essential linear part The gain may be 100 to 100,000 or more But V 0 cannot rise above some physical voltage V 0 < V +RAIL And V 0 cannot go below the lower “rail” V 0 > V -RAIL CMOS based amplifiers can often go all the way to their power supplies, perhaps ± 5 volts

16. 10/11/2004EE 42 fall 2004 lecture 1816 I-V Characteristics of a real high-gain amplifier Example: Amplifier with gain of 10 5, with max V 0 of 3V and min V 0 of  3V. V IN (  V) 12 3 V 0 (V) 0.1 0.2 33 22 11 .2 (a) V-V near origin 33 (b) V-V over wider range V IN (  V) 1020 30 V 0 (V) 1  30  20  10 22 11 2 3 upper “rail” lower “rail”

17. 10/11/2004EE 42 fall 2004 lecture 1817 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) V IN (V) 12 3 V 0 (V) 1 2 33 22 11 22 33 11 3 (c) Same V 0 vs V IN over even wider range 33 (b) V-V over wide range V IN (  V) 1020 30 V 0 (V) 1  30  20  10 22 11 2 3 upper “rail” lower “rail” Example: Amplifier with gain of 10 5, with upper rail of 3V and lower rail of  3V. We plot the V 0 vs V IN characteristics on two different scales

18. 10/11/2004EE 42 fall 2004 lecture 1818 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) V IN (V) 12 3 V 0 (V) 1 2 33 22 11 22 33 11 3 (c) V-V with equal X and Y axes Note: (a) displays linear amplifier behavior (b) shows limit of linear region – (|V IN | < 30  V) (c) shows comparator function (1 bit A/D converter centered at V IN = 0) where lower rail = logic “0” and upper rail = logic “1” Now plot same thing but with equal horizontal and vertical scales (volts versus volts)

19. 10/11/2004EE 42 fall 2004 lecture 1819 EXAMPLE OF A HIGH-GAIN DIFFERENTIAL AMPLIFIER OPERATING IN COMPARATOR (A/D) MODE Simple comparator with threshold at 1V. Design lower rail at 0V and upper rail at 2V (logic “1”). A = large (e.g. 10 2 to10 5 ) NOTE: The actual diagram of a comparator would not show an amplifier with “offset” power supply as above. It would be a simple triangle, perhaps with the threshold level (here 1V) specified. If V IN > 1.010 V, V 0 = 2V = Logic “1” If V IN < 0.99 V, V 0 = 0V = Logic “0” V0V0 V IN 12 0 1 2 +  V0V0 +  1V V0V0 V IN Comparator

20. 10/11/2004EE 42 fall 2004 lecture 1820 ONE-BIT A/D CONVERSION REQUIRED IN DIGITAL SYSTEMS  pulses in transmission  comparator regenerated pulses pulses out As we saw, we set comparator threshold at a suitable value (e.g., halfway between the logic levels) and comparator output goes to +rail if V IN > V THRESHOLD and to  rail if V IN < V THRESHOLD.

21. 10/11/2004EE 42 fall 2004 lecture 1821 OP-AMPS AND COMPARATORS A very high-gain differential amplifier can function in extremely linear fashion as an operational amplifier by using negative feedback. Negative feedback  Stabilizes the output R2R2 R1R1  + V0V0 V IN EXAMPLE We can show that that for A   (and R i  0 for simplicity) +  +  V0V0 AV 1 - + V1V1 RiRi R2R2 Circuit Model R1R1 V IN Stable, finite, and independent of the properties of the OP AMP !

22. 10/11/2004EE 42 fall 2004 lecture 1822 OP-AMPS – “TAMING” THE WILD HIGH-GAIN AMPLIFIER KEY CONCEPT: Negative feedback Circuit (assume V0V0 (+) ()() 1K V IN 9K R2R2 R1R1 +  V0V0 - + 1K V IN 9K R2R2 R1R1 Example:

23. 10/11/2004EE 42 fall 2004 lecture 1823 OP-AMP very high gain →predictable results Analysis: Lets solve for V - then find V O from V O = A (V + - V - )

24. 10/11/2004EE 42 fall 2004 lecture 1824 OP-AMPS – Another Basic Circuit Now lets look at the Inverting Amplifier V0V0 (+) ()() 1K V IN 9K R2R2 R1R1 +  V0V0 - + 1K V IN 9K R2R2 R1R1 Example: When the input is not so large that the output is hitting the rails, we have a circuit model:

25. 10/11/2004EE 42 fall 2004 lecture 1825 Inverting amplifier analysis Analysis: Solve for V - then find V O from V O = - AV -