1. 10/13/2004EE 42 fall 2004 lecture 191 Lecture #19 amplifier examples: comparators, op amps. Reminder: MIDTERM coming up one week from today (Monday October 18 th ) This week: Review and examples

2. 10/13/2004EE 42 fall 2004 lecture 192 Midterm Monday, October 18, In class One page, one side of notes

3. 10/13/2004EE 42 fall 2004 lecture 193 Topics Today: Amplifier examples –Comparator –Op-Amp

4. 10/13/2004EE 42 fall 2004 lecture 194 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

5. 10/13/2004EE 42 fall 2004 lecture 195 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

6. 10/13/2004EE 42 fall 2004 lecture 196 High gain Amplifier +  +  V IN We can make very high gain amplifiers by cascading lower gain amplifiers. For example, if we have two amplifiers, each with a gain of 100, then when the output of the first is feed into the input of the second, the total gain is 10,000. With a very high gain amplifier, a very small change in the input causes a large change in the output voltage, so the range of voltages over which the input results in a linear output is very narrow. V0V0 V IN

7. 10/13/2004EE 42 fall 2004 lecture 197 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. +  +  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?

8. 10/13/2004EE 42 fall 2004 lecture 198 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”

9. 10/13/2004EE 42 fall 2004 lecture 199 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

10. 10/13/2004EE 42 fall 2004 lecture 1910 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)

11. 10/13/2004EE 42 fall 2004 lecture 1911 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

12. 10/13/2004EE 42 fall 2004 lecture 1912 Conversion from signals to digital data  pulses in transmission  comparator regenerated pulses pulses out 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. Signals are conveyed as voltages, but signal levels must be converted into digital data. ( 1 bit A/D) The rails of the comparator are the logic levels, for example +rail = “1” or “true” and -rail→”0” or “false”

13. 10/13/2004EE 42 fall 2004 lecture 1913 OP-AMPS 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 will 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 !

14. 10/13/2004EE 42 fall 2004 lecture 1914 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: First of all, notice that if the input resistance of the amplifier is so large that the current into it is negligible, then R1 and R2 form a voltage divider to give the input to the negative terminal

15. 10/13/2004EE 42 fall 2004 lecture 1915 OP-AMP very high gain →predictable results Analysis: Lets solve for V - then find V o from V o = A (V + - V - )

16. 10/13/2004EE 42 fall 2004 lecture 1916 OP-AMP very high gain →predictable results

17. 10/13/2004EE 42 fall 2004 lecture 1917 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:

18. 10/13/2004EE 42 fall 2004 lecture 1918 Inverting amplifier analysis Analysis: Solve for V - then find V O from V O = - AV -

19. 10/13/2004EE 42 fall 2004 lecture 1919 Solving Op-Amp circuits We can take a very useful short-cut for OP- Amp circuits with high gain if we notice that if the circuit is in the linear range, then (V + -V - ) must be very small, and it goes to zero as the gain goes to infinity. The shortcut is just to assume (V + -V - ) =0, and then to check later to make sure that the amplifier is truly in the linear range.

20. 10/13/2004EE 42 fall 2004 lecture 1920 Capacitor in the feedback Now lets look at the Inverting Amplifier V0V0 (+) ()() 1K V IN R1R1 +  V0V0 - + 1K V IN R1R1 Example: In the linear range, the circuit model:

21. 10/13/2004EE 42 fall 2004 lecture 1921 Integrator Since the positive terminal is grounded, the negative terminal will be near zero volts The input terminal also takes in no current