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Lecture #19 amplifier examples: comparators, op amps.

Lecture #19 amplifier examples: comparators, op amps. Reminder: MIDTERM coming up one week from today (Monday October 18 th ) This week: Review and examples. Midterm. Monday, October 18, In class One page, one side of notes. Topics. Today: Amplifier examples Comparator Op-Amp. V IN.

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Lecture #19 amplifier examples: comparators, op amps.

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

  2. Midterm • Monday, October 18, • In class • One page, one side of notes EE 42 fall 2004 lecture 19

  3. Topics Today: • Amplifier examples • Comparator • Op-Amp EE 42 fall 2004 lecture 19

  4. VIN + + V0   Amplifier V+rail V+rail V0=AVIN Output is referenced to “signal ground” V0 cannot rise above some physical voltage related to the positive power supply VCC (“ upper rail”) V0 < V+RAIL V0 cannot go below most negative power supply, VEE i.e., limited by lower “rail” V0 > V-RAIL EE 42 fall 2004 lecture 19

  5. VIN + + V0   WHAT ARE I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER ? Circuit model gives the essential linear part The gain may be 100 to 100,000 or more But V0 cannot rise above some physical voltage V0 < V+RAIL And V0 cannot go below the lower “rail” V0 > V-RAIL CMOS based amplifiers can often go all the way to their power supplies, perhaps ± 5 volts EE 42 fall 2004 lecture 19

  6. + +   High gain Amplifier VIN VIN V0 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. EE 42 fall 2004 lecture 19

  7. Differential Amplifier Circuit Model in linear region V0 V+ + A AV1 Ri  V +  + + V1 V0 But if A ~ , is the output infinite? “Very high gain”   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. “Differential” V0 depends only on difference (V+  V-) EE 42 fall 2004 lecture 19

  8. (a) V-V near origin (b) V-V over wider range upper “rail” V0 (V) V0 (V) 3 0.2 2 0.1 1 VIN(V) VIN(V) 1 3 3 2 1 2 10 30 30 20 10 20 1 lower “rail” 2 .2 3 I-V Characteristics of a real high-gain amplifier Example: Amplifier with gain of 105, with max V0 of 3V and min V0 of 3V. EE 42 fall 2004 lecture 19

  9. (c) Same V0 vs VIN over even wider range V0 (V) 3 2 (b) V-V over wide range 1 upper “rail” 1 V0 (V) 2 VIN(V) 3 3 2 1 VIN(V) 1 3 3 2 1 2 10 30 30 20 10 20 lower “rail” 1 2 3 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) Example: Amplifier with gain of 105, with upper rail of 3V and lower rail of 3V. We plot the V0 vs VIN characteristics on two different scales EE 42 fall 2004 lecture 19

  10. (c) V-V with equal X and Y axes V0 (V) 3 2 1 1 VIN(V) 2 3 1 3 3 2 1 2 I-V CHARACTERISTICS OF AN ACTUAL HIGH-GAIN DIFFERENTIAL AMPLIFIER (cont.) Now plot same thing but with equal horizontal and vertical scales (volts versus volts) Note: • (a) displays linear amplifier behavior • (b) shows limit of linear region – (|VIN| < 30 V) • (c) shows comparator function (1 bit A/D converter centered at VIN = 0) where lower rail = logic “0” and upper rail = logic “1” EE 42 fall 2004 lecture 19

  11. V0 VIN V0 2 If VIN > 1.010 V, V0 = 2V = Logic “1” 1 1V VIN 0 1 2 If VIN < 0.99 V, V0 = 0V = Logic “0” + VIN + V0   Comparator 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. 102 to105 ) 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. EE 42 fall 2004 lecture 19

  12.  pulses out comparator transmission regenerated pulses pulses in We set comparator threshold at a suitable value (e.g., halfway between the logic levels) and comparator output goes to: +rail if VIN > VTHRESHOLD and to rail if VIN < VTHRESHOLD. Conversion from signals to digital data 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” EE 42 fall 2004 lecture 19

  13. R1 R2 R1 R2 V0 VIN AV1 Ri + EXAMPLE VIN  Circuit Model + - V0 V1 +  - + 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 We will show that that for A   (and Ri  0 for simplicity) Stable, finite, and independent of the properties of the OP AMP ! EE 42 fall 2004 lecture 19

  14. Example: R1 R2 9K 1K V0 VIN Circuit (assume R1 R2 V0 1K 9K () (+) VIN + - +  OP-AMPS – “TAMING” THE WILD HIGH-GAIN AMPLIFIER KEY CONCEPT: Negative feedback 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 EE 42 fall 2004 lecture 19

  15. OP-AMP very high gain →predictable results Analysis: Lets solve for V- then find Vo from Vo = A (V+ - V-) EE 42 fall 2004 lecture 19

  16. OP-AMP very high gain →predictable results EE 42 fall 2004 lecture 19

  17. Example: R2 R1 VIN 9K 1K V0 + - +  OP-AMPS – Another Basic Circuit Now lets look at the Inverting Amplifier When the input is not so large that the output is hitting the rails, we have a circuit model: R1 R2 VIN V0 1K 9K () (+) EE 42 fall 2004 lecture 19

  18. Inverting amplifier analysis Analysis: Solve for V- then find VO from VO = - AV- EE 42 fall 2004 lecture 19

  19. 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. EE 42 fall 2004 lecture 19

  20. + - +  Capacitor in the feedback Now lets look at the Inverting Amplifier Example: R1 VIN 1K V0 In the linear range, the circuit model: R1 VIN V0 1K () (+) EE 42 fall 2004 lecture 19

  21. Integrator • Since the positive terminal is grounded, the negative terminal will be near zero volts • The input terminal also takes in no current EE 42 fall 2004 lecture 19

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