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Lecture #18 Summary of ideal devices, amplifier examples

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. Midterm. Monday, October 18, In class One page, one side of notes. Topics. Today: Summary of ideal circuits

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Lecture #18 Summary of ideal devices, amplifier examples

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

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

  3. Topics Today: • Summary of ideal circuits • Amplifier examples • Comparator • Op-Amp EE 42 fall 2004 lecture 18

  4. Ideal devices Wire: Current in =current out No voltage differences Resistor EE 42 fall 2004 lecture 18

  5. Ideal devices 2 Inductor: Ideal diode: Reversed bias  no current, open circuit Forward bias  no voltage drop, just like a wire EE 42 fall 2004 lecture 18

  6. Ideal devices 3 + V1 - + V2 - Transformer N1 and N2 are the number of turns of wire EE 42 fall 2004 lecture 18

  7. 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 EE 42 fall 2004 lecture 18

  8. Ideal devices 5 + V1 - + V2 - Dependent Voltage source: Voltage given as a multiple of another Voltage or a current, current can be anything ~ + V1 - Dependent Current source Current given as a multiple of a different current or voltage, voltage can be anything EE 42 fall 2004 lecture 18

  9. NPN transistor Base Collector 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 Emitter EE 42 fall 2004 lecture 18

  10. NMOS transistor Drain Gate If VGS is higher than the threshold VTH, then the switch is closed. D G Source S The resistance from the source to the drain depends on the how much greater than threshold VGS is, and how wide the transistor is. EE 42 fall 2004 lecture 18

  11. PMOS transistor Source If VGS is lower than the threshold VTH, then the switch is closed. S G Gate Drain D The resistance from the source to the drain depends on the how much below threshold (more negative) VGS is. EE 42 fall 2004 lecture 18

  12. V0=AVIN But V0 cannot rise above some physical voltage related to the positive power supply VCC (“ upper rail”) V0 < V+RAIL And V0 cannot go below most negative power supply, VEE i.e., limited by lower “rail” V0 > V-RAIL VIN + + V0   Amplifier EE 42 fall 2004 lecture 18

  13. 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 VIN + + V0   Amplifier V+rail V+rail EE 42 fall 2004 lecture 18

  14. 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. Let’s see how! “Differential” V0 depends only on difference (V+  V-) 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”. EE 42 fall 2004 lecture 18

  15. 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 18

  16. (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 18

  17. (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 18

  18. (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 18

  19. 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 18

  20.  pulses out comparator transmission regenerated pulses pulses in 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 VIN > VTHRESHOLD and to rail if VIN < VTHRESHOLD. ONE-BIT A/D CONVERSIONREQUIRED IN DIGITAL SYSTEMS EE 42 fall 2004 lecture 18

  21. R1 R2 R1 R2 V0 VIN AV1 Ri + EXAMPLE VIN  Circuit Model + - V0 V1 +  - + 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 We can 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 18

  22. 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 EE 42 fall 2004 lecture 18

  23. 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 18

  24. 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 18

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

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