1. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California DIFFERENTIAL AMPLIFIER +  A V+V+ VV V0V0 Differential Amplifier “Differential”  V 0 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”. +  +  V0V0 AV 1 +  V1V1 RiRi Circuit Model in linear region RoRo Can add negative feedback to perform an “operation” on input voltages (addition, integration, etc.): operational amplifier

2. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California ANALYZING OPERATIONAL AMPLIFIER CIRCUITS: “IDEAL” ASSUMPTIONS For easier, approximate analysis of op-amp circuits: Rule 1: Assume A = ∞ Since V o finite (limited by rails), Vp-Vn = 0 Rule 2: Assume R i = ∞ No current flows into or out of input (+ and -) terminals

3. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California OPERATIONAL AMPLIFIER: HOW DOES IT DO THAT? Remember: current can flow out of/into op-amp output How? Op-amp is actually connected to positive and negative voltage supplies which set rails and deliver power to output load (via this output current) Utility of Voltage-Follower: If input voltage source cannot provide much power (current), use voltage follower at output to drive a high power load V0V0 +  V IN

4. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California ANALYZING AN OP-AMP: TIPS Step 1: KVL around input loop (involves V in and op-amp inputs) Use Rule 1: Vp-Vn = 0 Step 2: Find the current in the feedback path Use Rule 2: No current into/out of op-amp inputs Step 3: KVL around output loop (involves V o and feedback path) Remember current can flow in/out op-amp output

5. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California EXAMPLE: INVERTING AMPLIFIER V0V0 +  R1 R2 V IN Input Loop Feedback Path Output Loop

6. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California ANOTHER EXAMPLE “SUMMING JUNCTION” AMPLIFIER V1V1 V0V0 +  V3V3 V2V2 RFRF R1R1 R2R2 R3R3

7. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California IN GENERAL: DIFFERENTIAL AMPLIFIERS Amplifiers - needed to restore weak signals Amplifiers - key component in signal detection and conversion -- for example Analog to Digital Conversion Digital systems make extensive use of amplifiers Amplifiers “gone wild” = bistable circuits (flip-flops) Example: at the termination of every digital transmission line (take a pretty lousy-looking degraded pulse and decide if it’s a zero or a one). Example: interrogating a memory cell for its contents ( again, decide if the contents represent a zero or a one) Examples of single-bit Analog/Digital conversion

8. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California COMPARATORS Non-linear device used as 1-bit A/D, simple inverter, etc. Comparator Example with 2V threshold +  V0V0 V IN ++ 2V lower rail upper rail V0V0 Comparator transfer curve Slope is A V0V0 lower rail upper rail Rails are set by design or by power supplies or by “clipping” devices on output A large V0V0 +  High-gain differential amplifier

9. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California COMPARATORS (cont.) Inverter Example with 2V threshold V0V0 +  V0V0 V IN 2V  + V IN V0V0 Symbol lower rail upper rail Inverter transfer curve

10. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California ONE-BIT A/D CONVERSION REQUIRED IN DIGITAL SYSTEMS  pulses in transmission line  comparator regenerated pulses pulses out As we saw, we set comparator threshold at a suitable value (e.g., halfway between rails) Comparator output goes to +rail if V IN > V THRESHOLD and to  rail if V IN < V THRESHOLD.

11. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California D/A CONVERSION Example: Digital representation of sound to analog (so you can hear it!)  D/A conversion The summing junction op-amp provides a simple means of D/A conversion via weighted-adder D/A converter 00 1 01 00 11 0 1 00 1.5 2 0 1 1 0 0 111 1 000 2.5 3 3.5 4 1 00 1 1 0 1 0 11 11 00 11 0 1 111 0 1111 4.5 5 5.5 6 6.5 7 7.5 Binary number Analog output (volts) 0000 000 1 0.5 MSBLSB S1 closed if LSB =1 S2 " if next bit = 1 S3 " if " " = 1 S4 " if MSB = 1 Another way (not shown) is to sum charges instead of current with capacitor networks 4-Bit D/A 8V  + V0V0 5K 80K 40K 20K 10K S1 + -+ - S3 S2 S4  +

12. EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California CHARACTERISTIC OF A 4-BIT DAC Digital Input 0 1 2 3 4 5 6 7 8 0246810121416 Analog Output (V) 1111 1000 0100 0000 0001