EECS 40 Fall 2002 Lecture 12S. Ross and W. G. OldhamCopyright Regents of the University of California DIFFERENTIAL AMPLIFIER + A V+V+ VV 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
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
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
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
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
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
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
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
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
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.
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 Binary number Analog output (volts) 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 S S3 S2 S4 +
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 Analog Output (V)