Chapter 2. Operational Amplifiers

Transcription

1 Chapter 2. Operational Amplifiers Tong In Oh 1

2 Objective Terminal characteristics of the ideal op amp How to analyze op amp circuits How to use op amps to design amplifiers How to design more sophisticated op-amp circuits Non-ideal characteristics of op amps 2

3 Introduction Operational amplifier (op amp) Analog computation and sophisticated instrumentation Mid-1960 ma709 the first IC op amp : new era in electronic circuit design High quality op amps with extremely low prices Popularity Versatility Ideal characteristics Easy to design circuits using IC op amp Performance are quite close to those predicted theoretically IC op amp Made up of a large number of transistors, resistors, and a capacitor in complex It will be treated as a circuit building block Study its terminal characteristics and its applications 3

4 2.1.1 Op-Amp Terminals Two input terminals One output terminal dc power to operate Reference grounding point in op-amp circuits is just the common terminal of the two power supplies (no terminal) Other terminals For frequency compensation For offset nulling Figure 2.1 Circuit symbol for the op amp. 4 Figure 2.2 The op amp shown connected to dc power supplies.

5 2.1.2 Function and Characteristics To sense the difference between the two input signals (v 2 v 1 ) Differential-input, single-ended-output amplifier v 3 = A(v 2 v 1 ) Characteristics of the ideal Op Amp Infinite input impedance Zero output impedance Zero common-mode gain = infinite common-mode rejection Differential gain=open loop gain=a Infinite open-loop gain A Direct coupled or dc amplifiers Infinite bandwidth Not used in open-loop configuration To apply feedback to close the loop Table 2.1 Figure 2.3 Equivalent circuit of the ideal op amp. 5

6 2.1.3 Differential & Common-Mode Signals Differential input signal (v Id ): difference between the two input signals (v 1 and v 2 ) v Id = v 2 v 1 Common-mode input signal (v Icm ): average of the two input signals v Icm = 1 2 (v 1 + v 2 ) v 1 = v Icm v Id /2 v 2 = v Icm + v Id /2 6

7 2.2 The Inverting Configuration Not used op amps alone Connected to passive components in a feedback circuit R 2 connected from the output terminal back to the inverting or negative input terminal = Negative feedback If R 2 connected from the output terminal back to the non-inverting or positive input terminal = Positive feedback R 2 closes the loop around the op amp Output impedance level = ideally zero Inverting configuration Non-inverting configuration Figure 2.5 The inverting closed-loop configuration. 7

8 2.2.1 The Closed-Loop Gain Closed-loop gain, G v O v I Gain A is very large (ideally infinite) Difference voltage between input terminals = negligibly small (ideally zero) v 2 v 1 = v O A = 0, v 1 = v 2 Tracking each other in potential Virtual short circuit (whatever voltage is at 2 will automatically appear at 1 Because of the infinite gain A) Virtual ground Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps. 8

9 2.2.1 The Closed-Loop Gain Closed-loop gain: simply the ratio of the two resistances Depend entirely on external passive components Design it as accurate as possible Independent of the op-amp gain (due to negative feedback) R 2 /R 1 is much smaller than A, but stable and predictable Minus sign means signal inversion Inverting configuration Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps. 9

10 2.2.2 Effect of Finite Open-Loop Gain If the op-amp open-loop gain A is finite, i 1 = v I ( v o A ) R 1 = v vo I+ A R 1 v o = v o A i 1R 2 = v o A G v o v I = R 2/R 1 1+(1+ R 2 R1 )/A 1 + R 2 R 1 A v vo I+ A R 1 Figure 2.7 Analysis of the inverting configuration taking into account the finite open-loop gain of the op amp. 10

11 2.2.3 Input and Output Resistances Input resistance R i v I = v I v i I = R 1 1 R1 To make R i high, we should select a high value for R 1 Gain R 2 R 1 is also high, then R 2 could become impractically large Inverting configuration suffers from a low input resistance Output resistance of the closed-loop amplifier is zero Taken at the terminals of the ideal voltage source Ex

12 2.2.4 The Weighted Summer Figure 2.10 A weighted summer. Figure 2.11 A weighted summer capable of implementing summing coefficients of both signs. 12