Chapter: Operational Amplifiers / Operationsverstärker. Michael E. Auer

Electrical Engineering Chapter: Operational Amplifiers / Operationsverstärker Michael E. Auer Source of figures: Alexander/Sadiku: Fundamentals of Electric Circuits, McGraw-Hill

Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

OpAmp Basics (1) It is an electronic unit that behaves like a voltage-controlled voltage source. It is an active circuit element designed to perform amplification and mathematical operations of addition, subtraction, multiplication, division, differentiation and integration.

OpAmp Basics (2) A typical op amp: (a) pin configuration, (b) circuit symbol, (b) device (c)

OpAmp Basics (3) The equivalent circuit Of the non-ideal op amp Op Amp output: v o as a function of V d A Open Loop Voltage Gain v d = v 2 v 1 v o = A v d = A(v 2 v 1 )

OpAmp Basics (4) Typical ranges for op amp parameters Parameter Typical range Ideal values Open-loop gain, A 10 5 to 10 8 Input resistance, i 10 5 to 10 13 Ω Ω Output resistance, o 1 to 50 Ω 0 Ω Supply voltage, V CC 5 to 15 V

OpAmp Example Circuit Simulation model

Definition of the Ideal OpAmp An ideal op amp has the following characteristics: Infinite open-loop gain, A V d = 0 Infinite input resistance, i i 1 = i 2 = 0 Zero output resistance, o 0 Ideal Voltage source

Inverting Amplifier Basic Circuit Inverting amplifier reverses the polarity of the input signal while amplifying it v o = f 1 v i A V = f 1 Voltage gain in out = 1 = 0

Inverting Amplifier Equivalent Circuit Polarity!

Inverting Amplifier Example (1) efer to the op amp below. If v i = 0.5V, calculate: (a) The voltage gain, (b) the output voltage, v o and (c) the current in the 10kΩ resistor. Answer: (a) 2.5; (b) -1.25V; (c) 50μA

Inverting Amplifier Example (2) Determine the voltage v o in the circuit below. Answer: v o = 3 v a 12 = -6V

Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinv. Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

Noninverting Amplifier Basic Circuit Non-inverting amplifier is designed to produce positive voltage gain v o f = 1 + 1 v i in out AV = 1+ = =0 f 1 positive!

Noninverting Amplifier Example Calculate the voltage v o in the circuit below. Answer: v o = 7V

Unity Gain Amplifier (Voltage Follower) Special noninverting amplifier with: f = 0 ; 1 = Voltage follower Application as buffer amplifier to isolate one circuit from another

Summing Amplifier Basic Circuit Summing Amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs. + + = 3 3 2 2 1 1 v v v v f f f o ( ) 3 2 1 1 3 1 2 1 1 1 3 2 1 : if v v v v v v v v f o f f f o + + = + + = = =

Summing Amplifier Example Calculate the voltage v o and the current i o. Answer: v o = -8V; i o = - 4.8mA

Difference Amplifier Basic Circuit Difference amplifier is a device that amplifies the difference between two inputs but rejects any signals common to the two inputs. v o = (1 + (1 + / / ) v ) 2 1 2 2 2 v1 1 3 4 1 v o if = v 2 1 2 v = 1 3 4 = 1

Instrumentation Amplifier

Cascaded OpAmps It is an arrangement of two or more op amp circuits such that the output to one is the input of the next. v o = A v 1 with A = A1 A2 A3

Two-stage Amplifier Example Determine 1 to 5 so that v o = -5v 1 +3v 2 and in = 10kΩ. 4 5 2 Answer: 1 = 3 = 10kΩ 4 = 30kΩ 2 = 5 = 50kΩ

Cascaded OpAmps Example Find v o and i o in the circuit shown below. Answer: 350mV, 25μA

Application: DAC Digital-to Analog Converter (DAC) : it is a device which transforms digital signals into analog form. Four-bit DCA: (a) block diagram (b) binary weighted ladder type V f f f f 0 = V1 + V2 + V3 + V4 1 2 3 4 where V 1 MSB, V 4 LSB V 1 to V 4 are either 0 or 1 V

Summary The OpAmp is a high gain amplifier that has high input resistance and low output resistance. An ideal OpAmp has an infinite input resistance, a zero output resistance, and an infinite gain. For an ideal OpAmp, the current into each of its two input terminals is zero, and the voltage across its input terminals is negligibly small. In an inverting amplifier, the output is a negative multiple of the input. In a noninverting amplifier, the output is a positive multiple of the input. In a voltage follower, the output follows the input. In a summing amplifier, the output is the weighted sum of the inputs. In a difference amplifier, the output is proportional to the difference of the two inputs. OpAmp circuits may be cascaded without changing their input-output relationships. Typical applications of the OpAmp considered in this chapter include the DAC and the instrumentation amplifier.