Operational Amplifier: Design and applications PDF

Operational Amplifier: Design and applications Dr. Fahad Contents Introduction to Operational Amplifiers. Ideal Operational Amplifier The Inverting Configuration Non-Inverting configuration The Difference-Amplifier Circuit Integrators and Differentiators Challenges: Analog Computers. ...

Operational Amplifier: Design and applications Dr. Fahad Contents Introduction to Operational Amplifiers. Ideal Operational Amplifier The Inverting Configuration Non-Inverting configuration The Difference-Amplifier Circuit Integrators and Differentiators Challenges: Analog Computers.  Introduction to Operational Amplifiers. the IC op-amp is The first op-amp The op-amp is made up of was introduced in used in a vast several transistors 1960 and it had a variety of and some cost of tens of applications resistors usually dollars. nowadays. one capacitor.  Introduction to Operational Amplifiers. Symbols = = =  Ideal Operational Introduction Amplifier to Operational Amplifiers. Functions: Senses the voltage difference between two inputs Multiplies it by a number: For an ideal op amp, the following constraints are always applied:  Ideal Operational Introduction Amplifier to Operational Amplifiers. Characteristics Comments Infinite input resistance (ideal) Does not draw any current. Zero output impedance (ideal) Output voltage does not change with current Output in phase with noninverting input terminal “+” Out of phase with inverting input terminal “−” Infinite Differential/open-loop gain A responds only to difference Zero common-mode gain Infinite bandwidth amplify signals of any frequency with equal gain Single-ended output appears between terminal 3 and ground Output equation The voltage transfer characteristic { − 𝑉 𝐶𝐶 𝐴 ( 𝑣 𝑝 − 𝑣𝑛 ) +𝑉 𝐶𝐶  TheBasics Inverting Introduction to Configuration of Op-Amp Operational Operation Amplifiers. Circuit Configuration Closed loop gain Ideal Practical Input Output For ideal resistance resistance case  TheBasics Inverting Introduction to Configuration of Op-Amp Operational Operation Amplifiers. Derivation of closed loop gain 1 This also known as a virtual short circuit 2 We conclude from step 1 and This also known as a virtual short ground 3 Applying Ohm’s law across 4 Since Op-amp has infinite input resistance, the current flow in the op-amp is zero, hence 5 The current through is given as 6 Applying Ohm’s law to find for 𝐺=𝑣 𝑜 /𝑣 𝐼 =− 𝑅2 / 𝑅1  TheBasics Inverting Introduction to Configuration of Op-Amp Operational Operation Amplifiers. Example Find the output voltage in term of input voltage , a) Assuming ideal OpAmp. b) Assuming practical OpAmp with a) Ideal OpAmp b) Practical OpAmp  TheBasics Inverting Introduction to Configuration of Op-Amp Operational Operation Amplifiers. Application: Weighted Summer Amplifier  TheBasics Inverting Introduction to Configuration of Op-Amp Operational Operation Amplifiers. Example Design a weighted summer circuit based on the given equation: Compare: Obtain relations: =1 , Assume: ,  Non-Inverting Introduction Basics Ideal to ofvs. Realconfiguration Op-Amp Operational Op-Amps Operation Amplifiers. Circuit Configuration Closed loop gain Ideal Practical Input Output For ideal resistance resistance case  Non-Inverting Introduction Basics Ideal to ofvs. Realconfiguration Op-Amp Operational Op-Amps Operation Amplifiers. Derivation of closed loop gain 1 It is still a virtual short circuit 2 We conclude from step 1: and 3 Applying Ohm’s law across 4 Since Op-amp has infinite input resistance, the current flow in the op-amp is zero, hence 5 The current through is given as 6 Applying Ohm’s law to find for 𝑣𝑜 𝐺= =1+ 𝑅 1 / 𝑅2 𝑣𝐼  Non-Inverting Introduction Basics Ideal to ofvs. Realconfiguration Op-Amp Operational Op-Amps Operation Amplifiers. Example Design a noninverting amplifier with a gain of 6. Assume the OpAmp is ideal. Let 𝑅 𝑔=?  Non-Inverting Introduction Basics Ideal to ofvs. Realconfiguration Op-Amp Operational Op-Amps Operation Amplifiers. Application: Voltage follower When connecting a sensor (high impedance) to an analog-to-digital converter (low impedance), the voltage follower ensures the sensor’s signal is not loaded down or distorted.  The Difference-Amplifier Introduction Basics Ideal to ofvs. BasicOp-Amp Operational Real Op-Amps OperationCircuit Amplifiers. Configurations Circuit Configuration Setting =  The Difference-Amplifier Introduction Basics Ideal to ofvs. BasicOp-Amp Operational Real Op-Amps OperationCircuit Amplifiers. Configurations Derivation of differential gain Consider the circuit shown in Figure A, applying superposition as in Figures B & C. Analyzing Figure B, Fig A: Difference Amplifiers Analyzing Figure C, To have equal gain magnitude, we have Setting = to get , then Fig B: Superposition for. The differential gain For convenience, set and. Fig C: Superpostion for.  The Difference-Amplifier Introduction Basics Ideal to ofvs. BasicOp-Amp Operational Real Op-Amps OperationCircuit Amplifiers. Configurations Drawbacks For large differential gain , has to be small. Not easy to vary differential gain. low-input-resistance Solution: The Instrumentation Amplifier Two voltage followers are used to overcome the issue of low input resistance. These voltage followers also have gains for voltage amplifications in the first stage. Thus, the difference amplifier in the second stage has only the task of implementing the differencing function.  The Difference-Amplifier Introduction Basics Ideal to ofvs. BasicOp-Amp Operational Real Op-Amps OperationCircuit Amplifiers. Configurations Example Design a difference amplifier that amplifies the difference between two input voltages by a gain of 8, using an ideal op amp and ±8 V power supplies. So Let And  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations Role of Thump: Both OpAmps use Inverting configuration Consider the inverting closed-loop configuration with impedances Z1(s) and Z2(s)inverting Consider the replacingclosed-loop resistors R1 and R2, the configuration with impedances Z1(s) and Z2(s) replacing resistors R1 closed-loop and R2, the closed-loop gain, or transfer gain, function or transfer is function is given as given as  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations The Inverting Integrator The Inverting Integrator Also called Miller integrator Replace Z1 by R and Z2 by C ThevoltageacrossCisgivenas Since, Consider the inverting closed-loop configuration with impedances Z1(s) and Z2(s) replacing resistors R1 and R2, the closed-loop gain, or transfer function is given as Alternatively, substituting and Where  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations The Inverting Integrator: Drawback. When , at DC The Inverting Integrator: Solution.  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations The Inverting Integrator: Example. Find the output produced by a Miller integrator in response to an input pulse of 1-V height and 1-ms width. Let and. Assuming For = V For =  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations The Differentiator Replace Z1 by Cand Z2 by R Alternatively, substituting Consider the inverting closed-loop configuration with impedances Z1(s) and Z2(s) replacing resistors R1 Thus, and R2, the closed-loop gain, or transfer function is given as For s = jω , is the differentiator time constant  Integrators Advanced Introduction Basics Ideal to ofvs. Basic and Op-Amp Differentiators Configurations Operational Real Op-Amps Operation Amplifiers. Configurations The Differentiator: Example  Given an op-amp differentiator circuit with a 20k resistor 10 Microfarad capacitor, Vin =10V (constant). Find in the circuit after 10 seconds elapses. (Find)  Challenges: Introduction Basics Ideal Basic Analog Applications to ofvs. Op-Amp Operational Conclusions Real of Computers. Op-Amps Operation Op-Amps Amplifiers. Configurations Design OpAmp circuits for the following equation