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lecture 2 operational amplifiers

Goals. Understand behavior and characteristics of ideal op amps.Demonstrate circuit analysis techniques for ideal op amps.Characterize inverting, non-inverting, summing and difference amplifiers, voltage follower and integrator.Learns factors involved in circuit design using op amps.. 2. Ideal Operation Amplifier (Op Amp).

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lecture 2 operational amplifiers

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    1: Lecture 2 Operational Amplifiers

    3: Ideal Operation Amplifier (Op Amp)

    4: Ideal Op Amp Example

    5: Ideal Op Amp Example (Alternative Approach)

    6: Operational Amplifier Complete Model Represented by: A= open-circuit voltage gain vid = (v+-v-) = differential input signal voltage Rid = amplifier input resistance Ro = amplifier output resistance

    7: Operational Amplifier Mathematical Model: With Source and Load RL = load resistance RS = Thevenin equivalent resistance of signal source vs = Thevenin equivalent voltage of signal source

    8: Ideal Operational Amplifier Ideal op amp is a special case of ideal differential amplifier with infinite gain, infinite Rid and zero Ro . and If A is infinite, vid is zero for any finite output voltage. Vid = 0, v+=v- (Virtual Short Model) Infinite input resistance Rid forces input currents i+ and i- to be zero. Summary, Ideal op amp has following assumptions: A=8 , Where A is Open-loop gain i- = i+ = 0, Input resistance is infinite Zero output resistance Infinite bandwidth

    9: Inverting Amplifier: Configuration Positive input is grounded. Feedback network, resistors R1 and R2 connected between inverting input and signal source and amplifier output node respectively.

    10: Inverting Amplifier:Voltage Gain Negative voltage gain implies 1800 phase shift between dc/sinusoidal input and output signals. Gain greater than 1 if R2 > R1 Gain less than 1 if R1 > R2 Inverting input of op amp is at ground potential (not connected directly to ground) and is said to be at virtual ground.

    11: Inverting Amplifier: Example

    12: Non-inverting Amplifier: Configuration

    13: Non-inverting Amplifier:Voltage Gain, Input Resistance and Output Resistance Since i-=0 and But vid =0 Since i+=0

    14: Unity-gain Buffer A special case of non-inverting amplifier, also called voltage follower with infinite R1 and zero R2. Hence Av =1. Provides excellent impedance-level transformation while maintaining signal voltage level. Ideal voltage buffer does not require any input current and can drive any desired load resistance without loss of signal voltage. Unity-gain buffer is used in may sensor and data acquisition systems.

    15: Summing Amplifier Scale factors for the 2 inputs can be independently adjusted by proper choice of R2 and R1. Any number of inputs can be connected to summing junction through extra resistors. This is an example of a simple digital-to-analog converter.

    16: Difference Amplifier

    17: Difference Amplifiers

    18: Difference Amplifier Also called a differential subtractor, amplifies difference between input signals. Rin2 is series combination of R1 and R2 because i+ is zero. For v2=0, Rin1= R1, as the circuit reduces to an inverting amplifier. For general case, i1 is a function of both v1 and v2.

    19: Operational Amplifier Complete Model Represented by: A= open-circuit voltage gain vid = (v+-v-) = differential input signal voltage Rid = amplifier input resistance Ro = amplifier output resistance

    20: Non-ideal Operational Amplifier Various error terms arise in practical operational amplifiers due to non-ideal behavior. Some of the non-ideal characteristics include: v Finite open-loop gain that causes gain error Nonzero output resistance Finite input resistance Finite CMRR Common-mode input resistance v DC error sources v Output voltage and current limits

    21: Finite Open-loop Gain

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