“Op-Amp” Operational Amplifier Non Inverting Amplifier Inverting Amplifier Adder –(and Subtractor using an Inverter) Differential Amplifier Integrator Differentiator Op-Amp name derives from early usage of these elements in performing mathematical operations in analog computers.

Three Ways to Examine Op-Amp Behavior Consider as an Ideal Op-Amp Component Consider as a Feedback Model and Examine Behavior Perform Conventional Circuit Analysis

V E = V IN+ - V IN- V OUT = a * V E V IN+ V IN-

Ideal Op-Amp Model V E = V IN+ - V IN- V OUT = a * V E

Behavior of Feedback Model

of Non Inverting Amplifier

Behavior of Feedback Model

Summary

Circuit Analysis Approach

“Op-Amp” Operational Amplifier Non Inverting Amplifier Inverting Amplifier Adder –(and Subtractor using an Inverter) Differential Amplifier Integrator Differentiator Op-Amp name derives from early usage of these elements in performing mathematical operations in analog computers.

Differential Amplifier Circuit Analysis a (V + - V - )

Differential Amplifier Circuit Analysis a (V + - V - )

Differential Amplifier Circuit Analysis a (V + - V - )

Differential Amplifier Circuit Analysis a (V + - V - )

Differential Amplifier Circuit Analysis a (V + - V - )  Z F / Z G

Common Mode Rejection Ratio v icm v2v2 v1v1 vi1vi1 vi2vi2 v id / 2 v2v2 v1v1  Original Inputs Model of inputs with common- mode and differential-mode components

where A is the differential mode gain and A cm is the common mode gain Ideally: CMRR  Typically: 60 dB  CMRR  120 dB Common Mode Rejection Ratio CMRR

Assumes R 2 = R 4 and R 1 = R 3

Differential Amplifier Circuit Analysis with Component Imbalance

Differential Amplifier Circuit Analysis with Component Imbalance

Differential Amplifier Circuit Analysis with Component Imbalance

Differential Amplifier Circuit Analysis with Component Imbalance

Differential Amplifier Circuit Analysis with Component Imbalance

The Maximum Power Transfer Theorem simply states, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power.

To create the Thevenin Equivalent Circuit we need: 1.Value of the Thevenin Voltage Source 2. Value of the Thevenin Resistance

Input and Output Impedances of Noninverting Op-amp Configuration The unity gain buffer input impedance is much higher than the op-amp input impedance R d. The amplifier output impedance is much smaller than the op-amp output impedance R o. +  RdRd i RoRo RLRL CLCL ioio Av d vdvd vovo vivi + 

Instrumentation Amplifier v out R3R3 v1v1 R2R2 R3R3 v2v2 R1R1 R2R2 R4R4 R4R4 v ref

Instrumentation Amplifier Example Burr-Brown INA118 Parameters: Gain:

Instrumentation Amp (cont.) A feedback network may also be included with the instrumentation amplifier. v out R3R3 v1v1 R2R2 R3R3 v diff = v 2 - v 1 2R 1 R2R2 R4R4 R4R4 R C v2v2