Chapter 5: Operational Amplifiers

Current division of op amp

i(output)=i(invert) + i(non-invert) + i(V+) + i(V-)

Op amp funtions

Active circuit element designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation, and integration.

What exactly is an op amp?

An electronic device consisting of a complex arrangement of resistors, transistors, capacitors, and diodes. Just treat it as a circuit building block for now.

Linear region mode

-Vcc<=V0=Avd<=Vcc

Pins of an op amp

1, 5, and 8 are irrelevant to us 2 is the inverting input 3 is the noninverting input 6 is the output 7 is the positive power supply 4 is the negative power supply

Ideal op amp

1. Infinite open-loop gain, A is about infinity 2. Infinite input resistance, Ri is about infinity 3. Zero output resistance, R0 is about 0

Two important characteristics of the ideal op amp

1. The currents into both input terminals are 0, due to infinite input resistance. 2. The voltage across the input terminals is negligibly small, i.e. vd = v2-v1 is about 0 or: v1=v2 Thus, an ideal op amp has 0 current into its two input terminals and negligibly small voltage between the two input terminals.

Difference amplifier

A device that amplifies the difference between two inputs but rejects any signals common to the two inputs

What power source must an op amp use?

A voltage supply, though power supplies are often ignored in op amp circuit diagrams for the sake of simplicity

Op amp

An electronic unit that behaves like a voltage-controlled voltage source, also able to be used in making a voltage- or current-controlled current source. Can sum signals, amplify a signal, integrate it, or differentiate it.

Instrumentation ampliier

An extension of the difference amplifier in that it amplifies the difference between its input signals

Inverting and noninverting

An input applies to the noninverting terminal will appear with the same polarity at the output, while an input applied to the inverting terminal will appear inverted at the output

Noninverting amplifier effect

An op amp circuit designed to provide a positive voltage gain

Summing amplifier

An op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs (using the inverting and noninverting amplifier effects).

Cascade connection

Head-to-tail arrangement of two or more op amp circuits such that the output of one is the input of the next.

Thevenin resistance of op amp

Input resistance is the Thevenin equivalent resistance seen at the input terminals, while the ouput resistance is the Thevenin equivalent resistance seen at the ouput

Closed-loop gain

Negative feedback achieved when the ouput is fed back into the inverting terminal of the op amp The ratio of the output voltage to the input voltage when there is a feedback path from output to input. As a result of a negative feedback, it can be shown that the closed-loop gain is almost insensitive to the open-loop gain A of the op amp.

Summary of basic op amp circuits

Page 193 in PDF, table 5.3

Inverting amplifier effect

Reverses the polarity of the input signal while amplifying it

Noninverting amplifier

The input voltage vi is applied directly at the noninverting put terminal, and resistor R1 is connected between the ground and the inverting terminal. Using KCL, i1=i2, (0-v1)/R1=(v1-v0)/Rf, but v1=v2=vi so: v0=(1+Rf/R1)*v1

Practical limitation of the op amp

The magnitude of its output voltage cannot exceed |Vcc| i.e. the ouput voltage is dependent on and limited by the power supply voltage.

Inverting amplifier

The noninverting input is grounded, vi is connected to the inverting input through R1, and the feedback resistor Rf is connected between the inverting input and output i1=i2, and using KCL (vi-v1)/R1=(v1-v0)/Rf, and since v1=v2=9 for an ideal op amp, v0=-Rf*vi/Ri

What do all three modes of the op amp make up?

The total range of an op amp

Negative saturation mode

v0=-Vcc

Output voltage

v0=Avd=A(v2-v1) where A is the open-loop voltage gain, the gain of the op amp without any external feedback from output to input

Positive saturation mode

v0=Vcc

Differential input voltage vd

vd=v2-v1, where v1 is the voltage between the inverting terminal and ground and v2 is the voltage between the noninverting terminal and ground