Chapter 5: Operational Amplifiers

what is the relationship between Vi and Vo for the last shown ap amp inverted circuit

(Vi/R1) = (-Vo/Rf) or Vo = (-Rf/R1)Vi

inverting amplifier example of what it looks like

*NOTE* the voltage source is attached to the inverting terminal

picture of what a noninverting amplifier looks like

*NOTE* the voltage source is attached to the non inverting terminal

negative feedback

- output is fed back to the inverting terminal of the op amp

thus Vo is restricted by

-Vcc <= Vo <= Vcc

two properties of ideal amps are

1) currents into both input terminals are zero 2) Vd = 0

how many pin dual lines does an op amp have

8

which pins are irrelevant to us

8 (unused) 1 and 5 we don't really care about

*Cascaded op Amp circuits start here*

:P

*NOTE* in an ideal op amp, input currents (*i1 and i2*) are *equal to zero*. And *v2 == V1* so *Vd = 0* because V1 - v2 = 0 since they are equal.

:P

*REMEMBER IN IDEAL OP AMPS V1 = V2!*

:P

*start of summing amplifier*

:P

start of *Inverting Amplifier*

:P

start of *NonInverting Amplifier*

:P

cascade connection

A cascade connection is a head-to-tail arrangement of two or more op amp circuits such that the output of one is the input of the next.

voltage gain in decibels

A dB = 20log(A)

open loop voltage gain

A is called this because it is the gain of the op amp without any external feedback from output to input

rework this using *ideal* op amp model

Answer to this specific problem without reworking and using ideal is: 9.00041, 657 μA. I recommend you do this example as is and using the ideal thing

*WHAT DOES THIS MEAN*

As a result of the negative feedback, it can be shown that the closed-loop gain is almost insensitive to the open-loop gain A of the op amp. For this reason, op amps are used in circuits with feedback paths.

closed loop voltage gain *Av* is calculated how

Av = vo/vi = -Rf/R1

what is the voltage gain Av in a non inverting amplifier?

Av = vo/vi = 1 + Rf/R1 * polarity of output is the same as polarity of input*

what can be said about the equivalent circuit in terms of Ro, Ri, Vd?

Ro is the thevenin equivalent resistance as seen by the outputs Ri is the thevenin equivalent resistance as seen by the inputs Vd = V2 - V1

difference amplifier

The next cards will ask you to find KCL at node A, node B

(T/F) if Vd increases beyond the linear range, the *op amp* becomes saturated, that is Vo = Vcc or Vo = -Vcc

True

Vd = V2 - V1, meaning

V1 is the voltage between the inverting terminal and ground V2 is the voltage between the noninverting terminal and ground

what's vo?

Vo = A(Vd) = A(V2 - V1) multiplies the difference sensed by the op amp at the input terminals and multiplies it by the voltage gain A

difference amplifier

amplify the difference between two inputs but rejects any signals common to the two inputs

*op amp* (operational amplifier)

an electronic unit that behaves like a voltage controlled voltage source (VCVS) *AKA* voltage amplifier

why are the input currents equal to 0 in an ideal op amp

an ideal op amp has infinite resistance, which implies there's an open circuit, and open circuits have 0 current *however,* output current is not necessairly zero. Then what is it?

why do op amp circuits have the advantage that they can be cascaded without changing their input-output relationships

because each op amp's (*ideal*) input resistance is infinite and output resistance is 0

why is the voltage across the input terminals equal to zero?

because v2 == v1. why do they equal? because current is 0. V = IR

op amps are widely used because

cheap, fun, easy to use, and versatile

during negative feedback, the ratio of the output voltage to the *inverting* input voltage is called

closed loop gain

what types of gains are there when theres an inverting op amp circuit

closed loop voltage gain *Av* open loop voltage gain by the op amp itself *A*

summing amplified definition

combines several inputs and produces an output of their weighted sums

if Rf = 0 or R1 = infinity, or both, then what is the gain for a noninverting op amp?

gain is 1

what does it mean by a difference amplifier rejects an signals common to both inputs?

if v1 = v2, then the vo = 0, thus this is when a difference amplifier starts behaving like one

the original input signal in a cascade is increased by the gain of...

individual stages

pin 2

inverting input

In conclusion an inverter op amplifier does what to the inverting input?

it changes its polarity, while increasing its magnitude.

how to figure out the overall gain of a cascade

multiply the gain of each individual stage

pin 4

negative power supply V-

pin 3

non inverting input

pin6

output

pin 7

positive power supply V+

each circuit in a cascade is called a

stage

op amp can...

sum, amplify, integrate or differentiate signals

what is a limitation to the op amp

the magnitude of its output voltage cannot be greater than the abs value of the voltage source

(T/F) A non inverting amplifier in an op amp circuit is designed to provide a *positive* voltage gain

true

(T/F) gain for both inverting and noninverting op amp's is dependent on the *external resistors*

true

voltage followers are useful for what?

useful as an intermediate stage or buffer to isolate one circuit from another.

if Rf = 0 or R1 = infinity, or both, then what is vo? what about vi?

vo = vi

what is the name given to a noninverting amp that has Rf = 0 or R1 = infinity, or both? why?

voltage follower (unity gain amplifier) because the output follows the input.

op amps can be used in making

voltage or current controlled current sources

equivalent circuit

w\

when does v1= v2, v= 0 exist in a difference amplifier?

when

when does a difference amplifier become a subtractor?

when r1 = r2 and r3 = r4