3 Operational Amplifiers

Gain \=

Vout/Vin

features of an op amp

- one output, two inputs
- V+ and V- are connected high and low
- inverting and non-inverting inputs

open-loop mode

no feedback - no signal path between the output and its inputs

input impedance

resistance to current drawn from the input devices in an AC circuit

output impedance

resistance to current on the output

slew rate

how rapidly the output voltage can change (in V/s) in response to a change in input voltage

common-mode rejection ratio

the ability of the op-amp to reject input signals common to both input leads

ideal open-loop gain

infinite

ideal input impedance

infinite

ideal output impedance

zero

ideal slew rate

infinite

ideal CMRR

infinite

typical open-loop gain

\>100,000

typical input impedance

\>10MΩ

typical output impedance

50-75Ω

typical slew rate

0.5 V/µs to 16 V/µs

typical CMRR

3000-300,000

feedback

adding a fraction of the output signal to the input signal

positive feedback

- output connected to non-inverting input
- usually produces oscillation or saturation
- in phase

negative feedback

- improves stability
- uses part of the output signal to reduce the input signal
- out of phase

voltage difference between the two inputs of an op-amp with negative feedback

virtually zero - provided the output is not saturated

virtual earth

if one input is connected directly to 0 V, the other sits at 0 V provided that the output is not saturated.

open loop gain equation

VOUT \= G0 × (V2 - V1 )

circuit diagram for inverting amplifier

- feedback is delivered through the resistor Rf
- negative feedback, delivered to the inverting input
- non-inverting input is connected to ground
- Vin into Rin into the inverting input

gain of inverting amplifier

G \= -Rf / Rin

input impedance of inverting amplifier

R in

Resistor size in inverting amplifier circuit

\>1kΩ

circuit diagram for non-inverting amplifier

- feedback delivered through Rf to the inverting input
- input signal applied directly to the non-inverting input
- Rin is connected to ground from the inverting input

gain of non-inverting amplifier

G \= 1 + (Rf/ Rin)

input impedance for non-inverting amplifier

input impedance of the op-amp

Resistor size in non-inverting amplifier circuit

\>1kΩ

bandwidth

the frequency range over which the voltage gain is greater than 1/√2 of its maximum value

higher gain...

smaller bandwidth

gain-bandwidth product

Gain x Bandwidth

gain-bandwidth product is...

virtually constant for a particular amplifier

summing amplifier uses

- used as an audio mixer
- digital analogue converter

summing amplifier circuit

- negative feedback through Rf to the inverting input
- both inputs sit at the same voltage, non-inverting input connected to ground
- channel input signals fed through resistor to inverting input

output voltage gain in summing amplifier

Vout \= -Rf (V1/R1 + V2/R2 + ...)

gain of summing amplifier

G \= Vout/V1 \= -Rf/R1
(the output of the amplifier is equal to the sum of the separate inverting amplifier circuits)

voltage follower

a form of non-inverting amplifier

gain for a voltage follower

1

use of a voltage follower

the input impedance of an op amp is high compared to its output impedance and therefore the output impedance allows a higher current to flow than if no voltage follower was used. it is used as a buffer to limit current

clipping distortion

when an output exceeds the saturation level and the top of the waveform is clipped

how to reduce clipping distortion

- increase supply voltage
- reduce voltage gain of amplifier
- reduce amplitude of input signal

slew rate equation

ΔVout/Δt

slew rate required to produce a distortion-free output

2πfVp

f - maximum frequency of the signal.
Vp - peak voltage of the output.

comparator

a sub-system that compares two voltages. Its output indicates which is larger.

what type of gain is used in a comparator?

open loop gain, there is not feedback. the op amp amplifies the difference between the two input voltages

if V2 is bigger than V1...

the output will be in positive saturation (in theory, +VS)

if V1 is bigger than V2

the output will be in negative saturation (in theory, -VS)

comparator switching circuit

- one input is connected to the sensing subsystem
- the other is connected to a potential divider circuit at a reference voltage