ComparatorsSumming Amplifiers

Integrators and Differentiators

ComparatorsZero-Level DetectionNonzero-Level DetectionEffects of Input Noise on Comparator OperationReducing Noise Effects with HysteresisOutput BoundingA Comparator Application:

Over-Temperature Sensing CircuitA Comparator Application:

Analog-to-Digital (A/D) Conversion

Summing AmplifiersThe summing amplifier is an application of the inverting

op-amp configuration. It has two or more inputs, and its output is proportional

to the negative of the algebraic sum of its input voltages.

Summing AmplifiersSumming Amplifier with Unity Gain

A two-input summing amplifier

Summing AmplifiersSumming Amplifier with Unity Gain (cont…)

21 IIIT

fININ

fOUT

fTOUT

RR

V

R

VRIIV

RIV

2

2

1

121 )(

2121

ININININ

OUT VVRR

V

R

VV

If all three of the resistors are equal,

Summing AmplifiersSumming Amplifier with Unity Gain (cont…)

In general, a unity-gain summing amplifier with n inputs where all resistors are equal in value has a mathematical expression of

INnINININOUT VVVVV ...321

Summing AmplifiersExample Problem

Determine the output voltage (VOUT) of the circuit below.

If a fourth input of +0.5 V is added to the circuit with a 10 kΩ resistor, what is the output voltage?

Summing AmplifiersSumming Amplifier with Gain Greater than Unity

When , where R is the value of each equal-value input resistor, the gain of the amplifier is now equal to

The general expression for the output is

RR f

RR f

INnINININf

OUT VVVVR

RV ...321

Summing AmplifiersExample Problem

Determine the output voltage for the summing amplifier.

Determine the output voltage if the two input resistors are 2.2 kΩ and the feedback resistor is 18 kΩ.

Summing AmplifiersAveraging Amplifier

A summing amplifier can be made to produce the mathematical average of the input voltages.

This is done by setting the ratio Rf/R equal to the reciprocal of the number of inputs (n).

nR

R f 1

Summing AmplifiersExample Problem

Show that the amplifier produces an output whose magnitude is the mathematical average of the input voltages.

Specify the changes required in the averaging amplifier in order to handle five inputs.

Summing AmplifiersScaling Adder

A different weight can be assigned to each input of a summing amplifier by simply adjusting the values of the input resistors.

The output voltage can be expressed as

The weight of a particular input can be set by the ratio Rf to the resistance, RX, for that input (RX = R1, R2, … Rn).

INn

n

fIN

fIN

fOUT V

R

RV

R

RV

R

RV ...2

21

1

Summing AmplifiersExample Problem

Determine the weight of each input voltage for the scaling adder and find the output voltage.

Determine the weight of each input voltage if R1 = 22 kΩ, R2 = 82 kΩ, R3 = 56 kΩ, and Rf = 10 kΩ. Also find VOUT.

Summing AmplifiersScaling Adder Application:

Digital-to-Analog (D/A) ConversionD/A conversion is an important interface process for

converting digital signals to analog (linear) signals.One method of D/A conversion uses the scaling adder with

input resistor values that represent the binary weights of the digital input code.

Summing AmplifiersScaling Adder Application:

Digital-to-Analog (D/A) Conversion (cont …)

Binary-weighted resistor DAC

Summing AmplifiersExample Problem

Determine the output voltage of the DAC. The sequence of four-digit binary codes represented by the waveforms below are applied to the inputs. A high level is a binary 1, and a low level is a binary 0. The least significant digit is D0.

If the 200 kΩ is changed to 400 kΩ, would the other resistor values have to be changed? If so, specify the values.

Integrators and DifferentiatorsThe Op-Amp Integrator

An op-amp integrator simulates mathematical integration, which is basically a summing process that determines the total area under the curve of a function.

Integrators and DifferentiatorsThe Op-Amp Integrator (cont…)

How a Capacitor Charges RECALL: and Therefore, the capacitor voltage can be expressed as

This expression has the form of an equation of a straight line that begins at zero with a constant slope of IC/C.

RECALL: The capacitor voltage in a simple RC circuit is not linear but exponential.

tIQ C CCVQ

tC

IV CC

Integrators and DifferentiatorsThe Op-Amp Integrator (cont…)

How a Capacitor Charges

If Vin is constant,

Iin is also constant

(inverting input @ 0 V)

(very high input impedance)

i

inin R

VI

inC II

Integrators and DifferentiatorsThe Op-Amp Integrator (cont…)

The Capacitor Voltage

The Output Voltage

Integrators and DifferentiatorsThe Op-Amp Integrator (cont…)

Rate of Change of the Output

Integrators are especially useful in triangular-wave generators.Equation in Time Domain

CR

V

t

V

i

inOUT

dttvRC

tv IO )(1

)(

Integrators and DifferentiatorsExample Problem

Determine the rate of change of the output voltage in response to the first input pulse in a pulse waveform for the integrator. The output voltage is initially zero.

Describe the output after the first pulse. Draw the output waveform.

Integrators and DifferentiatorsExample Problem (cont…)

Modify the integrator to make the output change from 0 to -5 V in 50 µs with the same input.

Integrators and DifferentiatorsThe Op-Amp Differentiator

An op-amp differentiator simulates mathematical differentiation, which is a process of determining the instantaneous rate of change of a function.

Integrators and DifferentiatorsThe Op-Amp Differentiator (cont…)

Apply a positive-going ramp voltage to the input.

Ct

VI CC

fCfROUT RIRIV

CRt

VV f

inOUT

Cin VV

Integrators and DifferentiatorsThe Op-Amp Differentiator (cont…)

Output of a differentiator with a series of positive and negative ramps (triangle wave) on the input.

Integrators and DifferentiatorsThe Op-Amp Differentiator (cont…)

Equation in Time Domain

dt

tdvRCtv I

O

)()(

Integrators and DifferentiatorsExample Problem

Determine the output voltage of the op-amp differentiator for the triangular-wave input.

What would the output voltage be if the feedback resistor is changed to 3.3 kΩ?

BASIC OP-AMP APPLICATIONSREFERENCE:

BASIC OP-AMP APPLICATIONS