EMT 212/4 ANALOG ELECTRONIC

II

CHAPTER 2:OP-AMP APPLICATIONS & FREQUENCY RESPONSE

Content

1. Op-amp Application Introduction Inverting Amplifier Non-inverting Amplifier Voltage Follower / Buffer Amplifier Summing Amplifier Differencing Amplifier Integrator Differentiator Comparator Summary

2. Frequency Response

Op-amp Application

IntroductionOp-amps are used in many different applications. We will discuss the operation of the fundamental op-amp applications. Keep in mind that the basic operation and characteristics of the op-amps do not change — the only thing that changes is how we use them

Inverting Amplifier

Circuit consists of an op-amp and three resistors. The positive (+) input to the op-amp is grounded

through R2. The negative (-) input is connected to the input

signal (via R1) and also to the feedback signal from the output (via RF).

Inverting Amplifier

Assume that amplifier operates in its linearly amplifying region.

For an ideal op-amp, the difference between the input voltages V+ and V to the op-amp is very small, essentially zero;

V

V +

0 VV VV

Inverting Amplifier

Hence;

V

V +

11 R

V

R

VVi ininin

Inverting Amplifier

The op-amp input resistance is large, so the current into the +ve and –ve op-amp inputs terminal will be small, essentially zero

Finout RiVV

Fin

out RR

VVVV

1

0V

Fin

out RR

VV

1

1R

R

V

VA F

in

outv

Inverting Amplifier

Currents and voltages in the inverting op-amp

Inverting Amplifier - Example Design an inverting amplifier with a

specified voltage gain.Specification: Design the circuit such that the voltage gain is Av = -5. Assume the op-amp is driven by an ideal sinusoidal source, vs = 0.1sin wt (V), that can supply a maximum current of 5 µA. Assume that frequency w is low so that any frequency effects can be neglected.

Non-Inverting Amplifier

Circuit consists of an op-amp and three resistors.

The negative (-) input to the op-amp is grounded through R1 and also to the feedback signal from the output (via RF).

The positive (+) input is connected to the input signal.

Non-Inverting Amplifier

Input current to op-amp is very small. No signal voltage is created across R2 and hence

so it follows that;

invV

VV

invV

Non-Inverting Amplifier

so RF and R1 carry the same current. Hence vout is related to V through a voltage-divider relationship

+V +

V

I

0I

outF

vRR

RV

1

1

outF

in vRR

Rv

1

1

1

1R

R

v

vA F

in

outv

Non-Inverting Amplifier

The output has the same polarity as the input, a positive input signal

produces a positive output signal.

The ratio of R1 and RF determines the gain. When a voltage is applied to

the amplifier, the output voltage increases rapidly and will continue to rise until the voltage across R1 reaches the input voltage. Thus negligible input current will flow into the amplifier, and the gain depends only on R1 and RF

+V +

V

I

Non-Inverting Amplifier

The input resistance to the non-inverting amplifier is very high because the input current to the amplifier is also the input current to the op-amp, I+, which must be extremely small.

+V +

V

I

Non-Inverting Amplifier

1

2

2

1

1

1

21

2

12

1

11

21

1R

R

v

vA

R

vv

R

v

ii

R

vvi

R

vi

vv

in

outv

o

o

Voltage Follower / Buffer Amplifier This “buffer” is used to control

impedance levels in the circuit – it isolates part of the overall (measurement) circuit from the output (driver).

The input impedance to the buffer is very high and its output impedance is low.

The output voltage from a source with high output impedance can, via the buffer, supply signal to one or more loads that have a low impedance.

Voltage Follower / Buffer Amplifier High input impedance. Low output impedance. Voltage gain = 1

inout VV

1in

outv V

VA

Summing Amplifier

The inverting amplifier can accept two or more inputs and produce a weighted sum.

Using the same reasoning as with the inverting amplifier, that V ≈ 0.

The sum of the currents through R1, R2,…,Rn is:

n

nin R

V

R

V

R

Vi ...

2

2

1

1

Summing Amplifier

The op-amp adjustsitself to draw iin through Rf (iin = if).

The output will thus be the sum of V1,V2,…,Vn, weighted by the gain factors, Rf/R1 , Rf/R2 ….., Rf/Rn respectively.

ini

fi

N

fN

ff

finout

R

RV

R

RV

R

RV

RiV

...2

21

1

Summing Amplifier

Special Cases for this Circuit:1. If R1 = R2 =……= R then:

ini

fi

INnININf

out VVVR

RV .....21

1

Summing Amplifier

2. If R1 = R2 = … = R and VIN1, VIN2, … are either 0V (digital “0”) or 5V (digital “1”) then the output voltage is now proportional to the number of (digital) 1’s input.

ini

fi

Summing Amplifier - Application Digital to Analog Converter

- binary-weighted resistor DAC

Summing Amplifier - Application Digital to Analog Converter

- R/2R Ladder DAC

Differencing Amplifier

This circuit produces an output which is proportional to the difference between the two inputs

R 1

R F

v 1

v 2

R 1

R F

v out+

+

+

+

211

fout vv

R

Rv

Differencing Amplifier

The circuit is linear so we can look at the output due to each input individually and then add them (superposition theorem)

R 1

R F

v 1

v 2

R 1

R F

v out+

+

+

+

Differencing Amplifier

Set v1 to zero. The output due to v2 is the same as the inverting amplifier, so

R 1

R F

v 2

R 1

R F

v out+

+

+

v 1 = 02

12 v

R

Rv fout

Differencing Amplifier

The signal to the non-inverting output, is reduced by the voltage divider:

R 1

R F

R 1

R F

v out+

+

v 2 = 0

v 1+ +

v in

11

vRR

Rv

f

fin

Differencing Amplifier

The output due to this is then that for a non-inverting amplifier:

R 1

R F

R 1

R F

v out+

+

v 2 = 0

v 1+ +

v in

in1

fout v

R

Rv

11

Differencing Amplifier

11

vRR

Rv

f

fin

in1

fout v

R

Rv

11

111

1 1 vRR

R

R

Rv

f

ffout

11

1 vR

Rv fout

Differencing Amplifier

Thus the output is:

Thus the amplifier subtracts the inputs and amplifies their difference.

11

1 vR

Rv fout

2

12 v

R

Rv fout

21 outoutout vvv 211

vvR

R f

Integrator

The basic integrator is easily identified by the capacitor in the feedback loop.

A constant input voltage yields a ramp output. The input resistor and the capacitor form an RC circuit.

Integrator

The slope of the ramp is determined by the RC time constant.

The integrator can be used to change a square wave input into a triangular wave output.

Integrator

The capacitive impedance:sCCj

X c

11

Integrator

The input current:out

out

c

out

i

in sCV/sC

V

X

V

R

VI

1

Integrator

iin

out

sCRV

V 1

Integrator

Thus the output in time domain:

dtVCR

VCRj

V ini

ini

out

1

1

Differentiator

t 0 - t 1

++

0V in

V out

t 0 t 1 t 20

V in

tt 0

t 1t 2

0

V out

Differentiator

The differentiator does the opposite of the integrator in that it takes a sloping input and provides an output that is proportional to the rate of change of the input.

Note the capacitor is in the input circuit. The output voltage can be determined by

the formula below: dt

dVRCV

Cj

RV in

inout

1

Comparator

The comparator is an op-amp circuit that compares two input voltages and produces an output indicating the relationship between them.

The inputs can be two signals (such as two sine waves) or a signal and a fixed dc reference voltage.

Comparators are most commonly used in digital applications.

Comparator

Digital circuits respond to rectangular or square waves, rather than sine waves.

These waveforms are made up of alternating (high and low) dc levels and the transitions between them.

Transitions "High" dc level

"Low" dc level

Comparator

Example:Assume that the digital system is designed to perform a specific function when a sine wave input reaches a value of 10 V

Comparator

Variable voltage source

Digital system

V ref V +

V

Comparator

Comparator

With nonzero-level detection the voltage divider or zener diode sets the reference voltage at which the op-amp turns goes to the maximum voltage level.

(c) Zener diode sets reference voltage

V in

V outV Z

R

+V

+

Comparator

t

+V out (max)

t V out (max)

V out 0

V in 0

V REF

Comparator Waveforms

Comparator

Remember that the comparator is configured in open-loop, making the gain very high. This is open-loop configuration.

This makes the comparator very susceptible to unwanted signals (noise) that could cause the output to arbitrarily switch states.

Comparator

If the level of the pulse must be less than the output of a saturated op-amp, a zener-diode can be used to limit the output to a particular voltage. This is called output bounding.

Either positive, negative, or both halves of the output signal can be bounded by use of one or two zener diodes respectivelyD 2D 1

R i+V Z 2 + 0.7 V

00

V Z 2 0.7 V

V in

Comparator - Application

Over-Temperature Sensing circuit

Comparator - Application

Analog to Digital Converter

Summary

The summing amplifier’s output is the sum of the inputs.

An averaging amplifier yields an output that is the average of all the inputs.

The scaling adder has inputs of different weight with each contributing more or less to the input.

Integrators change a constant voltage input to a sloped output.

Differentiators change a sloping input into a step voltage proportional to the rate of change.

The op-amp comparator’s output changes state when the input voltage exceeds the reference voltage.

Frequency Response of Op-amp The “frequency response” of any circuit is the

magnitude of the gain in decibels (dB) as a function of the frequency of the input signal.

The decibel is a common unit of measurement for the relative magnitude of two power levels. The expression for such a ratio of power is:

Note: A decibel is one-tenth of a "Bel", a seldom-used unit named for Alexander Graham Bell, inventor of the telephone.

Power level in dB = 10log10(P1/P2)

Frequency Response of Op-amp The voltage or current gain of an amplifier

expressed in dB is 20 log10|A|, where A = Vout/Vin. The frequency response of an op-amp has a low-

pass characteristic (passing low-frequency signals, attenuating high-frequency signals).

fc

A

Gain (log scale)

Freq (Hz)

-3 dB point

Frequency Response of Op-amp The bandwidth is the frequency at which the

power of the output signal is reduced to half that of the maximum output power.

This occurs when the power gain A drops by 3 dB. In Figure shown before, the bandwidth is fc Hz.

For all op-amps, the Gain*Bandwidth product is a constant.

Hence, if the gain of an op-amp is decreased, its operational bandwidth increases proportionally.