C3 F5 Electronics R2

8/17/2019 C3 F5 Electronics R2

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C3 / F5 Electronics

F5.1 OPERATIONAL AMPLIFIERS

An operational amplifier (op-amp) is a voltage amplifier which amplifies the difference between the

voltages on its two input terminals. Op-amps often require a dual balanced d.c. power supply, e.g. ±

!". #owever, they will wor$ over a wide range of supply voltages from ±!" to ±!". %he power

supply connections are often omitted from circuit diagrams for simplicity. %he diagram below

shows the typical connections for an op-amp.

"& "

out

'"

&

"out

&"s

-"s

&

(

)*+,'.

"&

"-

"

%he & input terminal is $nown as the non-inverting input and the input terminal is $nown as the

inverting input terminal.

%he output voltage is given by

VVAVout

where A is the voltage gain.

An op-amp is assumed to behave ideally and the general properties of an ideal op-amp include/-• the voltage gain is very large (typically, '0 at low frequencies),

• the ma1imum output voltage is equal to the power supply voltage, (in practice it is about 2"

less),

• it has infinite input resistance so no current passes into the input terminals, (typically ' 3Ω,

so there is an input current of a few nano-amps),

• the output impedance is 4ero so it can supply any required current, (in practice many op-

amps are designed to limit the current to appro1imately !mA),

• the output voltage is 4ero when the two inputs are equal, (in practice there is a small offset

voltage which needs a variable resistor to balance out).

General Amplifier Definitions

An amplifier is designed to produce an output voltage or current which is a magnified copy of the

input voltage or current. 5hen power amplification occurs the e1tra power is provided by the

e1ternal power supply. %he pea$ power output is limited by the power supply voltage. %he gain is

calculated by the ratio of the output quantity to the input quantity.

)V(voltageinput

)V(voltageoutput =gainvoltage

in

out

)(Ppowerinput

)P(poweroutput =gainpower

in

out


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F5.2 VOLTAGE AMPLIFIERS

This section shows how operational amplifers can be used as voltageamplifers.

The Inverting Amplifier

6or most amplifiers, the voltage gain of an op-amp is too large to be of practical use. *t is not

possible to ad7ust the open loop voltage gain of an op-amp to enable them to be used in normal

amplifier circuits so Negative Fee!a"# is used to reduce the overall gain of the circuit. 5ith

negative feedbac$ a proportion of the output signal is 8fed-bac$8 to the input so that it cancels out

some of the input signal and reduces the apparent voltage gain of the whole circuit. 5ith an op-

amp, negative feedbac$ is the only way of controlling the voltage gain of the circuit. %he voltage

gain of the op-amp itself is unchanged but the overall voltage gain of the circuit is reduced

significantly. %he simplest e1ample of this is the Inverting Amplifier.

%he circuit diagram of an inverting amplifier is shown below. %he power supply connections are

not shown, but it is assumed that the circuit is operating from a dual voltage power-supply

e.g. &!". 9 f 7oins the output to the inverting input and provides the negative feedbac$.

9

9

f

'"

"out

"in

&

:

5ith an inverting amplifier, as the input voltage increases, the output voltage decreases and vice

versa. %his is represented in the diagram of an oscilloscope display shown below.

input

output


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*n this diagram, both the input and output traces are to the same scale and so it can be seen that the

output voltage is four times the si4e of the input voltage. %herefore the amplifier giving these traces

has a voltage gain of ; but the output voltage is inverted compared to the input voltage.

The Non$inverting Amplifier

%he circuit for a non-inverting voltage amplifier using an op-amp is very similar to the circuit forthe inverting amplifier. %he only difference is that the two inputs are reversed i.e. the signal is

connected to the non-inverting input of the op-amp and the free end of resistor 9 is connected to

'". %his is shown in the circuit diagram below. Again, the power supply connections are not

shown, but it is assumed that the circuit is operating from a dual voltage power-supply

e.g. &!".

9

9 f

'"

"out

"in

&

:

9 f 7oins the output to the inverting input and provides the negative feedbac$ for the circuit, so

reducing the overall voltage gain for the circuit.

5ith a non-inverting amplifier, as the input voltage increases, the output voltage increases and vice

versa. %his is represented in the diagram of an oscilloscope display shown below.

input

output

Again the output voltage is four times the si4e of the input voltage. %herefore the amplifier giving

these traces has a voltage gain of ; but the output voltage is not inverted compared to the input

voltage.

ince the input voltage is applied directly to the op-amp in this circuit, the input resistance of thisamplifier will be very large ('3Ω). %his should be compared with the input impedance of the

inverting amplifier where the input resistance is equal to % &.


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F5.3 VOLTAGE GAIN CALCLATIONS


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%

V

%

V

f

out

&

in

%he negative sign comes from the current passing from the virtual earth point to the output.


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9earranging gives

%

%

V

V f

in

out

%herefore the voltage gain of the inverting amplifier is determined solely by the two e1ternalresistors and the negative sign indicates that the amplifier is inverting.

*t should be noted that the voltage gain of the op-amp itself (open loop gain) has not been altered@ it

is still very large at low frequencies. ut the voltage gain of the overall circuit (closed loop gain)

has been reduced significantly. Also it is important to realise that the equation is only valid when

the open-loop gain is significantly greater than the voltage gain of the whole circuit. At high

frequencies the voltage gain of the circuit will decrease, since most op-amps are frequency

compensated to ensure that they are stable and do not oscillate.

The Non$inverting Amplifier

9

9 f

'"

"out

"in

&

:

5hen considering the voltage gain of the non-inverting voltage amplifier, it is important to

remember that the output voltage of an op-amp is equal to the differential input voltage multiplied

by the open loop voltage gain.

VVAVout

ince the open loop gain of the op-amp is very large at low frequencies, the voltage at the positive

input terminal and the voltage at the negative input terminal of the op-amp will be almost identical,

so long as the output has not saturated at the power supply voltage. %herefore the voltage at the

negative input terminal of the op-amp will be the same as that of the 7unction of the two resistors % f

and % 1

. %hese two resistors form a voltage divider as shown below.

9

9 f

'"

"-

"out

Vout causes a current to pass through % f and % &. %his current can be found from Ohm8s ?aw.


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% %

VI

&f

out

=

%his current causes a voltage to appear across % &, which is the voltage at the inverting input of the

op-amp. Bsing Ohm8s ?aw,

% IV & ubstituting for I

% % %

VV &

f &

out×

=

ut this will also be equal to the input voltage Vin

since the two op-amp input terminals must have

almost the same voltage, if the op-amp is not to saturate.

)% % (

% VV

&f

&outin

×

%

% &

%

)% % (

V

V

&

f

&

&f

in

out =

%he non-inverting amplifier has the same limitations at high frequencies as the inverting amplifierowing to the frequency compensation of the op-amp, but it does have the advantage of having a

very large input impedance.

F5.! T"E OP#AMP AS A COMPARATOR

%he output voltage of an op-amp is given by

)V$VA(=V $out

where A is the open loop voltage gain of the op-amp ('0) and (V+$V$) is the voltage difference

between the two inputs of the op-amp.

ince the op-amp has a very large open loop gain, A, only a very small difference between V& and

V$ is needed for the output voltage, Vout, to equal the supply voltages. Once this has occurred,

increasing the voltage difference between V& and V$ will not cause any further increase in Vout and

the op-amp is said to be saturated .

%he transfer characteristic for an op-amp is shown below, Vs is the power supply voltage.


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"s&

"s-

"out C volts

Cµ"

saturation

saturation

)*>+'.

-&" D "

- &" D "

-&" - "


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%his characteristic enables the op-amp to compare the two voltages on its input terminals.

*f V& is greater than V$ the output saturates at the positive supply voltage. *f V$ is greater than V&

the output saturates at the negative supply voltage. %his principle can be used to compare two

voltages, a reference voltage and a varying input voltage.

VVVV

VVVV

sout

sout

An op-amp can be used as a comparator either with a dual power supply or with a single power

supply. oth are considered below, as each have their own specific problems when used with real

op-amps.

As an e1ample of the use of a comparator circuit, consider an electronic fire alarm system.

A thermistor is a resistor made from semiconductor materials whose resistance changes with

temperature. %he symbol for a thermistor is shown below

%he most common type of thermistor has a negative temperature coefficient (ntc) which means that

as the temperature increases, the resistance of the thermistor decreases.

%he circuit diagram below shows how the thermistor can be used with an op-amp comparator to

sound an alarm if the temperature goes above a set temperature.

&

(

9

9 2

9 E

"&

"-

Fiode

&"s

("s)*>+'.

'"

Au44er

thermistor

&-

%he circuit operates from a dual power supply, +Vs and $Vs. 9esistors % and % - set the voltage at

the op-amp inverting input terminal, which gives the reference voltage for the comparison with the

non-inverting input terminal. *f % is equal to % -, then the reference voltage will be '", half way

between +Vs and $Vs.

9esistor % & forms a voltage divider with the thermistor. As the temperature of the thermistor

increases, its resistance decreases, and so the voltage at the non-inverting input of the op-amp will

increase. *f V+.V$, then the output of the op-amp will be at "s. %he diode prevents the bu44er

being damaged by being powered the wrong way round.


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5hen V+/V$, the output of the op-amp will switch to +Vs and the bu44er will switch on sounding

the alarm.

%he temperature at which the alarm sounds can be altered by changing the value of any of the

resistors, but the most convenient arrangement is to ma$e % equal to % -, (e.g. '$ Ω) and then use a

variable resistor for % &.

A similar circuit could be used to provide warning lights for a free4er. %he bu44er would bereplaced by two ?Fs (?ight mitting Fiodes), one red and the other green.

&

(

9

9 2

9 E

"&

"-

&"s

("s)*>+'.

'"

thermistor

$ Ω

redgreen

5hen the temperature of the thermistor is high, the output of the op-amp will be positive and the

red ?F will light. 5hen the temperature of the thermistor is low, the output of the op-amp will be

negative and the green ?F will light. %he $ Ω resistor limits the current passing through the

?Fs to a safe level.

I op-amps were ideal, then both o these circuits could be easily converted tooperate rom a single power supply. Unortunately, many real op-amps suerrom the problem that their outputs do not saturate at the power supplyvoltages but usually approximately two volts less. This can be a real nuisancewhen the output o the op-amp is connected to a transistor or even a red !",since both will be switched on permanently, irrespective o the output state othe op-amp, unless precautions are ta#en to prevent this rom happening.

The circuit diagram below shows the fre alarm circuit modifed to operate rom

a single power supply.


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&

(

9

9 2

9 E

"&

"-

&"s

)*>+'.'"

thermistor

Au44er &-red ?,F

$hen the temperature is low, the output o a real op-amp will also beapproximately %&. This is su'cient to ma#e some bu((ers sound, and so a red

!" can be connected in series with the bu((er to prevent this problem. ) red!" has a orward voltage o approximately %&, and so when the output o theop-amp is low, there will now be almost no voltage across the bu((er.

%he modified circuit diagram for the free4er alarm is shown below.

&

(

9

9 2

9 E

"&

"-

&"s

)*>+'.'"

thermistor $ Ω

red

green

$ Ω

%he two diodes provide an additional voltage drop of '.", which will ensure that each ?F hasinsufficient voltage available to light when it is not required.


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F5.5 T$e Sc$%itt tri&&er

5hen any signal is transmitted from one place to another it will suffer attenuation, (become

wea$er), dispersion (spread out) and it will gather noise and interference.

+'.

*f the received signal was 7ust amplified, as shown below, the original waveform would not be

restored and it would be unsuitable for use as a digital signal.

amplifier

received amplified

)*>+'.

*f the received signal was passed through a comparator, as shown below, the noise would cause

stray pulses which would again ma$e it unsuitable as a digital signal.

comparator

received compared

)*>+'.

*n order to restore the digital signal it is necessary to use a circuit called a chmitt trigger. %his

circuit uses positive feedbac$ to create two voltage switching levels instead of the single voltage

switching level of a comparator. %his produces hysteresis, the voltage level needed to ma$e theoutput go high is different from the voltage level needed to ma$e it go low. As a result the circuit

can be set so that it will ignore the ma7ority of the noise on the signal and so not produce stray

pulses.

chmitt trigger

received regenerated

)*>+'.


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%he circuit diagram for an inverting chmitt trigger operating from a single power supply is shown

below.

'"

&

:

"in "out

" (

"&

&2"

'$ Ω

'$ Ω

'$ Ω9

)i$es''

*n this circuit the op-amp functions as a comparator but the reference voltage, produced by the two

'$ Ω resistors connected across the power supply, changes with the value of Vout. Assuming an

ideal op-amp, if Vout is '", then the feedbac$ resistor, 9, will effectively be in parallel with the

lower '$ Ω resistor as shown in the left diagram below.

'"

"&

&2"

'$ Ω

'$ Ω

'$ Ω9

)i$es''

'"

"&

&2"

!$ Ω

'$ Ω

)i$es''

%he two parallel resistors form a !$ Ω resistor as shown in the diagram above on the right. Bsing

the voltage divider formula

V0&(

)'

(&'

(&,V

×

*n order for the output to go high, Vin must go below this voltage. 5hen it does, V 1 will be less

than V+ and so Vout will become 2". %he feedbac$ resistor, 9, is now effectively in parallel with

the upper '$ Ω resistor and so, using the technique above, the reference voltage at V+ will be G".

*n order for the output to go low, Vin must go above this voltage. %his circuit therefore has two

switching levels (;" and G") which are separated by ;" and is less susceptible to the effects of

noise than a comparator circuit.

F5.' O(#)%( (ro*le%s.

>lease see the tudent 5or$ oo$ for suitable tas$s and problems together with appropriate responses.

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C3 F5 Electronics R2