Operational amplifiers
1) Amplifier differentiates them:
It is a circuit that it supplies in escape marks them
proporziona them to the two marks them of income 
where To1 it is the
amplification reported to not inverting door 1 when door 2 is in short
circuit. If To1= To2= Tod it is had that 
while if To1 ¹ To2 I can write generator V1 as sum of two generators 
and equally for generator V2 has 
and therefore applying the
superimposition of the effects has that Vu equal feeding is sum of the V
u deriving from the application to the circuit of one and
of the Vu deriving from the
application to the circuit of un0' uneven feeding, that is 
con 
e 
naturally for an amplifier differentiates them
ideal is had Tos infinitesimal
respect to Tod and comes
therefore defined 
the which it determines the
quality of the amplifier differentiates them, as well as more good how
much h®¥ .
2) Amplifier differentiates them with emettitore connection:
It is come true by means of two npn having in common the emettitore that through a R resistanceand is connected to a various battery from that one which the resistances of collector are connected both, in such a way increases dynamics.
On the bases of the transistors the two are applied mark them of famous income and that one of the two does not come invert while the other comes sfasato of 180°. 3 exited different can be had:
to) exited canted between the collector of Q1 and mass
b) exited canted between the collector of 2Q and mass
c) exited balanced between the collector of Qthe 1 and collector of Q2
The gain of common way Tos can be calculated through Bartlett considering the
semicircuit with the resistance of emettitore 2Rand , 
is obtained
while for the calculation of Tod the circuit considering it has a short circuit on the
emettitore and the generator is worth 
, is
obtained 
. Dividend the two values finds to you
finds that 
and therefore as well as more is
elevated the how much largest one is Rand .
3) Amplifier differentiates them with generator of constant current:
This configuration has been developed in how much in order
to approach itself the amplifier condition differentiates them ideal
is necessary to have a Rand much
high one, but this on the escape characteristics is equivalent to
diminish the slope of the straight one of cargo, and therefore to
lower the job point in such a way, reducing dynamics, in order to
obviate to this problem could be increased the value of the battery
but that could damage the emettitore splice base if the inverse
polarization is too much intense. The problem comes resolved
replacing Rand with a generator
of constant current constituted from npn having a collector connected
to the emettitori of Q1 and
2Q and the emettitore
connected through R3 a - VEE which goes to feeding
also the partitore of tension of base R1, R2 with Rhaving in 2 series a
diode valve, obtains for the currentthe 0 that slides in the collector the value 
that it is simplified in 
the if putting in series two diode valves is
succeeded to verify 
.
4) Characteristic of transfer of the amplifier differentiates them:
It expresses the value ofthe C1 and ofthe C2 in function of the potential difference them present to the
clips of income, being 
e 
, has 
deriving it
respect a vB1 â " vB2 obtains the
transconduttanza that in the casethe C1 =the C2 is worth 
employee therefore fromthe 0 therefore the amplifier
differentiates them can be used like circuit AGC. It is observed
moreover that the linear region in which is had that the escape
current is proporziona them to the difference of the income tensions
is limited to the region in which such difference he is smaller of
50mv therefore such circuit can be used also like limiter.
5) Characteristics amplifier operational:
to) infinite Gain of tension
b) infinite Stiffness of income
c) Stiffness of null escape
d) Relationship of common reiezione infinitely
and) infinite Band
It observes that in the linear behavior if Tov® ¥ it imposes that for having one exited ended must be vin = v - v- = 0 while being R = the ¥ must be = the 0 therefore operatingly is = the 0, V = 0 that is virtual mass.
6) inverting Amplifier:
The inverting clip does not find to mass while 1
marks themv is applied to
the clip inverting through Z1 and finally Z2 realizes the negative feedback. For the analysis he
is sufficient to observe that if the inverting clip is not to mass, it
is also the inverting clip and therefore 
e
moreover-= 0 thereforethe 1=the 2 is reached therefore the
relation 
that in the Z case1 = Z2 realizes an invester but a stage buffer in how much will
not be able to be never had the income stiffness is not infinite
inasmuch as the income through the stiffness Z 1 is
applied .
7) Sommatore:
The inverting clip is not found to mass while it marks them coming from from n generating are applies you to the clip inverting through n stiffnesses, is then a stiffness that realizes the negative feedback. With the same observations made for the inverting amplifier one obtains that it marks them of escape is the sum weighed of marks them of income.
8) not inverting Amplifier:
1 marks themV is applied on the not inverting clip while the inverting
clip is connected to mass through Z1 and the escape through the stiffness of reaction Z2. In virtue of the structure
i differentiate them must be hadv = v = v1 and therefore characterizing
in the two stiffnesses a partitore of tension 
from which 
and therefore pu² to
come true a stage buffer or pursuer of tension is had is replacing Z2 with a short circuit that
replacing Z1 with an open
circuit.
9) Amplifier differentiates them:
1 marks themV comes applied al to clip inverting through R1 while the resistance R2 realizes the negative feedback, al
inverting clip does not come instead applied marks them V2 through the partitore of tension R3 , R4 . Through the superimposition of the effects the
expression of the V and the V is estimated- and uguagliano obtaining for the escape tension the
expression 
placing 
and
grouping R2 it is reached the
condition, if it is verified has 
however in order to realize the difference well is
necessary to place a buffer on everyone of the two incomes, in fact us
in such a way svincola from the fact that the resistances of income of
the two channels are various.
Il CMRR currency adding and removing the 
amount to 2° the member of the and
observing that if V12 "V have 
, the value of To s and fromit the is obtained therefore 
that stretches to infinite if the relationships of
resistances are much precise.
10) Integrator:
A condenser in the operational feedback is placed of in
configuration inverting, that it determines 
that is the function of transfer of an integrator in how much to
divide for jw in the dominion
of Fourier is equivalent to integrate in the dominion of the time.
The circuit introduces problems to the vlves in how much the
condenser becomes a circuit open and therefore the amplifier more is
not retroazionato and it is behaved like a opened circuit, in the
practical one puts one resistance in parallel to the ability imposing
therefore one frequency of advanced cut.
It is observed that the circuit is behaved as low-pass filter and integral in the feature to slope â?"20dB/decade.
11) Shunt:
It is had operational in configuration inverting with an
ability in place of Z1 that it
determines 
that it is the function of
transfer of a shunt in how much to multiply for jw in the dominion of Fourier is equivalent to derive
in the dominion of the time. The circuit introduces problems to
vhf in how much the condenser to vhf becomes a short circuit and
therefore tension v is had on the inverting clipin and on the inverting clip the mass while for
definition the two clips must be found to the same one does not
upgrade them, in the practical one puts one resistance in series to
the ability imposing therefore one frequency of inferior cut.
It is observed that the circuit is behaved as high-pass filter and derives in the feature to slope 20dB/decade.
12) Realization of a generator of reference tension:
The tensions of reference realized with batteries or zener
are in kind distributed current function, in order to resolve such
problem an not inverting amplifier is used having on clip the
battery or the tension of zener that it can be obtained using the
feeding of the operational one, the escape tension is therefore 
can therefore be obtained greater tensions of
reference of VZ while in order
to obtain inferior tensions is necessary to insert a partitore of
tension to goes them of the zener. The previous outline has the
defect that the feeding of the operational one can be slices from
ripple then convene to directly feed the zener with the escape
tension, in particular it comes inserted in place of the resistance of
negative feedback, the circuit is completed from trimmer a place
between the clip of escape of operational and the having mass and the
connected mobile contact to the positive clip. The equality of
the tensions to the income clips is 
from which
is obtained therefore acting on the trimmer
can compatibly be obtained in escape whichever greater tension ofV Z with the feeding.
13) stabilized Local p0wer source:
It is a circuit that independently supplies in escape
always the same tension from the value of the cargo which it is
connected, such function can demand also high currents that for
dissipation reasons cannot be supplied from a integrated circuit like
the operational one that also very it would be lend in virtue of the
low resistance of escape. One uses therefore a pursuer of
emettitore in how much the gain in tension is unitary but the gain in
current is approximately 100, its tension of escape is is sended
through a partitore R1 , R2 to the clip inverting of an
operational one that used for feeding one zener connected to the clip
not inverting of the same one. Uguagliando the tensions to the
clips of income of the operational one 
is obtained and therefore pu² to obtain one
stabilized tension of greater escapeV u of the tension of zener. The circuit is
completed placing of the resistances of protection on the base and on
the collector of the transistor and a condenser
that in short shapes operational as an integrator and avoids that
variations ininfluenti repentine but of the escape tension determine
the instability of the circuit, is observed then that the feeding of
the operational one comes captured to the income of the stabilized
local p0wer source.
Not linear circuits with operational amplifiers
14) Limiter to a level:
A diode valve in parallel to the resistance of reaction is
come true with an inverting amplifier having, in such a way when the
diode valve is blocked (V2 > -
Vg) an operational normal
school is had inverting while when the diode valve leads (V2 < - Vg) is necessary to consider its
direct resistance much lowland in parallel to the resistance of
feedback and therefore one is had in escape tension much lowland.
To the aim to limit to a various tension from vg I can insert one zener in
contropunta with the diode valve that regarding the previous case has
been invert, is had that sin when V2 < VZ Vg2
the diode valve are interdetto and therefore 
, when instead 2 passes in 2
conductionis had V =VZ Vg constant .
15) Limiter to two levels:
It is come true with operational in configuration
inverting with two diode valves zener in contropunta places in
parallel to the resistance of feedback, in such a way alternatively
one of the two zener is behaved from diode valve in conduction and
other from zener, one for the negative tensions and the other for the
positive tensions in how much the positive clip is to mass and
consequently also the clip negative, when instead one 
of the two diode valves is is had
in how much is behaved as the highest resistance and
therefore opens that branch of the circuit.
16) Limiter of precision:
The outline is the same one of the limiter to a level but
it comes added a diode valve (…with the anode towards the
escape) in series to the resistance of feedback and escape V3 comes taken between these two members,
it is had that if V1 < 0 then
V2 > 0 therefore the diode
valve D2 lead and they have 
, if instead V1 > 0 has V2 < 0
therefore D2 is interdetto and
D1 it leads, in short the
escape is 0 in how much comes captured through the R resistance from
one virtual mass.
17) Rectifier to double semiwave:
1 marks themV goes to a sommatore to two incomes is directly that passing
through a limiter of precision whose exited is 
if V < 0 oppure V3 = 0 if Vthe > 0, the resistances of the circuit have all the R
value except that one in series to the diode valve of the precision
limiter that is worth 
in such a way obtains that
the escape of the sommatore is worth
Vi if Vi < 0 or â?"Vi se Vi > 0.
18) Converter AC-DC:
A rectifier to double semiwave with in series to the income two opposite elettrolitici with polarity in how much is had electrolytic if it does not have a head to mass differently draft positive semiwaves and negative semiwaves, in this way at least one of the two works correctly and the introduced errors are equal in the two backs, they have the task to cut via continuous the overlapping one to the sinusoide that agrees to straighten. In the making sommatore part of the rectifier has a electrolytic condenser in parallel to the resistance of reaction, in such a way it comes realized a pass-low filter whose frequency of cut is set up through a trimmer so as to to satisfy the specific one on the ripple moreover be a matter itself of a converter adapted for precision measures is necessary that the escape of the operational ones is 0 when the income is 0, to such aim in order to compensate the offset one puts one resistance between the every not inverting clip of operational and the mass.
19) logaritmico Amplifier:
It is had operational in configuration inverting with a
diode valve polarized directly in place of the resistance of feedback,
for it has 
from which applying to the
logarithm to both the terms 
replacing in it V
is obtained2 = - V ha
. The defect of this configuration is that
it is behaved as amplifier single logaritmico on 3 decades in how much
has one fallen of tension in the body of the diode valve and the
tension applied to the clips is not the same one that have the heads
of the splice, however can be arrived in particular until to 7 decades
inserting a transistor with the base to mass in place of the diode
valve in the which case applying the equations of Ebers-Moll and
replacing 
the nella 
and
observing that VCB @ 0 e 2 V EB =V
, it is obtained 
.
20) antilogaritmico Amplifier:
It is had operational in configuration inverting with a
diode valve polarized directly in place of R1, for it
pertanto 
is had and therefore the escape
tension is proporziona them to the exponential of the income tension.
The problem of this configuration is that much lowland has a
resistance of income therefore needs of a buffer.
21) Realization of an analogic multiplier:
Draft of a circuit that takes advantage of the property of the second logarithm which the sum of the logarithms is equal to the logarithm of the product therefore taken two largenesses of income, if of ago the logarithm, is added and finally the product of the departure largenesses is made the antilogarithm obtaining.
Moreover multiplying the logarithm for one constant the operation of elevation to power can also be realized while changing of sign to the logarithm through an invester the division operation can be realized.
22) Comparatore:
It is a device with an income for marks them and an income for the reference tension, is had that the escape is to the high state when the tension of income v is inferior to the tension of reference vr while the escape is low when the tension of income v is advanced to the tension of reference vr .
23) Operational used like comparatore:
On the two incomes of an inverting sommatore the tension
of reference V is had and it marks them of income V2 while in place of the resistance of
feedback an ideal diode valve is had zener supposed which being the
positive clip of operational to mass (…and therefore also
the that negative) it imposes to the escape the value VZ or - Vg to second of the current that covers it 
, remembering the characteristic of the zener is had that
the release happens for i=0 from which it is obtained that the
reference tension is 
, in agreement with the
comparatore definition if V1 > VR the escape is
low (Vg) otherwise is high (VZ).
24) Comparatore with hysteresis:
It is a device that concurs to make that the escape of the
comparatore commuti from high to lowland for a tension of reference VRH and commuti downstairs to
high for one tension of reference VRL ¹ VRH . The circuit is realized with an operational one in
which income v negative is applied to
the clip while one tension V comes applied to clip through a
resistance R1 , finally the
resistance R2 supplies to the
positive feedback therefore the escape can assume only i values high Vlow 2H and V2L . The reference tension is that
one to the positive clip, its value is estimated with the
superimposition of the effects and changes to second of the state of
the escape in fact if the escape is high V2H has 
while if the escape is
low V2L it has 
. A simplified analysis of the circuit is carried out
placing V=0, the cycle of hysteresis characterized from an amplitude
is determined therefore
(…than it can be varied acting on the resistances and
tensions V2H and V2L ) and from valor the medium 
that concurs of simply traslare the hysteresis cycle
acting on V. It is observed that tensions V2H and V2L is the saturation tensions and can be fixed to i values
VZ and Vg placing one zener between the escape and the clip
inverting from which diparte one resistance towards mass.
25) Detector of peak:
It has the scope memorizzare the maximum value of the shape of wave in income, have 4 possible evolutions:
to) an ideal diode valve with a condenser on the cargo, when the tension on the condenser is greater of the income tension, the diode valve is blocked and therefore the continuous condenser memorizzare the maximum tension that it had, if it marks them of income exceeds this last one, the diode valve leads and the condenser is loaded to the new value.
b) the problem of the previous configuration is that the condenser can be unloaded is on the cargo that on the diode valve the which if blocked it introduces a high resistance but not infinite, moreover it must be considered also fall of upgrades them ai heads of the diode valve when it leads. In order to resolve these problems the group is placed diode valve-condenser in escape from operational having on the clip a negative the Vout captured i heads of the condenser while it marks them of income V comes applied on the positive clip, if it is advanced to tension v0 in escape the diode valve leads and the operational one is behaved like a pursuer, and the condenser is loaded while if vi < v0 in escape from the operational one have a negative tension, the interdice diode valve and the condenser are remained loaded to the maximum previous value.
c) the problem of the previous configuration is that if the diode valve is opened, the feedback ring is opened also and therefore the operational one retroazionato does not stretch to saturate, moreover the condenser can be still unloaded on an eventual cargo, in order to avoid that comes loaded from an operational one in configuration to tension pursuer while the group diode valve-condenser comes carried outside from the feedback of the comparatore of income and the same one comes instead carried out through a diode valve that leads when the other is opened in such a way the operational one does not go in saturation but it follows always the Vin . It marks them of escape comes moreover brought back in income through one resistance RC in order to concur with 1° the operational comparatore to behave itself as a pursuer during the phase of loads.
26) Sample-Hold:
The circuit essentially is constituted from a FET that
leaves to pass only marks them of income when it marks them of
sampling the door in conduction concurring therefore loads with the
condenser place to goes them, when the interdice FET instead the
condenser is maintained memorizzato the last value and in order to
avoid that drainages in this phase have been closed on the resistance
of income of a tension pursuer. Analogous in order to avoid that
during the loaded phase of sampling the circuit the previous stage
comes inserted also in income a tension pursuer. The
dimensioning of the condenser must satisfy two opposite necessity in
fact during the holding phase of it would have to be much large one
while during the phase of sampling it would have to be much small so
as to to load itself instantaneously to the value of the income
tension or would have to be closed on a resistance much lowland
moreover has the problem that if the sampling interval is much short
one, being 
comes demanded of the currents that
the operational one is not in a position to supplying. Part of
the previous problems comes resolved inserting a complementary
symmetry a stage to goes them of the FET with a resistance of
polarization mails between the base and the emettitore, is had that in
the phase of it loads works the npn while in the phase of discharge
works the pnp.
27) Generator of wave quadrant:
An operational comparatore is had in which the tension of
escape V0 is brought back is to
clip through a partitore R2 ,
R3 that through one R' net to
the clip â " connected to mass through a condenser. Be a
matter itself of a comparatore, in escape tensions V can be had only0H and V0L that it implies that to clip the reference
tensions are 
e 
Supponiamo that in escape the condenser isV 0H then begins to load sinché joined to
value VRH the escape with the
comparatore becomes V0L and
therefore the condenser begins to unload itself sin when caught up
value VRL commuta still and
therefore via giving place to a rectangular wave whose width of
T1 = TH obtains imposing 
while the width of T2 = TL is obtained
imposing 
, is observed that if!V0H| = |V0L| 
is had therefore acting on
R' has a rough variation of the period while acting on the
relationship R3/R2 if of it fine variation has one.
So that the condition very is respected places a brace of zener
in contropunta in escape from the operational one separates to you but
from same through one the resistance.
28) Generator of impulses:
Quadrant with a diode valve in parallel to the condenser is constituted from a wave generator place on the inverting clip.
We suppose that in escape there is negative tension VOL , it directly polarizes
the diode valve therefore to the clip â " the tension is had -
Vg while to clip the
tension is had 
therefore if 
is had that V- > V therefore
in escape has VOL that
turns out to be the stable state. The monostable behavior is
obtained sending to a wave quadrant in income to a shunt from which it
exits a positive peak and a peak negative, this last one cut through a
diode valve, such marks applied them to clip renders V > V- and therefore the escape of the comparatore becomes VOH therefore the interdice
diode valve and the condenser is loaded with constant of time t = CR' stretching to VOH but when the comparatore catches
up valueV RH commuta
the escape to value VOL and
therefore the condenser begins to unload itself stretching to
value VOL but reached the
value - Vg the diode valve
in parallel begin to lead and the interdice. The duration of
the interval of time in which V0 = VOH are
given from the 
relation, is obtained 
.
29) Generator of rampa:
A rampa of tension a lot can be obtained simply loading a
condenser ¬, but the linear course has itself for smaller times much
of the time constant in fact replacing the development of Taylor of
the exponential in the expression of only loads with the 
condenser looks at that the course is a rampa but the
development is valid single if the argument of the exponential is
infinitesimal therefore t > >t moreover for having of the times of the order of some
second must be had one VCC much
large one. Naturally VCC great and large R convene to simulate them more than to
implement them really and in order to make that must understand
physics.
From 
the it is observed that if is
constant then integrating it has V=kt that is a rampa therefore if a
rampa is not had is because he is not constant and this because the
condenser is loaded then puts in the circuit a pursuer whom moment for
moment a tension supplies to the mesh that cancels that one of the
generator. The circuit is constituted from the condenser that
must be loaded having a head to mass while the other is fed through
the R resistance from condenser C0 much large one which it comes loaded to VCC through one diode valve cassonetto.
The mesh is closed through a tension pursuer that for as it is
put gives to the mesh a tension that embezzles to that one the heads
of the condenser. An impulse negative on gate of a FET the place
in parallel to the condenser from beginning to loads, the interdice
diode valve and C0 begins to
yield charge to C, the current that slides in the mesh is equal to the
current that loads the condenser and is worth 
that, replacing the budget of loads 
and
collecting Vc(t) it gives back 
with 
and 
which as intentional C e To @ 1 aremuch large in how much C0>>, after all being V'CC > > vc(t), has thatthe c(t) is constant and therefore the escape is one rampa.
