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```Operational Amplifier
Ä
It is a three-terminal device with two
inputs, one inverting (- symbol) and the
other non-inverting (+ symbol). The
output signal of the op-amp is given by
the difference between the voltages
applied to the two inputs, multiplied by
the gain A, of the op-amp.
v1
i1 = 0
+
A(v1-v2)
v2
i2 = 0
vo
+
-
-
Features of an “ideal” op-amp:
The input resistance is infinite so that
no current flows into either input of the Circuit diagram of an “ideal” op-amp
op-amp. (note that on the equivalent
circuit they are shown as not connected
to anything inside the op-amp!)
r
r
The output resistance is zero. I.e., the op-amp can drive any load to any
voltage.
r
The open-loop gain (A) is infinite.
r
The output voltage is zero when the input voltage difference is zero.
r
The bandwidth is infinite.
However, there aren’t many truly ideal things around!
Sure I’m not perfect,
but what do you expect
for \$0.80? Every thing?!
+
-
What would op-amps be good for?
•
•
•
•
•
•
•
•
amplifiers,
integrators,
differentiators,
comparators,
precision rectifiers,
oscillators,
filters,
and a whole mess of other things!
Op-amps with feedback:
a
a
+
Positive feedback, is not great for
amplifiers, but good for oscillators.
-
Negative feedback is great (not
always the case when used with
people)! It is used in most
amplifiers and improves your
circuit in several ways.
+
Finally what can you do with Op-amps?
Voltage Follower
It is the simplest op-amp circuit. It is used where an identical “copy” of an
input signal is desired.
V-
Vout
Vin
+
-
V+
+
As for all op-amp circuits using negative feedback, the circuit automatically keeps
the voltage difference between the two inputs at zero (or very nearly so!).
Clearly V- = Vout
A
The basic op-amp equation: Vout = A.(V+ - V - ) => Vout = A + 1V+
Since op-amp’s open-loop gain is very large (infinity for the ideal op-amp), the
output voltage thus equals the input voltage.
The Inverting Amplifier
The next op-amp configuration is the inverting amplifier, which produces
an inverted output with respect to the input signal. The output signal
is also amplified by a factor that is determined by the ratio of the the
two resistors (some gain at last!).
ifb
R2
R1
Vin +
-
V-
iin
V+
V+ = V− = 0
Vout
+
To see why the V- input must be at or
near ground in this case, consider that
V o u t = A (V + − V − ) ⇒ V − = −
∴ V − → 0 as A → ∞
iin = i fb
V
Vin
and i fb = − out
R2
R1
V
V
R2
Vin
or in = − out ⇒ V out = −
R1
R2
R1
iin =
V out
A
The Non-Inverting Amplifier
i2
R2
R1
V-
i1
Vin +
-
V+
Vout
+
V− = V+ = Vin
Since no current flows into an ideal op - amp, i1 = i2 or
Vout − V− V−
V
R2
=
⇒ out = 1 +
R2
R1
Vin
R1
BASIC PARAMETERS OF OP-AMPS
Offset voltage- If an op-amp were perfectly balanced, the DC output voltage, Vo,
would be zero when no differential voltage is applied to the inputs. owing to
minor unbalances, this is not the case. A real op-amp can be thought of as a
perfect op-amp with a small offset voltage, Voff, applied differentially to the
inputs.Owing to the large voltage gain, even a small Voff can result in a large Vout.
Many op-amps have two pins to which an external potentiometer connected to a
DC voltage can be connected to “null” out Vout.
Slew Rate (SR)- Since op-amps are not infinitely fast, their gain decreases as
the input frequency increases. This makes sense, since for a higher frequency,
the transistors inside must swing the output faster and faster to reach the same
output amplitude. This brings us to the term slew rate, which specifies the
maximum rate at which the op-amp can swing its output. Slew rate is traditionally
given in units of V/ µs.
Bandwidth- A very important fact is that the product of the gain and the
frequency is constant at any point on the response curve of the amplifier. That
means that you are always trading off gain for frequency response. The more
gain, the sooner the response begins to roll off. The gain-bandwidth product is a
key parameter in the selection of op-amps since it expresses the limits for
amplification / frequency response performance.
Common-Mode Signal Rejection- If op-amps were perfect difference
amplifiers, then the output should always be zero if you apply the same signal to
the non-inverting and inverting inputs at the same time. Well, op-amps are not
perfect at this either! Such a signal, applied to both inputs at the same time, is
called, a common-mode signal. Common-mode rejection is important to consider
because often external noise (such as 60 Hz hum) is applied to op-amps
unintentionally.
Output Voltage Swing- While the op-amp can swing its output nearly to the
supply voltages (usually +/- 12 or 15 volts), it obviously cannot swing them
farther. If an input signal is so large that the op-amp circuit’s gain calls for a
swing beyond the supply voltages, the amplifier’s output will clip. In another
word, for an op-amp to function linearly, the output voltage and output current
must be less than saturation voltage and saturation current. This is the effect
that causes the nasty audio distortion when you turn an amplifier up too loud.
(Attention for rock & roller fans!)
Other Op-Amp Parameters- There are some other op-amp parameters that are
often considered (but will not discussed here), such as noise performance of the
op-amp, stability, its power consumption, its input resistance (sorry folks, it is not
infinity!) and still some other parameters. The interested student (is there any