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Operational
Amplifiers Explained (part 2)
Bill Naylor, Electronworks Ltd
The article Operational Amplifiers Explained (part
1) should be read before proceeding. The following
article explains some further theory behind the
function of an operational amplifier. You can use
one of our electronic kits to evaluate the theory.
If you have any suggestions for improving this
application note, please drop us a line at:
enquiries@electronworks.co.uk
The operational amplifier is often taught by
examining an ‘ideal’ part. Many amplifiers today are
so good that an ideal part can sometimes be assumed
in circuit design, thus greatly simplifying the
theory behind how an op amp circuit works.
This is best explained by referring to a typical non
inverting configuration shown in FIG 1.
FIG 1
In an ideal op amp the following are true:
-
The input connections (+) and (-) have infinite
input resistance hence take zero current from
the surrounding components.
-
The output can provide enough current to power
any load.
-
The part has infinite gain when amplifying the
input voltage difference at the input
(the voltage between the inputs (+) and (-)),
thus:
 where
A is infinite.
Point 3 is often tricky to understand. It can be
considered in another way: If the amplification (or
gain) is infinite then for any output, the voltage
difference at the inputs is theoretically zero. This
definition is more applicable to how op amps are
used in practical circuits.
In practice, we apply a voltage to one of the inputs
and then feed a fraction of the output voltage back
to the inverting input. This has the effect
of allowing the output voltage to adjust itself to
make sure the two input terminals are at the same
voltage, thus adhering with point 3 above. If the
output is too high, the fraction fed back to the
inverting input tells the amplifier to reduce the
output. Thus we have a self correcting action
happening.
Consider again FIG 1. Let’s apply a voltage (Vin) of
1V to the non inverting pin (+). If the inverting
pin (-) is at zero, the difference between the input
pins is 1V. If the gain of the amplifier is
infinite, the output voltage of the op amp rises (on
its way to infinity). This causes a current to flow
in R2 and R1. This current, by Ohm’s Law, is
represented by:
From our ideal op amp model, if the resistance of
the inputs is infinite, then no current flows into
the (-) input, hence all of the current from the
output flows through R2 and R1.
The voltage developed across R1, again from Ohm’s
Law is:
Or
Now, we know that the output adjusts itself to make
the two inputs equal. From FIG 1 we can see that the
voltage across R1 is the same as the voltage at the
(-) pin of the op amp. If the output adjusts itself
then the voltage at the (-) pin is the same as the
voltage at the (+) pin, or the input voltage.
In fact, rearranging the above equation, we can see
that
or
or
This is our original gain equation for a non
inverting op amp as shown in Operational Amplifiers
Explained (part 1).
The method of applying a small amount of the output
voltage back to the inverting input is called
‘Negative feedback’ and is a trick used in nearly
all op amp circuits. The benefits to the circuit are
that it ensures the gain of the circuit is dependent
purely on the external components around the
amplifier and not on the gain of the amplifier
itself.
Just for the sake of completion, let’s do the same
for the inverting op amp configuration shown in FIG
2.
FIG 2
We can see that the (+) input is at 0V. With
negative feedback, we know that the (-) input will
also be at 0V.
Applying a voltage (Vin) as shown of 1V causes a
current to flow in R1 (from left to right). If the
input resistance to the (-) pin is infinite, no
current flows into this pin, hence all the current
from R1 flows into R2. The output voltage adjusts
itself to make sure both input pins are at the same
voltage (in this case 0V). To ensure the current
continues to flow from left to right, the output
voltage has to go negative with respect to the
voltage at the (-) pin which is 0V.
If the input voltage is Vin then the input current,
from Ohm’s Law, is represented by:
This current has to flow in R2 and flows from left
to right. This current is represented by:
Therefore, equating the current through R1 with the
current through R2
So
Hence
This is the equation for an inverting op amp circuit
as shown in Operational Amplifiers Explained (part
1).
In conclusion, we have now shown how the inverting
and non inverting gain equations are derived. In
fact, if you consider all the currents flowing into
and out of each circuit node in any op amp circuit,
the gain equation (how the output responds to a
given input) can be determined.
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