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E
R
-E
S
E
S
-E
O
I
R
=
R
R
=
R
P
(1)
Then multiplying both sides by RRRP, we obtain
E
R
R
P
= E
S
R
P
+ E
S
R
R
–E
O
R
R
.(2)
Figure 4 yields a second equation relating the amplifier output to its gain and voltage input
E
O
=E
S
(-A) (3)
which when substituted in equation (2) and solved for Es yields
E
R
R
P
E
S
=
R
P
+ R
R
(1+A)
(4)
Normally, the operational amplifier gain is very high, commonly 10,000 or more. In equation (4)
If we let A → ∞
(5)
Then Es→ O
This important result enables us to say that the two input voltages of the comparison amplifier of Figure 4 (and
Figure 3) are held equal by feedback action.
In modern well-regulated power supplies, the summing point voltage Es is at most a few millivolts. Substituting
Es = 0 into equation (1) yields the standard gain expression for the operational amplifier
R
P
E
O
= -E
R
R
R
(6)
Notice that from equation 6 and Figure 4, doubling the value of R
P
doubles the output voltage.
To convert the operational amplifier of Figure 4 into a power supply we must first apply as its input a fixed dc
input reference voltage E
R
(see Figure 5).