IR = | = | |||
RR | RP | |||
|
|
Then multiplying both sides by RRRP, we obtain
ERRP = ESRP + ESRR –EORR.
Figure 4 yields a second equation relating the amplifier output to its gain and voltage input
EO =ES (-A)
which when substituted in equation (2) and solved for Es yields
ES = | ER RP | |
RP + RR (1+A) | ||
|
Normally, the operational amplifier gain is very high, commonly 10,000 or more. In equation (4)
If we let | A → | ∞ |
Then | Es→ | O |
(1)
(2)
(3)
(4)
(5)
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
| RP | |
EO = |
| (6) |
| ||
| RR |
Notice that from equation 6 and Figure 4, doubling the value of RP 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 ER (see Figure 5).
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