```6.070 Spring 2019
Dr. James W. Bales
Op Amps:
An op-amp is a 5-terminal device. Two terminals are inputs (the inverting input, IN+ and
the non-inverting input, IN-), One terminal is an output (VOUT), and two are the power
connections (VCC+ and VCC-).
Figure 1. Two symbols for the op-amp.
At times, the power connections (V+ and V–) are omitted from the schematic, but a real
op-amp still needs to be connected to power to work!
Sometimes we power the op-amp off of symmetric positive and negative power supplies
(e.g., +/- 12 V), other times we use a positive voltage and ground (e.g., +5 V and GND).
Golden Rules:
Our model of an op-amp is that it follows the two golden rules.
1) The Op-Amp Inputs draw no current.
2) With Negative Feedback, the output will change to make the inputs be at the same
voltage (i.e., makes +IN = –IN).
(Negative feedback means that there is a path for current to flow between output and the
inverting input (–IN).
Here is the circuit you built during the second lab (note that I labeled the voltage at –IN
as V–:
IF
I IN
RF
VIN
-
VOUT
RI
I IN
+
V −V
= IN −
RI
From Ohm’s lab, we get IIN = (VIN – V-) / RI. Then:
Golden Rule #2 tells us
V− = 0
⇒ I IN =
VIN
RI
Golden Rule #1 requires
I F = I IN
0
⇒ (V− − VOUT ) = I F RF
⇒ −VOUT =
VIN
RF
RI
!R
⇒ VOUT = − % F
' RI
&quot;
&amp; VIN
(
This is known as the Inverting Amplifier. The output voltage is equal to the input voltage
multiplied by a negative constant, with the value of the constant set by the ratio of the
two resistors.
(Notice the minus sign on the right-hand side. By writings Ohm’s law as DV=IR it arises
naturally in our derivation.)
Dr. James W. Bales
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