UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201
CIRCUIT THEORY I
CIRCUITS WITH OP AMPS
The OP AMP has three distinct operating regions – the linear region, in which the output voltage
is proportional to the difference between the two input voltages, and two saturation regions,
where the output voltage takes on the value of either the positive or the negative power supply
voltage. With two simplifying assumptions, we can readily analyze circuits containing these
devices. The assumptions are:

The OP AMP is ideal. The input resistance is infinite, the open-loop gain is
infinite, and the output resistance is equal to zero. There is no current flowing
into the input terminals and there is no voltage difference across them when the
OP AMP is operating in the linear region.

The OP AMP is operating in its linear region. To make this assumption, the
circuit must have a negative feedback path from the OP AMP output terminal to
the OP AMP inverting input terminal.
To analyze a circuit containing an OP AMP, begin by making the above assumptions. Then write
one or more node equations at the OP AMP input terminals. (We don’t write a node equation at
the OP AMP output terminal because we have no way to determine the current flowing into that
terminal.)
4- Step Analysis Process
1. Assume that the OP AMP is ideal and operating in its linear region. Label the two input
nodes of the OP AMP, usually vp for the non-inverting terminal and vn for the inverting
terminal. Label the OP AMP output node, usually vo.
2. If possible, calculate the numerical value of the node voltage at the non-inverting input.
Remember that the ideal OP AMP assumption tells us that there is no current flowing into
the OP AMP. If a numerical calculation is not possible, calculate the voltage at the noninverting input as a function of the source voltage or voltages connected to that terminal.
3. Write a KCL equation at the inverting input. Remember that by assumption, the voltage
at the inverting input is the same as the voltage at the non-inverting input. The node
voltage equation at the inverting input will always involve the output voltage because of
the negative feedback path that allows the OP AMP to operate within its linear region.
Solve the node voltage equation for the voltage at the output node.
4. Examine the voltage at the output node. If the OP AMP is actually operating within its
linear region, the output voltage will be between the two power supply voltages. If it is,
your analysis is complete. If it is not, then the output voltage is not the value that you
calculated, but instead will saturate to the closest power supply voltage.
EXAMPLE
Determine the output voltage.
V1
6V
Rf
20k
R1
vn
4k
4
U1
2
6
R2
vo
3
10k
vp
7 1 5 741
V3
2V
V2
6V
1. Assume that the OP AMP is ideal and operating in its linear region. This allows us to
assume that the currents flowing into the input terminals are equal to zero, and that the
voltage difference between them is equal to zero.
2. Calculate the voltage at the non-inverting input. Since there is no current flowing into the
non-inverting input, there is no voltage drop across the 10 kΩ resistor. Therefore, the
voltage vp = 2 V.
3. Write a node voltage equation at the inverting input.
vn
4000
+
vn - vo
20,000
=0
v n = v p = 2V
v o = 12V
4. Examine the value of the output voltage. If the OP AMP is within its linear region of
operation, the output voltage should be between -6 V and +6 V. Since the calculation
gave the output voltage as 12 V, the OP AMP must be saturated, and the output voltage
is the same as the value of the power supply closest to +12 V, or the output voltage is
equal to +6 V.
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