The analysis of various op-amp circuits can be further simplified by the following approximation:
Based on these approximations, the analysis of op-amp circuits can be much simplified than before, as shown in the following examples.
As the input current is negligible, i.e.,
, applying
KCL to the node of
, we have
In general,
and
in the inverter can be replaced by two networks
(with impedances
and
respectively) containing resistors and capacitors
and the analysis of the circuit can be carried out easily in frequency domain:
As the input current
is negligible, we have
(
First define
As the input currents are zero, the currents flowing through
and
are equal for both sides, i.e.,
Note 2: If one of the input, e.g.,
is connected to a constant
voltage treated as a reference
, then the differential amplifier
can also be used aa a level shifter. As
Express the output voltage
as a function of both inputs
and
. Find the gain
.
Hint: Analyze the three opamps separately. Assume the voltage at
the middle point of
is zeor, i.e., the
input of each of the
two opamps is grounded through
.
Without feedback, the output of an op-amp is
. As
is
large,
is usually saturated, equal to approximately either the
positive or the negative power supply, depending on whether or not
is greater than
. These two possible outputs, positive and negative,
can be treated as ``1'' and ``0'' of the binary system. The figure shows
an A/D converter built by three op-amps to measure voltage
from 0 to
3 volts with resolution 1 V.
Due to the voltage dividor, the input voltages to the three opamps are, respectively, 2.5V, 1.5V and 0.5V. The output of these opamps are listed below for each of the voltages:
| Voltage (volts) | 0 | 1 | 2 | 3 |
| Opamps Outputs | 000 | 001 | 011 | 111 |
| Binary Representation | 00 | 01 | 10 | 11 |
Integrator
In time domain, as
and
, we have
Differentiator
If we swap the resistor and the capacitor, we get in time domain:
Low-pass filter:
High-pass filter:
Band-pass filter:
Higher than first order systems can be built with multiple integrators, as shown here for a third order system:
From the diagram, we can get
From the diagram, we can get