EE 420L
Analog
Integrated Circuit Design Laboratory
Laboratory
Report 5: Op-Amps III, the Op-Amp Integrator
AUTHOR:
Bryan Kerstetter
EMAIL:
kerstett@unlv.nevada.edu
JANUARY
30, 2019
General
Overview
This laboratory even further introduces operational
amplifiers. While also introducing the op-amp integrator topology. The frequency
response of the op-amp integrator topology will be addressed. Additionally, an
integrator will be designed that will convert a square wave into a triangle
wave.
Prelab
I watched Dr. Baker’s
third video about Op Amps while also reviewing the concepts covered in
my Laboratory
Report 4.
Description
of Laboratory Procedures
{The LM324 is exclusively used
throughout this laboratory}
{During this laboratory we assume that VCC+
= +5V and VCC- = 0V.}
{For oscilloscope images, assume that the
yellow and blue traces are the input and output signals, respectively}
Figure 1
The topology of an op-amp integrator can be seen
below. The output of the integrator is described in equation 1.
[1]
Frequency Response of
the Integrator
The frequency
response of an integrator can be described by equations 2-4.
[2]
[3]
[4]
Figure 2
The circuit as seen in Figure 2 was implemented on the
breadboard. In Figure 2, R1 must be a resistor of a great value. This
resistance is meant to minimize the effect of the op-amp’s offset voltage.
Interestingly, R1 can be neglected throughout calculation because it can be
treated as an open. The circuit will continue to work if R1 remains in the
circuit. However, the offset voltage will influence the output waveform. The unity-gain frequency can be calculated to
be:
[5]
The unity gain frequency is the frequency at which the output
waveform is -3dB the input waveform.
[6]
Therefore, we must determine at what frequency the output
waveform has a magnitude of 141.42 mVpp.
Experimentally we determined the unity-gain frequency to be 220 Hz (Figures 3
and 4).
Figure 3
Figure 4
In simulation and hand calculations, removing the
resistor does not affect the response of the circuit. However, practically an
op amp has an offset voltage. We then removed the 100k resistor. There was
little effect. The output voltage slightly increased in magnitude. The 100k resistor
has little effect on frequency response. The phase shift between the two
signals is around 90. This is to be expected.
[7]
Therefore, we can conclude:
For input signal of 
the output signal will be 
,
see Figure 6. Therefore, we can conclude that when an integrator’s input signal
is a sine wave, the output signal will have a difference in magnitude and a 90-degree
phase shift. Where the difference in magnitude is dependent upon the values of
R, C and the frequency.
Figure 5
Figure 6
The Design of a Square-Wave to Triangle
Wave Generation Circuit
A square-wave to triangle-wave generation circuit can
be designed based upon the following parameters and the topology given in
Figure 2.
·
Input/output signal frequency at 10 kHz
·
Output ramp to swing from 1V to 4V
centered around 2.5V
For this design, we will have the input square wave
that will go from 0V to 5V. The common mode voltage will be 2.5V. The circuit’s
resistor can be found in the following manner:
Based
upon Equation 1:
[8]
[9]
[10]
Let
Vout be 
[11]
[12]
Where,
[13]
[14]
{experimentally measured} [15]
[16]
Therefore,
[17]
The following LTspice model can be
created bases upon the design parameters.
Figure 7
Figure 8
As seen in Figure 8, a triangle wave that meets the
design requirements is achieved. We experimentally implemented the circuit on a
breadboard. As seen in Figure 9, our circuit was successful.
Figure 9
A smaller resistor value or capacitance value, results
in a triangle wave that is larger in magnitude. If the magnitude of the
triangle wave is too large, then the triangle wave will clip.
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420L Spring 2019 Page
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