Lab 3 - EE 420L
This lab report contains the following:
-
Lab instructions
-
Part 1: LM324 Operational Questions
-
Part 2: Basic Op-amp analysis
-
Part 3: Offset voltage measurements of 4 different
Op-Amps
-
Part 4: Conclusion
Lab instructions:
Lab
instructions can be viewed and referenced from here
Part 1 – LM324 Operational Questions
This lab will utilize
the LM324 op-amp (LM324.pdf).
Review the data sheet for this op-amp.
For the following questions and experiments assume
VCC+ = +5V and VCC- = 0V.
- Knowing the non-inverting
input, Vp, is at the same potential as the inverting input, Vm, (called
the common-mode voltage, VCM) what are the maximum and minimum allowable
common-mode voltages? Support your answer with an entry from the
electrical characteristics table in the datasheet.
This data can be found in the datasheet for the LM324. The 
is the input common voltage range, which explains
precisely what the maximum and minimum allowable common-mode voltages are. At an
ambient temperature of 
the minimum allowable 
is 0V and the maximum allowable is 
. Therefore, the
maximum allowable voltage is:
.
Figure
1: Common mode input voltage range
- What is a good estimate for
the op-amp's open-loop gain? Support your answer with a plot from the
datasheet and an entry from the electrical characteristics table.
We can use the information detailed in the datasheet provided with
the op-amp to estimate the devices open-loop gain. The open loop frequency
response detailed below shows that at 1kHz the open-loop gain will be about
60dB. Or given 
we will have a gain of 1000. Given this information
and the support from the graph, we can say that 1000 is a fair estimate for the
. Using figure 2 and 4
we can determine that the voltage gain at is approximately 108dB, and that using figure 3,
the gain is 100dB at an entry voltage at most power supply voltages.
Figure
2: Large signal voltage gain
Figures
3,4,and 5: Voltage Gain(left), Large Signal Voltage Gain(center), Open Loop
Frequency Response(right)
- What is a good estimate for
the offset voltage? For worst case design what value would you use?
Given an ambient temperature of we should expect a 2mV as the typical offset
voltage. I would assume a voltage of 9mV as the worst-case scenario as
indicated in the table.
Figure
6: Input offset voltage table
Part 2 – LM324 Operational Questions
Build, and test, the following circuit. Note that a precise value for the 5k
resistors isn't important. You can use 4.7k or a 5.1k resistors.
Figures
7 and 8: Circuit schematic in question(left) and the LTSpice simulated
circuit(right)
- What is
the common-mode voltage, VCM? Does VCM change? Why or why not?
The
common-mode voltage is the voltage at which the small signal voltage will
oscillate. In the circuit above we have 2.5V as our
. This is created by the voltage divider below
the op-amp.
Figure 9: 2.5V DC offset indicated
in our oscilloscope measurement
- What is
the ideal closed-loop gain? (Calculate gain of circuit)
Given the we are using the topology of an
inverting op-amp, the gain can be calculated as follows 
- What is
the output swing and what is it centered around?
The output swing is 100mV as indicated by the SINE
wave input signal in the simulation and is centered around 2.5V. The simulation
of the circuit can be observed in figures 10,11, and 12. Our oscilloscope
measurements produced smoother waves while the function generator was
functioning on the 50
mode, so all inputs and outputs were cut in
half.
can be calculated as follows since it is a
voltage divider:
Figure 10: LTSpice simulation output for Vout and Vin
Figure 11: DC coupled oscilloscope
measurement of the circuits input and output. It can be observed that our
offset is slightly off. This is due to the noise being received from the
circuit implemented on the breadboard. Long wires that cross each other can pick
up ambient noise from neighboring electronics, which can affect the signal. Theoretically
the offsets will be exactly the same for both the input and output.
Figure 12: AC coupled oscilloscope measurement of the
inputs and outputs of the circuit.
- What
happens if the input isn't centered around VCM, that is, 2.5 V?
If the input isn’t centered around then the small signal input and output swings
would oscillate around a different DC offset. This can be more easily observed
below in figure 13. A simple change in produces a different point for the small signal
to swing about. In the case below, the common mode voltage is switched from 2.5V
to 3.0V.
Figure 13: DC offset change
- Provide a
detailed discussion illustrating that you understand what is going on. What
is the maximum allowable input signal amplitude? Why?
The op-amp is receiving a VCM of 2.5V, which is
the voltage that the small signal of 100mV will oscillate around. The gain of
the circuit is determined by 
,
which indicates that the output signal will experience a 
phase shift as indicated in figures 10-12. Additionally,
the op-amp is being operated with a 
and a 
,
so the max input AC voltage can’t exceed 2.5V. The max amplitude can’t exceed 5V
combined. Any higher and we can observe clipping in the circuit.
- What is
the maximum allowable input signal if the magnitude of the gain is
increased to 10? Why?
Maximum allowable input signal would be a 10th
of what was previously stated. We don’t want the total amplitude to exceed 5V,
so we must limit the input to 
.
- What is
the point of the 0.01 uF capacitors from VCC and VCM to ground? Are
these values critical or could 0.1 uF, 1,000 pF, 1 uF, etc. capacitors be
used?
The capacitors serve as decoupling capacitors.
In short, these components serve to limit the amount of noise experienced by
the circuit by discharging any noise detected. The specific values are also not
critical and either of the values listed can be used.
- The data
sheet shows that this op-amp has an input bias current that flows out of
the op-amp's inputs of typically 20 nA. This current flows out of both
the non-inverting and inverting inputs through the resistors connected to
these inputs. Show how the operation of the circuit can be affected if,
for example, R1 and R2, are much larger. Explain what is going on. What
is the input offset current? What does this term describe?
Larger amounts of resistance will lead to much
larger voltage drops, which when added to VCM can lead to an output that is
greater than the before specified max input voltage. If the resistors are
increased to the gigaohm or megaohm range, then the circuit may experience a
different Vcm and may also experience clipping. The input offset current is the
difference between the input bias current at the terminals of the op-amp. As
indicated in the below chart, the typical input offset current is 2nA. These
currents are intended to make sure that current does not flow into the terminals.
Figure 14: input offset current
Figure 15: Our op amp circuit implemented onto a breadboard
Part 3 – Offset
Voltage Measurements of 4 different Op-Amps:
-
Explain
how the following circuit can be used to measure the op-amp's offset voltage.
The following circuit can be used to measure the inputs
offset voltage by observing the topology of the circuit. The inverting terminal
is in series with a 1k resistor and the non-inverting terminal is connected to
VCM. Given the equation for gain that was previously stated for an inverting
topology, we know the gain is -20. Using this information we can ascertain that
the equation for the offset is 
- Note that
if the output voltage is precisely the same as VCM then the op-amp has no
offset voltage (this is very possible). To measure small offset voltages,
increase the gain by increasing RF to 100k or larger. Explain what is
going on.
Increasing Rf to 100k will lead to a gain of
100. This is due to the equation for gain for this specific topology as 
.
The increase in gain will make a more visible difference in offset voltage.
Measure the offset voltage of 4 different op-amps
and compare them.
Part 4 – Conclusions
This lab presented an invaluable insight into the realistic
operation of op-amp devices. Accounting for the offset in an op-amp device allows
the observer to be able to account for differences between their theoretical and
actual observations when designing a circuit. By testing for the offset in the
3rd portion for the lab we were also able to see that the measured
offsets feel within the ranges listed in the datasheets making them a reliable
source to reference when designing circuits. It was also refreshing to see the
comparison of ideal and non-ideal op-amp observations, and how they can change
the outcomes of your circuit design.
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