EE 617 Sensors in Instrumentation 2024
Problem set 1
1. Derive expressions for common mode gain and differential
gain for a difference amplifier that has all resistors unequal
(assume R1, R2, R3, R4 that are unequal).
2. Consider the load cell connected as shown. The strain gages
were all rated at 120 in unstrained condition, however the
values we measure are: P = 116, Q = 125, R = 115, S =
120. Input voltage Vin = 10V is used in the circuit.
a. Calculate the bridge voltage output (Vb) in unstrained
condition. This is the offset voltage of the bridge.
b. You need to make the bridge voltage output zero by
connecting just one resistor as a shunt across one of the
arms of the bridge. Explain with the help of a circuit
diagram, how will you modify the circuit to achieve this.
Calculate the required resistance value.
3. You have joined a company where your manager has asked you to use a pressure sensor
IC that he found at a discount on some company website, in a pressure-sensitive mat that
your company wants to design for analyzing walking patterns of individuals. The pressure
sensitive element has bandwidth of 20kHz, and is connected to an amplifier with signal
bandwidth 100kHz internally inside the IC. To digitize the signal from the pressure sensors,
what is the smallest sampling rate that you must choose for the ADC? Explain your answer.
4. Upon performing a Gage R&R study, the variance due to operators was measured to be
far greater than variance due to equipment error and variance of product characteristic.
Your managers suggest that re-calibration of the equipment will improve the overall
measured variance. Do you agree with their opinion? If you disagree, what would you do
differently?
5. The attached dataset (dataset.txt) was collected from a sensor that generated a voltage
output, using a sampling rate of 20Hz. The measurement was conducted in absence of
any stimulus, so it contains only recording of the sensor noise. Does the measurement
have any flicker noise? You are free to use any programming language of your choice and
corresponding built in libraries to examine power spectral density.
6. You recently joined a start-up company, that has invented a revolutionary sensor (to
measure concentration of pathogen ‘X’) which they claim is the ‘next big thing’ in the field.
One of the engineers who worked with the company had made some measurements on
these sensors before deciding to leave for better options. One of the limitations in the
method used to perform measurements is that each sensor can be used only for one
measurement (use-n-throw mode). Therefore, one cannot measure multiple
concentrations using the same sensor, and has to rely on population statistics. The
engineer had conducted 15 measurements for each concentration, using a new sensor for
each measurement. The company is desperate to announce the revolutionary sensor in
the market and want to publish a datasheet to attract potential customers. Since your
transcript says that you have taken EE617 course at IIT Bombay, they entrust you with this
critical task. The measurements are provided in the file ‘nextbigthing-EE617.xlsx’ (same
data in Sheet1 and Sheet2, use whichever or both sheets as per your convenience. Please
use JMP for this question).
a. Suggest a methodology for quantifying the sensitivity in units of [mV/pg/ml]. ([pg/ml]
is the unit for measurement of pathogen concentration, and the sensor output is
reported in [mV]).
b. Based on the measurements, suggest numbers to be used for min/max spec for
sensitivity [mV/pg/ml]. Justify your answer.
7. Try to recreate Figure 3 and Figure 4 of this paper: Kluge et al. Sensors 17.7 (2017): 1522.
https://www.mdpi.com/1424-8220/17/7/1522
The dataset is freely accessible here: https://osf.io/cfb7e/. Only the file
stride_parameters.csv is relevant for this question. The paper uses R for analyzing this
data and generating the plots. You will find that JMP is much easier to use. Of course, you
will have to figure out how to easily generate the plot. Please look for resources on the
internet and proceed.
8. Dr. Quick and Dr. Quack sell diet plans for weight loss. Some data from participants who
participated in their weight loss plans is attached in the file ‘Diet.xlsx’. Which plan would
you recommend to a friend, for highest chances of success? Analyze using JMP.
9. For the op-amp based inverting amplifier circuit discussed in class using TL072 opamp and
R1 = 10k and R2 = 20k (i.e. inverting gain of –2), calculate RTI noise for each noise
source in the circuit, and find total RMS noise voltage assuming same noise gain for all
noise sources.
10. Let us analyze the impact of feedback on noise.
Consider the feedback loop shown on the right
with noise sources, where n1* is input referred
noise for A and n2* is input referred noise for
B. For simplicity, assume that A and B are
constants (no zeroes or poles).
a. Obtain an expression for the closed loop transfer function, i.e. obtain expression for y
in terms of u, A and B (ignore noise sources).
b. Obtain an expression for input referred noise power un*2.
c. What is the output referred noise power yn*2?
d. For large open loop gain A (e.g. in op-amps, A → ), what parameters does yn*2
depend on?
11. Consider the instrumentation amplifier (INA) circuit shown in the figure below (left).
The equivalent noise model for the INA is shown in the figure on the right below,
where eni is the input-referred voltage noise, eno is the output-referred voltage
noise, and in is the input-referred current noise of the INA. Assume all these noise
sources to be independent.
Now consider the circuit shown below, where an INA is used to amplify the output of
a Wheatstone bridge, and an op-amp (OPA) is used as a buffer to generate the
reference voltage for the INA. The relevant noise numbers for the INA and OPA are
also provided below.
• GBWP: gain-bandwidth product
• All voltage noise numbers are input referred
Calculate the following noise contributions towards RMS voltage noise at the output
(OUT): (please write down expression, and also calculated RMS noise voltage)
a) Noise due to INA
b) Thermal noise due to sensor resistance i.e., Rs/2
c) Noise due to OPA and associated resistors (RF, R1, R2)
d) Total output-referred RMS voltage noise of the circuit, comprising of
contributions from a, b and c above.
