BMED 4490 Sensors and Instruments
Spring 2001
MiniProject #3: Filters and Networks
This project has two parts. The first part is due Wednesday March 7. The second part is
due on Monday March 19 after the Break. You can obtain help on either part this next
Tuesday March 6 at 4pm in JEC4304. Or send an email if you have questions that can be
addressed by that route.
1. Narrow Band Filter (See separate sheet with equations).
The purpose of this part of the project is to show how analysis can be done that
provides information on the performance of a narrow-band filter in reducing noise
levels. This part begins with the information in the presentation by Heather Pichette.
The spreadsheet ‘MINIPROJ.xls’ in the 010228 folder plots the magnitude and phase
angle of the frequency response function against frequency for a two pole narrowband filter. The bandwidth of the filter changes with the damping coefficient. The
filter has a gain of unity when the frequency of the filter input matches the undamped
natural frequency of the filter. Note that the values of  (zeta) and n can be adjusted
in cells directly above the plots of the frequency response.
The transfer function of the two pole narrow-band filter is:
2 n s
H s   2
2
s  2 n s   n
where,
n = undamped natural frequency,
 (zeta) = damping coefficient,
s = j ; =2f; j=  1
The first step in your work is to write down the complete equations that were used to
generate the two plots in MINIPROJ.xls. Your final result should be a single
equation for each plot.
The second step is to add to the spreadsheet to show the noise spectral output of the
filter for representative noise input. The equation for the effect of the filter on the
noise is:
G y ( f )  H ( f ) Gx ( f )
2
where
Gx(f) = Noise Power Spectra at Input,
Gy(f) = Noise Power Spectra at Output, and
2
H ( f ) = Magnitude squared of the filter frequency
response function
For present purposes to illustrate the effect of the filter on noise, please use the
following representation for the Noise Power Spectra at the input.
Gx ( f ) 
1
2
aj  1
where, “a” is A Noise Bandwidth Parameter. A representative value for “a” is
(2*2*104)-1.
This equation shows the noise that would be seen if very broadband white noise (e.g.
electron motion due to thermal influences) was low-pass filtered by an electronic
circuit. Your addition to the spreadsheet should result in a plot of Gy(f) in which a is
an adjustable parameter, located in a spreadsheet cell directly above the plot.
2. Resistance Estimates
This part of the project is concerned with using impedance information to determine
equivalent circuit components for elements in the glove safety instrument design.
Starting with Dan Casimiro’s presentation (slide 3), we can find the resistance and
capacitance equivalents for the surgeon’s skin. To quote from Dan’s PowerPoint:
At a minimum, the surgeon’s impedance due to his skin is approximately
200 k at 1 Hz and 200  at 1 MHz
The skin is modeled to a first order representation as
parallel resistance and capacitance, as shown to the
left. The impedance is given by:
Z ( s) 
R
; where s=j; =2f
sRC  1
(1)
In this instance, when  is very small, Z=R. Therefore, as a first approximation, R is
200K. Equation (1) above is then solved for C at a frequency of 1MHz. To do this
we work with the magnitude of Z, which is 200  at 1MHz. The magnitude of the
numerator of equation (1) is just R. The magnitude of the denominator of equation (1)
is (CR) 2 . The calculation should yield a value for C of 8*10-10 f. Please check
to see if you obtain the same value.
The same approach can be applied to the spreadsheet ‘glove data.xls’, which
contains information about impedance under a variety of experimental measurement
conditions. The starting point is equation (1), which shows the relationship of
impedance to resistance, capacitance and frequency. The remainder of project is to
obtain numerical values for the glove hole resistance and glove capacitance, with
adjustment for the multimeter impedance and for that of the rest of the circuit. The
approach described here builds upon the presentation by Jean Riedell.
The column in the spreadsheet labeled SG volt (signal generator voltage) is for the
circuit shown below. We see that the Multimeter is able to read a result of 6 volts
from 20Hz to 20KHz.
Next we look at Z1=inf, in which case the circuit includes the series resistor of 1M
as follows. There is no glove, just the multimeter with its internal resistance and
capacitance. The capacitance CMM may also include capacitance of the wiring to the
multimeter.
For this arrangement, the data shows 5.3 volts at low frequencies, and we ignore the
capacitance at low frequencies, as a first approximation. The voltage divider has 6
volts from the signal generator and 5.3 volts across the Multimeter. What is the
resistance RMM? The answer is 7.6 M. Please check to see if you obtain the same
answer.
The next step is to find the capacitance CMM. At a frequency of 2KHz and Z1=inf,
the Multimeter reads 4 volts. The voltage divider impedance relationship is shown in
equation (2). The brackets are present to show that we are looking just at magnitudes
of the complex impedance, although the equation without brackets and including
phase applies as well. In equation (2), ZMM is the impedance of the Multimeter. This
equation has only one unknown, which is C and the equation can be solved for C.
What is the value of C?
VMM
10 6
 6
VSG
10  Z MM
(2)
The spreadsheet column labeled Z1no hole shows what happens when the glove is
present and its capacitance CG is in parallel with CMM. Since parallel capacitances
add, the previous procedure for calculation of capacitance can be repeated, but now
with a voltage of 1.2 volts. The calculated capacitance is the sum of the parallel
capacitances. What is CG?
Finally, we have the hole present. The approach is similar to previous calculations,
but not only is the glove capacitance present, the hole resistance is present. The hole
is in parallel with RMM. What is the value of RMM?
You could consider using any frequency between 20Hz and 2 KHz for the
calculation. Note that at 20Hz, the glove capacitance appears to have an effect, albeit
small, on impedance (or else our assumption of infinite resistance without a hole is
only approximately correct). If you want to ignore this small effect, go ahead. For
extra credit, you could check at more than one frequency to see if the result is similar
at different frequencies.
This Miniproject uses measurements of impedance magnitude only. It should be
noted that Sarah Pluta’s presentation on Lissajous figures is the basis for
measurement of impedance phase as well as magnitude, and would allow for simpler
calculation in some instances, and for calculation in the presence of more complex
circuit configurations.