CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
PORTABLE CARDIOTACHOMETER
A thesis
submitted in partial satisfaction
of the requirements for the degree of
Master of Science in Engineering
by
Joseph D. Perret, III
/
January 1976 ·
I
I
The thesis of Joseph D. Perret, III is approved:
California State University, Northridge
December 1975
ii
I
TABLE OF CONTENTS
i.
Page
LIST OF FIGURES
lV
LIST OF SYMBOLS
v
Chapter
l.
INTRODUCTION
1
2.
SIGNAL ANALYSIS
4
3.
SYSTEM DESCRIPTION
14
4.
CIRCUIT DESCRIPTION
17
EGG Preamplifier
17
R-Wave Detector
20
Tach Generator and Comparators
26
Modulator and Tone Generator
30
Power Supply and Tept Oscillator
33
5.
SIMULATOR DESIGN
36
6.
GONG LUSIONS
41
44
BIBLIOGRAPHY
iii
LIST OF FIGURES
Figure
Page
2. 1
Normalized ECG Waveform
6
2.2
Normalized Plot of the Frequency
Distribution of the ECG Waveform
and that of the (sina/a) 2 Function
8
2.3
Isosceles-Triangle Wave
7
3. 1
Block Diagram
Portable Cardiotachometer
15
4. 1
Schematic Diagram of the ECG
Preamplifier
18
4.2
Matched Filter Response
20
4.3
Frequency Response of Two-Pole
Butterworth Filter
22
4.4
Filter Response Versus .Frequency
for the Ideal Matched Filter and
the Bandpass Filter
24
4.5
Schematic Diagram of the R-Wave .
Detector
27
4.6
Schematic Diagram of the Tach
Ge_nerator and Comparators
28
4.7
Schematic Diagram of the Modulator
and Tone Generator
32
4.8
Schematic Diagram of the Power
Supply and Te.st Oscillator
34
5. 1
Schematic Diagram of the ECG
·simulator
37
iv
LIST OF SYMBOLS
Symbol
Definition
An arbitrary angle
cn
Fourier series coefficient
A
Average value of the amplitude
av
Time from zero to 1/2 the triangle wave's base
Period of the waveform
p
Ratio of spectral power density of a known
deterministic signal to that of white noise
S(t)
Spectral power density of known deterministic signal
N(t)
Spectral power density of white noise
so (t)
Resultant power spectral density caused by S(t)
N (t)
Resultant noise spectral density caused by N(t)
H(w)
Filter transfer function with respect to frequency
0
;f -1(
·Inverse Fourier transform
S(w)
1-l (N(t))
1-l (S(t))
t
Maximum time response of the filter
S (w)
n
m
Arbitrary functions
Conditional density function of r given M
r
Output
M
Indicates presence of the input signal
M
Indicates absence of the input signal
E
r
Means value of r
v
i.
I
Symbol
Definition
a
Threshold value of the filter 1 s response
ca
Cost associated with a false alarm
cd
Cost associated with a false denial
P(M/r=R)
A conditional probability which is defined as the
probability of M given that r has value of R
vbatt
Battery voltage
v sat
Saturation voltage
vi
ABSTRACT
A PORTABLE CARDIOTACHOMETER
BY
JOSEPH D. PERRET, III
MASTER OF SCIENCE IN ENGINEERING
JANUARY 1976
In rehabilitative and preventative cardiac patient programs,·
subjects are stress tested in order to establish a target training
heart rate and are then assigned an exercise program based on this
target rate.
As part of their exercise routine, the subjects· m1,1st
stop and palpate the carotid artery and record their pulse :rate.
The next phase of exercise is then adjusted in order to remain just
below or at this pre-established rate.
Research has shown that these rates are often exceeded during
the exercise session due to errors in measurement.
There exists
therefore a critical need for a portable, inexpensive electronic
device which can signal the user instantant::ously when his target
heart rate is not met or exceeded.
A design was presented, in this
study using integrated circuits, to realize the design of a portable
cardiotachometer.
The design included a signal analysis of the
EGG of an exercising subject.
The portable cardiotachometer uses disposable monitor
electrodes to obtain the EGG signal, and produces a solid tone on
vii
a small internal speaker to signify the existence of a low limit in
the heart rate, or a modulated tone to signify that the target rate
is exceeded.
This feedback signal allows the subject to constantly
update his output to remain within the preset limits.
viii
Chapter 1
INTRODUCTION
Within the past few years, the clinician has witnessed the
rapid evolution of the field of electrical monitoring of the heart {35).
Continuous electrical monitoring in corona'ry and intensive care
units has been extended to more sophisticated forms of automatic
electrical monitoring on the general hospital floor {36, 37).
Long
term monitoring with a portable ECG tape recorder has become
increasingly popular for outpatient use.
Telemetry has also been
widely applied to transmit e~ectrocardiogram {ECG) information
from the patient to a remote observer {23).
All of these techniques
require bulky and costly equipment limiting their application.
Data accumulated in recent years strongly suggest that a
lifetime pattern of moderate or heavy regular physical exertion in
an apparently healthy populatio·n,. provides some protection against
sudden cardiac death and myocardial infarction with its resultant
mortality (3, 10, 18).
The means whereby exercise might
accomplish these ends is not totally clear, but it may be possible
that exercise may act directly to retard the progress of arteriasclerosis (8).
It may act to increase or decrease the demand for
cardiac output through more efficient use of the skeletal muscles.
Although, theoretically, exercise could promote intercoronary
collateral circulation, studies using intracardiae angiography have
1
not borne this out (14).
Whatever the reason, however, physical
training is not only prophylactic in the general population, but it
also may increase longevity in those already afflicted with overt
manifestations of coronary heart disease (15, 27).
Exercise also
ameliorates the symptoms of angina pectoris (9).
In rehabilitative and preventative cardiac patients, subjects
are stress tested in order to establish a target training heart rate
(4, 34).
As part of their exercise routine, the subjects must stop
and record their radial or carotid pulse.
They then adjust their
exercise routine to remain just below or at the predetermined
rate (7).
This process has two major disadvantages.
One, the target
heart rate may be exceeded or not maintained during the exercise
periods between measurements (24, 25), thus the correction is
similar to a bang-bang servo system whose time constant is long
in relation to the desired output.
The second disadvantage is the
error due to the measurement procedure.
A subject usually counts
his own pulse for a 10 or 15 second interval, then multiplies the
result by six or four to derive his heart rate in beats per minute
(34).
Due to the rigors of exercise, the physical stature of the
subject, the undesirable competition between subjects, and the
lack of expertise, the subject might easily err in the measurement
(24, 34).
Physicians and physiologists are presently debating formulas
to establish target heart rates.
The results differ by only a few
percent, whereas the actual clinical conditions dictate a measurement and maintenance ability of 10 to 20 percent (24, 34).
It is intuitive that a portable cardiotachometer with instantaneous feedback to the subject in order to assist him in the
maintenance of his target heart rate, would be beneficial.
A study
of the literature did not reveal the existence of such a device.
Several companies are marketing a portable ECG transmitter which
utilizes acoustical coupling for transmission (38).
This device is
primarily designed for remote recording of the ECG waveform but
could conceivably be used to determine heart rate, by counting the
audio phase shifts.
This would still require that the subject stop
and note the beats per minute.
A review of the schematic reveals
no attempt to filter artifact, which would result in false readings
of exercising subjects.
The purpose of this paper is to present the design of a small,
inexpensive, portable cardiotachometer which will provide audible
outputs to an exercising subject when he has ceased to maintain a
predetermined heart rate limit.
The device will utilize conven-
tional monitor adhesive electrodes to process the ECG potential for
heart rate detection.
Chapter 2
SIGNAL ANALYSIS
The ECG signal, which is to be processed, is a rather weak
biopotential associated with the depolarization and repolarization of
the heart muscle tissue. , Depolarization on the surface of the heart
muscle fiber causes the fiber to become electrically negative with
respect to adjacent regions ·of polarized fiber.
Repolarization
makes it electrically positive.
This electrical activity, which starts and coordinates the
heart's mechanical-muscular activity, originates in the rear of the
atrium, in an area called the sinoatricular node.
This SA node, as
it is also called, is the heart's natural pacemaker.
The electrical
depolarization spreads over the cardiac muscle in a chainlike
progression.
As soon as depolarization starts, a current flows
from the inactive region to the active, changing the poiarization
and initiating a response in the inactive region.
The progre:;;sion of changes in membrane polarization over
the heart muscle is called the cardiac potential; its recording is the
ECG or electrocardiogram.
Design specifications for ECG amplifiers or signal conditioners are determined primarily by signal characteristics,
electrode characteristics and application.
4
Signal characteristics
determine such specifications as gain, noise and bandwidth.
Electrode characteristics determine the required input impedance,
the maximum injection current ratio (current that flows in the
source due to connection of the amplifier) and the required common
mode rejection.
The application influences all these specifications
and imposes others such as distortion, linearity, and gain stability.
The spectrum analysis of the ECG waveform shows that
essentially all of the signal is produced with a frequency domain of
from DC to 3000 Hz.
However, to limit the high frequency noise
content, one can limit the amplifier response to 100 Hz and still
capture the ECG signal adequately (12).
This then defines the
bandwidth of the ECG preamplifier.
The noise generated with such an amplifier is derived from
two sources: "Johnson noise'' and ''excess noise''.
Examination of
the equation relating the Johnson noise produced within an amplifier
to its bandwidth indicates that the noise produced is proportional to
the square root of the bandwidth.
Thus one can see that limiting the
amplifier's bandwidth will be of great value in limiting the resultant
Johnson noise.
The excess noise's bandwidth is less than 3000Hz.
Its value also decreases with bandwidth, although not as markedly
as that of Johnson noise (31).
Electrodes are a source of amplifier disturbance.
Their
selection dictates that the amplifier's input impedance be high
(100 KJ1.. or greater) and have a gain of 50.
In addition, AC coupling
must be used to eliminate the electrode offset potential.
The ECG waveform is divided into sections for identification
(6).
As seen below in Figure 2. I, the predominant feature of this
normalized ECG waveform is the R-wave.
R
Q
s
Figure 2. I
Normalized ECG Waveform
Studies (19, 28) have shown 80o/o of the energy of the ECG
waveform is contained in the R-wave._ The R-wave is caused
~y
the repolarization of the atrial and depolarization of the ventricular
section of the heart which occur almost simultaneously.
The
spectral response of the ECG, which can predominantly be attributed
to the R-wave, lies in a band from 0 to 30 Hz (5, 12, 19, 28).
In addition to the signal from the ECG input, the amplifier
will be subjected to an intense level of noise signals resulting from
random noise, pick up, muscle artifact, head movement, stray
radiation, etc.; .all of which can be best defined as white noise in
the region of interest, from 0 to IOO Hz.
An approximation of the ECG waveform can be seen from the
normalized plot of the frequency distribution of the ECG waveform
which is presented in Figure 2. 2.
This curve suggested that a good
.
t"1on can b e ma d e b y us1ng
.
.
approx1ma
a (sina
- - )2 curve, a 1so s h own 1n
a
Figure 2. 2.
An analysis of these curves yields a mean square
error of 0. 014 and a correlation coefficient of 0. 003.
The (sinal a)
2
curve can be realized by an isosceles -triangle
pulse show·n below in Figure 2. 3.
The Fourier analysis of the
waveform yields:
A
av
=
A (t /T)
1
Figure 2. 3
Isosceles-Triangle Wave
It can be seen from the above analysis that the parameters to
.
..
.
be varied are the amplitude, the pulse width and the repetition rate.
The nominal values for the best curve fit to the ECG spectrum are:
2t
1
= 27.8msec
T > 4t
1
This can be seen in Figure 2. 2.
1.0
5NORMA.l.IZ.E.O EC~
,
Figure 2. 2
0.9
Normalized Plot of the Frequency Distribution
of the ECG Waveform and that of the {sino</« )2 Function
0.8
lLI
0
..5(51~(.() 2
:::> 0.7
1~
~
o.o
~
0 0.5
w
t-J
~0.4
:2
Ol
0 0.3
:z
O.l
0.1
.,.,..
4
1'f
"[
3T'I'
511
ff
4
4
FRE:Q.UE:NC.Y
(c.v)
311'
z
7'ii
4
A matched filter can be used to detect the presence of a known
If we define a symbol p
train of pulses which is masked by noise.
which equals the ratio of the spectral power density of a known
deterministic signal to that of white noise, we can define a matched
filter whose transfer function is designated as H(w).
The Schwartz inequality states:
·I
too
J
- 00
F 1 (w) F 2 (w) dw
and if F
1
(w)
=k
I
too
2
:s;
.
J
IF 1 (w)
-oo
2
I
too
dw
2
J IF 2 (w) I
dw
-oo
F /"(w}, the equality holds
Noting that:
and letting: F
1
(w) = H{w) and F
2
p becomes:
too
too
2
2
jH{w) 1 dw
I S{w) 1
-CO
1 -oo
p :s; 1TN
I
(w) = S{w) E"j wtm
J
too
:s;
I
2
I S{w) 1
-CO
-CO
an upper bound
P
=
s
2
{t )
o
m
2
N (t )
o
:s;
1
1TN
I S{w) I
2
dw
m
in order to force an equality
H(w)
= kS~~(w)
:. h(t)
E" -j w tm
= k;it-1 t(-w)
,-iwt~
this then defines the matched filter.
Thus for an isosceles-triangle pulse train, the time response
of the filter, due to symmetry, is that of the triangular wave, but
shifted in time.
There is still an unsolved problem as to the threshold value
of the output which can be used to detect its presence.
A cost
analysis may be run which will yield an optimal value for the
threshold detector.
For the following system:
S (t)+ N (t)
H(w)
S(t)+N(t)
0
0
The resultant signal which.passes through the filter- is:
= r~-1 [S{w)H(w)J
S 0 (t)
1 +co
s 0 (t)
=
2
1i
.
· t
J H(w)S(w)E"J w dw
-co
Where S (t) is a deterministic signal
0
The power spectrum of the noise signal which passes through
the filter is equal to:
E [N
].
2
o
Where:
(t)
1 +oo
= -2 1T j'
-00
I
S (w) H(w)
n
2
I
dw
t1:"'- 1 (N(t))
Sn::o ·,;r
For white noise:
Sn
= ~ - 1 (N{t)) = ~
1
2rr
=
IH(w) I
z· J
-oo
+oo
1
=
N 2 (t) = (2rr) 2
IJ
+oo
=
IJ
where
t
I
· t
·
H(w)S(w)EJw m dw
-oo
+oo
1
1TN
· t
2
H(w)S(w)EJ w m dw
-oo
0
p
dw
p becomes:
Therefore
p
2
+oo
N
2
I
2
J-oo jH(w) I dw
is the maximum time response of the filter.
m
If the signal is pre sent, a conditional density function may
be defined as:
1
=
f (r /M)
r
where
f
r
where
and
E
.;z;,r;;
1
2
r
E
(r/M) =the density function of the output given that
the signal is pre sent
r(t) = S (t)
0
r
--z
(r -E )
+ N 0 (t)
is the mean value of r(t)
M is the fact that the event is pre sent
=
f (rIM)
r
1
vz;~
where f (r /M) =
r
e:
the density function of the output given
that the signal is absent
A value of "a", a constant less
tha~
E, may be chosen which
will be defined as a threshold value .. With this type of system, there
are two errors possible:
present;
1) A false alarm= r <a, the signal is not
2) A false di.smissal = r > a, the signal is present.
A cost may then be assigned to each of these conditions: the
probability of a false alarm. P (FA) has a cost of C a.; the probability
of a false dismissal P (PD) has a cost of Cd.
P (M)
+P
(M) = l.
The total probability:
A conditional probability may be defined such
that:
P(M/r = R) =
P(M/ r = R)
=
probability signal is present, given that its
amplitude is equal to the mean value
probability signal is not pre sent given that its
amplitude is equal to the mean value.
And of course two decisions may be made based on the
condition that r
= R;
that the message is present, and that it is not.
At the ideal threshold value, the average cost of a false alarm
error and that of a false dismissal error are the same.
Ca. P(M/r=R) = Cd . P(M/r=R)
f {r /M)
Noting that:
P(M/ r=R)
=
r
f (r)
.
P(M)
r
f (r /M)
f (r/M)
ca
r
r
f
f (r)
r
r
{r)
P(M)
Assume F {r/M) is Gaussian
r
P(M)
c
a
. P(M)
= cd
E
_ {E-2R)
N
P(M)
At threshold R=a
E-2a
N
c
=
£
solve for
a
=
E
2
a
cd
P(M)
P(M)
a
N
+2
i,n
[ca ~J
Cd P(M)
Thus the value of the threshold can be determined.
Chapter 3
SYSTEM DESCRIPTION
The portable cardiotachometer is realized by the circuits
depicted in. the block diagram shown in Figure 3. 1.
Each of these
blocks is described in the subsequent paragraphs.
The ECG signal is picked up by floating, silver- silverchloride electrodes and secured to the chest wall by adhesive
collars in the vicinity of the heart.
The electrodes are generally
kept close to each other to avoid large DC·skin potential differences.
The resultant signal is then amplified by a differential preamplifier.
The preamplifier produces a nominal six volt signal from the one
millivolt input.
A matched filter is used, along with a level detector to
determine the presence of the R-wave in a normal ECG waveform
complex.
The matched filter is tuned to the frequency response of
the R-wave and will produce its maximum output at the peak of the
R-wave.
The self-correcting level detector is used to detect the
threshold value to signal the occurrence of an actual R-wave and
produce a pulse output when the threshold is exceeded.
A feedback
signal from the tachometer generator (tach gen) circuit provides a
cutoff signal to the self-correcting circuit within the level detector.
This results in a variable threshold which compensates for the
-'
14
[EC.TROOE
A
D'SC
L'EVE:L ~
DE:TECTOR
TACI-\
~ENt:RATDR
~~/
6
t:Lt::C.Tl<OOE.
JUt.
l"bNE:
GSNERA.TOR
MATCHED
FILTER.
r
TEST
OSCI LLA1bR
Fig:ure 3.1
Block Diagram
Portable Cardiotachometer
LIMIT
DETECTORS
subject to subject threshold value of the R-wave response from the
matched filter.
The level detector's output may be switched out of the circuit
and substituted with a test oscillator.
This built-in test oscillator
produces precalibrated pulses representing both high and low limits.
This is provided as a self-test capability .
. The tachometer generator converts the input pulse from the
level detector into an analog voltage proportional to the heart rate
of the user.
This circuit also provides the feedback signal to the
self-correcting level detector.
This analog voltage is compared against preset values in the
limit detectors.
Variance of this signal to the preset limits
produces either a high or low heart rate signal.
A high limit will
trigger a one -cycle oscillator, whereas a low limit will produce a
low signal to the tone generator.
These two signals are diode ORed
to the input of a tone generator,
The tone generator will produce a 1000 cycle audio output
through a built-in speaker.
If the heart rate is below the preset
level, a solid tone will result; if, however, the heart rate is too
high, a one cycle off, one cycle on, 1000 cycle tone will result.
These two tones will signal the subject to either increase or
decrease his exercise level to match the preset limits.
Chapter 4
CIRCUIT DESCRIPTION
This chapter contains descriptions of the circuits used to
implement each of the functional blocks described in Chapter 3.
The circuits were designed using readily available components_ and
made liberal use of existing integrated circuits to reduce the
circuit's complexity.
Each is described in subsequent paragraphs.
ECG Preamplifier
The technique chosen for the ECG preamplifier 1 s first stage
was a differential input instrument amplifier with direct coupling.
This permits input transients due to electrode movement 'and static
charges without waiting several seconds for the amplifier to recover
from the overload.
This amplifier circuit exhibits very high input
impedance· and negligibly small injection current.
With DC
coupling, however, the electrodes may see differential DC voltages
up to +100 mv on the skin of the subject, whereas the input signal
is about 1 mv.
Therefore, the subsequent stage is a conventional
differential amplifier, referenced to ground, which is AC coupled.
The resultant ECG preamplifier will have a large dynamic range .
at the output to accommodate the DG offset signal, while still
maintaining a high common mode rejection ratio at the input.
The preamplifier's circuit schematic is presented in
Figure 4. 1.
The circuit utilizes an integrated circuit designated
17
EC~
iN
7
R.S
200K 1%
C61nj
Cl !hf
RZ. 300 K
tOJ.,
~5
12KI%
"':)I
R4
300 K IOJ'o
I'
(A
1t:> R-V•./AV'E.
C2 3hf
d.
0
•
t!
·9V
CS ...._
R9
lnf
2.00K 1%
ECG.~
Figure 4. 1
Schematic Diagram of the ECG Preamplifier
DETECTOR
Al, which contains two operational amplifiers in a single package
and is used as a DC differential instrument amplifier configuration.
The dual amplifier's input circuitry has extremely high input
impedance, both differential and common mode.
This high input impedance results from the two noninverting
inputs, which have an input impedance of 30 x 10
6
.n..
As a result,
the circuit is quite insensitive to imbalances in the source impedances that might occur if one of the electrodes is not properly
connectec1 to the patient.
The output of the amplifier's Al-l and
Al-2 are:
v.tn
el =
v em
e2 =
v em + v.tn
( R2
Rs
+.!.)
2
(4 + .!.)
R
5
2
Hence the differential output will be:
The cross -couplin..g between the amplifiers via R
5
reduces
the common mode gain to unity but amplifies the differential signal,
unlike a pair of voltage followers.
The component values shown
provide a differe·ntial gain of 50, which leaves a margin on the
output swing capability of the amplifier, for a maximum common
mode swing of +5 v,- and a differential DC offset of+ 100 mv, for
the normal input signal of 1 mv.
The third amplifier A2-l,
converts the differential signal to a single-ended one, and boosts
the gain to 1000.
Capacitor
c 1, c 2 , c 5 ,
and
c6
limit the bandwidth
to 100 Hz to reduce the high frequency noise.
R-Wave Detector
The R-wave detector used a matched filter and a selfcorrecting level detector to signal the presence of the ECG waveform complex.
From the foregoing analysis in Chapter 2 it was
determined that the matched filter should have a frequency response
of:
.
. t
H(w) = kS*(w)e -J w m
For a triangle wave input with the following characteristics;
~
A
E
~-¥i~~aT
o t=27. 8 msec
2rr
/t
The resultant power spectrum of this waveform is then:
4
S(w) =A
2
sin (wT /2)
2
(Tw)
S*(w) = S( -w) = S(w), from symmetry
The area of interest in the frequency domain can be limited
to the left hand plane from zero to 21T/t.
The resultant matched
filter is to have a frequency response as shown below in Figure 4. 2.
A~
__...L.__J_....,.:e-,--,.~ w
t
Figure 4. 2
Matched Filter Response
An approximation of this filter could be achieveg using a
Butterworth filter.
In order to build this bandpass filter with a
minimum number of components, yet guarantee sharp cut-off, a
multiple feedback bandpass active filter de sign was used.
In
addition to narrow bandpass response and a moderate Q, the
amplifier delivers a substantial gain, and requires no inductive
components.
The filter response shown in Figure 4. 3 has a
transfer function of:
E
-S(liR
0
C )
10 8
E:(S)=~2--------------------------------~-------
s + s ( 1 I R 12 ) • (1 I c 7+ 1 I C 8 )+ ( 1 I R 12 . c 7. c 8 ).
I
( 1I R
10
+ 1 I R 11)
the center frequency gain is:
the center frequency is determined by:
112
1
-=a=
Q
.1112
::o u)J
1
+R
Bandpass filter design:
H
0
=
30 +3o/o
1
= -0: = 5 -t5o/o
2
wo = 27Tfo = 1. 25 x 10
c7 = c 8 = c = 0 . 1 p,f + 1 o/o
Q
R1o
=
Q
H w c
0 0
= 13. 33K
+lo/o
0
·10
.D
0
~-Zf)
]aJ
1/J
R
t/1
~
-~
ct
w
~
u:
-4¢
"Figure 4. 3
Frequency Response of Two-Pole Butterworth Filter
I
s
10
1:')
l=I'Z.E.QUE:.NC:.'(
20
\N \-\'a
2~
30
3'5
R
=
11
R
12
Q
(2Q2 -Ho)
=
_g_
w e
woe
=20K+l%
= BOOK +1%
0
A plot of the filter 1 s frequency response versus that of the
ideal matched filter is shown in Figure 4. 4.
The component tolerances were chosen to maintain the center
frequency within 3% and the Q within 5%, based on the following
sensitivity analysis:
= -0. 3
SR
(Q)
12
=
1
2
2. 08
X
10 -2
.
2.08
X
10
-2
0
MATC.H£0 FILTER ~
--......
I
-10
\
\ \'_.5"
I
-20
w
'\
I
l
"'z
0
0(/'J
w
ct
ol
\
I
Q
-3Db
+\
I
JJ
!
~
\
-39
I
w
!J
u:
I
~
+
5I
I
I
I
I
10
~\LiaR
NORMJ!..LlZ.ED A.T '2.0
~z
\
\
Filter Response Verses
Frequency for the Ideal Matched
Filter and the Bandpass Filter
J
;l----~------~------~-------I=Rt:.QUENC.Y
Bt...N'OP"SS
\
Figure 4. 4
15
2.. POLE
IN
2.0
;.!;!
25
30
\
\
""
se,
~40
In the threshold detection of the R -wave input, the error to be
·,_.:l-
·.;._.;~~
.·---.-.·.
-:avoided .is that of the false alarm in the presence of noise.
The
false dismissal is of lesser importance since it occurs less
frequently, and the tachometer will integrate the resultant error.
-~
)'
False alarms will result from artifact, causing a noise input within
the
respo~se
band of the filter.
A value of Ca
= 5,
and Cd
=1
can
be assigned to the equation derived in Chapter 3.
The signal probability is given a nominal value based on the
pulsed signal's width with respect to a nominal expected repetition
rate.
A typical value would be:
30 msec/0. 6 sec = 0. 05 = P(M)
E+N
a
=
a
= E+N
2
2
E
2
2
4.55
2
1 +oo
IS(w) dw
2
J-co
=
I
=A2
T
_2
ex
T
teo
J
2
_jH(w)
I dw
-co
1 +oo
E
=2
E
=
E (N)
J-oo js(w) I2 dw = A 2 TTo
2
= A • o. 05• 30
2
I.5•A =1.5
=
1 NI +j.m
2
IH(w) I dw
2 1T 2
-m
= 211T
N
2
T
2 30(A /2)( o/T)
N
=
0. 59 .. N
a
=
1. 5/2 +
1
where N
N • 0.59
1
2
1
= 3S:i
• 4. 55
= 4. 776
The schematic of the R-wave detector is presented in Figure 4. 5.
Because of the wide variation in pulse repetition rate and
because N is a variable, a self-adjusting comparator was used.
1
Amplifier A3, in Figure 4. 5
i~
a noninverting comparator.
filter's response is rectified and averaged by CR , CR and
1
2
and R
14
.
17
The nominal value of the comparator is set by R
to the value calculated
a~ove
of this threshold is modified by R
R
19
, CR
c 10
The time constant of the filter is chosen to be 60% of the
pulse width.
and R
The
4
and
c 12 .
detected signal.
18
for the threshold.
16
The value
, which derives its input from
This forms a voltage level proportional to each
Thus the threshold is modified by a feedback
signal which is proportional to the input from the filter.
The
comparator 1 s input is clamped to prevent further charging of the
modification to the threshold by the input
11
C" which is derived
from the following one- shot stage.
Tach Generator and Comparators
Once the presence of the ECG waveform is detected, a
voltage proportional to the repetition rate of the signal needs to be
generated in order to perform an analog comparison, which will
signify the heart rate limits have been exceeded.
schematic of the tach generator and comparators.
Figure 4. 6 is a
To generate
C8
o .• ..,.:f
~----------~1--~
r------------lC
CR3
Cl\
R\1
£2.6K
l~o
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I "lo
j
Rl~
FILTER
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~ 1001<.
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R\5
C.R4
330K
J
.J± CIZ
t.o..yf
ALL 0\00E.S lH 941.
COM PARA.lOR
Figure 4. 5
Schematic Diagram of the R-Wave Detector
.01~
11\V
R\9
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•
Rl4
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a>
I
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Ul
Q\
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LOW
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CR9Y--v
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.LeD
~
'U I
RZ8
IOK
Figure 4. 6
Schematic Diagram
of the. Tach Gene.rator and Comparators
COMPAQ..ATORS
'E
this voltage, a nonretriggerable one-shot multivibrator, whose
output duration is less than the maximum input pulse period is used.
The value of the one- shot 1 s output would be:
l pulse
=
Vee . t n (volt seconds)
0
Where Vee is the output voltage of the one shot; t n is the
0
ti;rne the one shot is on.
The resultant pulse train may be averaged and stored in an
analog memory element (a capacitor), which will produce a voltage
output which is proportional to the repetition rate of the detector
output.
Vout
=
+co vee· t
on
pulse
-co
J
+cox.ve
J
x pu1ses dt =
sec
·-co
e
sec
.T
on dt
The one shot uses an integrated circuit Ul, shown in
Figure 4. 6, which is one half of NE556V.
one shot is pin 8.
inverted by Q l.
The trigger input to the
The trigger is capacitively coupled in and
The one shot time is determined by R
23
and e
13
•
The equation is:
Tc =
l. l Re
Tc = 220 msec
The output of the one shot is pin 9.
R
38
and CR , which is a
9
light emitting diode, serve as a visual indication that the EeG
waveform is
b~ing
detected.
Q2 is used as a feedback signal to
the self-learning comparator described above.
The one-shot output will have a volt-second output which is
averaged by capacitor C
ECG waveform rate.
produce a voltage at
14
to produce a voltage proportional to the
The one shot's time on is adjusted by R
c 14
equal to 6. 3 vat a rate of 200 bpm.
to
23
The
time constant of the averaging circuit is chosen to be 0. 5 sec in
order to smooth any transmit, yet reward the user quickly for an
increased heart rate.
A dual comparator can then be used to detect a repetition
rate which is below or above a preset limit.
The comparator tdp
levels are chosen to be:
High Limit:
50 to 200 bpm
Low Limit:
30 to 170 bpm
The dual comparator uses a divider chain derived from the
battery to develop the reference voltage.
The one shot's time
constant is relatively insensitive to battery voltage, but the voltage
level ofthe pulse is directly proportional to it.
Therefore, the
voltage comparator makes use of a ratio-metric measurement.
The comparator uses two variable resistors, R
to adjust the high and low limit alarm levels.
26
and R
27
,
The high limit is
adjustable from 200 to 50 bpm, and the low limit from 170 to 30
bpm.
R
39
and R
40
are used to provide 1% of hysteresis in order
to prevent comparator chatter.
Modulator and Tone Genera tor
The modulator and tone generator serve to provide the
feedback signal to the user which results from a high or a low limit
detection of the ECG rate.
The low limit, which indicates that the
subject's heart rate is below a preset limit causes the tone
generator to produce a solid tone.
A high limit, because of
potential seriousness and for distinction, produces a burst of the
same tone at one second intervals.
If neither of the two limits is
exceeded, no tone is produced.
This circuit is realized using a phase shift oscillator for the
tone generator and a free running multivibrator for the one second
modulation.
The tone generator formed by the phase-shift oscil-
lator is held off until it receives an output from either the low limit
input or the modulator.
The modulator, which is a free running
multivibrator, is held off untii it receives
a high limit input.
The
schematic for this circuit is presented in Figure 4. 7.
The one cycle modulator uses the other half of U 1, a NE556 V,
as a free running multi vibrator.
is held from charging by Q4.
The oscillator 1 s timing capacitor
A grounded input to point D, will
turn off Q4, allowing the oscillator to function.
oscillation is determined by R
30
, R
31
, and
c 15 .
The period of
The oscillation
will have a period of two seconds, with a duty cycle of 1/2.
The tone generator uses an integrated circuit audio amplifier
connected with a feedback circuit to form a phase shift oscillator.
The oscillatiol'l: frequency of 1 KHz is chosen in order to take
advantage of the response of a small speaker and help insure
detection by the subject.
The transistor Q3 is biased on the R
32
,
+c:>V
-l-<:lV
R30
R29
100\(
lOOK
e
Rol
<
lOOK~
II
lss~
2
CRS
IN9\4
Ul
+9V
St------1
..._---<11~-j z
"
HI~H
liM IT
D
4
"
t_a3_ _ _ __.
O~"+- ~
2N2Z2'21\I
'~-
po"l"-f.-. .CIS
R34 V
~
CR7 IN914
~
j_C\10
o.1"1f
~
l.:*---1
Q3
"
_l C\7
ll MIT
1
'\7
MOOV LA.. TOR
TONE
~------------~--------~
.
Fig~re
j_Ct8 _Let'?
To· 't5 To.l..,.fJo·•"''f
,.
IN914T-
tow
R3Ci>
3.3K_
3.3~--,
2NZ222A
CR8
'R35
3.3K
4. 7
.Schematic Diagram
of the Modulator and Tone Generator
~ENERA.TOR
SPEA.K~
to ground the feedback and prevent oscillation.
The transistor is
turned off by a ground input signal through either CR
7
or CR .
8
If
the input is from CR , a solid tone will result, whereas, if the
8
modulated input is through CR , it will produce a burst of tones on
7
a one second interval.
Power Supply and Test Oscillator
The integrated circuits used in the portable cardiotachometer
require both a positive and negative nine volt power supply.
The
positive voltage is derived from a common nine volt transistor
radio battery.
This battery type was chosen because of its size
and availability.
The negative supply could use another nine volt
battery, but this idea was discarded due to weight, volume, cost
and maintenance considerations.
In order to generate a negative
supply, an artificial reference level could be used or an inverter
could be built.
The inverter was chosen due to its small size, low
power dissipation, low output impedance, and lack of level shifting
problems.
The circuit also contains a built-in oscillator which may be
used to adjust and self test the voltage comparator.
The oscillator
generates either a high limit rate or a low limit rate, which is
selectable by a switch.
Another switch is used to switch the unit
from the operate to the test mode.
The schematic is presented in
Figure 4. 8.
The nine volt battery is switched on and off by SW 1.
Its
+9V
SWI
OFF" o
~ON
R41
IK
10
9
0.0'-1
CZI
~-
-& SSG
LEO
.
I
•
~
R4'2.
U2.
CR\0
I))
14
33K
?
e-j~2.""
IOOOp
c c. f
•
Ill
+9V
. 'R431-~~-~
lOOK ~ SW2.
R44
~ 20K
<
Low., .J
~~t
Figure 4. 8
CZ.5
Schematic Diagram
4?.;-,f T
of the Power Supply & Test Oscillator
\7
,...-----...,
CIMITI
\
!_ 5 Sf>
2
U~
2
51----T-ES-\
j.r
o-----CI.
~
0<
e
I
position is indicated by CR
10
, a light emitting diode.
The minus
nine volt supply utilizes a transformerless power converter.
The
circuit consists of a NE556V used in the self-triggering mode as a
squarewave generator, followed by a voltage -doubling rectifier.
The frequency is determined by R
42
and c
22
and is chosen to be
20 KHz to _provide good filtering with a relatively small capacitor
c24·.
The built-in test oscillator uses the other half of the NE556 V
as a free running multivibrator oscillator.
either R
43
or R
44
and c
25
.
The frequency is set by
The frequency is chosen by SW2 to be
either a high limit signal or a low limit signal.
The value of the
signal is set using a test instrument or a stop watch.
These levels
are adjusted to the prescribed EGG waveform rate in order to just
produce a high and a low trip limit. · SW3 is used to place the· unit
in either the test or operate mode.
In the test mode, the signal
from the oscillator is fed to the tach generator's one-shot input to
·emulate the R-wave detector's output.
Chapter 5
SIMULATOR DESIGN
In order to verify the functioning of the device, it was
necessary to design a simulator that would adequately emulate the
salient properties of the ECG waveform.
The property of interest
in this study is the frequency spectrum of the ECG waveform, and
to have the ability to vary both the repetition rate and output bandwidth within the range expected from an actual study.
A detailed
analysis of the ECG waveform is presented in Chapter 2.
In the design of the ECG simulator circuit, it was desirable
that· the circuit meet the following specifications:
Input Power - +9 vdc battery
Output a.
Signal level:
2 mv max
b.
Output imped·ance:
c.
Repetition rate: 200 bpm, 20 bpm
d.
Pulse width:
lOOK
50 msec
The resultant design would produce an easy to use, portable
device to check the functioning of the portable cardiotachometer.
A circuit schematic is presented in Figure 5. 1.
The design was accomplished utilizing two integrated circuits,
the 556 dual timer and the 5558 dual operational amplifier, both of
36
+~V
R1
lOOK
A
~b
I
~
.._
.0.
+9V <>--
4
f
1oo.n..s
z·
Cl1
14
SSG
Ul ·
3
\0
5
--rr.· - 8
Ul
~
O.l..,S.T
T
-=. 9VDC
R5
4.7K
9
1'2
9
'7
4-9V
i
tOKt
7.
·JUL
OSCILLATOR
RE.
lss~
Bl.
1.. Bm"ErG.Y
___..
R3 ~ ~~6
4iJ.yf I
'--1
I
+C4
I C3
1
o.1-"li
l.yf
ONE SHO'T
'k
C5
.22.0"'1;.
~I-
Figure 5. 1
Schematic Diagram of the ECG Simulator
~9V
lJl.l
R\\'ZOOl<
C6
__/\____/\__
100-'ff Rl2. lOOK
Rl4 lOOK
Rl3
R7
'<>tOO..Q.
IOK
lNVER.TER
INTEGRATOR
~ AiTENUA.TOR.
which are available from several vendors.
The 556 dual timer is
used here first as the free running oscillator and secondly as the
one shot.
f
=
The oscillator 1 s frequency is determined by the:
1/T
The pulse width of the oscillator's output must be less than
the minimum desirable one shot timer of 5 msec.
This time is
determined by:
Due to the required hias current requirements of the device,
the total resistance must be less than l 0 M.n..
conventional value of 4 7 J.Lf.
t2 R 3: R
T
3
1
is chosen to be a
Therefore to satisfy:
-3
:::; 5 X 1 0
6
3
0.64-47-10-
Choose R
C
~ 15 3
.!l..
= 100 .n.
1 min
= 5 x 10-3 min = 300 msec/beat
.
=
200 beats
beats
m1n
which yields R
T max
=
2
1
30 bpm
= 726 .n., choose 680 .n.
=
0. 5 sec
39
The one shot pulse width is determined by:
t
.
m1n
=
4 msec
and
c4 =
1. 0 J.Lf
are arbitrarily chosen, then:
l
6 msec
1. 1. 1
Choose
R
5
X
10
5.45
-6 =
50 msec
1. 1. 1
R
4
10
3
= 4. 7K
Finally,
Choose
X
=
X
10
-6 -4. 7K
=
40K
SOK
The inverter circuit utilizes a 5558 as an inverting comparator.
When the incoming pulse goes below one half the battery voltage
{Vbatt), the output goes to within one volt of Vbatt•
Conversely,
when the output is greater than one half V batt' the output of the
inverter goes to within one volt of ground.
The one volt offset is a
result of the amplifier's saturation characteristics.
The integrator is a classical inverting integrator with a selfrestoring resistor R
11
The integration time constant is determined by the product of R
and
c 5. ·
c5.
, to prevent precharging of the capacitor
9
It is chosen long with respect to the integrated pulse to
prevent errors due to the exponential change rate near the V
the amplifier.
sa
t of
The output attenuator results in a signal amplitude
of 1/1000, or the desired 2 mv maximum.
Chapter 6
CONCLUSIONS
In the foregoing chapters, a design for a portable cardiatachometer is described.
As a result of the waveform analysis
presented in Chapter 2, the circuitry described in Chapters 3 and 4
was implemented.
This circuitry meets the following specification:
30
Input Sensitivity
100 J.LV to 10 mv
Common Mode Rejection
Ratio
50 db
Maximum Input Offset
Voltage
+100 mv
Input Frequency Response
100Hz
X
10
6
Input Impedance
.n.
Settings
High Limit Trip Point
Range
50 to 200 bpm
Low Limit Trip Point
Range
30 to 170 bpm
Adjustment
1% of full scale
, __ TeJl1pe;rature Drift--·-
30 ppm
Output (Audio)
Low Limit
1KHz +20%
High Limit
1 KHz +20% with 1 Hz +20%
modulator
Audio Power Output
1 watt RMS
The input impedance is dictated by the electrodes and their
interface to the subject's epidermis, and is to be greater than
41
lOOKn..
Using the technique presented in Chapter 4, an input
impedance of 30M.ll.. was obtained.
This will insure that impedance
mismatch and variable skin resistance will not adversely affect the
operation of the cardiotachometer.
The bandwidth of the ECG preamplifier is limited to 100 Hz,
in order to adequately capture the ECG waveform complex and yet
provide for noise rejection.
The offset potential is maximized, but
limited by the output potential of the integrated circuits.
There
exists a trade-off between the desired input sensitivity, which is
derived from the gain, and the input offset voltage.
The nominal
value of the ECG waveform's amplitude is 1 mv, therefore the
sensitivity range is plus and minus 20 db.
The common mode
rejection ratio is made as high as possible.
The high and low limit ranges were chosen based upon the
studies referenced in Chapter 1.
It is felt that these limits will
span the requirements of both the athlete and rehabilitative patient.
The adjustment setting was dictated by the most conservative
formulas used to establish target. heart rates.
This portable cardiotachometer could be produced for $119,
assuming a minimum production lot of 1000 units.
This may be .
broken down as follows:
$ 30
Component Cost
Printed Circuit Board
Molded Plastic Case
5
10
3
Leads, Molded
Package of 100 Electrodes
20
Assembly Labor
36
Test Labor
15
Total
$119
A selling price would be three times the production cost,
plus $30 per unit for the nonrecurring cos:t for electrical and
mechanical engineering as well as setup cost.
This would yield a
price of $400 per unit.
The circuitry, including the battery, can be packaged into a
box measuring no greater than 12 em x 12 em x 3 em.
pased on using 2 cm
2
discrete components.
This is
for integrated circuits, and 0. 5 cm
2
for
BIBLIOGRAPHY
1.
Aschman, R., Hull, E.
Macmillan, 1945.
Essentials of electrocardiography.
2.
Astrand, P. 0., Rhyming, I. A nomogram for calculation of
aerobic capacity from pulse rate during submaximal work.
J. Appl. Physiol. J: 218, 1974.
3.
Brown, J., Jourke, G. J., Gerty, G. F. Nutritional and
epidemiologic factors related to heart disease. World Rev.
Nutr. Diet, 12:1, 1970.
4.
Bruce, R. A. , Lerman, J. Exercise testing and training in
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1975.
5.
Cooley, J. W., Lewis, P., Welch, P. Computer analysis of
the power spectral density of the nominal electrocardiogram.
IEEE Biomed., September: 49, 1973.
6.
Cromwell, L., Weibell, F. J., Pfeiffer, E. A., Usselman,
L. B. Biomedical instrumentation and measurement.
Prentice -Hall: 1973.
7.
Edwards, M. A. The effects of training at predetermined
heart rate levels for sedentary subjects. Med. and Sci. in
Sports, 6:14, 1975.
8.
Ferguson, R. J., Pititcler, R., Choquette, G., et al. Effects
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circulation and progression of coronary disease. Am. J.
Cardiol., 34:764, 1974.
· 9.
Foster, L., Reeves, T. J. Hemodynamic response to
exercise in clinically normal middle -·aged men and in those
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10.
Fox, S.M. InNaughton, J.P., andHellerstein, H. K.
(editors). Relationship of activity habits to coronary heart
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11.
Frank, E. K. , Braunstein, J. R. Spectrum analysis of the
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Biophysical Society Meeting, Boston, 5 Feb. 1958.
12.
Fuso, P. M. Analyse harmonique de l'electro cardiogramme.
Arch. Mal du Coeur, 58:1022, 1965.
44
13.
Gills, J. N. Fairchild semiconductor linear integrated
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14.
Gottheimer, V. Long-range strenuous sports training for
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15.
Hellerstein, H. K. The effect of physical activity: patients
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16.
Hellerstein, H. K. Exercise therapy in coronary disease.
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17.
Hiller, F., Lieberman, G. Introduction to operations
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18.
Kannel, W. B. Habitual level of physical activity and risk of
coronary heart disease. Can. Med. A. J., 812, 1967.
19.
Langer, P. H., Geselowitz, D. B. Characteristics of the
frequency spectrum in the normal subject and in subjects
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20~
Langer, R. H., Geselowitz, D. B. High frequency components
in the electrocardiograms of"normal subjects and of patients
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21.
Laning, J. H., Battin, R. H. Random processes in automatic
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22.
Mitra, S. K.
23.
Nagel, E. L. , Hirshman, T. J., Nas senfield, .S. R., et al.
Telemetry-medical command in coronary and other mobile
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24.
Naughton, J. P., Hellerstein, H. K. Exercise testing and
exercise training in coronary heart disease. New York,
Academic Press, 1973.
25.
Naughton, J. P. The contribution of regular physical activity
to the ambulatory care of cardiac patients. Postgrad. Med.,
57:51, 1974.
26.
Papoulis, A. Probability, random variables and stocastic
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27.
Rechnitzer, P. A., Pickard, H. A., Daivis, A. N., et al.
Long term follow up study of survival and recurrence ratio
following myocardial infarction in exercising and control
subjects. Circulation, 45:853, 1972.
Active inductorless filters.
IEEE Press, 1971.
28.
Scher, A. M. , Young, A. C. Frequency analysis of the
electrocardiogram. Cir. Res., VIII:344, 1960.
29.
Staff.
Linear applications.
30.
Staff.
555/556 timers.
31.
Strong, P. A.
1970.
32.
Swan,_ H. P. Biological engineering.
Hill Book Company, 1971.
33.
Taccardi, B. Distribution of heart potential on the thoracic
surface of normal human subjects. Cir. Res., 12:341, 1963.
34.
Travel, M. E. How much exercise for your cardiac patient.
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35.
Uhley, H. N. Electrical monitoring of the acutely ill patient.
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