the electrocardiogram
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The electrocardiogram
Op-amps, instrumentation amps, filters
This is your data
Time (sec)
V (a
rb)
EKG
The EKG is a powerful diagnostic tool. Regularly used by cardiologists.
Disclaimers
• We are not real doctors. Neither are you. Do not try to interpret your EKG.
Safety
Safety
• We will review this in lab, but basically– 100 K resistors between you and breadboard.– Unplug your laptop while collecting data.
Privacy
• Your EKG could be considered private medical information under Federal HIPAA laws.
• If using this data makes you at all uncomfortable – then use one of the instructors as your subject.
The circuit
C 3
1uF
+ 5 V
R 5
1M
+ 2.5 V
DAQ(A0+)
R 6
1k
R 8
2K
R 7
10K
R 1
100K
Arm
ArmC 1
1 uF
+ 2.5 V
U 3 A
L M C 6 48 4
1
3
2
411
O U T
+
-
V+
V-
Foot
+ 2.5 V
U 1 A
A D 6 2 3 A N
4
3
6
2
5
81
7-V
S
+I N
O U TP U T
-I N
R E F
+R G-R G
+VS
R 2
100K C 2
0.1 uF
R 3
10K
+ 5 V
R 4
100K
AD623 – Instrumentation amplifier
The Op-Amp
Dynamic model of an op-amp
out
Subtract Saturation
1s
Integrator
1e6
Gainin -
in +
out
in +
in -
The op-amp follower
3
21
411
-
+
U1A
TL084
+15V
-15V
OutIn
Dynamic model of the follower
out
Subtract Saturation
1s
Integrator
1e6
Gainin -
in +
out
in +
in -
Simplification for op-amp circuit analysis
• If the op-amp is wired with negative feedback, and - • Changes are “slow” (less than ~100 kHz), then –
– Assume no current flow through into the inputs. – The two input voltages are equal.
What does this circuit do?
What does this circuit do?
What does this circuit do?
AD623
Data sheet
Let’s look at the filters now…
C
R21
V in p u t
Vout
Impedance (Z)General form of Ohm’s Law V = I Z
CjjCZ
ejCeti
etv
dttdv
Cti
tjtj
tj
1
)(
)( :response AC
)()(
VV
IV
VI
V
Example: capacitor
RC circuit (via impedances)
C
R21
V in p u t
RZ 1
CjZ
1
2
21
2ZZ
ZVV inout
Voltage divider
Vout
Do you remember how to plot Vout/Vin ?
w = logspace(0,4,100);j = sqrt(-1);R = 10e3;C = 1e-6;
Z1 = R;Z2 = 1./(j*w*C);
loglog(w,abs(Z2./(Z1+Z2)));
Resistors in series and parallel
Impedances in series:
Impedances in parallel:
21 ZZZ
21
111
ZZ
Z
Can you derive these relationships?
What about two filters in series?
C 3
1uF
+ 5 V
R 5
1M
+ 2.5 V
DAQ(A0+)
R 6
1k
R 8
2K
R 7
10K
R 1
100K
Arm
ArmC 1
1 uF
+ 2.5 V
U 3 A
L M C 6 4 8 4
1
3
2
411
O U T
+
-
V+
V-
Foot
+ 2.5 V
U 1 A
A D 6 2 3 A N
4
3
6
2
5
81
7-V
S
+I N
O U TP U T
-I N
R E F
+R G-R G
+VS
R 2
100K C 2
0.1 uF
R 3
10K
+ 5 V
R 4
100KVin Vout
The circuit
C 3
1uF
+ 5 V
R 5
1M
+ 2.5 V
DAQ(A0+)
R 6
1k
R 8
2K
R 7
10K
R 1
100K
Arm
ArmC 1
1 uF
+ 2.5 V
U 3 A
L M C 6 48 4
1
3
2
411
O U T
+
-
V+
V-
Foot
+ 2.5 V
U 1 A
A D 6 2 3 A N
4
3
6
2
5
81
7-V
S
+I N
O U TP U T
-I N
R E F
+R G-R G
+VS
R 2
100K C 2
0.1 uF
R 3
10K
+ 5 V
R 4
100K
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