Biomedical Engineering Reference
In-Depth Information
gured such
that the apparent impedance between
x
1
and the output is proportional to the control volt-
age at
y
1
. This makes the cutoff
where
z
is an of
ff
set input. In the tunable
fi
filter of Figure 2.16, the AD633 is con
fi
ff
frequency of the high- and low-pass
fi
filter outputs, as well
as the center frequency of the bandpass section,
c
o
n
tr
o
R
l
e
v
)
o
(
l
C
ta
1
g
)
f
c
2
0
π
(
3
PSpice simulation results shown in Figure 2.17 demonstrate the e
ect of varying the con-
trol voltage presented to the
y
1
inputs of the AD633s. Although the circuit is shown set up
for PSpice simulation, it can be built using real components. Output bu
ff
ff
ering using Burr-
Brown BUF634 bu
ff
ers make this a very useful stand-alone lab instrument that can be used
to
ed biopotential signals selectively prior to recording. A digitally program-
mable version of the tunable
fi
filter ampli
fi
filter can be made by substituting two multiplying D/A con-
verters for the AD633s. In this case, the control voltage is replaced by a digital control
word supplied to the input of the D/A converters.
fi
50/60-Hz NOTCH FILTERS
Probably the most common problem in the detection and processing of biopotential signals
is power line interference. Sixty hertz (50 Hz in Europe) and its harmonics manages to creep
into low-level signals despite the use of di
cation methods and active body
potential driving which attempt to eliminate common-mode signals. Unfortunately,
50/60 Hz falls right within the band where biopotentials and other physiological signals
have most of their energy. The usual solution to reject unwanted in-band frequencies is the
notch
ff
erential ampli
fi
filter.
As shown in Figure 2.18, simple implementation of a notch
fi
fi
filter known as a
twin-T
fi
filter
requires only three resistors and three capacitors. If C1
C3, C2
2C1, R1
R3, and
R2
R1/2, the notch frequency occurs where the capacitive reactance equals the resistance
(
X
C
R
) and is given by
1
f
notch
2
π
(R1
)(C1)
As such, the twin-T notch
filter works by phase cancellation of the input signal. When the
phase shift in the two sections is exactly
fi
90 and
90, the tuned frequency is canceled
completely. Signals passed by the
filter will experience some distortion since the twin-T
notch shifts the phase of low-frequency components (
fi
f
notch
) by
90 and high-frequency
components (
filter will depend on the load that
is connected to the output, so the resistors should be of much lower value than the load for
minimal loss. The depth and width of the response can be adjusted somewhat with the
value of R2 and by adding some resistance across the capacitors.
Twin-T notch
f
notch
) by
90. The insertion loss of the
fi
filters can achieve very good suppression at their center frequency.
However, the use of precise and tightly matched components is extremely important to
yield a deep notch at the required frequency. The depth of the notch is de
fi
ned as the out-
put signal ratio between an out-of-notch component and a component at the notch fre-
quency. In practice, a twin-T notch built with tightly matched components can yield pretty
good notch-frequency attenuations. Passive notch
fi
filters can be built into small enclosures
and placed between equipment stages. For example, the notch
fi
filter of Figure 2.19 was
built inside a Pomona Electronics model 2391 box, which comes with BNC connectors on
each end, making it easy to place it at the input of oscilloscopes and signal recorders.
For most practical applications, however, an op-amp needs to be added to the twin-T
network to increase its notch depth as well as to make it insensitive to the impedance of
fi
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