4B15 Introduction to Bioengineering
Electrodes and Transducers
Lecture 4: Biomedical Measurements and Transducers
4.1 Introduction
There are many physical measurements which are made in medicine.
These can be either invasive or non-invasive. Measurements can be made
without physical contact with the body, such as in the case of CT or MRI scans.
Other measurements can be made with the aid of miniature transducers, such as
an endoscopy or the measurement of intra-arterial blood pressure. Many
measurements, however, are carried out in the form of blood tests, where the
reaction of the blood samples to chemical reagents provide information on the
condition of an organ or the efficiency of a bodily function. Such tests usually
also involve the use of instrumentation to monitor the status of the reactions,
such as the change of colour of a test strip.
In general terms a transducer is a device which measures a physical
phenomenon and converts the variation in this phenomenon into an electrical
signal. This is so that the signal can then be conditioned and processed with the
sophistication and precision offered by electronic instrumentation and
equipment and then usually stored in electronic or hardcopy form for record
and subsequent referral.
4.2 Common Physical Measurements
Many physical parameters are commonly measured in both invasive and
non-invasive settings. Among the most widespread are the following:
Electricity - Surface Potentials:
These are signals that can be measured from the surface of the body using
electrodes and sereval examples have been mentioned already such as the ECG
and the EEG as shown in Fig. 1.
Fig. 1 Measurement of EEG and ECG
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Pressure:
Pressure can be measured externally as in the case of blood pressure
measurement, where the gauge pressure in the compression cuff is measured as
this is deflated to estimate the internal pressure in the artery as shown in Fig. 2.
Solid-state pressure transducers are available for the purpose in a variety of
ranges and accuracies. Miniature pressure transducers allow intra-arterial
pressure measurement and catheterised insertion of transducers into the heart
for long term monitoring. They are also available for other locations such as the
eye.
Fig. 2. Measurement of Pressure in Clinical Scenarios
Temperature:
As with pressure, temperature can be measured internally or externally.
Sensors can be mounted on the body or inserted at suitable sites. They usually
exploit the property of thermal expansion of a metal, or the differing rates of
thermal expansion of two different metals. Examples of temperature monitors
are shown in Fig. 3.
Fig. 3 Examples of Temperature Measurement Transducers
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Flow:
The rate of flow of air into and out of the lungs is important in the
diagnosis and treatment of diseases such as asthma and lung cancer as well as
other pulmonary complaints. The flow of blood in narrowed arteries which have
suffered stenosis or through damaged valves in the heart is also an important
measurement, which can be accomplished through the use of miniature
transducers that can be inserted through catheters.
Fig. 4 Examples of Flow Rate Monitoring
Strain:
Damage to muscles, tendons and ligaments, as is common in sporting
injuries, can be assessed with the aid of transducers which can measure the
stress and strain which they have been subjected to and can help in monitoring
the healing process.
Fig. 5 Examples of Strain Measurement
Acceleration:
The technology behind accelerometers has improved much in recent years,
allowing such transducers to become more compact in shape and size. These can
be used to measure the forces placed on the body in high speed activities such as
space travel or in general studies of walking gait or limb movement. They have
also been used more recently to aid independent living among the elderly, where
they have been used to monitor falls or unsteadiness in the balance of the elderly
in their own homes.
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Fig. 6 Examples of the Measurement of Acceleration
4.3 Typical Transducer Characteristics
Many solid-state pressure transducers are constructed in the form of a
Wheatstone bridge which is implemented directly on Silicon. The associated
interfacing and signal conditioning amplifier and any other electronics needed
can often be mounted on the same chip as is used for the sensor itself. An
example of the construction of the Sensym SPX50 pressure transducer is shown
in Fig. 7. This is fabricated as a piezo-resistive sensor in the form of a
Wheatstone bridge, consisting of four ion-implanted resistors etched onto an
integral silicon diaphragm which transform the shear stress due to applied
pressure into an electrical output. The diaphragm is mounted and bonded over
an access port where the input pressure is applied. The bridge is exited using an
external supply voltage and can operate over a wide voltage range.
Photo
Fig. 7 The Physical Construction of a Solid-State Pressure Transducer
An electrical equivalent circuit of the transducer is shown in Fig. 8, which
can be seen to be that of an elementary Wheatstone bridge providing a
differential output signal. With zero pressure applied to the transducer, the
potential at both output terminals relative to ground is half the supply voltage.
When input pressure is applied to the transducer, the potential at the positive
output terminal increases from half the supply voltage, while that at the negative
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Fig. 8 Equivalent Circuit of the SPX 50 Pressure Transducer
output terminal decreases. The difference between these two potentials is a small
signal voltage which is proportional to the applied pressure.
The performance characteristics of the transducer are given in Table I.
This table shows the parameters which describe how the transducer operates
and the ranges which apply to the values of these parameters, due to
manufacturing variations and the ambient conditions in which the transducer is
used.
Table I The Performance Parameters of the SX 50 Pressure Transducer
Parameter
Min.
Typ.
Max.
Unit
Pressure Range:
0
-
100
kPa
Supply Current:
-
2.7
-
mA
Full-scale Span:
75
110
150
mV
Sensitivity:
750
1100
1500
µV/kPa
Offset Voltage:
-35
-20
0
mV
-
+48
-
µV/OC
-2400
-2150
-1900
ppm/OC
-
4.65
-
kΩ
+690
+750
+810
ppm/OC
-
+0.2
+0.5
%FS
Offset T. C.:
Sensitivity T.C.:
Bridge Resistance:
Resistance T.C.:
Lin & Hys Error:
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Fig. 9 shows a plot of the transducer transfer characteristic, from which it
can be seen that there considerable variation in the transducer properties due to
manufacturing variation.
non-linear
characteristic
output
voltage
sensitivity
variation
offset
variation
ideal linear
characteristic
applied pressure
Fig. 9 Transfer Characteristic of the SX 50 Pressure Transducer
The output voltage at the positive output terminal, pin 2, of the transducer is
given as:
𝑽+ =
𝑹𝑩 (𝟏 + ∆)
𝑹𝑩 (𝟏 + ∆)
𝑽𝑩 =
𝑽𝑩
𝑹𝑩 (𝟏 − ∆) + 𝑹𝑩 (𝟏 + ∆)
𝟐𝑹𝑩
where RB is the change in the resistance, RB, of an arm of the bridge, which is
proportional to the applied pressure and VB is the bridge supply voltage.
The output voltage at the negative output terminal, pin 4, of the
transducer is given as:
𝑽− =
𝑹𝑩 (𝟏 − ∆)
𝑹𝑩 (𝟏 − ∆)
𝑽𝑩 =
𝑽𝑩
𝑹𝑩 (𝟏 + ∆) + 𝑹𝑩 (𝟏 − ∆)
𝟐𝑹𝑩
The differential output of the sensor is then given by:
𝑽𝒐𝒖𝒕 = 𝑽+ − 𝑽− = [
𝑹𝑩 (𝟏 + ∆) 𝑹𝑩 (𝟏 − ∆)
𝟐∆𝑹𝑩
∆𝑹𝑩
−
𝑽𝑩 =
𝑽
] 𝑽𝑩 =
𝟐𝑹𝑩
𝟐𝑹𝑩
𝟐𝑹𝑩
𝑹𝑩 𝑩
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If a span sensitivity, S, is specified for the transducer as the output voltage in
mV per unit of supply voltage, VB, per unit of applied pressure, p, that is as
mVV-1kPa-1, then the ideal transducer output can be expressed as:
𝑽𝒐𝒖𝒕 = 𝑽+ − 𝑽− = 𝑺𝑽𝑩 𝒑
In practice, there are large deviations from the ideal in the transducer
characteristic, as can be seen in Fig. 9. The bridge output is not zero for zero
applied pressure, but an offset voltage, VOS, exists which has an associated range
due to manufacturing variations. That is to say, when zero input pressure is
applied, the two output terminals of the transducer do not sit at a potential of
VB/2, i.e. half of the bridge supply voltage, but can both differ slightly from this.
This means that the differential output voltage measured between the two
terminals may be some positive or negative value which is not zero. This
modifies the output voltage to:
𝑽𝒐𝒖𝒕 = 𝑽+ − 𝑽− = 𝑽𝑶𝑺 + 𝑺𝑽𝑩 𝒑
where the offset voltage, VOS, is small in relation to the bridge supply voltage but
can be quite large when considered in relation to the differential output voltage
associated with the pressure measurement range.
In addition, most transducers have a large manufacturing variation in the
sensitivity of the diaphragm and consequently there is a large variation in the
span sensitivity from one transducer to the next. This means that the parameter
S has a large variation so that the full-scale output voltage from the transducer
for a given bridge supply voltage varies considerably. In addition, both the offset
voltage and the span sensitivity vary with temperature and consequently have
associated temperature coefficients. This means that if nominal values of these
parameters are quoted at a given temperature, T0, they will vary as the
temperature deviates from this value, so that they must be treated effectively as
functions of temperature. In this case the transducer output is given as:
𝑽𝒐𝒖𝒕 = 𝑽+ − 𝑽− = 𝑽𝑶𝑺𝟎 [𝟏 + 𝜶(𝑻 − 𝑻𝟎 )] + 𝑺𝟎 [𝟏 + 𝜷(𝑻 − 𝑻𝟎 )]𝑽𝑩 𝒑
where
T0 is the reference temperature at which nominal parameter values are quoted
T is the actual operating temperature
VB is the bridge supply voltage
p is the applied input pressure
VOS0 is the nominal value of the offset voltage
S0 is the nominal value of the span sensitivity
α is the temperature coefficient of the offset voltage
β is the temperature coefficient of the span sensitivity
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To complicate matters further, the transducer characteristic has some
degree of non-linearity over its range of operation and deviates from the ideal
straight-line output voltage vs. pressure relationship as shown in Fig. 9. Finally,
properties such as hysteresis and ageing effects can also give rise to
measurement errors.
4.3 Transducer Calibration and Compensation
These sources of error can only be only be counteracted by passing the
output of the transducer through a signal conditioning amplifier as shown in
Fig. 10.
Fig. 10. Signal Conditioning of a Silicon Pressure Transducer
The offset voltage is cancelled by adding an equal and opposite
cancellation voltage, VOC, in the conditioning amplifier. This is done in the first
instance at the reference temperature, T0. The variation in span sensitivity is
counteracted by adjusting the gain of the amplifier at the reference temperature
to give the required maximum output voltage for full-scale input pressure. The
bridge supply voltage can also be used for this purpose.
The temperature coefficient of the offset voltage is compensated for by
ensuring that the equal and opposite offset cancellation voltage has a
temperature coefficient of the same magnitude as that of the offset voltage. The
bridge supply voltage can also be made to vary with temperature and must have
a temperature coefficient which is equal and opposite to that of the span
sensitivity. When this is implemented, the output voltage from the conditioning
amplifier is given as:
𝑽𝒐𝒖𝒕 = 𝑽𝑶𝑺𝟎 (𝟏 + 𝜶∆𝑻) + 𝑽𝑶𝑪𝟎 (𝟏 + 𝜸∆𝑻) + 𝑮𝑺𝟎 (𝟏 + 𝜷∆𝑻)𝑽𝑩𝟎 (𝟏 + 𝜹∆𝑻)𝒑
where:
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ΔT = T - T0 is the deviation in temperature from the nominal reference value
γ is the temperature coefficient of the offset cancellation voltage
δ is the temperature coefficient of the bridge supply voltage
and the other parameters are as above.
In order to obtain full cancellation and calibrate the output voltage to be
independent of temperature requires:
𝑽𝑶𝑺𝟎 (𝟏 + 𝜶∆𝑻) + 𝑽𝑶𝑪𝟎 (𝟏 + 𝜸∆𝑻) + 𝑮𝑺𝟎 (𝟏 + 𝜷∆𝑻)𝑽𝑩𝟎 (𝟏 + 𝜹∆𝑻)𝒑 = 𝑮𝑺𝟎 𝑽𝑩𝟎 𝒑
This requires:
𝑽𝑶𝑺𝟎 (𝟏 + 𝜶∆𝑻) + 𝑽𝑶𝑪𝟎 (𝟏 + 𝜸∆𝑻) + 𝑮𝑺𝟎 𝑽𝑩𝟎 (𝟏 + 𝜷∆𝑻 + 𝜹∆𝑻 + 𝜷𝜹∆𝑻𝟐 )𝒑
= 𝑮𝑺𝟎 𝑽𝑩𝟎 𝒑
If the second order term in ΔT2 is ignored as negligible then full compensation
requires:
𝑽𝑶𝑪𝟎 = −𝑽𝑶𝑺𝟎 ; 𝜸 = 𝜶 ; 𝜹 = −𝜷
More accurately if the first two conditions are satisfied we need:
𝜷∆𝑻 + 𝜹∆𝑻 + 𝜷𝜹∆𝑻𝟐 = 𝟎
𝜷∆𝑻 + 𝜹(𝟏 + 𝜷∆𝑻)∆𝑻 = 𝟎
Since ΔT cannot be taken as zero this requires:
𝜷 = −𝜹(𝟏 + 𝜷∆𝑻)
so that:
𝜹=−
𝜷
(𝟏 + 𝜷∆𝑻)
→ −𝜷
These values are only calculated for design purposes and perfect matching for
compensation is achieved during the calibration process. A simple calibration
procedure is:






Set the ambient temperature to the lower value ( this may be the reference
temperature T0 but does not have to be)
Set input applied pressure to zero
Adjust the nominal value of the offset cancellation voltage, VOC0, to get an
output voltage of zero from the conditioning amplifier
Set the applied pressure to its full-scale value
Adjust the gain, G, or the nominal bridge supply voltage, VB0, to bring the
output of the conditioning amplifier to the specified full-scale value
Raise the ambient temperature to its higher value
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



Set the applied input pressure to zero
Adjust the temperature coefficient of the offset cancellation voltage to obtain
zero output voltage from the conditioning amplifier
Raise the applied input pressure to its full-scale value
Adjust the temperature coefficient of the bridge supply voltage to bring the
output voltage of the conditioning amplifier to its full-scale value.
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