U.S. patent application number 14/158416 was filed with the patent office on 2014-05-15 for control circuit for use with a four terminal sensor, and measurement system including such a control circuit.
This patent application is currently assigned to ANALOG DEVICES, INC.. The applicant listed for this patent is Donal BOURKE, Dennis A. DEMPSEY, Patrick KIRBY, Colin LYDEN, Dermot G. O'KEEFFE. Invention is credited to Donal BOURKE, Dennis A. DEMPSEY, Patrick KIRBY, Colin LYDEN, Dermot G. O'KEEFFE.
Application Number | 20140132325 14/158416 |
Document ID | / |
Family ID | 49303701 |
Filed Date | 2014-05-15 |
United States Patent
Application |
20140132325 |
Kind Code |
A1 |
LYDEN; Colin ; et
al. |
May 15, 2014 |
CONTROL CIRCUIT FOR USE WITH A FOUR TERMINAL SENSOR, AND
MEASUREMENT SYSTEM INCLUDING SUCH A CONTROL CIRCUIT
Abstract
A control circuit for use with a four terminal sensor, the
sensor having first and second drive terminals and first and second
measurement terminals, the control circuit arranged to drive at
least one of the first and second drive terminals with an
excitation signal, to sense a voltage difference between the first
and second measurement terminals, and control the excitation signal
such that the voltage difference between the first and second
measurement terminals is within a target range of voltages, and
wherein the control circuit includes N poles in its transfer
characteristic and N-1 zeros in its transfer characteristic such
that when a loop gain falls to unity the phase shift around a
closed loop is not substantially 2.pi. radians or a multiple
thereof, where N is greater than 1.
Inventors: |
LYDEN; Colin; (Baltimore,
IE) ; BOURKE; Donal; (Mallow, IE) ; DEMPSEY;
Dennis A.; (Newport, IE) ; O'KEEFFE; Dermot G.;
(Blarney, IE) ; KIRBY; Patrick; (Raheen,
IE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LYDEN; Colin
BOURKE; Donal
DEMPSEY; Dennis A.
O'KEEFFE; Dermot G.
KIRBY; Patrick |
Baltimore
Mallow
Newport
Blarney
Raheen |
|
IE
IE
IE
IE
IE |
|
|
Assignee: |
ANALOG DEVICES, INC.
Norwood
MA
|
Family ID: |
49303701 |
Appl. No.: |
14/158416 |
Filed: |
January 17, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
13626630 |
Sep 25, 2012 |
8659349 |
|
|
14158416 |
|
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Current U.S.
Class: |
327/306 |
Current CPC
Class: |
H03F 2200/462 20130101;
G01N 27/49 20130101; G01N 27/028 20130101; H03F 1/34 20130101; G01N
27/3273 20130101; H03L 5/00 20130101; H03F 2200/261 20130101; H03F
3/45475 20130101 |
Class at
Publication: |
327/306 |
International
Class: |
H03L 5/00 20060101
H03L005/00 |
Claims
1. A method of operating an instrument loop comprising a multi
terminal sensor and an excitation circuit, wherein the
multi-terminal sensor has at least one drive terminal which is
distinct from a first sense terminal, and wherein the
multi-terminal sensor has further terminal, and wherein the
excitation circuit is arranged to measure a voltage difference
between the first sense terminal and the further terminal, and to
use this voltage difference to control an excitation signal applied
to the at least one drive terminal so as to maintain the voltage
difference between the first sense terminal and the further
terminal to a target value or to within a target range, and wherein
the excitation circuit is arranged to have at least one zero in its
transfer characteristic such that it satisfies the Barkhausen
stability criterion.
2. The method of claim 1, wherein the excitation circuit has N
poles and N-1 zeros in its transfer characteristic.
3. The method of claim 2, wherein the poles are provided as
integrators.
4. The method of claim 1, further comprising providing the
excitation signal with or as an AC component at a plurality of
frequencies, and measuring a complex impedance of the
multi-terminal sensor at a plurality of frequencies.
5. The method of claim 4, further comprising using the measurement
of complex impedance to compensate a parameter of the
multi-terminal sensor.
6. The method of claim 5, wherein the sensor includes a chemical or
biological sensing cell, and the parameter that is compensated is
temperature within the sensing cell.
7. The method of claim 1, wherein the N-1 zeros occur at
frequencies at which the control loop has a gain of more than
unity.
8. The method of claim 1, wherein the N-1 zeros occur at
frequencies at which the control loop has a gain of more than
0.5.
9. The method of claim 1, wherein the N poles occur at frequencies
at which the control loop has a gain of more than unity.
10. The method of claim 1, wherein the sensor is a four terminal
glucose sensor.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This is a Divisional Application of U.S. Utility application
Ser. No. 13/626,630, filed Sep. 25, 2012, which is incorporated
herein in its entirety.
FIELD OF THE INVENTION
[0002] The present invention relates to a control circuit for use
with a four terminal sensor, a combination of a four terminal
sensor and a control circuit, and a method of improving accuracy of
a measurement system when used with four terminal sensor. The
sensor may, for example be a biological sensor such as a glucose
sensor.
SUMMARY OF THE INVENTION
[0003] According to a first aspect of the present invention there
is provided a control circuit for use with a four terminal sensor,
the sensor having first and second drive terminals and first and
second measurement terminals, the control circuit arranged to drive
at least one of the first and second drive terminals with an
excitation signal, to sense a voltage difference between the first
and second measurement terminals, and to control the excitation
signal such that the voltage difference between the first and
second measurement terminals is within a target range of voltages,
and wherein control circuit includes N poles in its gain-frequency
transfer characteristic and N-1 zeros in its gain-frequency
transfer characteristic such that when a loop gain falls to unity
the phase shift around a closed loop is not substantially 2.pi.
radians or a multiple thereof, where N.gtoreq.2 and is an
integer.
[0004] It is thus possible to perform impedance measurements of the
impedance of the four terminal sensor at a plurality of frequencies
using a higher gain in the control circuit than would have been the
case if stability had been achieved merely by reducing the open
loop gain at low frequency until such time as the closed loop gain
in the control circuit had fallen to unity whilst maintaining the
change in gain with frequency at substantially -20 dB per decade
change in frequency.
[0005] The N poles and N-1 zeroes referred to above are poles and
zeroes occurring at frequencies where the control circuit has
sufficient gain for oscillation to occur. This means, for example,
that the gain in a forward path within the loop is greater than
unity. Preferably a gain margin is included in the loop to allow
for manufacturing variation or temperature variation, and hence the
N poles and N-1 zeroes referred to in the summary of the invention
occur at frequencies where the gain is more than unity as modified
by the gain margin, so say at gains of 0.5, or less, such as
0.3.
[0006] Poles occurring in the frequency space above the frequency
at which the controller gain or loop gain has fallen to less than
unity, preferably as modified by a gain margin, such that the gain
is, for example, less than 0.5 do not give rise to instability and
can be ignored.
[0007] The use of higher gains in the control circuit means that
the voltage difference between the first and second measurement
terminals can be more tightly controlled to a target value or
target range of values and consequently measurements of other
parameters will also be correspondingly improved.
[0008] Advantageously the control circuit has first and second
reference voltage input terminals for accepting a differential
reference voltage. The differential reference voltage sets the
target voltage for the voltage difference between the first and
second measurement terminals.
[0009] Advantageously the four terminal sensor comprises a load
whose impedance varies, amongst other things, as a function of
concentration of a chemical, enzyme, or biological material.
Alternatively the impedance of a load may vary as a function of a
reaction. It is known that sensors for electrical detection of
biological parameters can be produced. Examples of such
electrically readable biological sensors in widespread use include
blood glucose measurement strips that are used in the care of
diabetes.
[0010] According to a second aspect of the present invention there
is provided a control circuit constituting an embodiment of the
first aspect of the invention in combination with a four terminal
sensor.
[0011] According to a third aspect of the invention there is
provided a method of operating an instrument loop comprising a
multi terminal sensor and an excitation circuit, wherein the
multi-terminal sensor has at least one drive terminal which is
distinct from a first sense terminal, and wherein the
multi-terminal sensor has further terminal, and wherein the
excitation circuit is arranged to measure a voltage difference
between the first sense terminal and the further terminal, and to
use this voltage difference to control an excitation signal applied
to the at least one drive terminal so as to maintain the voltage
difference between the first sense terminal and the further
terminal to a target value or to within a target range, and wherein
the excitation circuit is arranged to have at least one zero in its
transfer characteristic such that it satisfies the Barkhausen
stability criterion.
[0012] Preferably the at least one zero is positioned below a
frequency at which a forward gain of the excitation circuit has
fallen to less than unity such that a closed loop involving the
excitation circuit cannot undergo self sustaining oscillation.
DESCRIPTION OF THE FIGURES
[0013] The present invention will now be described, by way of
non-limiting example, with reference to the accompanying Figures,
in which:
[0014] FIG. 1 is a circuit diagram of a measurement circuit
constituting an embodiment of the present invention;
[0015] FIG. 2 is a circuit diagram of a current measurement
circuit;
[0016] FIG. 3 is a circuit diagram of a further current measurement
circuit;
[0017] FIG. 4 is a graph representing an excitation signal that may
be applied in electrochemical analysis to a suitable measurement
cell;
[0018] FIG. 5 is a graph of the idealized evolution of current with
respect to time for an electrochemical glucose measurement
cell;
[0019] FIG. 6 is a graph of impedance versus frequency for a blood
glucose test sensor;
[0020] FIG. 7 is a gain-frequency transfer characteristic of an
operational amplifier that has been stabilized by its manufacturer
to guard against self oscillation;
[0021] FIG. 8 is a plot of phase shift versus frequency for the
amplifier whose gain-frequency response is shown in FIG. 7;
[0022] FIG. 9 shows part of the circuit of FIG. 1, but with the
inclusion of parasitic components;
[0023] FIG. 10 is a plot of a gain-frequency characteristic for the
circuit of FIG. 1 in the absence of any compensating zero in its
response characteristic;
[0024] FIG. 11 is a plot of the phase-frequency response for the
circuit having the gain-frequency response shown in FIG. 10;
[0025] FIG. 12 is a plot of a gain-frequency response for an
embodiment of the invention;
[0026] FIG. 13 is a phase-frequency plot for the embodiment whose
gain-frequency response is shown in FIG. 12;
[0027] FIG. 14 is a circuit diagram of a circuit in which the first
two stages may be used to introduce two poles and one zero, or all
three stages may be used to introduce three poles and two
zeros;
[0028] FIG. 15 is a diagram of a differential instrument loop that
can be stabilized in accordance with the invention; and
[0029] FIG. 16 is a circuit diagram of a further circuit for
introducing a pole zero pair.
DESCRIPTION OF EXAMPLE EMBODIMENTS
[0030] FIG. 1 is a circuit diagram of a measurement circuit
comprised of a four terminal sensor, generally designated 2, in
combination with a control circuit, designated 4, and a current
measurement circuit designated 8. The four terminal sensor
comprises a load 10 whose impedance varies as a function of a
measurand. Thus, for example, the load may be a cell for biological
measurement whose impedance varies as a function of an analyte
concentration. The analyte may, for example be blood glucose. The
cell may be attached to a substrate and connected to terminals on
the substrate such that the cell 10 can be electrically excited and
the current flow through the cell monitored. As part of this
measurement it may be desired to know, with significant accuracy,
the voltage across the cell 10 as well as the current through it.
Connections to and from the cell 10 may be subject to manufacturing
variation and may exhibit impedance, and indeed changes in
impedance, which would effect the accuracy of the voltage
measurement. In order to overcome such impedance issues, the cell
is provided as part of a four terminal sensor. The four terminal
sensor comprises a first drive terminal 20, notionally connected to
one end of the cell, and a second drive terminal 22 notionally
connected to an opposing end of the cell. An impedance, represented
by resistor 24 may exist between the first drive terminal 20 and
the first end of the cell 10. This first impedance 24 may be
deliberate or it may simply be a function of the properties of the
cell 10 and the connections made to it and hence may be regarded as
being a parasitic component. Similarly a second resistance 26 may
exist in the path between the second side of the cell 10 and the
second drive terminal 22. The four terminal sensor overcomes the
problem of these resistances 24 and 26 by having first and second
measurement terminals 30 and 32 connected to the first and second
ends of the cell 10, respectively. These connections may also
exhibit deliberate or parasitic impedance as represented by
resistors 34 and 36, respectively. Although the word "terminal" has
been used here, it is to be understood that it can be replaced by
the term "node".
[0031] The cell output voltages occurring at the first and second
measurement terminals 30 and 32 will accurately represent the
voltage difference across the cell 10 if no current, or
substantially no current, is taken by a measurement circuit
connected to those first and second measurement terminals 30 and
32. This condition can, to all intents and purposes be achieved by
operational amplifiers employing high impedance front ends. Such
high impedance front ends typically use insulated gate field effect
transistors as input devices. As a consequence such circuits draw
substantially no current from the measurement terminals.
[0032] The control circuit 6 has been schematically represented as
an operational amplifier. This is substantially correct, because
although it has first to fourth inputs 41 to 44 its action within
the closed loop shown in FIG. 1 is to drive the voltage at its
output node 50 so as to minimize the sum of the voltage difference
between the voltage occurring at input 41 with respect to the
voltage occurring at input 42 and the voltage difference between
the signal occurring at signal input 44 with respect to the signal
occurring at reference voltage input 43. Each of these differences
can be formed by operational amplifiers i.e. the difference between
the signals at inputs 41 and 42, and the difference between the
signals at inputs 43 and 44, and then each of these differences can
act as inputs to a further operational amplifier.
[0033] It will be appreciated that a small voltage difference
exists between the value of the first input 41 and the second input
42, and also between the voltage at the input 43 and the input 44,
but that the magnitude of this voltage difference depends upon the
gain of the control circuit 6. In broad terms, the magnitude of the
voltage difference decreases proportionately with the increase in
gain of the control circuit 6. Thus high gains within the control
circuit 6 result in the voltage difference across the cell 10 being
controlled such that it accurately matches the voltage difference
generated by a reference circuit 52 and supplied to reference
inputs 42 and 43 of the control circuit 6. The effect of the input
offsets have been ignored, and it is assumed that appropriate
techniques, such as auto-zeroing, will be employed to reduce these
sources of error.
[0034] In order for the voltage across the cell 10 to be
controlled, current must flow through the cell, for example from
the first drive terminal 20 to the second drive terminal 22. As
part of the measurement of the biological material to which the
cell is responsive, it is necessary to know the magnitude of the
current passing through the cell. To this end, a current
measurement circuit 8 is provided. In the example shown in FIG. 1
the measurement circuit 8 has been positioned between the second
drive terminal 22 and a small signal ground 60. However the current
measurement circuit 8 could also be provided in the feedback loop
between the output node 50 of the control circuit 6 and the first
driven node 20 of the four terminal sensor 2. The person skilled in
the art is free to make this choice depending, to some extent, on
what current measuring technology or circuit he finds most
convenient to implement.
[0035] The voltage reference 52 may be arranged to generate a DC
voltage pulse, in which case it is desirable to measure the
evolution of current with respect to time. However, for checking
and calibration purposes it may also be desirable for the voltage
reference 52 to generate a changing signal, for example an
alternating sinusoid, and in which case it becomes desirable for
the measurement circuit 8 to have knowledge of the phase of the
sinusoidal signal such that a magnitude and phase change of the
current flow may be measured, for example to deduce a complex
impedance of the cell 10. The complex impedance may be determined
by comparing the magnitude and phase of the voltage difference
between the first and second measurement terminals with the
magnitude and phase of current flow through the sensor.
[0036] FIG. 2 schematically illustrates a first current measurement
circuit which comprises a sense resistor 70 disposed in series
between the second driven node 22 and the small signal ground 60.
The voltage occurring across the resistor 70 can be measured by a
analog to digital converter 80. The analog to digital converter 80
may be implemented in any suitable converter technology, such as
sigma-delta, successive approximation or flash technologies
depending on the speed and accuracy requirements required by the
circuits designer.
[0037] FIG. 3 shows a variation on FIG. 2 in which the current
sense resistor is placed in the feedback loop of a operational
amplifier 90 having its inverting input connected to the second
drive terminal 22 and its non-inverting input connected to the
small signal ground 60. This configuration may be advantageous as
it means that the voltage at the second drive terminal 22 is held
substantially constant by virtue of the amplifier 90 forming a
virtual earth, and the impedance of the resistor 70 may be selected
so as to give a greater output voltage range at the output of the
amplifier 90. Once again, the output voltage can be digitized by an
analog to digital converter 80.
[0038] The load 10 may, for example, be an electronically measured
electrochemical strip, of which a glucose strip is a common
example. An amperometric measurement protocol for such a strip is
illustrated in FIG. 4. During the amperometric measurement, a DC
voltage is applied across the strip at time T.sub.0 and held
constant until time T.sub.1. The difference between time T.sub.1
and T.sub.0 is substantially 1 second and the magnitude of the
voltage may be around 500 mV. During the measurement protocol the
current across the cell varies substantially as shown in FIG. 5.
Thus the current quickly rises to an initial value I.sub.0 and
decays to a value I.sub.1. The curved shape is a cottrellian curve
(it follows a Cottrell equation) whose shape varies substantially
as
K T . ##EQU00001##
The value of the parameter K varies as a function of analyte
concentration. However, the value of K may also vary as a function
of other parameters, a common one being temperature, but it may
also vary in the presence of contaminants. In a more complex form
of the Cottrell equation, the value of K varies as the square root
of a diffusion coefficient for a species being measured, and it is
the diffusion coefficient which is a function of temperature It is
therefore desirable to make some correction measurements, either
before or after the main test, to deduce factors which may be used
to modify the value of K, such that, for example, a glucose test
becomes more accurate.
[0039] It has been observed by workers in the field that some of
these error sources, such as temperature and some interfering
chemicals can be deduced by measuring the complex impedance of the
cell 10. Thus, for example, it has been observed for a glucose
measurement cell that the variation of impedance with respect to
frequency as shown in FIG. 6, has a turning point generally
indicated 100. The position of the turning point can, as known to
the person skilled in the art, be used to derive a correction
factor, for example, for measurement of temperature. Thus measuring
the impedance as a function of frequency enables the temperature of
the cell 10 to be deduced. It is expected that this approach can be
extended to many biological sensors responsive to respective
analytes.
[0040] If, for example, one wished to measure the temperature, it
might be thought that temperature measurement would be better
performed by fabricating a temperature sensor within the cell, but
this is not as desirable as might first be supposed. Firstly, a
temperature sensor would almost certainly tend to measure the
temperature of the substrate upon which the cell is formed rather
than a temperature of the cell. Thus, when a biological sample,
such as blood, is introduced into the measurement cell the cell's
temperature will differ from that of the substrate and an
equalization time would be required during which a reaction may
occur between chemicals (analytes) in the sample, such as glucose,
and the agents within the cell used to test for those chemicals.
Additionally the formation of a temperature sensor would require
additional processing steps and the temperature sensor itself would
probably be subject to manufacturing error and hence may not
actually improve the temperature measurement, and hence estimates
of related parameters such as diffusivity.
[0041] Typically the complex impedance of the cell is measured by
inducing a low voltage sine wave across the cell, for example of
the order of 15 mV, at a range of frequencies such as 1 kHz, 2 kHz,
10 kHz and 20 kHz. This impedance can be used, in a known way, to
apply a correction factor for temperature. This, however, brings
its own measurement problems.
[0042] As mentioned before, the control circuit can be regarded as
operating much like a operational amplifier. Electronic engineers
are generally aware that an amplifier connected in a feedback loop
has the capability of entering self sustaining oscillation.
Furthermore, most engineers are aware that manufacturers of
operational amplifiers guard against self oscillation by
deliberately inserting a low frequency pole, i.e. a low pass filter
in the amplifier, so as to modify the gain versus frequency
response of the amplifier. In broad terms, and as illustrated in
FIG. 7, the insertion of a single pole 110 in the frequency
response characteristic causes the gain (expressed in decibels) to
decrease by -20 dB per decade. This introduces a phase shift as
function of frequency of -90.degree. at frequencies above the
position of the pole 110, as illustrated at FIG. 8. Most electrical
engineers leave University with a working "rule of thumb" that an
amplifier or a feedback loop will remain stable as long as the gain
of the loop only decreases at -20 dB per decade as the gain in the
loop crosses unity.
[0043] A consequence of this is that stability can be ensured as
long as only one pole exists below the unity gain frequency of the
operational amplifier. However, in general it is difficult to
ensure that only one pole exists.
[0044] FIG. 9 illustrates the four terminal sensor of FIG. 1 in
greater detail, but this time includes the effect of parasitic
components, and in particular parasitic capacitors 120 and 122. It
can be seen that the parasitic capacitance 120 acts in conjunction
with the resistor 34 to form a low pass filter whose break point
will be determined by the resistance of resistor 34 and the
capacitance of the parasitic capacitor 120. This low pass filter
places a further pole in the frequency response of the forward
signal path within the control circuit. Similarly resistor 36 and
parasitic capacitor 122 also form a low pass filter. For simplicity
it will be assumed that these two poles are at the same frequency
hence can be regarded as being a single low pass filter. If it is
not the case that the poles can be regarded as forming a single low
pass filter, the generally one will be more troublesome than the
other, and measures described herein to restore loop stability will
be applied to the more troublesome one of the poles as a matter of
preference.
[0045] FIG. 10 schematically illustrates frequency response
characteristic for the circuit shown in FIG. 1 where a primary pole
110 exists in the control circuit frequency response by virtue of
it being included by design in order to provide loop stability, and
a further pole 140 exists as a result of the filter inadvertently
formed between resistor 34 and parasitic capacitor 120 and resistor
36 and parasitic capacitor 122. If the parasitic pole 140 occurs at
a frequency where the open loop gain of the control circuit 6 has
not fallen below 0 dB (below unity) then the frequency response has
the capability of falling at -40 dB per decade over a region,
generally designated 150, where unity gain is reached. Similarly, a
second pole will add a further 90.degree. of phase shift in the
frequency response, as shown in FIG. 11, such that at the unity
gain frequency the phase shift within the control circuit is
substantially 180.degree.. This combines with a 180.degree. phase
shift by virtue of the negative feedback loop giving a total phase
shift of around 360.degree. and consequently placing the circuit in
a position where it can undergo self sustaining oscillation.
Typically an engineer when faced with this problem knows that the
instability can be solved by reducing the open loop gain of the
amplifier to a lower value, as indicated by curve 160 of FIG. 10
such that the intercept with the 0 dB line occurs at -20 dB per
decade. However whilst this technique brings stability it reduces
the open loop gain and consequently increases the error voltage
between the reference voltage and the measured voltage difference.
Furthermore, the gain necessarily reduces with frequency so the
gain at 2 kHz will be 6 dB less than that at 1 kHz, the gain at 10
kHz will, by definition, be 20 dB less than that at 1 kHz and the
gain at 20 kHz will be 26 dB less than that at 1 kHz. The errors
between the target voltage difference and the reference voltage
difference will be correspondingly increased. Thus, it can be seen
that this approach to introducing circuit stability carries a
significant penalty in measurement accuracy.
[0046] Stability against self sustaining oscillation may be
resolved by, for example, introducing a zero 170 in the frequency
response below the unity gain frequency such that the slope of the
frequency response is modified from being -40 dB per decade at
frequencies below the zero 170 to -20 dB per decade at frequencies
above the zero 170 and at the unity gain frequency. Such an
arrangement is shown in FIG. 12. FIG. 12 also shows a further pole
172 occurring at a frequency above the unity gain (zero dB)
frequency merely to point out that a pole here does not introduce
self sustaining oscillation. FIG. 13 shows a generalized phase plot
for such a transfer function which shows the phase change being
substantially -180.degree. below the zero 170, rising to
substantially -90.degree. between the position of the zero 170 and
the pole 172 and reverting back to -180.degree. at frequencies
above that of the pole 172.
[0047] It is worthwhile pointing out that having a gain change of
-40 dB per decade, as shown as occurring at frequencies below that
of the zero 170 does not cause oscillation. This is
counterintuitive to many electronic engineers. However whether or
not a circuit oscillates is determined by the Barkhausen stability
criteria. Barkhausen's criteria applies to linear circuits within a
feedback loop. It states that if A is the gain of an amplifying
element in the forward path of the circuit and .beta. (J.omega.))
is the transfer function of the feedback path so that PA is the
loop gain around the feedback loop of the circuit, then the circuit
will sustain steady state oscillation only at frequencies for
which:
[0048] i) the loop gain is equal to unity in absolute magnitude,
that is |.beta.A|=1; and
[0049] ii) the phase shift around the loop is zero or an integer
multiple of 2.pi..
[0050] The Barkhausen criteria is a necessary condition for
oscillation but it is not a sufficient condition. Some circuits
which satisfy the criteria do not oscillate. However if a circuit
does not satisfy the criteria then it will not oscillate. This
confirms that high gain at relatively low frequencies, as shown in
FIG. 12 even though it is accompanied by a phase shift of
-180.degree. in the forward path plus a further -180.degree. by
virtue of forming the feedback loop (thus corresponding to
substantially 2.pi.) will not in itself create an oscillatory
condition.
[0051] The gain-frequency characteristic of FIG. 12 may be modified
by the introduction of further poles and zeros, it being merely
sufficient that the frequency response as it crosses the unity gain
value falls by only 20 dB per decade. Thus the response towards the
lower frequency end of the graph may fall by -40, -60, -80 or more
dB per decade depending on how many poles have been introduced in
the frequency response characteristic.
[0052] FIG. 14 illustrates a circuit which provides three poles and
two zeros in the frequency response, with a circuit for
illustrative purposes only being drawn as a single ended circuit
which receives a first input 200 representative of the negated
magnitude of the cell output signals and a second input 202
representative of the magnitude of the reference signals. Each of
these signals are input via respective impedances 210 and 212 to a
inverting input 214 of a first operational amplifier 216. The
operational amplifier 216 has its non-inverting input connected to
a small signal ground and a capacitor 220 connected between an
output 222 of the first amplifier 216 and its inverting input 214.
The existence of a capacitor 220 in the feedback loop of the
amplifier 216 will be recognized by the person skilled in the art
as forming an integrator. An ideal integrator places a pole at 0
Hz. However, given that in reality the amplifier 216 has a finite
gain, then the pole is, in reality, positioned close to but not
actually at 0 Hz. An output node 224 may be provided so as to
selectably allow operation of the circuit as described in the prior
art.
[0053] However, in accordance with an embodiment of the present
invention one or more poles are further provided in conjunction
with associated zeros. A pole and zero pair can be provided by a
circuit block, generally indicated 240, of which, in this example,
two such blocks 240, 240a have been provided in series. However the
invention can be practiced with the inclusion of only one circuit
block 240, or indeed three or more of such circuit blocks. The
circuit block 240 includes a further operational amplifier 250
having its non-inverting input connected to a small signal ground.
An input resistor 252 is provided between the inverting input of
the further operational amplifier 250 and the circuit which
supplies a signal to it, which in this instance is the integrator
formed around amplifier 216. A feedback loop around the further
amplifier 250 comprises a capacitor 254 in series with a resistor
256. It can be seen, that at low frequencies the impedance of the
capacitor 254 dominates and hence the feedback loop behaves as an
integrator. In this particular arrangement the further pole
provided by the circuit block 240 occurs substantially at 0 Hz. It
can also be seen that as the frequency rises the impedance of the
capacitor 254 reduces and starts to become less significant than
that of the further resistor 256. In fact, the value of the
capacitance C.sub.254 of the capacitor 254 and the resistance
R.sub.256 of the resistor 256 inserts a zero at
1 2 .pi. R 256 C 254 . ##EQU00002##
It can further be observed, by inspection, that at frequencies
above the frequency of the zero introduced in block 240, the gain
of block 240 is determined by the ratio of resistor 256 to the
ratio of resistor 252. An output node 260 is provided, such that a
signal picked off from this node 260 corresponds to the output node
50 of FIG. 1. Provided that the zero formed by capacitor 254 and
resistor 256 occurs below the unity gain frequency of the control
circuit 6, then stability will be ensured.
[0054] A further block similar to the first block, but with similar
parts designated by an appended "a" may also be provided to
introduce a second pole zero pair. The zero introduced by the
further circuit block need not be positioned at the same frequency
as the zero provided by the first block.
[0055] FIG. 15 illustrates a further variation of the circuit shown
in FIG. 1 where two control circuits are provided. An upper control
circuit, including additional pole-zero compensation as described
hereinbefore receives a first reference voltage from a first
reference voltage generator 270 and controls the voltage at the
first measurement terminal 30 to match that reference voltage
provided by the first reference voltage generator 270. A second
control circuit 302 receives a second reference voltage from a
second reference voltage generator 307 and controls the voltage at
the second measurement terminal 32 to be equal to the voltage from
the second reference voltage generator 307. Thus upper and lower
limbs of the sensor are driven to respective voltages in a dual
ended manner. A current measuring resistor 70 may be inserted in
either of the control loops (as by definition the current must be
the same in each control loop, and the voltage occurring across the
resistor 70 can be digitized by a differential input analog to
digital converter 80.
[0056] FIG. 16 is a circuit diagram of a further circuit that can
be used to provide a pole zero pair as is known to the person
skilled in the art. It comprises an operational amplifier 320
having a non inverting input that acts as a signal input. A
capacitor 322 is connected between an output of the amplifier 320
and an inverting input of the amplifier 320. A resistor 324
connects the inverting input to a small signal ground.
[0057] It should be noted that the designer may also place zeros in
the transfer characteristic without forming an associated pole.
Such a zero can be implemented as a high pass filter, either as an
active filter of a passive filter, as is known to the person
skilled in the art.
[0058] It is thus possible to modify the frequency response of the
or each control circuit by the appropriate insertion of additional
poles (preferably as integrators) and zeros (preferably as high
pass filters) so as to enable much higher loop gains to be employed
than would be the case if stability was ensured by merely reducing
the open loop gain of the control circuit by use of gain reduction
alone rather than by introduction of additional pole zero
pairs.
[0059] The claims presented here are written in single dependent
format so as to be suitable for filing at the USPTO. However, for
use in other jurisdictions where multiple dependent claims are
frequently used, each dependent claim is to be assumed to be
multiply dependent on all preceding dependent claims sharing the
same independent claim, except where this is clearly not
technically feasible.
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