Capacitance measuring apparatus with means for nulling the resistive component

A circuit and method for measuring the capacitance of a medium independent of the resistivity of the medium. A triangular voltage is applied to plates immersed in the medium to generate both a resistive current component in phase with the triangular voltage and a capacitive current component in phase with a differential of the triangular voltage. The resistive and capacitive current components are summed with a selectable current which is provided having a phase .pi. radians out of phase with the triangular voltage and having an amplitude related to a control signal. The summed current is sampled over a time period phase shifted from the capacitive current component and then integrated so that the capacitive current component integrates to zero and the integral of the resistive current component minus the selectable current provides the control signal. In response to the control signal, the selectable current is varied until the sum of the selectable current and resistive current component are nulled. This summed current is then sampled in phase with the capacitive current component thereby obtaining a measurment of capacitance independent of resistance.

BACKGROUND 
The field of the invention relates to the measurement of capacitance, in 
particular the measurement of lossy capacitance. Stated another way, the 
measurement of capacitance shunted by a low resistance. 
As the world's petroleum reserves become depleted, interest has increased 
in adapting vehicles to run on a mixture of gasoline and alcohol 
(including ethanol and methanol). With present technology, vehicles may be 
adapted to run on a gasoline/alcohol mixture by altering the engine's 
air/fuel ratio and/or ignition timing to compensate for the lower energy 
density of these fuel mixtures. Since the fuel mixture may vary depending 
upon both gasoline and alcohol availability in a specific locality, it is 
desirable to have an on-board sensor for providing an engine controller 
with an indication of gasoline/alcohol mixture in the fuel tank. 
Gasoline and alcohol have substantially different dielectric constants. 
Accordingly, measurement of the capacitance between two parallel plates 
suspended in the fuel tank may provide an approximation of the 
gasoline/alcohol mixture. However, the gasoline/alcohol mixture contains 
contaminants, such as sodium or calcium ions, from dessicants, thereby 
adding a resistive component between the plates. This parallel resistive 
component may be sufficiently low to overwhelm capacitive measurement 
unless very high frequencies, such as 10 MHz, are used. For example, when 
measured at 30 KHz, the resistive current component between the plates may 
be approximately 20 times greater than the capacitive current component. 
A prior approach for on-board measurement is disclosed in IEEE Transactions 
on Vehicular Technology, Volume VT-27, No. 3, August 1978, page 142, 
entitled "An On-Board Sensor For Percent Alcohol", by J. W. Hille and P. 
R. Rabe. This approach requires a tuned circuit for comparing the 
capacitance to be measured to a calibrated reference. A disadvantage with 
this approach is that variations in the reference will adversely affect 
the measurement. Further, the problem of a high resistive current 
component does not appear to be addressed. 
An approach to measurement of capacitance in general, rather than the 
capacitance of a gasoline/alcohol mixture, is disclosed in U.S. Pat. No. 
3,947,760. A circuit is disclosed for measuring both the resistance and 
capacitance of a capacitor. The ratio of charging and discharging times of 
two integrative capacitors is compared to determine the desired 
measurements. This circuit has the disadvantage of requiring a variable 
voltage source. In addition, the problem of a high resistive component 
overwhelming the capacitive current component does not appear to be 
addressed. 
SUMMARY OF THE INVENTION 
An object of the invention described herein is to provide both an apparatus 
and a method for accurately measuring capacitance having a low shunting 
resistance. 
The above problems and disadvantages are overcome, and object achieved by 
the apparatus and method described herein for measuring the capacitance of 
a medium independently of the resistivity of the medium. In one aspect of 
the invention, the apparatus comprises: means for applying a periodic 
voltage to plates immersed in the medium to generate both a resistive 
current component flowing through the medium in phase with the periodic 
voltage and a capacitive current component flowing through the medium in 
phase with a time derivitive of the periodic voltage; current providing 
means coupled to both the periodic voltage and a control signal for 
providing a selectable current .pi. radians out of phase with the periodic 
voltage and having an amplitude related to the control signal; current 
summing means coupled to both the medium and the current providing means 
for summing the selectable current and the resistive current component and 
the capacitive current component; sampling means for sampling the summed 
current over a time period in phase with the resistive current component; 
averaging means coupled to the sampling means for averaging the capacitive 
current component to zero and for averaging the resistive current 
component minus the selectable current to generate the control signal; 
means for coupling the control signal to the current providing means so 
that the current providing means provides the selectable current 
substantially equal to the resistive current component and .pi. radians 
out of phase with the resistive current component thereby nulling the 
resistive current component from the summed current; and detecting means 
coupled to the summing means and in phase with the capacitive current 
component for detecting the capacitive current component independently of 
the resistive current component. 
By nulling the resistive current component, as described hereinabove, an 
advantage is obtained of obtaining a measurement of the capacitive current 
component which would otherwise be overwhelmed by the resistive current 
component. An additional advantage is that an accurate measurement of 
capacitance is obtained without the need of an accurately calibrated 
reference. A further advantage is that a variable source of periodic 
voltage is not required. Still another advantage obtained is that a high 
frequency periodic voltage is not required. 
In another aspect of the invention, an accurate measurement of the 
alcohol/gasoline fuel mixture in an automobile is provided by measuring 
the capacitance between two plates in the fuel mixture independently of 
the resistivity of the fuel mixture. More specifically, this apparatus 
comprises: a voltage source applying a periodic voltage accross parallel 
capacitive plates positioned in the mixture to generate both a resistive 
current component in phase with said periodic voltage and a capacitive 
current component in phase with a time derivitive of said periodic 
voltage; a current generator coupled to both the periodic voltage and a 
control signal for providing a selectable current .pi. radians out of 
phase with the periodic voltage and having an amplitude related to the 
control signal; current summing means coupled to both the parallel plates 
and the current generator for summing the selectable current and the 
resistive current component and the capacitive current component; sampling 
means for sampling the summed current over a time period in phase with the 
resistive current component; an integrator coupled to the sampling means 
for integrating the capacitive current component to zero and for 
integrating the resistive current component plus the selectable current to 
define the control signal; a feedback loop for coupling the control signal 
to the current generator so that the current generator provides the 
selectable current substantially equal to the resistive current component 
and .pi. radians out of phase with the resistive current component thereby 
nulling the resistive current component from the summed current; measuring 
means coupled to the summing means and in phase with the capacitive 
current component for measuring the capacitive current component 
independently of the resistive current component; and means for converting 
the measurement of said capacitive current component into an indication of 
the alcohol/gasoline fuel mixture.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring first to FIGS. 1 and 2, a block diagram (FIG. 1) and associated 
electrical signal wave forms (FIG. 2) illustrate an example of one circuit 
wherein the invention is used to advantage. More specifically, capacitance 
measuring circuit 10 is shown for measuring the capacitance of a 
gasoline/alcohol fuel mixture in the fuel tank (not shown) of a motor 
vehicle. In response to the measurement of capacitance, look up table 14 
provides engine fuel controller 16 with a measurement of the alcohol 
content of the gasoline/alcohol fuel mixture for proper air/fuel ratio 
control. Since the dielectric constant of alcohol is approximately an 
order of magnitude greater than the dielectric constant of gasoline, an 
accurate measurement of capacitance is converted, by look up table 14, 
into a measurement of the alcohol content of the gasoline/alcohol fuel 
mixture. 
Capacitor 18 and resistor 20 schematically illustrate the respective 
capacitance and shunt resistance between two spaced capacitive parallel 
plates 22 having a medium therebetween. In this example, the medium is the 
gasoline/alcohol fuel mixture. Resistor 20 is representative of the 
resistance caused by contaminants such as sodium or calcium ions in the 
fuel mixture. These contaminants may have sufficient concentration to 
render the fuel mixture conductive. For example, measurements by the 
inventor herein have indicated that 800 ohms is not unusual for a 10 
picofarad capacitor. Measurements have also indicated that the resistive 
current component can be approximately 20 times greater than the 
capacitive current component. Accordingly, previous approaches to 
measuring the capacitance of capacitor 18 have been frustrated by the 
resistive current component. As described in greater detail hereinafter, 
capacitive measuring circuit 10 solves the problem of providing an 
accurate measurement of capacitance when shunted by a low resistance. 
Continuing with FIGS. 1 and 2, a general description of circuit 10 is 
presented. A more detailed description of circuit 10 is provided 
hereinafter with particular reference to FIG. 3. Conventional square wave 
generator 26 provides a voltage square wave V.sub.SW to triangular wave 
generator 30. Square wave V.sub.SW is integrated by triangular wave 
generator 30 to generate a triangular voltage wave V.sub.T. It is seen 
that the zero crossings of V.sub.T are .pi./2 radians shifted from the 
zero crossings of V.sub.SW. Stated another way, V.sub.T is .pi./2 radians 
out of phase with V.sub.SW. 
V.sub.T is shown applied across capacitive plates 22 immersed in the 
gasoline/alcohol mixture. Capacitive plates 22 are schematically shown 
represented as capacitor 18, with a dielectric constant determined by the 
percent of alcohol in the gasoline/alcohol mixture, and a parallel shunt 
resistor 20. In response to V.sub.T, resistive current component i(R) 
through resistor 20 and capacitive current component i(C) are generated. 
Resistive current component i(R) is in phase with V.sub.T and capacitive 
current component i(C) is essentially the time derivitive of V.sub.T. That 
is, i(C) is proportional to d V.sub.T /d(T). Accordingly, i(C) is 
essentially a square wave having zero crossings in phase with the 
directional changes of V.sub.T. It is to be noted that the relative 
amplitudes shown in FIG. 2 are not to scale. For example, as stated 
previously herein, resistive current component i(R) may be approximately 
20 times greater than capacitive current component i(C). 
In general terms, resistive current component i(R) and capacitive current 
component i(C) are summed in current summer 32 with a selectable current 
i(ST) from current providing circuit 34. Selectable current i(ST) is .pi. 
radians out of phase with resistive current component i(R) and has an 
amplitude which varies with electronic control signal E(R). For reasons 
described herein after, E(R) is generated through a feedback loop for 
nulling resistive current component i(R). 
More specifically, current providing circuit 34 is shown having V.sub.T 
applied across it and is also shown including, in this particular example, 
the parallel combination of variable resistor 78 and negative current 
generator 38. The resistance of variable resistor 78, RV, varies in 
proportion to the amplitude of E(R). Since V.sub.T is applied across 
variable resistor 36, variable current i(RV) therethrough is a function of 
both VT and E(R), and in phase with V.sub.T. Negative current generator 38 
provides negative current i(T) shown .pi.0 radians out of phase with 
V.sub.T and, accordingly, i(R). Thus, selectable current i(ST)=i(RV)-i(T). 
Continuing with FIG. 1, and also referring to FIG. 3, the output of current 
summer 32 is a voltage V(S) proportional to the summed current i(S) where 
i(S)=i(R)+i(C)-i(T)+i(RV). The output of current summer 32 is coupled to 
both resistive sampling circuit 42 and capacitive sampling circuit 44. 
Resistive sampling circuit 42 samples i(S) in phase with the zero 
crossings of V.sub.T as determined by sampling signal S(T) from zero 
crossing detector 42A. The sampled summed current is then integrated in 
integrator 46, the integral thereof defining E(R). Since capacitive 
current component i(C) is essentially a square wave having zero crossing 
points .pi./2 radians out of phase with S(T), capacitive current component 
i(C) will integrate to zero. Accordingly, E(R) represents the integral of 
the summed current components without capacitive current component i(C) as 
follows: 
EQU E(R)=.intg. i(R)+i(RV)-i(T) dt 
In response to E(R), variable resistance RV of variable resistor 36 is 
changed such that i(R)+i(RV)-i(T)=zero. This is diagramatically shown in 
FIG. 3. After the above steady state operation is achieved, summed current 
i(S) is then equal to capacitive current component i(C). As previously 
described herein, resistive current component i(R) has been nulled so that 
an accurate measurement of capacitive current component i(C) and, 
accordingly, the capacitance of the gasoline/alcohol mixture, is obtained. 
Continuing with FIG. 1, capacitive sampling circuit 44 samples summed 
current i(S) in phase with sampling signal S(SW) from zero crossing 
detector 44. Sampling signal S(SW) is in phase with the change in 
direction of V.sub.T and, accordingly, in phase with capacitive current 
component i(C). The output of capacitive sampling circuit 44 is a voltage 
V(C) having an amplitude directly proportional to the capacitance of the 
medium measured, in this case the gasoline/alcohol mixture. Continuing 
with this illustrative use of capacitive measuring circuit 10, V(C) is 
converted by look up table 14 into an indication of the alcohol content of 
the gasoline/alcohol mixture for use by engine fuel controller 16. Since 
alcohol has a lower energy density than gasoline, engine fuel controller 
16 increases the fuel delivered to the internal combustion engine (not 
shown) as a function of the alcohol content in the gasoline/alcohol 
mixture. 
In view of the above, it is seen that an advantage is obtained of providing 
an accurate measurement of capacitance by nulling out the resistive 
current component. Otherwise, in applications where the resistive current 
component is significantly larger than the capacitive current component, 
an acceptable measurement of the capacitive current component would not be 
obtainable. A further advantage is obtained because the high frequencies 
used in prior approaches to obtain a measurement of capacitance are not 
required here. In one application in which the invention was used to 
advantage, a 30 KHz square wave generator was used. With the low 
frequencies utilized, as compared to prior approaches, less expensive 
electronic components are used. For example, referring to the detailed 
electronic schematic shown in FIG. 4, nine conventional operational 
amplifiers are used. 
Referring now to FIG. 4 wherein like numerals refer to like parts shown in 
FIG. 1, a detailed example of a circuit which may be used to advantage for 
capacitance measurement circuit 10 is shown. Square wave generator 26 is 
shown in this example as a square wave oscillator including operational 
amplifier 50 having feedback to the positive input terminal through 
capacitor 52 and a resistive voltage divider defined by resistors 54 and 
56. Feedback is also shown to the negative input terminal through a 
resistive voltage divider defined by resistors 58 and 60. Triangular wave 
generator 30 is shown in this example as an integrator circuit including 
operational amplifier 64 for integrating V(SW) from square wave generator 
26 to generate V.sub.T. Operational amplifier 64 is shown configured as an 
integrator with feedback through capacitor 66. A conventional DC 
eliminator shown defined by resistors 68 and 69, and capacitor 70, is 
shown as another feedback loop to eliminate the DC component. Capacitor 72 
is shown coupled to the negative input terminal for DC blocking. 
Variable resistor circuit 36 of current providing circuit 34 is shown as 
resistor 78, having a light sensitive resistance, optically coupled to 
optical diode 80 which is responsive to electronic control signal E(R). 
Voltage translation of E(R) is shown through a conventional resistive 
voltage divider, resistors 82 and 84, coupled to a supply voltage 
V.sub.Ref. Negative current generator 38, of current providing circuit 34, 
is shown as conventional operational amplifier 86, configured as a phase 
inverter with gain provided by the ratio of feedback resistor 90 to 
negative input resistor 94. Adjustable capacitor 92, shown connected 
parallel to input resistor 94, aligns the phase of a negative current i(T) 
from operational amplifier 86 with V.sub.T. Resistor 88 is shown to 
convert the voltage output of operational amplifier 86 to i(T). 
Current sensing means 32 is shown as operational amplifier 98 having 
feedback resistor 102 coupled to the negative input terminal. In a 
conventional manner, the negative input terminal acts as a virtual ground 
wherein i(R), i(C), i(T), and i(RV) are summed. Operational amplifier 98 
also acts as a current to voltage converter providing an output voltage 
V(S) directly related to the summed currents to resistive sampling circuit 
42. 
Resistive sampling circuit 42 is shown including operational amplifier 104 
having feedback resistor 106, negative input resistor 108, positive input 
resistor 110, and zero crossing detector 42A coupled to the positive input 
terminal. Zero crossing detector 42A is shown including operational 
amplifier 112 with a negative input coupled to V.sub.T and an inverted 
output coupled to the gate of FET 114. Sampling signal S(T) is provided by 
coupling ground to the positive input terminal of operational amplifier 
104 through FET 114 in response to V.sub.T. In accordance with the above 
description, sampling signal S(T) is .pi. radians phase shifted from 
V.sub.T and switches at the zero crossings of V.sub.T. Thus, the output of 
resistive sampling circuit 42 is phase inverted from V(S) when S(T) is 
shorted to ground and its output is directly related to V(S) when S(T) is 
floating. 
Referring to FIGS. 2 and 3, resistive sampling circuit 42 positively 
rectifies i(R) and i(RV), and negatively rectifies i(T). Since i(C) is 
.pi./2 radians phase shifted from S(T), i(C) is integrated to zero by 
integrator 46. 
Referring back to FIG. 4, integrator 46 is shown as a conventional 
operational amplifier 116 configured as an integrator with feedback 
capacitor 118 and negative input resistor 120. Since integrator 46 nulls 
capacitive current component i(C), the output of integrator 46 is 
therefore representative of the integral, ER, of the remaining recitified 
currents: i(RV) +i(R)-i(T). As previously discussed, variable resistance 
RV is varied in response to ER so that i(RV)+i(R)-i(T)=zero. 
The output of current summing means 32 is also coupled to capacitive 
sampling circuit 44. This circuit is shown including operational amplifier 
122 having feedback resistor 124, negative input resistor 126, positive 
input resistor 128 and zero crossing detector 44A coupled to the positive 
input terminal of operational amplifier 122. Zero crossing detector 44A is 
shown having operational amplifier 129 with an negative input coupled to 
V.sub.SW and output coupled to the gate of FET 130. Sampling signal S(W) 
is provided by a coupling ground to the positive input terminal of 
operational amplifier 122 through FET 130 in response to V.sub.SW. 
Accordingly, sampling signed S(W) is .pi. radians phase shifted from 
V.sub.SW. 
When S(W) is shorted to ground, capacitive sampling circuit 44 inverts 
V(S), and when S(W) is floating, capacitive sampling circuit 44 passes 
V(S) through resistors 124 and 126. Since S(W) is in phase with i(C), and 
i(R) has been nulled as previously described, the output of capacitive 
sampling circuit 44 is a voltage related to the capacitive current 
component i(C). 
This concludes the description of the preferred embodiment. The reading of 
it by those skilled in the art will bring to mind many alterations and 
modifications without departing from the spirit and scope of the 
invention. For example, although analogue components, such as operational 
amplifiers, are shown in the detailed electrical schematic presented in 
FIG. 4, those skilled in the art will recognize that other circuits may be 
used such as digital circuits with appropriate sampling signals. 
Accordingly, it is intended that the scope of the invention be limited 
only by the following claims.