METHOD AND APPARATUS FOR MEASURING CAPACITY VARIATIONS OF A CONDENSER

The present invention relates to a method for measuring the capacity of a condenser, and in particular its capacity variations with respect to a nominal capacity value. The present invention also relates to an apparatus which carries out said method.

Known methods and apparatuses for measuring capacity variations of a condenser employ a bridge, known also as De Sauty-Wien bridge, which comprises two electric lines connected in parallel, in which the first line includes two resistors, while the second line includes said condenser, as well as a reference resistor and a reference condenser.

However, said known methods and apparatuses are relatively complex to be employed, since the balance condition of the bridge is determined by varying two parameters, for example the resistance of the reference resistor and the capacity of the reference condenser. Furthermore, the capacity of the reference condenser may vary due to its sensitivity to external factors, for example the humidity or the temperature or the ageing, so that the measurements may be imprecise.

It is therefore an object of the present invention to provide a method and an apparatus which are free from said disadvantages. Said object is achieved with a method and an apparatus, the main features of which are disclosed in claims 1 and 25, respectively, while other features are disclosed in the remaining claims.

Thanks to the measurement of the phase shift in the measurement bridge, the method and the apparatus according to the present invention provide accurate measurements in a simple and quick manner, especially if a phase comparator connected to the bridge is employed.

Furthermore, the reference condenser can be eliminated, so as to reduce the measurement complexity, costs and errors. For measuring the capacity variations it is in fact possible to measure also the phase shift only or another parameter of the bridge, in particular the frequency of the reference signal or the resistance of the reference resistor, if the bridge is balanced again after the phase shift.

The method and the apparatus according to the present invention preferably

employ a particular phase comparator, easy and precise, for providing a continuous electric signal proportional to the phase shift in the bridge.

Said phase comparator is preferably connected to an electronic control unit for automatically carrying out the calculations of the capacity variation and/or for automatically vary with a feedback the parameters of the bridge, so as to provide accurate measurements in real time.

The condenser to be measured is preferably provided with a temperature sensor connected to the control unit, so that the measurements are always correct even with temperature variations. Further advantages and features of the method and the apparatus according to the present invention will become clear to those skilled in the art from the following detailed and non-limiting description of some embodiments thereof with reference to the attached drawings, wherein:

- figure 1 shows a scheme of the bridge of the apparatus; - figures 2 and 3 show vector diagrams of the bridge of figure 1;

- figure 4 shows a scheme of the bridge of figure 1 connected to the phase comparator of the apparatus; >

- figure 5 shows a scheme of the phase comparator of figure 4;

- figures 6 and 7 show diagrams of the phase comparator of figure 5; - figure 8 shows a scheme of a first embodiment of the apparatus;

- figure 9 shows a scheme of a second embodiment of the apparatus;

- figures 10 and 11 show schemes of the condenser of the bridge of figure 1; and

- figure 12 shows a vector diagram of the bridge of figure 1 with the condenser of figure 11. Referring to figure 1, it is seen that the apparatus according to the present invention comprises in a known way a variable voltage generator OSC, for example an oscillator which supplies a reference signal to a bridge comprising two electric lines connected in parallel through two outer connections C and D. The first line includes a first resistor Rl connected in series through a first inner connection A to a second resistor R2, while the second line includes a condenser Cx to be measured connected in series through a second inner connection B to a reference resistor Rx. The position of

condenser Cx and of the reference resistor Rx can be inverted. The resistances of the first resistor Rl and of the second resistor R2, as well as the nominal capacity of condenser Cx and the resistance of the reference resistor Rx, are determined before carrying out the measurement and remain substantially constant during the ' measurement. For example, the resistances of the first resistor Rl and of the second resistor R2 are fixed and the same, while for balancing said bridge the resistance of the reference resistor Rx is varied for being substantially equal to the capacitive reactance Xcx of condenser Cx, so that the reference resistor Rx is preferably a variable resistor, for example a rheostat or a potentiometer. Generator OSC provides to the outer connections C and D of said bridge a reference signal which oscillates with a frequency fo lower than the frequencies in which condenser Cx undergoes phenomena of dielectric relaxation.

Referring also to figure 2, it is seen that, according to the invention, the subject- matter of the measurement is the phase shift between vector V _a t, relative to the voltage between the inner connections A and B and vector V _ca relative to the voltage between the outer connection C and the inner connection A, i.e. to a signal in a phase concordance with the reference signal provided by generator OSC.

Figure 2 discloses the arrangement of the vector present in the bridge in its balance condition, wherein: V cd = Vca + Vad = ^cb + V _b d

Since vector V _c £ is in a phase concordance with the current in condenser Cx, it will be always phase shifted of 90° with respect to V^ (for simplicity, the loss current of condenser Cx is assumed null). Point B is therefore always on the semicircle with center A and radius AB. Without varying the resistance of the reference resistor Rx, the method and the apparatus according to the present invention can measure the variation δc of the capacity of condenser Cx with respect to its nominal value.

Figure 3 shows this new circumstance, in which the difference with respect to the previous case consists of angle θ of the phase shift of vector V _a b which is proportional

o δc, i.e. 9- = 0 when δc =0.

The new capacitive reactance is now equal to:

X(Cx + δc)

Angle α formed by vectors V ₀ ^ and V _ca is: α = (180° - 90° - θ) / 2 = (90° - θ) / 2 = arctg (V _bd I V _cb ) = arctg (X _{(Cx + δc)} / Rx) so that:

X( _{Cx + δc)} / Rx = tg [(90° - θ) / 2] = tgα i.e.:

1 / [ω Rx (Cx + δc)] = tgα where ω is the pulsation at frequency fό of the reference signal.

Therefore:

1 = ω Rx tgα (Cx + δc) i.e.:

1 = ω Rx Cx tgα + ω Rx δc tgα and thus:

δc = (1 - co Rx Cx tgα) / (ω Rx tgα)

Thereby, by carrying out the suitable reductions the following formula is obtained:

δc = 1 / (co Rx tgα) - Cx Finally, since Xc _x = Rx = 1/ω Cx = l/2π fo Cx , for the balance condition of the bridge the following formula is obtained:

δc = 1/2 π f ₀ Rxtgα - 1/2 π f ₀ Rx = 1/ (2π f ₀ Rx) * (1/ tgα - 1) i.e.:

δc = 1/ (2π fo Rx) * (1/ tg[(90° - θ) / 2] - 1) This formula provides the capacity variation δc of condenser Cx by knowing frequency fo of the reference signal, the resistance of the reference resistor Rx and angle θ depending on vectors V _a b and V _ca .

Since frequency f ₀ of the reference signal and the resistance of the reference resistor Rx are known, said phase comparator must determine only angle 0 for

obtaining the capacity variation δc.

• Referring to figure 4, it is seen that for said purpose the phase comparator PC is connected to the inner connections A, B and to the outer connection C of the above described bridge for comparing the phases of the two vectors V _a £, and V _ca by supplying to its output Vout a continuous voltage proportional to angle β, which corresponds to the angle between the two vectors reduced by 90°, i.e. to the additional phase shift between the two vectors with respect of the balance condition of the measurement bridge in which the phase shift is 90°. The voltage at output Vout of the phase comparator PC further depends on the input reference voltage Vref. The phase comparator PC outputs a null voltage Vout when the two vectors V _ca and V _a b are phase shifted by 90°, while it outputs a voltage equal to a reference value Vref when the two vectors V _ca and V _α & are in a phase concordance. The conversion is linear with the intermediate phase shifts.

In the following description it is assumed, for a greater clarity, that the phase comparator PC is a device with an infinite input impedance, a null input capacity and a null hysteresis.

Referring to figure 5, it is seen that the phase comparator PC preferably comprises two voltage comparators CMPl, CMP2 and a logic gate XOR, which are powered with the reference voltages +Vref and -Vref. The non- inverting input (+) of the first voltage comparator CMPl is connected to the inner connection B between condenser Cx and the reference resistor Rx, while the inverting input (-) of the first voltage comparator CMPl is connected to the inner connection A between the first resistor Rl and the second resistor R2.

The non-inverting input (+) of the second voltage comparator GMP2 is connected to the inner connection A between the first resistor Rl and the second resistor R2, while, the inverting input (-) of the second voltage comparator CMP2 is connected to the outer connection C between the second resistor R2 and the reference resistor Rx.

As an alternative, since the phase of vector V _ca coincides with the phase of vectors V _c d and V _a d, the inputs of the second voltage comparator CMP2 can be connected to the

outer connections C and D or to the inner connection A and to outer connection D, respectively. In general, it is sufficient that the signal supplied to the second voltage comparator CMP2 is in a phase concordance with the sine signal generated by generator OSC. The outputs of the voltage comparators CMPl and CMP2 are connected to the inputs of the logic gate XOR. The output of the logic gate XOR is in turn connected to a low pass filter LPF, comprising for example a RC circuit of the known kind which performs the function of a mean value detector. The cutoff frequency of this circuit RC is much lower than frequency f ₀ of the reference signal. The . output of filter LPF is connected to output Vout of the phase comparator PC.

Figures 6 and 7 show the variations during the time of signals V _α £ and V _ca and of the corresponding output signals from components CMPl, CMP2, XOR and LPF of the phase comparator PC when the bridge is balanced (figure 6: θ = O and Vout = O) or when the bridge is unbalanced (figure 7: θ > 0 and Vout > 0), respectively. Values Vout and θ are directly proportional and their ratio is linear.

Filter LPF extracts the mean value Ymed of the output of the logic gate XOR, i.e.:

Vout = Ymed = l/(T/2) ζ' ² y(t)dt where T is the period of the reference signal at frequency f ₀ . If θ = 0, the function y(t) is a square wave with a duty cycle of 50% and its mean value is obviously Ymed = 0. If θ = 45°, then Ymed = Vref / 2, while if θ = 90°, then Ymed = Vref.

Referring to figure 8, it is seen that in a first embodiment of the apparatus according to the present invention the output of the phase comparator PC is connected to an electronic control unit CU of a known kind, for example a microcontroller, through an amplifier GA and an analog-to-digital converter ADC, so that the digital value corresponding to signal Vout can be processed by the control unit CU. For this purpose, the control unit CU is provided with a digital memory DM in which conversion tables, working and/or correction parameters can be stored. The control unit

CU can also be connected to a data interface DI and/or to input and/or output devices 10, for example a keyboard and a display.

The control unit CU is suitably connected to resistor Rx for varying with a feedback the value of its resistance according to value Vout, so as to automatically zero the bridge. For this purpose, resistor Rx is preferably a digitally controlled potentiometer or DCP. The control unit CU is also connected to a second variable resistor Rg ₅ also preferably consisting of a digitally controlled potentiometer, so as to vary with a feedback the gain of amplifier GA according to value Vout for obtaining the maximum resolution in the measurement of the capacity variation of δc. Furthermore, condenser Cx is preferably provided with a temperature sensor TS, for example of the PTlOO kind, connected to the control unit CU through a sensor interface SI. The digital memoiy DM therefore contains a correction ^■ table according to the temperature measured by the temperature sensor TS for correcting the values of the capacity variation of δc due to the variation of the dielectric constant of condenser Cx according to the temperature variation of the latter.

Referring to figure 9, it is seen that a second embodiment of the apparatus according to the present invention comprises again a phase shift bridge connected to a phase comparator PC, however the frequency of the reference signal output by the voltage generator OSC is varied with a feedback so that the balance condition of the bridge is always satisfied, i.e. it is always θ = 0.

In this embodiment the frequency of the reference signal generated by generator OSC is varied in an aiitomatic manner until the capacitive reactance Xc — X( _{Cx + δc)} of condenser Cx is equal to the resistance of resistor Rx.

In other embodiments of the invention the resistance of the reference resistor Rx can be varied for balancing the bridge.

If fo is the frequency in which the bridge is balanced at the beginning of the measurement, when the bridge is unbalanced due to the capacity variation δc the new frequency fi of the reference signal must be determined so that the bridge is balanced again, i.e. R _x = X _c = X(Cx + δC>

The frequency difference f ₀ - f _\ depends on value δc in the way described hereinunder. The capacitive reactance Xc _x of condenser Cx at frequency f ₀ is:

Xcx= l / (2π f ₀ Cχ) so that: . since Rx = Xc _x for the balance condition of the bridge at frequency f ₀ . The total reactance Xc generated by the parallel contribution of Cx and δc at frequency I ₁ is: Xc= 1 / [2π fi(C _{x +} δc)] = 1 / (2π f, C _x + 2π ft δ _c ) = 1 / (2π fi / 2π f ₀ R _x + 2π ft δ _c ) =

=1 / ( ft / foRx + 2π ftδ _c ) = f ₀ Rχ/ ( ft + 2π ft f ₀ δ _c R _x ) but also in this new circumstance Xc = R _x , so that: R _x ( ft+ 2π ft fo δ _c Rx) = f ₀ R _x

R _x ft + 2π ft fo δ _c R _x ² = f ₀ R _x and by dividing all by f ₀ Rχ _: f ₁ / f _o + 2π ft fo δ _c Rχ = l so that: which becomes:

Since 1/2 π Rx can be considered a constant of the measurement bridge, this formula can be more conveniently written as: δ _c = K * ( fo - ft) / fo ft

The latter formula clearly express that the capacity variation δc of condenser Cx is proportional to the difference of the frequencies f ₀ and ft (before and after the measurement) and inversely proportional to their product. hi the present embodiment, the output of the phase comparator PC is connected to a zero detector, in particular to the non-inverting input of a voltage comparator ZD having the inverting input connected to earth. The output of comparator ZD therefore assumes only two values 0 and 1, corresponding to an "up" or "down" signal, sent to generator OSC, which suitably comprises a voltage controlled oscillator or VCO.

Generator OSC therefore follows the balance point of the bridge (condition 0 = 0) by supplying a reference signal, the frequency ft of which increases or decreases according

to the received "up" or "down" command. Frequency JE ₁ associated to the signal of generator OSC is sent in a digital form to the control unit CU, which obtains the value of δc thanks to the above cited formula.

It is therefore clear that the first embodiment of the apparatus according to the present invention works as a two pan balance in which, after the tare has been zeroed, the weight variation is indicated by the position of the pointer on the graduated scale.

Also the second, embodiment works as a two pan balance in which the tare is zeroed, however the weight variation is measured by adding weights on a pan for taking the pointer again to the zero of the graduated scale. The advantage offered by the second embodiment, exactly as in the case of the balance, consists of a much wider scale end, i.e. of a wider range of measurable values.

In the present description condenser Cx has been assumed as ideal, i.e. without any loss member. In fact any real condenser, including condenser Cx, can be represented by the circuit of figure 10, in which L and RA represent the eddy inductance and the eddy resistance, respectively, which are caused by the electric connections between the terminals of condenser Cx and the relevant connections B and C of the bridge, while RB represents the resistance caused by the loss in the dielectric inserted between the plates of condenser Cx. Since the inductive reactance X _L is generally negligible at frequency f ₀ of the reference signal, the circuit of figure 11 can suitably approximate the circuit of figure 10.

In this approximate circuit Req and Cep are the equivalent resistor and the equivalent condenser, respectively, the respective resistance and capacity of which can be calculated in a known way through the knowledge of the values of resistances RA, RB and of the capacity of condenser Cx. The vector diagram of figure 12 represents in an emphasized manner the circuit of figure 11. The vector calculation for the value of the capacity variation δc is this more complex. In particular, the vector between the inner connections A and B of the bridge is vector V _a ι • and angle θ is, in fact, 9-'. hi the practice, the tests carried out on some materials of industrial importance have pointed out that the eddy members are so small that can be neglected. For being

employed as a laboratory instrument, for which high precisions are required, memory DM of the apparatus according to the present invention contains a series of correction parameters relating not only to said eddy members, but also to all the mechanical, electric and electronic members of the apparatus, so that the control unit CU can calculate and supply measurements always accurate and reliable on the base of these correction parameters.

Further modifications and/or additions may be made by those skilled in the art to the hereinabove described and illustrated embodiments while remaining within the scope of the following claims.