This invention relates to a high accuracy, easy to fabricate. linear variable capacitive transducer for sensing planar angles. The transducer provides a linearly proportional analog or digital output for full circle range of angles (0 to 360°) and beyond. The bask transduction is accomplished using capacitive elements and the sensor part is made of plates that can be fabricated easily with good accuracy and precision.
Two signal evaluating circuits are proposed, one analog and the
other digital
Angle sensors are required in many application areas like automobile, marine, aerospace and industrial automation.
The present invention proposes a capacitive type transducer that provides an output thai: is linearly proportional to the angle being sensed. The measurement range of the proposed transducer covers the full circle ranee of angles, namely, 0 to 360° and beyond. The sensor part is made of simple shaped plates that can be easily fabricated with good accuracy. As stated above, two different means for signal evaluation are proposed, namely, the analog and the digital. The analog means provide an analog voltage output proportional to the angle being sensed. Since the proportionality constant in the analog signal evaluation means is dictated only by a pair of dc reference voltages, high accuracy is obtained bv using a couple of stable, precision dc reference voltages. In the digital means, the sensor capacitances become an integral part of a modified twin-dual slope GDCs and hence a direct digital output proportional to the angle being sensed is obtained there from. The output from the digital circuitry is dependent only on a dc reference voltage and a high frequency clock. Hence, high accuracy is obtained by employing a single stable dc reference voltage and clock- An added advantage of the digital technique is that the output from the transducer is insensitive to

changes in temperature, moisture, vertical displacement in the moving parts and parasitic capacitances.
The linear variable capacitive angle transducer, according to this invention, comprises a sensor part and a signal evaluating part, the sensor part consisting of three circular conducting plates mounted concentrically on a spindle, the top and bottom plate being made of four identical quarter circle parts, and immovably fixed, the four quarter circle parts of the top plate being positioned such that each top quarter circle part is aligned with the corresponding quarter circle part at the bottom plate, respectively, while the middle plate is semicircular and is freely rotatable between the top and bottom plates, the top, middle and the bottom plates being electrically insulated from one another, the spindle being
mechanically linked to the element whose angular position 0 is to he measured; a guard ling consisting of an electrically insulated annular ring immovably fixed to the spindle whose outer radius is exactly equal to the outer radius of the top or bottom plate, surrounding the middle plate, the radius of the middle plate rnip being such that it is slightly less than that of the inner radius of the annular guard ring whereby the guard ring encircles the middle plate but circumferentially spaced therefrom without any mechanical or electrical contact, a pair of dielectric plates interposed between the top and middle plate and between the middle plate and bottom plate, said dielectric plates being immovably fixed, the arrangement being such that if the annular ring, the middle plate and the four bottom quarter circle plates are all kept at the same potential, the resulting four capacitances
between the respective quarter circle plates vary as the said angle 0 varies; means for evaluating the capacitive output signal in accordance withthe relationship

between the said capacitive output and angle 6.
The proposed transducer will now be described with reference to Figs 1 to 7 of the accompanying drawings which illustrate by way of example and not by way of limitation embodiments of this invention.

The proposed transducer is made of a sensor part and a signal evaluation part part. The sensor part of the proposed transducer. shown in figure L consists of three circular shaped conducting plates mounted concentrically. While the top and bottom plates aw made of four quarter circle parts and firmly fixed, the middle plate MP, having a semi-circular shape, freely rotates between the top and bottom plates. The top. middle and the bottom plates are electrically insulated from one another. The tour, quarter circle parts of the top and bottom plates are identical in dimensions and are insulated from each other.
The four, quarter circle parts of the top plate (marked as TP1„ TP2? TP3 and TP4) are positioned such that each top quarter circle part is aligned with the corresponding quarter circle part at the bottom, marked as BPL BP2, BP3 and BP4 respectively. The middle, half circle plate MP mounted on a spindle and suitably anchored, rotates freely between the top and bottom plates. The spindle attached to the middle plate MP is mechanically linked to the element whose angular position Oh to be measured. An annular ring AP, whose outer radius is equal to the outer radius of the top or bottom plate, serves as the guard ring. The radius of the middle, half circle plate rmp is chosen to be slightly less than that of the inner radius of the annular guard ring AP and thus AP encircles the half circular plate, without any mechanical or electrical contact. If the annular ring AP, firmly fixed and insulated from the other parts of the sensor, the middle plate MP and the four bottom quarter circle plates are all kept at the same
potential it nicely turns out that the resulting four capacitances C\f C% C3 and C4 between lead pairs TP1-BP1, TP2-BP2, TP3-BP3 and TP4-BP4 respectively vary as (9 varies. The dimensions of the plates and the dielectric constant of the insulator employed determine the maximum value CMthat any of these capacitances (C1 C2, C3 and L\) can attain when the middle plate MP is in a position such that it is

completely outside the corresponding pair of plates of that capacitance. Here Cm [εσπ rm2/4(rMP+(2T1/Er}}] where sQ is the
permittivity of tree space, sr is the dielectric constant of the insulator employed, rMPand r1 are the thicknesses of the middle plate and the
insulator respectively. Minimum value of nearly zero occurs when the middle plate MP is positioned such that it covers the complete area of a pair of plates of a capacitance. Figure 2(a) shows the middle plate MP at the initial (0°) position for which C1 and C2 will be nearly zero and C3 and C4 will be equal to CM. If the middle plate is moved by an angle (l. ()-. 90°, as indicated in figure 2(b), the value of Cx will increase and that of C3 will decrease in equal proportions [=cM(0/90)|
and the values of C2 and C4 remain unaltered. As Ovaries from 0° to
3(30°. the values of capacitances C1 C2 C3 and C4 will vary as indicated in figure 3, resulting in two push-pull or differential pairs of capacitances, namely, C1 - C2 and C2- C4. It is easily seen that the values of the capacitance pair C3 and C3 change only in the intervals O°<0 <90° and 1.80°<# >270° and remain constant during 90° < 0 180° and 270° < 0 < 360°. Similarly C2 and C4 vary in a push-pull manner but in 9O°<0<18O° and 270°<&<360° intervals and remain constant during 0°s 0 <90° and 180°< 9 <270°. The values of



Substituting the values of Ch C^ C3 and C4, we get:
f {C\,C^Ci,Cs) = (9(8/360)-4, if 0 is measured in degrees or
(2)
^d{4liv)-A, if 6 is expressed in radians.
(3)
Here the function sgn(x) will be -1 for x < 0 and equal to +1 otherwise. The value of f (C1 C2 C3, C4) is also portrayed in figure 3. Equation (I) can be solved either using (a) an analog method or (b) digital method.

The schematic diagram of the signal evaluating circuitry that evaluates equation (1), using analog signal processing technique, is shown in figure 4. The differential capacitances C1 and C3, opamp OAl, Comparator OC1, four single pole double throw (SPDT) switches S1, S2, S3 and S4 along with resistor R\ constitute a relaxation oscillator, OSC-a. Similarly C2 and C4, opamp OA2, Comparator OC2, SPDT switches S5, S& S7, S8 and resistor R2 forms a second relaxation oscillator, OSC-p. In both oscillators, +Vp and -Vnare the dc reference voltages. First the working of OSC-a is explained here. Switches S1 S2, S3 and S4 are all controlled by the output of the comparator OC1 and hence change state simultaneously.
Let us assume that switches S1 S2, S3 and S4 are all at position 1. Then capacitor C1 is included in the feedback path of opamp OAl and C3 simply becomes a load on the output of OAl. However, it should be noted that, at any given instant, the voltage across C\ would be equal to that of C3, The opamp OAl with capacitor C1 in feedback path and resistor RI at the input becomes an integrator. Since S1i is in

position L the voltage connected to this integrator is VN and hence its output voitage will increase in the positive direction with a slope
as shown in figure 5. This situation will continue until voia
reaches 4- Vp, As soon as voi(y reaches -t- VF, say after 7# s, comparator OCI will change stale forcing switches S1 S2 S3and S4 to position 2. In this condition sensor capacitance C3 will come into the feedback path of OA1 and C\ will be connected to ground. Since S1 is now in position 2, +Vp will be connected to the input of the integrator and its
output voltage voiα, Yvill decrease gradually with a slope of
readies Vn As soon as voia reaches Vn say after a time period TL, comparator OCI will revert to its earlier state and will set switches S1, S2, S3 and S4 to position 1. Now the circuit will operate as explained earlier, leading to sustained oscillations. Figure 5 also portrays the output of switch S4 along with the output of the integrator. It is easily seen that
(4) The output of S4 is fed as input to a low pass filter LPFa. Now, if we
choose VF - VN = VR and the cut off frequency of the low pass filter LPFa to be very low as compared to the frequency of oscillation foa, [foa 1/T, T = TH + TL] then the output of the filter voa will be
(5) Substitution for TH and TL in terms of C1 and C2 in equation (5) we
get:
(6)

Similarly, switches S5, S6, S7 and S8 along with opamp OA2, comparator OC2, and resistance R2 combine with sensor capacitances C2 and C4 to form the second relaxation oscillator OSC-p whose operation is exactly same as OSC-a. Therefore the expression for output voltage vap from the low pass filter LPFp will be
(7) The voltage signals voa, vap and -VN are fed to an inverting three input
summer formed by four resistors and opamp OA3. The gain for voa and v0β is kept as -1 and the gain for -¥N is chosen to be -2. The output of OA3 is again inverted with opamp OA4 configured as an inverting unity gain amplifier. The output voltage vol from this
Voltage signals v0 C2 then the output of integrator OA1, v0u will ramp in the positive direction in small steps of value vR(cx -c3)/cFA for every clock period Tc as shown in figure 7.
If Ci C3 then the output of integrator OAL voiA will ramp in the negative direction in small steps of value for every
clock period 1\■_-.

Similarly depending on the values of C2 and C4? the output of integrator OA2, voiB will be either positive, zero or negative at the end of T1. At the end of T1, the second integration time T2 starts. At the beginning of T2, the outputs of the integrators OA1 and OA2 are sensed by the control unit through the comparators OC1 and OC2 respectively. During T2, if the output of OC1 is high (voiA is positive) then when the clock is low, S3 is set to position 1 and S1 and S2 are kept at position 2 and hence discharging C1 and C3. When the clock turns high, S3 is set to position 2 and S1 and S2 are kept at position 1 and hence C1 and C3 get charged to +VR. The charging currents of both C1 and C3 will now enter CFA and hence the output of the integrator OA1 will ramp down with small steps of value vR (cx + c3 )/cFA for every cock, as indicated in figure 7. The time taken

for the output yoiA to reach zero is measured as T24 (= +N24)- If at the end of TI the comparator output is zero (voiA is negative) then during the second integration time T2, when the clock is high switches S1, S2 and S3 are kept at position 1 and C1 and C3 get charged to +VR. When the clock turns low, these switches are toggled, transterring the charges in C\ and C3 cumulatively to CFA. Then for every clock cycle, a net charge of VR(CI + C3) is transferred to CFA and the output of the integrator OA1 will ramp up with small steps of value.
Here too the time taken for the output voiA to reach zero is measured as T2A and the polarity of T2A is taken as negative (= -N24))- During the second integration, simultaneously a similar process is carried out for CDC-B and depending on the values of C2 and C4, the second integration period T2B (+N2B or -N2B) is obtained. Figure 7 portrays the condition that would exist when 9 is 90°.
Since the net charge gained by either CFA or CFB is zero at the end of T2A or T2B , whichever is larger, we get


The control unit is programmed to evaluate (9) or (10) after obtaining N24 and .N2B, to obtain a digital value directly proportional to the angle being measured either in degrees or in radian respectively.

Claim:
1. A linear variable capacitive angle transducer comprising a sensor part and a signal evaluating part, the sensor part consisting of three circular conducting plates mounted concentrically on a spindle, the top and bottom plate being made of four identical quarter circle parts, and immovably fixed, the four quarter circle parts of the top plate being I positioned such that each top quarter circle part is aligned with the corresponding quarter circle part at the bottom plate, respectively, while the middle plate is semicircular and is freely rotatable between the top and bottom plates, the top, middle and the bottom plates being electrically insulated from one another, the spindle being mechanically linked to the element
whose angular position 0 is to be measured; a guard ring consisting of an electrically insulated annular ring immovably fixed to the spindle whose outer radius is exactly equal to the outer radius of the top or bottom plate, surrounding the middle plate, the radius of the middle plate being such that it is slightly less than that of the inner radius of the annular guard ring whereby the guard ring encircles the middle plate but circumferentially spaced therefrom without any mechanical or electrical contact, a pair of dielectric plates interposed between the top and middle plate and between the middle plate and bottom plate, said dielectric plates being immovably fixed, the arrangement being such that if the annular ring, the middle plate and the four bottom quarter circle plates are all kept at the same potential that the resulting four capacitances between the respective quarter circle plates vary as the said angle varies;


obtain a linear relationship between the said capacitive output and angle 9.
2. A transducer as claimed in Claim 1 wherein the said means is
analog based.
3. A transducer as claimed in Claim 1 wherein the said means is
digital based.
4. A linear variable capacitive angle transducer substantially as
herein described with reference to, and as illustrated in, the
accompanying drawings.