A novel readout circuit for interfacing single element resistive sensors is presented in this paper. The proposed scheme is based on a new relaxation oscillator (RO). The RO, along with a timer ...counter provides a digital output proportional to the resistance of the sensor. The output characteristic of most of the existing readout circuits for resistive sensors suffers from gain, offset, and nonlinearity errors. The sources of errors include various nonideal circuit parameters and their drift. The output of the proposed readout circuit has a special feature that it is not a function of the circuit parameters such as: 1) offset voltages of the opamps and comparators; 2) bias currents of the opamps and comparators; 3) gain of various units employed; 4) ON-resistance of the switches; 5) value or mismatch in the magnitudes of the reference voltages employed; 6) delay of the switches and comparator; 7) leakage current of the switch; and 8) slew rate of the opamp. Such a scheme will be useful for high accuracy measurements, even when the parameters 1)-8) may vary or drift, due to variation in the measurement environment. A prototype of the proposed readout scheme has been developed in the laboratory and the performance has been evaluated under various conditions. The output was found to be linear with a worst-case nonlinearity of 0.05%. Test results from a prototype developed show that the proposed scheme possesses all the features, described above, as expected.
This paper presents a new capacitance-to-frequency converter (CFC) with high linearity and accuracy. In the CFC, the capacitance-to-frequency conversion is achieved using a negative feedback ...mechanism. In the feedback, the output frequency controls the charge injected by a switched-capacitor (SC) network such that the difference error is automatically minimized. The feedback mechanism ensures that the final output is insensitive to the nonlinearity errors of the units employed to realize the forward path, namely, a capacitance-to-voltage converter and a voltage-to-frequency converter. A simple error correction mechanism employed ensures that the digital output obtained is insensitive to the number of nonideal circuit parameters. The proposed converter uses a dc reference voltage for the excitation and helps to achieve high accuracy. A prototype of the improved CFC has been developed and tested for sensor capacitance <inline-formula> <tex-math notation="LaTeX">C_{x} </tex-math></inline-formula> in the range of 5-25 pF. A prototype of the conventional open-loop CFC was also developed, and the linearity has been evaluated. The proposed closed-loop approach has lower (0.1%) nonlinearity error compared to the conventional CFC (0.8%). This improvement is achieved without the use of any error-compensating schemes, and hence the complexity level of the system remains the same as that of any typical CFC. The response time of the CFC designed is about <inline-formula> <tex-math notation="LaTeX">400~\mu \text{s} </tex-math></inline-formula> for a 5-25 pF step change in <inline-formula> <tex-math notation="LaTeX">C_{x} </tex-math></inline-formula>. The results obtained from the prototype CFC confirmed its usefulness.
In this paper, a new digitizer, which accurately provides the values of the change in the capacitor C x and resistor R x of a parallel R-C sensor, is presented. Conventional measurement schemes for ...parallel R-C sensors require a precision sinusoidal excitation, followed by a signal conditioner, a demodulator and an ADC. This increases the cost and complexity of the scheme. Hence, a dc excitation and an ADC modified to measure R x and C x directly is preferred, by the design engineers. But, such a scheme has not been reported. Another challenge is the low-modulation nature of such sensors, i.e., the change in resistance ΔR and capacitance ΔC can be very small compared with the nominal values R 0 and C 0 of the sensor. This introduces a large offset in the digital output, leading to an inefficient conversion. The proposed digitizer employs a dc excitation and provides accurate digital values of change AR in R x and ΔC in C x of the sensor. The digitizer employs a simple, but effective automatic calibration, with the help of an improved switched capacitor controlled voltage and obtains an output independent of the nominal values (R 0 and C 0 ) of the sensor leading to an efficient conversion compared with the existing schemes. A detailed analysis of the sources of errors affecting the output of the digitizer has been conducted. A prototype of the proposed digitizer has been developed and tested in the laboratory for a wide range of R 0 and C 0 . The results show that the output of the proposed digitizer is independent of the R 0 and C 0 and can accurately measure the AR and AC without any cross-sensitivity.
A capacitance-to-digital converter (CDC) designed to possess negligible sensitivity to non-ideal circuit parameters is presented in this paper. The scheme is based on switched capacitor integrating ...technique and the conversion process is such that the final output is fundamentally insensitive to leakage resistance and stray capacitance of the sensor, offset voltage and bias current of the opamp, delay, offset voltage, and bias current of the comparator, leakage current, delay, and charge injection of the switches employed, and so on. Such a characteristic is highly useful for precision measurement. The proposed CDC achieves it without any special compensating circuits, unlike some of the existing CDCs that partially meet the above feature. The performance of the CDC has been experimentally evaluated. Results show high insensitivity to the non-ideal circuit parameters. In addition, the worst case non-linearity error of the prototype CDC was found to be less than 0.1%, when tested for a range of 10 to 400 pF.
A new capacitance-to-digital converter (CDC) that gives a digital output proportional to the measurand kx, independent of its nominal capacitance, is reported in this paper. Various CDCs are ...available in the market, but their output is a function of the nominal value C 0 of the sensor. Thus, a manual correction is required in the output, whenever a new capacitive sensor is interfaced to such CDCs. Moreover, the C 0 of the sensors is usually a large value compared with the change in capacitance due to kx. Thus, in a typical CDC, a large percentage of the output counts/bits is used to measure and represent the C 0 leading to an underutilization of the hardware as far as the measurement of kx is concerned. The proposed CDC uses a new automatic calibration (AC), employing a switched-capacitor (SC) circuit-based voltage source in a feedback topology, and provides an output independent of the C 0 of the sensor employed. The proposed CDC is based on an SC dual-slope technique and possesses the advantages of the dual-slope conversion method. The CDC circuit is designed such that the entire full scale can be used for representing the change in the kx. In addition to this advantage, the AC helps to remove the dependence on the accuracy of the reference capacitor employed in the CDC. A detailed analysis of the effect of various sources of errors in the CDC has been conducted and presented in this paper. A prototype of the proposed CDC has been developed and tested. The results obtained show that the output of the CDC is not a function of the C 0 (C 0 varied from 60 pF to 1.46 nF) of the sensors interfaced.
This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the ...tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann–Lemaître–Robertson–Walker spacetimes is straightforward.
In this article, an efficient differential voltage amplifier scheme for interfacing piezoelectric sensors that is insensitive to cable parasitic capacitance and immune to common mode interference ...(CMI) is presented. The scheme is beneficial for improving the sensitivity and signal-to-noise ratio (SNR) performance of high piezoelectric voltage constant (piezopolymer) piezo-sensor-based applications involving long cables between the piezo-sensor and electronics. In many piezo-sensor applications operating in harsh environments, the piezo-sensor and electronics need to be separated using long cables. The cable introduces signal loading, the triboelectric effect, and the picking up of external interference, resulting in poor sensitivity and SNR performance. Piezopolymer-based sensors e.g., polyvinylidene fluoride (PVDF) have high voltage sensitivity compared to charge sensitivity, which results in improved sensitivity performance if a voltage amplifier is used instead of a charge amplifier for interfacing these sensors. Hence, an enhanced differential voltage amplifier scheme insensitive to cable parasitic capacitance and immune to triboelectric effect and CMI is presented in this article. The proposed scheme has been simulated using LTspice, and a prototype has been implemented. The performance has been evaluated in the presence of cable parasitic capacitance and common-mode interference. The experimental result shows that the sensitivity is improved by 4.55 dB in comparison with a normal differential amplifier when a 5-m dual-core cable is used to connect a piezo-sensor (Airmar AT200). The proposed differential scheme improved the rejection of CMI by 18 dB compared with the single-ended configuration of the scheme.
A novel inductance-to-digital converter (LDC) that outputs a digital value corresponding to the change in inductance (<inline-formula> <tex-math notation="LaTeX">\Delta L ...</tex-math></inline-formula>) independent of offset inductance (<inline-formula> <tex-math notation="LaTeX">L_{01} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">L_{02} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">L_{03} </tex-math></inline-formula>), mismatch in offset inductance (<inline-formula> <tex-math notation="LaTeX">L_{01} \neq L_{02} </tex-math></inline-formula>), and series coil resistance (<inline-formula> <tex-math notation="LaTeX">R_{C1} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">R_{C2} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">R_{C3} </tex-math></inline-formula>) is presented in this work. In most cases, the change in sensor inductance <inline-formula> <tex-math notation="LaTeX">\Delta L </tex-math></inline-formula> due to the measurand will be very small as compared with <inline-formula> <tex-math notation="LaTeX">L_{0} </tex-math></inline-formula>. Thus, the existing architectures that measure the sensor inductance <inline-formula> <tex-math notation="LaTeX">L_{Xi} (=\!\!L_{0i} \pm \Delta L; i=1,2,3 </tex-math></inline-formula>) leads to underutilization of the output range. The proposed scheme is effective in measuring <inline-formula> <tex-math notation="LaTeX">\Delta L </tex-math></inline-formula> insensitive to <inline-formula> <tex-math notation="LaTeX">L_{0i} </tex-math></inline-formula> for both single-element type inductive sensor (SIS) and differential-type inductive sensor (DIS). For most of the DIS, in practice, it is very difficult to obtain the matched offset inductance <inline-formula> <tex-math notation="LaTeX">L_{01} </tex-math></inline-formula> = <inline-formula> <tex-math notation="LaTeX">L_{02} </tex-math></inline-formula> for the differential pair <inline-formula> <tex-math notation="LaTeX">L_{X1} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">L_{X2} </tex-math></inline-formula>. This will introduce a noticeable error in the output for existing DIS readout schemes. Whereas, for the proposed LDC's automatic offset elimination (AOE) mechanism ensure that digital output is made independent of the offset inductance <inline-formula> <tex-math notation="LaTeX">L_{03} </tex-math></inline-formula> (for SIS) and associated mismatch <inline-formula> <tex-math notation="LaTeX">L_{01} \neq L_{02} </tex-math></inline-formula> (for DIS). The LDC presented here uses dual-slope conversion technique and employs dc source for digitization. This eliminates the need for ac excitation source and possesses high measurement accuracy and noise immunity. The proposed LDC also measures coil resistance with negligible cross-sensitivity for SIS and DIS, which further enhances the practical efficacy of the proposed scheme. The developed prototype demonstrated a worst-case linearity error of 0.59% for <inline-formula> <tex-math notation="LaTeX">\Delta L </tex-math></inline-formula> in the range of ±9 mH and a linearity error of 0.48% for coil resistance measured in the range of 100-<inline-formula> <tex-math notation="LaTeX">1000~\Omega </tex-math></inline-formula>. The proposed approach paves path toward the use of a single readout in measuring <inline-formula> <tex-math notation="LaTeX">\Delta L </tex-math></inline-formula> for both SIS and DIS, even with large nominal inductance values and coil resistance.
In this article, a novel <inline-formula> <tex-math notation="LaTeX">\pi </tex-math></inline-formula>-model capacitive readout circuit that measures changes in sensor capacitance independent of ...offset capacitance is presented. The <inline-formula> <tex-math notation="LaTeX">\pi </tex-math></inline-formula>-model capacitor consists of three capacitances (<inline-formula> <tex-math notation="LaTeX">C_{x2} </tex-math></inline-formula>: between electrodes, and <inline-formula> <tex-math notation="LaTeX">C_{x1} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">C_{x3} </tex-math></inline-formula>: between each electrode and ground), effective for sensing both the measurand detection and its relative position. The final output of the switched-capacitor converter is insensitive to the parasitic capacitance from shielding cables or sensor structures, and its use of a dc source further enhances the measurement accuracy. The measurement update rate is increased by a settling time enhancement unit (STEU). The proposed feedback mechanism reduces the worst case linearity error from 3.5% (during open-loop configuration) to 0.24%. The developed prototype automatically eliminates offset capacitance (from 20 to 240 pF) and has a negligible cross-sensitivity error (<0.12%) between capacitance measurements in the <inline-formula> <tex-math notation="LaTeX">\pi </tex-math></inline-formula>-model. This CFC can provide the best update rate (typically 150 Hz), in comparison to the existing <inline-formula> <tex-math notation="LaTeX">\pi </tex-math></inline-formula>-model capacitive sensing architectures.
A Capacitance-to-Time Converter (CTC) that measures the change in capacitance <inline-formula><tex-math notation="LaTeX">\Delta C</tex-math></inline-formula> of a Differential-type Capacitive Sensor ...(DCS) is presented in this work. Most of the existing measurement circuits for DCS assumes its offset capacitance (<inline-formula><tex-math notation="LaTeX">C_{01}</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">C_{02}</tex-math></inline-formula>) be exactly matched. While in practical cases, it is difficult to have matched offset capacitance (<inline-formula><tex-math notation="LaTeX">C_{01} = C_{02}</tex-math></inline-formula>) due to sensor structure or manufacturing defects. This mismatch (<inline-formula><tex-math notation="LaTeX">C_{01} \ne C_{02}</tex-math></inline-formula>)will introduce a noticeable error in output of existing schemes. Moreover, the conversion time for most of these schemes are large, which is not suitable for high speed applications. The proposed CTC implements a closed loop system that generates a pulse width modulated output whose on-time is proportional to <inline-formula><tex-math notation="LaTeX">\Delta C</tex-math></inline-formula>. It implements an Automatic Offset-mismatch Nullification (AOFN) process that eliminates the effect of mismatch between the offset capacitances of DCS. The developed prototype of CTC showed a worst case linearity error of 0.3% for <inline-formula><tex-math notation="LaTeX">\Delta C</tex-math></inline-formula> in range of <inline-formula><tex-math notation="LaTeX">\pm</tex-math></inline-formula>180 pF and a conversion time of 2 ms. This result demonstrates the usefulness of the CTC for accurate and high-speed measurement applications.
PDF
