Abstract: An electronic device includes a flexible substrate and a conductive wire. The conductive wire is disposed on the flexible substrate and includes a metal portion and a plurality of openings disposed in the metal portion. The metal portion includes a plurality of extending portions and a plurality of joint portions, and each of the openings is surrounded by two of the plurality of extending portions and two of the plurality of joint portions. A ratio of a sum of widths of the plurality of extending portions to a sum of widths of the plurality of joint portions is in a range from 0.8 to 1.2.

Abstract: An analytical synthesis method (ASM) for designing a higher-order voltage-mode operational trans-resistance amplifier and capacitor (OTRA-C) based filter is disclosed. A decomposition of a complicated nth-order transferring a function is converted into a set of equations corresponding to a set of sub-circuitries. Then, a circuit structure is constructed by combining said sub-circuitries.

Abstract: An analytical synthesis method (ASM) for designing a higher-order voltage-mode operational trans-resistance amplifier and capacitor (OTRA-C) based filter is disclosed. A decomposition of a complicated nth-order transferring a function is converted into a set of equations corresponding to a set of sub-circuitries. Then, a circuit structure is constructed by combining said sub-circuitries.

Abstract: A complimentary single-ended-input OTA-C universal filter structures in terms of integrated circuits is provided. The integrated circuit comprises a plurality of amplifiers and a plurality of capacitors. In some capacitors, one electrode is electrically connected to the positive input of its corresponding amplifier, and the other electrode can be electrically connected to an electrical source. In addition, the negative input of one amplifier is electrically connected to the negative input of another amplifier. Besides, there are a head amplifier and a tail amplifier. The output of the head amplifier is electrically connected to the negative input of the head amplifier, and the positive input of the tail amplifier can be electrically connected to an electrical source.

Abstract: Nth-order voltage- and current-mode arbitrary phase shift oscillator structures are synthesized using n operational trans-conductance amplifiers (OTAs) or second-generation current controlled conveyors (CCCIIs) and n grounded capacitors. Linking up the I/O characteristics of the OTA and the CCCII and the reactance of grounded capacitor, the step of synthesis is first based on the algebraic analysis to oscillatory characteristic equations, resulting in a quadrature oscillator structure. Secondly, instead of the quadrature characteristic, to control each output signal with one another by a desired phase difference > or <90°, selectively superposing any of two fundamental OTA/CCCII-C sub-circuitries benefits the transformation of quadrature to arbitrary-phase-shift characteristic for the sinusoidal oscillator structure. Furthermore, several compensation schemes are presented for reducing the output parameter deviation due to the non-ideal effects.

Abstract: A voltage-mode nth-order differential difference current conveyor (DDCC) and fully differential current conveyor (FDCCII)-resistor and capacitor filter structures are proposed using a new effective analytical synthesis method (ASM), a succession of innovative algebra operations until a set of simple equations are produced, which are then realized using n integrators and a constraint sub-circuitry, A new ASM can effectively carry out (i) use of all the grounded capacitors and grounded resistors, and (ii) employment of the minimum number of active and passive components and then enjoys the low sensitivities, lower parasitics, power consumption, noise, and smaller chip area leading to simultaneously achieving two important features: (i) higher output performance and (ii) lower cost, without tradeoff. Moreover, the component value variations of all the relative sensitivities have the same incremental percentage or decrement.

Abstract: A complimentary single-ended-input OTA-C universal filter structures in terms of integrated circuits is provided. The integrated circuit comprises a plurality of amplifiers and a plurality of capacitors. In some capacitors, one electrode is electrically connected to the positive input of its corresponding amplifier, and the other electrode can be electrically connected to an electrical source. In addition, the negative input of one amplifier is electrically connected to the negative input of another amplifier. Besides, there are a head amplifier and a tail amplifier. The output of the head amplifier is electrically connected to the negative input of the head amplifier, and the positive input of the tail amplifier can be electrically connected to an electrical source.

Abstract: Nth-order voltage- and current-mode arbitrary phase shift oscillator structures are synthesized using n operational trans-conductance amplifiers (OTAs) or second-generation current controlled conveyors (CCCIIs) and n grounded capacitors. Linking up the I/O characteristics of the OTA and the CCCII and the reactance of grounded capacitor, the step of synthesis is first based on the algebraic analysis to oscillatory characteristic equations, resulting in a quadrature oscillator structure. Secondly, instead of the quadrature characteristic, to control each output signal with one another by a desired phase difference > or <90°, selectively superposing any of two fundamental OTA/CCCII-C sub-circuitries benefits the transformation of quadrature to arbitrary-phase-shift characteristic for the sinusoidal oscillator structure. Furthermore, several compensation schemes are presented for reducing the output parameter deviation due to the non-ideal effects.

Abstract: An analytical Synthesis Method (ASM) is clearly and effectively demonstrated in the realization of current/voltage-mode Operational Trans-conductance Amplifier and Capacitor (OTA-C) circuits, where a complicated nth-order transfer function is manipulated and decomposed by a succession of innovative algebra operations until a set of simple equations are produced, which are then realized using n integrators and a constraint circuitry. The circuits realized includes voltage-mode nth-order OTA-C universal filter structures, tunable voltage/current-mode OTA-C universal biquad filters, voltage-mode odd/even-nth-order OTA-C elliptic filter structures, voltage/current-mode odd-nth-order OTA-C elliptic high-pass filter structures, and OTA-C quadrature oscillators. Some realized OTA-C circuits can be simplified to be OTA-only (OTA-parasiic C) circuits which fit for the operation at high frequencies.

Abstract: A voltage-mode nth-order differential difference current conveyor (DDCC) and fully differential current conveyor (FDCCII)-resistor and capacitor filter structures are proposed using a new effective analytical synthesis method (ASM), a succession of innovative algebra operations until a set of simple equations are produced, which are then realized using n integrators and a constraint sub-circuitry, A new ASM can effectively carry out (i) use of all the grounded capacitors and grounded resistors, and (ii) employment of the minimum number of active and passive components and then enjoys the low sensitivities, lower parasitics, power consumption, noise, and smaller chip area leading to simultaneously achieving two important features: (i) higher output performance and (ii) lower cost, without tradeoff. Moreover, the component value variations of all the relative sensitivities have the same incremental percentage or decrement.

Abstract: Nth-order OTA-C (Operational Transconductance Amplifiers and Capacitors) filter structures are realized by using the analytical synthesis method to achieve the following three important criteria simultaneously: filters use just n grounded capacitors, each of which is located at each of just n nodes in the realized circuit, because they use smaller area in the IC, and they can absorb equivalent shunt capacitive parasites; filters employ only single-ended-input OTAs to overcome the feed-through effects due to finite input parasitic capacitances associated with double-input OTAs to replace the same positions of the n given capacitors; and filters have the least number-of components (passive and active) for a given order to reduce power consumption, chip areas, and noise. Both the first and the second criteria lead to the minimum parasitic distortion and make the most precise output signals. And the third criterion produces the cheapest chip.

Abstract: Nth-order OTA-C (Operational Transconductance Amplifiers and Capacitors) filter structures are realized by using the analytical synthesis method to achieve the following three important criteria simultaneously: filters use just n grounded capacitors, each of which is located at each of just n nodes in the realized circuit, because they use smaller area in the IC, and they can absorb equivalent shunt capacitive parasites; filters employ only single-ended-input OTAs to overcome the feed-through effects due to finite input parasitic capacitances associated with double-input OTAs to replace the same positions of the n given capacitors; and filters have the least number-of components (passive and active) for a given order to reduce power consumption, chip areas, and noise. Both the first and the second criteria lead to the minimum parasitic distortion and make the most precise output signals. And the third criterion produces the cheapest chip.