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This paper presents a sensor readout integrated circuit (ROIC) using a capacitively coupled instrumentation amplifier (CCIA)-embedded continuous-time ΔΣ modulator (CT ΔΣM) incorporating chopping artifact rejection. Chopping is an essential technique for suppressing the offset and 1/ƒ noise. However, the chopping artifacts in the modulator loop degrade the in-band noise, linearity, and loop stability. In the proposed design, chopping aliasing is avoided by setting the chopping frequency (ƒch) same as the sampling frequency (ƒs). The chopping ripple is mitigated using the ripple reduction loop (RRL), and the shaped quantization noise-folding resulting from the RRL is prevented by minimizing the loop gain and bandwidth of the RRL. The residual ripple and spikes are filtered out using the alias rejection band of CT ΔΣM. The third-order loop filter enables sufficient noise-shaping with a low oversampling ratio (OSR). The chip is implemented in a 180-nm CMOS process with an active area of 1.65 mm2, drawing 232.2 μA at a 1.8 V supply. The proposed capacitively coupled (CC)-CT ΔΣM has a 19.4 nV/√Hz input-referred noise density, 1.9 μ V offset, 0.08% gain error, 16 ppm integral nonlinearity (INL), and 140 dB common-mode rejection ratio (CMRR) within an input range of 60 mVpp. With −110.1 dB total harmonic distortion (THD), excellent dynamic linearity performance is achieved owing to the CCIA-integrated design and chopping artifact rejection technique. [ABSTRACT FROM AUTHOR]

First-in first-out (FIFO) queues are ubiquitous building blocks in modern system-on-chips. Big FIFOs are often realized as static random access memories (SRAMs), and in many cases account for a significant portion of the area and power consumption of integrated circuits (ICs). Gain-cell embedded DRAM (GC-eDRAM) technology is an embedded memory alternative to the pervasive SRAM technology in ICs. It consumes less silicon area and less power than SRAM, but has the drawback of access blockage caused by its periodic data refreshing. In this paper we leverage the unique access patterns implied by the FIFO scheme to design a FIFO realized with GC-eDRAM. We show that such a FIFO is functionally indistinguishable from a FIFO realized with SRAM. The proposed FIFO has no access blockage time due to refresh, and no data integrity issues, and so can be used as an out-of-the-box replacement for FIFOs in existing and future designs, while providing as much as a $2\times $ reduction in both area and power as compared to SRAM. [ABSTRACT FROM AUTHOR]

This paper considers a large class of memristor circuits of arbitrary order, and containing an arbitrary number of flux- or charge-controlled memristors, for which a state equation (SE) description can be obtained. By means of the SEs, it is shown that the state space of each circuit can be decomposed in infinitely many manifolds, and that in the autonomous case, each manifold is positively invariant and is characterized by a different reduced-order dynamics and attractors. These results are the basis for extending the analysis to the non-autonomous case, where time-varying independent sources are present. In particular, the chief result obtained in this paper shows how to analytically design external pulses for programming memristor circuits, i.e., how invariant manifolds and attractors can be changed and controlled by applying suitable charge or flux sources via time-varying voltage and/or current pulses with finite time duration. The main results are obtained by relying on a recently introduced technique for the analysis of memristor circuits in the flux-charge domain. [ABSTRACT FROM AUTHOR]

In this paper, different methodologies are employed to improve the linearity performance of a prototype CMOS image sensor (CIS). First, several pixel structures, including a novel pixel design based on a capacitive trans-impedance amplifier (CTIA), are proposed to achieve a higher pixel-level linearity. Furthermore, three types of digital linearity calibration methods are explored. A prototype image sensor designed in 0.18- $\mu \text{m}$ , 1-poly, and 4-metal CIS technology with a pixel array of $128 \times 160$ is used to verify these linearity improvement techniques. The measurement results show that the proposed CTIA pixel has the best linearity result out of all pixel structures. Meanwhile, the proposed calibration methods further improved the linearity of the CIS without changing the pixel structure. The pixel mode method achieves the most significant improvement on the linearity. One type of 4T pixel attains a nonlinearity of 0.028% with pixel mode calibration, which is two times better than the state of the art. Voltage mode (VM) and current mode (CM) calibration methods get rid of the limitation on the illumination condition during calibration operation; especially, CM calibration can further suppress the nonlinearity caused by the integration capacitor $C_{\textit {FD}}$ on the floating diffusion node, which is remnant in VM. [ABSTRACT FROM AUTHOR]

This paper presents a fully on-chip mixed-mode low-dropout (LDO) regulator with improved regulation and transient responses. With the help of the digital regulation part, the supported maximum load current is significantly improved, while the chip area overhead is very small. A Miller compensation capacitor and a buffer stage are used to achieve stability and improve power MOS gate slew rate. The ultra-fast voltage buffer helps further improve the load transient recovery speed and reduce the chip area due to its wider voltage swing. A proof-of-concept LDO design is fabricated in a standard 0.18- $\mu \text{m}$ CMOS technology. The maximum load current is 150 mA, the output voltage is 1 V, and the dropout voltage is 0.2 V. The load regulation is 0.17 mV/mA, which is more than 480% improved over the traditional design without digital assistance. [ABSTRACT FROM AUTHOR]

This paper presents a 24-channel time-shared 8-bit digital-to-analog converter (DAC) with dual sampling to minimize the effective channel area of the column driver integrated circuit (IC) for high-resolution active-matrix organic light emitting diodes (AMOLED). The proposed time-shared DAC significantly reduces the effective channel area of the column driver IC, since a single high-speed DAC is shared among multi channels. The dual-sampling architecture for the output amplifiers also reduces the power consumption of the column driver IC, where the operating time of the time-shared DAC and the output amplifier is efficiently handled during the limited 1-horizontal time. The sampling accuracy of the dual-sampling architecture is improved by a simple dummy switch and a source follower. The proposed time-shared DAC with the dual sampling is implemented by a 0.13- $\mu \text{m}$ high-voltage complementary metal-oxide-semiconductor process and integrated in a 960-channel column driver IC, while the effective channel area of the column driver IC is 5520 $\mu \text{m}^{2}$. As a result of driving an 11-inch-wide quad extended graphics array AMOLED panel by using the prototype column driver IC, the panel uniformly generates a clear image. [ABSTRACT FROM AUTHOR]

This paper demonstrates a completely on-chip implementation of expansion and compression of continuous-time, wideband, analog pulses. The input pulse is fed to a continuous-time filter whose delay exceeds the pulse duration. Once the pulse is completely inside the filter, it is stored in the form of the filter’s state-variables, which can completely reconstruct the pulse. Instantaneously decreasing or increasing the filter’s bandwidth at this instant results in the output pulse being expanded or compressed, respectively, compared with when the bandwidth is unchanged. A 1.6 mm2, 370 mW, 0.13 $\mu \text{m}$ prototype has a delay filter whose bandwidth can be switched between 870 and 472 MHz. It achieves $1.8\times $ pulse expansion and $1.7\times $ pulse compression with an rms error which is 33 dB below the peak-peak pulse amplitude. [ABSTRACT FROM AUTHOR]

This paper presents a PLL supporting diverse low-power clocking needs including wide input (6–200 MHz) and output (0.15–5 GHz) frequency ranges and SSC operation. Fabricated in 14nm FinFET CMOS, a low-power switched-cap loop filter is employed to enable high −3dB PLL bandwidth (>40% of $f_{\mathrm{ REF}}=19.2$ MHz), and the proposed reference current generator (IrefGen) provides accurate current with <4% tolerance without the need for external components or on-chip precision resistors. IrefGen decouples PLL loop dynamics from feedback divide ratio and provides immunity to systematic capacitor variation. Power gating of switched-cap loop filter’s bias circuits results in more than 10% PLL total power savings. The PLL achieves 1.6-ps integrated RMS jitter at 4 GHz using 100-MHz reference while consuming 2.6 mW from 0.95 V. The PLL performance satisfies the stringent PCIe Gen2/3 jitter specifications without resorting to inductors. [ABSTRACT FROM AUTHOR]

An efficient self-powered synchronous electric charge extraction CMOS interface circuit dedicated to piezoelectric harvesters is proposed in this paper. Self-powered peak detection (PKD) and switch circuits are used to reduce quiescent current so that the backup or pre-charged power can be saved. A new low phase lag (LPL) PKD circuit is designed to improve the synchronous extraction efficiency, which only requires one detection capacitor to perform positive and negative PKD. The circuit can be set at general mode (G-mode) or LPL mode (LPL-mode). Under LPL-mode, the phase lag can be reduced typically by 50%, the synchronous extraction efficiency can obtained up to 94%, while the output power can reach 659~\mu \textW when the piezoelectric transducer original open-circuit voltage V\mathrm{ oc,org}=5 V, which is 3.56 times of that of full-bridge rectifier standard energy harvesting circuit at the maximum power point. The minimum harvesting startup voltage is 1.7 V and is independent of the energy storage capacitor voltage V\mathrm{ DC} . The harvesting efficiency can still reach 71.3% at V\mathrm{ oc,org}=5 V. The size of the active area is 0.5 mm2 in a 0.18- \mu \textm CMOS technology. Circuit may be invoked as a functional block for energy autonomous wireless sensor network node of the Internet of Things. [ABSTRACT FROM PUBLISHER]

This paper presents a piezoelectric-based power management solution for battery-free wireless remote switches (BWSs). The proposed BWS IC, including a piezoelectric (PE) energy harvester and a buck converter, can collect the energy generated by a single PE-button press, and then supply that energy to a wireless transmitter to send a message. By combining a rectifier using the synchronized switch harvesting on inductor technique and a 6:1 series–parallel switched-capacitor converter, the proposed PE energy harvester can maximize the collected amount of energy, while supplying it at a low output voltage. In addition, by employing a switching-based start-up scheme and a variable ON-time pulse-frequency modulation scheme, the proposed buck converter can reduce the loss associated with charging the output capacitor during start-up, and then deliver the largest possible energy to the load, while maintaining low voltage ripples and high-power efficiency. A prototype BWS IC fabricated with high-voltage 250-nm CMOS technology was shown to be capable of harvesting a total energy of 246~\mu \textJ from a single button-pressing of a 300-mm2 lead magnesium niobate-lead titanate PE disc. More than 200~\mu \textJ was delivered to the load, sufficient to transmit a 4-B-long message via a 2.4-GHz wireless USB channel over a 10-m distance. [ABSTRACT FROM AUTHOR]

With reference to 48-V systems, used in electric and hybrid vehicles and for telecom and networking power supply, this paper presents the circuit/transistor-level design, implementation, and test of an inductorless dc/dc converter. Its architecture is a cascade of three switched-capacitor converters with step-up/down capabilities plus linear converters, working in parallel at the end of the cascade. It provides multiple regulated voltages, which are isolated from input failures. The design also includes on-chip control unit and a serial interface toward an external host. Experimental tests carried out on the chip, fabricated in 0.35- \mu \textm CMOS technology, proves that the design is suitable to face harsh operating environments, including the 48-V automotive one. Compared with the state-of-art, the proposed design stands for its wide input voltage regulation range, load/line regulation, power supply rejection ratio, and low electromagnetic interference emissions. [ABSTRACT FROM PUBLISHER]

This paper presents a low-power compact analog circuit for processing time varying signals. The proposed circuit implements temporal differentiation, amplification and rectification, i.e., separation of outputs into on and off pathways. It is based on a hysteretic differentiator circuit, commonly used in neuromorphic vision sensors to implement temporal edge detection. This paper presents a thorough analysis of the original circuit and identifies the source of the problems and limitations it has for processing real-world sensory signals. The steps required to solve this problem are presented as well as an extended circuit with tunable gain and adaptable threshold that allows thresholding of small temporal changes (noise) and high-pass filtering of large temporal changes. The new circuit proposed is particularly suited for focal plane implementation of both gradient based and token based motion algorithms that require robust detection of temporal discontinuities. The circuit has been designed and successfully integrated into a 64 × 1 test prototype motion chip, fabricated in standard 350 nm CMOS technology. The paper provides extensive experimental characterization results. [ABSTRACT FROM PUBLISHER]

This paper presents a mutual capacitive touch screen panel (TSP) readout IC (ROIC) with a differential continuous-mode parallel operation architecture (DCPA). The proposed architecture achieves a high product of signal-to-noise ratio (SNR) and frame rate, which is a requirement of ROIC for large-sized TSP. DCPA is accomplished by using the proposed differential sensing method with a parallel architecture in a continuous-mode. This architecture is implemented using a continuous-type transmitter for parallel signaling and a differential-architecture receiver. A continuous-type differential charge amplifier removes the common-mode noise component, and reduces the self-noise by the band-pass filtering effect of the continuous-mode charge amplifier. In addition, the differential parallel architecture cancels the timing skew problem caused by the continuous-mode parallel operation and effectively enhances the power spectrum density of the signal. The proposed ROIC was fabricated using a 0.18-$\mu$m CMOS process and occupied an active area of 1.25 \text{mm}^{2}. The proposed system achieved a 72 dB SNR and 240 Hz frame rate with a 32 channel TX by 10 channel RX mutual capacitive TSP. Moreover, the proposed differential-parallel architecture demonstrated higher immunity to lamp noise and display noise. The proposed system consumed 42.5 mW with a 3.3-V supply. [ABSTRACT FROM PUBLISHER]

In this paper the power losses of efficient capacitive converters with multitude transfer ratio values are discussed. The loss mechanism circuits, based on general transposed series parallel (GTSP) topology, is studied and the losses are calculated, which in turn enables the “bottlenecks” to be identified and overcome. The calculations show that for a given number of switching cells the power losses of such converters are mainly dependent on the voltage conversion ratio, the topology function, the resistances of the switches in on and off states, the ESR of the capacitors, the switching frequency, the voltage drop, and the load. The theory explains the fact that was observed in experiments, that for low voltage conversion ratio values, efficiency decrease was measured. It is shown that for these low voltage ratio values the mechanism associated to the off resistance of the switches is more dominant and reduces the efficiency. This power loss estimation can be used as a powerful tool for the performance optimization of capacitive converters. The theoretical results are verified experimentally on a 10-cell GTSP converter prototype. The experimental results show good agreement with the proposed theory. [ABSTRACT FROM PUBLISHER]

This paper proposes a column-parallel two-step single-slope analog-to-digital converter (SS ADC) for high-frame-rate CMOS image sensors. The proposed two-step SS ADC circuit does not utilize an analog memory capacitor to store the value of the first ramp step. Instead, to handle problems such as the slope errors of the second ramp and the stored charge error from charge feed-through, it utilizes a very simple digital column circuit consisting of a coarse counter (coarse step counter) and a 4-to-16 decoder. The second ramp (fine ramp) slope has only one slope generator, regardless of the results of the first ramp decisions, to eliminate the slope mismatch between fine ramp slopes. A prototype sensor comprising 640 \times 480 pixels was fabricated with a 0.13-\mum CMOS process. The results of experiments conducted indicate that the proposed ADC can achieve a conversion time of 6.4 \mus at a main clock frequency of 62.5 MHz, which is 10.2 times faster than the conventional SS ADC. The maximum frame rate of the proposed VGA CMOS Image Sensor (CIS) is 320 frames per second (fps). Further, the proposed circuit employs redundancy error correction logic to calibrate the error between the coarse and fine steps. The total power consumption is 72 mW from supply voltages of 2.8 V (analog) and 1.5 V (digital). The figure of merit (FoM) of the proposed VGA CMOS image sensor is 2.01 [e^-\ nJ]. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-bit incremental analog-to-digital converter (ADC) based on successive approximation (SA) for column-parallel readout circuits. The proposed ADC suppresses the random noise and enhances the resolution by embedding the conventional SA ADC with an integrator and decimation filter. In addition, the operating speed is increased through the two-step operations of coarse conversion with the proposed ADC and fine conversion with the embedded SA ADC. A residue fitting method is adopted to adjust the residue voltage to the fine conversion range after the coarse conversion. The proposed ADC with 12-bit resolution was fabricated using a 0.13 \mum CMOS image sensor process with a pixel array that has an image format of 648 \times 488 and a pixel size of 5.6\ \mum\times 5.6\ \mum. The measured results show a random noise of 108 \muV, a dynamic range of 60.9 dB, a differential nonlinearity of +1.02/-0.34 least significant bit (LSB), and an integral nonlinearity of +0.64/-0.54 LSB. [ABSTRACT FROM AUTHOR]

This paper presents the analysis and design of a quadrature charge-domain down-conversion sampling mixer with embedded finite-impulse-response (FIR), infinite-impulse-response (IIR), and 4-path bandpass filters. An in-depth investigation of the principles of periodic impulse sampling, periodic windowed sampling, and periodic N-path windowed sampling is presented and their characteristics are compared. A detailed mathematical treatment of charge-domain windowed samplers with built-in sinc, FIR and IIR filters is provided. A quadrature charge-domain sampler with embedded FIR, IIR, and 4-path band-pass filters is proposed and its performance including the effect of the non-idealities of devices is investigated. The proposed design is implemented in an IBM 130 nm 1.2 V CMOS technology. Simulation results demonstrate that the proposed design is tunable over 50–250 MHz frequency range. For an 100 MHz input, the proposed design exhibits 70 dB aliasing rejection, 60 dB stop band attenuation while consuming current of 145 \muA. The performance of the proposed design is further validated using the results of on-wafer measurement of the fabricated microchip. [ABSTRACT FROM AUTHOR]

An analytical approach to evaluate performance of analog integrated circuits and make a comparative study in different technology nodes is presented. To provide closed-form solutions, this article proposes using $\mathscr {C} = \text {C}/\text {I}_{\text {DS}}$ as an independent design variable, where C refers to any physical or parasitic capacitance associated with a Field-Effect Transistor (FET) biased at IDS. The proposed $\mathscr {C}$ -based methodology is used to study speed versus power trade-offs in both continuous-time (CT) and discrete-time (DT) circuits. Predictive Technology Models (PTMs) have been used to study performance of both MOSFET and FinFET (i.e. FET) devices in different technology nodes. This analysis shows that FinFET transistors exhibit a wider medium-inversion region compared to MOSFET devices, making them more convenient for high-speed and low-power designs. Additionally, this study proves that a lower sub-threshold slope factor results in an improved energy-efficiency of analog circuits. [ABSTRACT FROM AUTHOR]

In this article, first integrated circuit (IC) implementation of parallel synchronized switching harvesting on inductor (p-SSHI) is presented for triboelectric energy harvester targeting 1 Hz to 5 Hz mechanical motions. It is accompanied by on-chip buck and switched capacitor DC-DC converters, all capable of handling 70 V levels. Unlike piezoelectric harvesters, triboelectric nanogenerators (TENGs) can produce very high open-circuit voltages; thus, the proposed system utilizes this property within the technology limits to maximize the extracted power. An in-house manufactured TENG using steel and polytetrafluoroethylene (PTFE) is modeled for sub-5 Hz motions. The energy is extracted and stored in an external capacitance until its voltage reaches 70 V, which is achieved in three press-and-release mechanical cycles. 70-to-2 V down conversion is carried on by 70-to-10 V buck converter followed by a 10-to-2 V switched capacitor DC-DC converter. A chip is manufactured in $0.18~\mu \text{m}$ HV BCD process with an active area of 6.25 mm2. End-to-end peak efficiency is measured as 32.71% for 1 Hz motion with a 722 $\mu \text{W}$ total power delivery to the load for 4 ms. [ABSTRACT FROM AUTHOR]

A design methodology for an area-optimized integrated charge pump is described suitable for on-chip high-voltage reverse bias of single-photon avalanche diodes (SPADs). The high-voltage generation block is implemented in a general-purpose 0.13- $\mu \text{m}$ CMOS process and is capable of generating a maximum regulated output voltage of 17.7 V from an input of 1.8 V. An ON–OFF regulation scheme with dynamic charging and discharging capability of the charge pump provides fast recovery of the output bias voltage during SPAD transients, where overshoot and undershoot must both be corrected during active quench and reset. Following a SPAD avalanche current pulse, the measured transient recovery time is 500 ns from a 150-mV overshoot and a 500-mV undershoot to reach 99% of steady-state output. The implemented SPAD bias generation system occupies 0.175-mm2 chip area, without requiring an off-chip load capacitor. [ABSTRACT FROM AUTHOR]

Conventional capacitance-to-digital converters (CDCs) suffer limitations either on narrow capacitance range or low resolution for jitter-induced noise and high power consumption. In order to avoid these limitations, a 13-b 1 pF–10 nF generic CDC is presented. In the proposed CDC with the oversampled $\Delta \Sigma $ modulation, the zero-crossing-based circuits (ZCBCs) are used to replace the operational transconductance amplifier to avoid feedback loop stability issues. However, the ZCBCs inevitably incur the non-idealities and thus, a novel calibration scheme is presented for efficient non-ideality-error cancellation. In addition, for the purpose of making the proposed CDC sufficiently intelligent to adapt to a wide capacitance-sensing range, an adaptive auto-range mechanism is proposed. The above three techniques complement each other and work as a whole leading to the proposed CDC with wide range, high resolution, high linearity, and low power consumption. A prototype fabricated using 0.18- $\mu \text{m}$ CMOS technology is experimentally verified using a MEMS capacitive humidity sensor. The measurement results show that the CDC achieves a 13-b root-mean-square noise equivalent resolution with a 128- $\mu \text{s}$ conversion time and a 230 fJ/conversion-step figure of merit. The calibration scheme enhances the linearity from 7 to 11.4 b in the 1 pF–10 nF compatible capacitance range. [ABSTRACT FROM AUTHOR]

A new fS/4 bandpass $\Delta \Sigma$ -analog-to-digital converter (ADC) architecture is realized by feeding back the delayed quantization noise inherently produced by a pipelined ADC. Designed in a 55-nm global foundry (GF) LP-CMOS process, the prototype ADC sampling at 250 MHz achieves an Signal-to-Noise+Distortion Ratio of 72, 75.8, 80.1, and 85.3 dB in a 15.64-, 7.82-, 3.91-, and 1.953-MHz band, respectively, around a center frequency of 62.5 MHz with only first-order noise shaping, while consuming 103 mW of power, and achieving a maximum figure-of-merit of 158 dB. [ABSTRACT FROM PUBLISHER]

The longitudinal waveform relaxation (WR) proposed by Gander and Ruehli converges faster than the classical WR method. For the former, a free parameter \alpha is contained, which has a significant effect on the convergence rate. The optimization of this parameter is thus an important issue in practice. Here, we apply this new WR method to the fractional-order RC circuits, and optimize such a parameter at the continuous and discrete levels (this gives two parameters \alpha ^{c}_{\mathrm{ opt}} and \alpha ^{d}_{\mathrm{ opt}} ). We consider three simple but widely used convolution quadrature for discretization, based on the implicit-Euler method, the two-step backward difference formula, and the trapezoidal rule, and we derive the parameter \alpha ^d\mathrm{ opt} for each quadrature. Interestingly, it is found that for the former two quadratures, the optimized parameter \alpha ^d\mathrm{ opt} results in a much better convergence rate than \alpha ^c\mathrm{ opt} , while for the quadrature based on the trapezoidal rule, \alpha ^d\mathrm{ opt} and \alpha ^c\mathrm{ opt} result in the same convergence rate. [ABSTRACT FROM AUTHOR]

A new 96 \times 96 array of 30\ \mu\text{m}\times 30\ \mu\text{m} readout integrated circuit (ROIC) with an individual pixel tunable bias control is demonstrated. Detailed IC design, test structures, readout circuit building blocks, and applied techniques are discussed. The new ROIC is capable of providing a large voltage swing for the bias in both positive and negative polarities to each individual pixel, independently. These enhanced functionalities are achieved by modifying a capacitive transimpedance amplifier (CTIA) CMOS ROIC architecture. An FPGA-based test bench has also been developed to test and characterize the new ROIC system, for which software and hardware are described in detail. The test chip has been fabricated with 2P4M 0.35 \mu\text{m}$ high-voltage CMOS technology, where the bias voltage range is ±5 V and the output swing range is ±3.9 V. The demonstrated ROIC is an ideal infrastructure for implementation of region of interest enhancement and a solid base for infrared multispectral acquisition targeting an infrared retina. [ABSTRACT FROM PUBLISHER]

Memristor-based circuits are widely exploited to realize analog and/or digital systems for a broad scope of applications (e.g., amplifiers, filters, oscillators, logic gates, and memristor as synapses). A systematic methodology is necessary to understand complex nonlinear phenomena emerging in memristor circuits. The manuscript introduces a comprehensive analysis method of memristor circuits in the flux-charge $(\varphi,q)$-domain. The proposed method relies on Kirchhoff Flux and Charge Laws and constitutive relations of circuit elements in terms of incremental flux and charge. The main advantages (over the approaches in the voltage-current $(v,i)$-domain) of the formulation of circuit equations in the $(\varphi,q)$-domain are: a) a simplified analysis of nonlinear dynamics and bifurcations by means of a smaller set of ODEs; b) a clear understanding of the influence of initial conditions. The straightforward application of the proposed method provides a full portrait of the nonlinear dynamics of the simplest memristor circuit made of one memristor connected to a capacitor. In addition, the concept of invariant manifolds permits to clarify how initial conditions give rise to bifurcations without parameters. [ABSTRACT FROM PUBLISHER]