• Journal of IKEEE
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• v.3 no.1 s.4
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• pp.39-49
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• 1999

This paper describes a 1 GHz, low-phase-noise CMOS fractional-N frequency synthesizer with an integrated LC VCO. The proposed frequency synthesizer, which uses a high-order delta-sigma modulator to suppress the fractional spurious tones at all multiples of the fractional frequency resolution offset, has 64 programmable frequency channels with frequency resolution of $f_ref/64$. The measured phase noise is as low as -110 dBc/Hz at a 200 KHz offset frequency from a carrier frequency of 980 MHz. The reference sideband spurs are -73.5 dBc. The prototype is implemented in a $0.5{\mu}m$ CMOS process with triple metal layers. The active chip area is about $4mm^2$ and the prototype consumes 43 mW, including the VCO buffer power consumption, from a 3.3 V supply voltage.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.9
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• pp.650-656
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• 2004

This paper presents block and timing diagrams of the DWA(data weighted averaging) to optimize a feedback time delay of the sigma-delta modulator. Through the Matlab modeling, the optimized coefficients of the integrators are obtained to design the modulator. And then the fully differential SC integrators, feedback DAC, 9-level quantizer, and DWA are designed by considering the nonideal characteristics of the modulator. The designed second-order multibit modulator is fabricated in a 0.35$\mu\textrm{m}$ CMOS process. The designed modulator achieves 73dB signal-to-noise ratio and 72dB dynamic range at 1.2Vp-p 585kHz input singal and 52.8MHz sampling frequency.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.10
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• pp.513-519
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• 2001

This paper proposed a random sigma-delta modulator(RSDM), which is constructed by a 1st order sigma-delta modulator(SDM) and a simple structured random binary generator(RBG). The 1st order SDM produces a switching pulse waveform which has the same low-frequency component as the reference input, while the RBG spreads the distribution of the number of sampling per switching cycle, and thus disperses the spectrum spikes in the output. The relationship between the harmonic spectra and the number of sampling per switching cycle is studied through computer simulations, and the frequency spectra of the RSDM are confirmed in an experimental setup.

• Proceedings of the KIEE Conference
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• 2000.07b
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• pp.1321-1323
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• 2000

Sigma-delta modulation can perform A/D conversion with a high-resolution. It is useful for simplifing the system and spreading out inband signal noise. When the sigma-delta modulation is applied to a switching converter, it can suppress the harmonic frequencies of output signal and be realized with a simple structure. In this paper, some methods of sigma-delta modulation are discussed so as to find the suitable structure for a switching converter. Noise characteristics are calculated and analyzed through simulations.

• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.2
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• pp.170-183
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• 2013

This paper gives an overview of fractional-N phase-locked loops (PLLs) with practical design perspectives focusing on a ${\Delta}{\Sigma}$ modulation technique and a finite-impulse response (FIR) filtering method. Spur generation and nonlinearity issues in the ${\Delta}{\Sigma}$ fractional-N PLLs are discussed with simulation and hardware results. High-order ${\Delta}{\Sigma}$ modulation with FIR-embedded filtering is considered for low noise frequency generation. Also, various architectures of finite-modulo fractional-N PLLs are reviewed for alternative low cost design, and the FIR filtering technique is shown to be useful for spur reduction in the finite-modulo fractional-N PLL design.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.361-364
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• 2003

In this paper, a high-resolution multibit sigma-delta modulator implemented in a.0.35-um CMOS technology is introduced. This modulator consists of two switched capacitor integrators, 3-bits A/D converter, and 3-bits D/A converter For the verification of the internal function blocks, HSPICE simulator is used. This circuit is normally operated at 130 MHz clock and the total power dissapation is 70 mW.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.10a
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• pp.29-37
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• 1996

A ductile fracture criterion, which has already proposed, namely, ($\Delta$1/1o)f at $\Delta$$\sigma$ m=(($\Delta$1/1o)f+(-1/tan$\theta$)$\Delta$$\sigma$m(where ($\Delta$1/1o)f is fracture elongation, $\Delta$$\sigma$m is mean stress variation) was made use of to study the working limit in axisymmetric extrusion. The present investigation is concerned with the application of theory on flow and fracture to the prediction of workability of materials in axisymmetric bar extrusion, with special reference to central bursting. The influenced of die geometry and manufacturing conditions on the central bursting are predicted.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.8
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• pp.65-73
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• 2007

This paper presents a low power CMOS continuous-time $\Sigma\Delta$ (sigma-delta) modulator for UMTS receivers. The loop filter of the continuous-time $\Sigma\Delta$ modulator consists of an active-RC filter which performs high linearity characteristics and has a simple tuning circuit for low power operating system The architecture of this modulator is the $3^{rd}-order$ 4-bit single loop configuration with a 24 of OSR (Oversampling Ratio) to increase the power efficiency. The modulator includes a half delay feedback path to compensate the excess loop delay. The experimental results of the modulator are 71dB, 65dB and 74dB of the peak SNR, peak SMR and dynamic range, respectively. The continuous-time $\Sigma\Delta$ modulator is fabricated in a 0.18-um 1P4M CMOS standard process and dissipates 15mW for a single supply voltage of 1.8V.

• Journal of IKEEE
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• v.18 no.1
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• pp.119-127
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• 2014

This paper presents a CMOS readout circuit for MEMS(Micro Electro Mechanical System) acceleration sensors. It consists of a MEMS accelerometer, a capacitance to voltage converter(CVC) and a second-order switched-capacitor ${\Sigma}{\Delta}$ modulator. Correlated-double-sampling(CDS) and chopper-stabilization(CHS) techniques are used in the CVC and ${\Sigma}{\Delta}$ modulator to reduce the low-frequency noise and DC offset. The sensitivity of the designed CVC is 150mV/g and its non-linearity is 0.15%. The duty cycle of the designed ${\Sigma}{\Delta}$ modulator output increases about 10% when the input voltage amplitude increases by 100mV, and the modulator's non-linearity is 0.45%. The total sensitivity is 150mV/g and the power consumption is 5.6mW. The proposed circuit is designed in a 0.35um CMOS process with a supply voltage of 3.3V and a operating frequency of 2MHz. The size of the designed chip including PADs is $0.96mm{\times}0.85mm$.