桑名 杏奈

In this paper, an investigation of the operating regions of the Kerwin-Huelsman-Newcomb filters based on the characteristics of Nichols charts is presented. In recent research papers, the idea of loop gain cannot be used in many feedback systems because the mathematical relationships between loop gain and closed-loop gain do not exist. Moreover, both Nyquist and Nichols charts of loop gain do not describe three different behaviors of high-order networks. Furthermore, the Kerwin-Huelsman-Newcomb topology is one of the most important filters in modern telecommunication systems while the behaviors of phase margin in this architecture are not well analyzed. Hence, the ringing test for three different cases of the second-order Kerwin-Huelsman-Newcomb filters is proposed and described in detail. The experimental measurements of the phase margins are 50 degrees (under-damping region), 77 degrees (critical damping region), and 83 degrees (over-damping region). It shows that the ringing test has a very clear electronic technical meaning and reflects the important role of the Nichols chart in the high-order networks.

This paper describes details of floating-point square root calculation algorithms using Taylor-series expansion and mantissa region division in the viewpoint of the efficient dedicated hardware design. Taylor-series expansions of the square root are examined at the center points of divided mantissa regions, and based on these, square root calculation hardware design balances among accuracy, numbers of basic floating point arithmetic operations (multiplications and additions/ subtractions) as well as the required look-up table size are clarified quantitatively. These results lead to obtaining the suitable algorithm for floating-point square root calculation, and building its corresponding hardware architecture for the digital processor designer.

In LSI testing, equivalent time sampling techniques are frequently used because the input signals to the device under test and the sampling clock are controllable when the repetitive input signals are applied to the analog device under test, its output signals can be also repetitive. In this paper, we investigate an efficient waveform acquisition method with the equivalent-sampling using the metallic ratio of the sampling frequency and the input frequency, which is expected to be used for on-line, short-time and simple analog/RF/mixed-signal IC testing.

This article improves ADC sampling efficiency of the histogram method by investigating the ratio between the input saw frequency and the sampling frequency the goal is to shorten ADC test time, and thus cost. Using a saw wave signal, the histogram RMS error within a certain range is simulated for the golden ratio, silver ratio, bronze ratio and prime number ratios. Golden ratio can halve the test time compared to the conventional method. We simulate an increase in output bins (the number of histogram bins), and find bronze ratio yields the best sampling efficiency.

This paper studies a current-driven IGBT driver circuit to reduce the collector voltage overshoot and switching loss during its turn-off. The gate voltage operating region is divided into 4 and for each region, the optimal amount of the pulling current from the IGBT gate is used. Our simulations show that with the current-driven IGBT driver, the overshoot voltage is reduced by 31 % and the switching loss is by 35%, compared to the voltage-driven IGBT driver usage case.

This paper presents design and analysis of DACs based on the non-uniform current division resistive ladder, and proposes a new configuration DAC with segmentation of binary, quaternary and unary resistive-ladders, which enables two times gain with equivalent chip area and current sources to the conventional. Also, Monte Carlo simulation considering resistor and current source mismatches shows that the DNL deviation of the proposed one is a little better than the conventional one.

This paper presents several proposed motion models of high-order physical systems in three main concepts called macro-scale, regular-scale, and nano-scale. In fact, it is very difficult to find an exact numerical solution for the high-order differential equations because all numerical methods only yield the approximate solutions. In addition, loop gain is not widely used in many negative feedback systems because it is an approximation value. To overcome the limitations of the high-order differential equations and the loop gain, the waveforms of the physical periodic motions are expressed by helix functions at time variation, and the characteristics of complex functions are used to examine the behaviors of the transmission spaces and the transmission networks in the different motion models including the Earth's motion, the simple pendulum systems, and the electronic systems. Furthermore, the force of attraction and the friction or the resistance in the different scales obey the conservation law and the superposition principle therefore, three superposition formulas are introduced to derive the transfer functions in high-order mechatronic systems. The operating regions, the effects of the overshoot phenomena, the breaking chemical bonds, and the difference between negative and positive feedbacks in these systems are also introduced. As a result, the use of complex functions, helix waves, and superposition principle leads to a complete control theory with which many behaviors of the physical systems can be explained and predicted easily.

<title>Abstract</title> On the basis of the intimate relation between Nambu dynamics and the hydrodynamics, the hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as “hydrodynamics of granular material”. In Part 1, the quantization of space is done by Moyal product, and the hydrodynamic simulation is performed for the so obtained two dimensional fluid, which flows inside a canal with an obstacle. The obtained results differ between two cases in which the size of a fluid particle is zero and finite. The difference seems to come from the behavior of vortices generated by an obstacle. In Part 2 of quantization, considering vortex as a string, two models are examined; one is the “hybrid model” in which vortices interact with each other by exchanging Kalb-Ramond fields (a generalization of stream functions), and the other is the more general “string field theory” in which Kalb-Ramond field is one of the excitation mode of string oscillations. In the string field theory, Altarelli-Parisi type evolution equation is introduced. It is expected to describe the response of distribution function of vortex inside a turbulence, when the energy scale is changed. The behaviour of viscosity differs in the string theory, being compared with the particle theory, so that Landau theory of fluid to introduce viscosity may be modified. In conclusion, the hydrodynamics and the string theory are almost identical theories. It should be noted, however, that the string theory to reproduce a given hydrodynamics is not a usual string theory.

This paper presents some limitations of the classical concept of loop gain in many mathematical motion models of the real objects. It is well known that there are some advanced concepts in control theory and a lot of them are very heavy on the loop gain. Therefore, the loop gain is heard in many topics like frequency compensation, phase-gain margins, negative feedback systems. However, the loop gain cannot be used to analyze the overshoot phenomenon in many feedback amplifiers because it doesn't show the operating regions of high-order mechatronic systems. In addition, the theoretical calculation, the laboratory simulation and the practical measurement of loop gain are not unique. As a result, this is the biggest limitation in mathematical models of motion that a lot of engineers have trouble with loop gain. To overcome some disadvantages of the loop gain, the use of the self-loop function allows engineers to do the ringing test simpler because it is easily verified in MATLAB calculator, SPICE simulator, and Network Analyzer. In order to extend the application range of the Nichols chart of self-loop function in high-order mechatronic systems, the feasibility of complex functions and the explanation of overshoot phenomena are described in detail. It is shown that complex functions are useful tools for mathematical motion models of mechatronic systems.

This paper explores the use of the Pascal's triangle to study the operating regions and compute the phase margins of second-order Rauch low-pass filters. Inspection of the Pascal's triangle allows the determination of the exact values of the phase margin at unity gain of the self-loop function in a transfer function. The phase margin on Nichols chart allows the prediction of the ringing that drives the system unstable. Several illustrative examples of high-order linear systems are provided. Experimental measurement results of the implemented circuit show that the proposed method is quite effective.

This paper presents a study of helix functions and multi-source Rauch filters using complex functions. Complex functions which imaginary unit j represents a 90-degree phase shift are used to express both analogue signals and transmission networks. Helix waves are proposed to analyze the behaviors of analogue signals such as sinusoidal signals, differential signals, and complex signals in both time and frequency domains. A general superposition formula is also introduced for deriving the transfer functions of multisource transmission networks such as fully differential amplifiers, fully differential low-pass filters, polyphase filters, complex filters, and quadrature signal generation circuits. In addition, the advantages of Rauch filters are an easiest selection of circuit components and a simplest design in fully differential forms and complex topologies. As a high-order feedback system operates in the under-damping region, ringing occurs and makes the network unstable. Therefore, the Nichols chart of self-loop function is used to do the stability test of a 4th-order fully differential Rauch low-pass filter because it can be easily integrated in Network Analyzers. The simulation results of the phase margin at unity gain of the self-loop function in a proposed design of this filter are 74 degrees (over-damping region), 68 degrees (critical damping region), and 59 degrees (under-damping region). With the proposed superposition formula, the transfer function and the image rejection ratio of a 4th-order Rauch complex filter are easily derived and investigated in both positive and negative frequency domains. The image rejection ratio of the Rauch complex filter is 32 dB. It's shown that complex functions play an important role in mathematical models of motion in multisource networks. The innovation of this work is the Nichols chart of self-loop function which is a useful tool for the stability test of feedback networks. The observation of the phase margin at unity gain of the self-loop function helps us determine the operating regions of high-order systems quickly. In addition, the use of the superposition formula is a fast network analysis method for high-order multi-source systems.

This paper explores the use of the Nichols chart to study the operating regions and compute the phase margins in electronic amplifiers. Inspection of the Nichols chart allows the determination of the exact values of the phase margin at unity gain of the self-loop function in a transfer function. Hence, there is no need to use the Nyquist criterion which is an important stability test with applications to adaptive feedback systems. Furthermore, the phase margin allows the prediction of the ringing that drives the system unstable. Several illustrative examples of feedback amplifiers are provided. Experimental results are also presented which confirm the theoretical development of the stability test.

This paper presents a ringing test for 2nd-order Sallen-Key low-pass filters. A comparison measurement is constructed, which takes into account the measurement of a self-loop function in a transfer function. Based on the phase margin at unity of the self-loop function, a general stability criterion for second-order linear systems is proposed in terms of operating regions. In case of under-damping region, the ringing occurs and makes the system unstable. The advantage of the proposed criterion lies in its simplicity than some of the existing results. The new stability criterion is applied to the network based negative feedback issues. Experimental results show that the proposed method is quite effective.

This paper investigates floating-point division algorithms based on Taylor-series expansion. Taylor-series expansions of 1/x are examined for several center points with their convergence ranges, and show the Taylor-series expansion division algorithm trade-offs among division accuracy, numbers of multiplications/additions/subtractions and LUT sizes the designer can choose the optimal algorithm for his digital division, and build its conceptual architecture design with the contents described here.

This paper presents a ringing test for 2nd-order Tow-Thomas low-pass filters. A new concept of self-loop function in a transfer function for a class of linear negative feedback systems is introduced. The introduction of the self-loop function allows the extension to the stability test for high-order linear systems. Based on the proposed comparison measurement technique, the self-loop function is derived directly from the measurement results of the transfer function without breaking the feedback loop. The phase margin at unity of the self-loop function on the Nichols chart determines the operating region of a linear system. As a high-order system operates on the under-damping region, the damped oscillation noise causes ringing and makes the network unstable. In case of the second-order system, if the phase margin is smaller than 76.3 degrees, the ringing occurs and makes the system unstable. The measurement results of the magnitude of the transfer function in the implemented circuit at around the cutoff frequency 25 kHz are -10 dB (over-damping region), 0 dB (critical damping region), and 15 dB (under-damping region). The measurement results of the phase margin are 95 degrees (over-damping region), 77 degrees (critical damping region), and 40 degrees (under-damping region). Experimental results show that the proposed method is quite effective on the ringing test for high-order linear negative feedback systems.

This paper describes the similarity of the crest factor reduction effect among the four algorithms (Newman, Kitayoshi, Schroeder and Narahashi) and unifies their initial phase setting equations using the derivation of the Narahashi phase. When testing the frequency characteristics of analog/mixed-signal ICs, a multi-tone (sum of multiple sine waves) signal is often used instead of a single tone signal, to reduce their testing time. However, as the amplitude of each tone signal becomes smaller if multiple sine waves are simply added without care of their initial phases, the SNR of the test result becomes worse and the test accuracy becomes lower. To alleviate this problem, it is necessary to generate a multi-tone signal using a crest factor reduction algorithm. There are four representative multi-tone signal generation algorithms for reducing crest factor, and their study results are presented.

This paper describes an accurate and fast testing technique for a precision voltage reference. Our proposed DC-AC conversion and FFT spectrum analysis method is applied and its experiment results show that measurement accuracy within ±100μV and measurement variation (repeatability) within ±10μV are feasible.

This paper proposes a summing node test method for the operational amplifier and shows the followings: (i) It can be used for parallel testing of multiple AC characteristics (such as open loop gain (AOL), PSRR and CMRR) of one operational amplifier simultaneously with the equivalent accuracy but much faster compared to the NULL method. Also it can measure them even for multiple operational amplifiers at the same time. (ii) It can measure THD, SNR and THD+N of the operational amplifier with the comparable accuracy to the audio analyzer usage case, by applying proper analog filters. In other words, it can measure them with remarkable accuracy at very low cost. These have been verified with simulations and experiments. The proposed summing node test method uses an inverting operational amplifier under test and its negative input is amplified by an auxiliary non-inverting operational amplifier. The input and power supply voltages for the operational amplifier under test are modulated by AC signals with different frequencies. The auxiliary amplifier output is digitized after analog filtering and FFT is performed to the digitized data. This proposed method can reduce operational amplifier test time with good accuracy but without expensive instruments at mass production shipping, to meet the requirements for IoT and automotive as well as audio applications.

A proposed ringing test for linear negative feedback amplifiers is presented. As a negative feedback amplifier operates in the under-damping region, the ringing occurs and makes the system unstable. A comparison measurement technique is proposed to measure the self-loop function in a transfer function. The ringing test for the shunt-shunt feedback amplifier, the unity-gain amplifier, and the inverting amplifier are demonstrated by the simulation results. The theoretical concepts of the stability test for 2nd-order Åkerberg-Mossberg low-pass filters are verified by the practical measurements.

This paper presents a design of a sixth-order passive quadrature signal generation network for verifying the behavior of the passive polyphase filters in RF front-end low-IF transceivers applications. The transfer function of this network is derived based on the superposition principle and there are two maximum values (at frequencies 45 kHz, 100 MHz), and one minimum value at frequency 2 MHz. The IQ mismatch occurred at below 40 kHz and above 2 MHz in the observed frequency range 1 kHz to 10 MHz.

This paper discusses the practical measurements of self-loop functions in second-order low-pass filters based on an alternating current conservation technique. From the view point of transfer function of a network, the measurement of phase margin at unity gain of the self-loop function can verify the operating region of a high-order transfer function which can be over-damping, or critically damping, or under-damping. The overshoot and undershoot voltages will occur in both passive and active linear systems when they work on the under-damping region. Therefore, measurements of self-loop function have been useful not only in passive networks but also in feedback systems.

This paper proposes the design of an LC harmonic notch filter to improve the output ripple in an inductor type step-down DC-DC buck converter. To examine the overshoot voltage of the converter, the transfer function and its self-loop function of the power stage were analyzed. The LC network was designed at the 180 kHz harmonic frequency and added at the output node of the power stage of the converter. As a result, the ripple was reduced by 3 dB (from -35 dBV to -42 dBV at 180 kHz). The ripple level was kept below 5 mVpp, which is small enough compared to 5 V desired voltage.

This paper introduces our production testing research results for analog and mixed-signal SoC in IoT era, such as operational amplifier, ADC, sampling circuit, timing related testing technologies. Notice that production testing and measurement / characterization for ICs are similar but different, and this paper introduces the former. The analog / mixed-signal testing plays a very important role in achieving both reliability and low cost for IoT and automotive systems. It also is a big technological challenge because there is no general method, but it requires state-of-The-Art combination and optimization of a wide variety of technologies including circuit and system design as well as signal processing, control and measurement algorithms. Their overview including future technology challenges is described.

A proposed ringing test for 3rd-order ladder low-pass filters is presented. As a high-order network operates in under-damping, ringing occurs and makes the system unstable. The alternating current conservation technique is proposed to measure the self-loop function in a transfer function. The values of theoretical calculation are verified by the SPICE simulation and practical measurement results.

This paper describes an improved Nagata current source insensitive to temperature utilizing MOSFET drain current temperature characteristics, as well as supply voltage variation. The proposed circuit does not require a start-up circuit or special resistors, and it is simple-yet-effective as a stable reference current source. Its circuit operation principle and SPICE simulation results are presented.

This paper presents the nonlinearity simulation results for N-Ary resistive ladder-based current-steering digital-To-Analog converters (DACs) using the Monte-Carlo method. Differential nonlinearity (DNL) of the R-2R based current-steering DAC deteriorates due to the mismatch of both current sources and resistors. It is inferred that when an N-Ary resistive ladder that divides the current into the non-binary ratio is used, its DNL standard deviation becomes the largest at the boundary codes of the ranges divided into N.

In this paper, we have examined two crest factor controlled multi-Tone signal generation algorithms: modified Newman and Fibonacci sequence initial phase setting methods. We have found with simulation that the former can realize relatively wide crest factor control range but the waveform quality degrades as the crest factor increases, compared to the latter. These algorithms can be used, such as for effective test of the transmission characteristics of OFDM systems, where the frequency dependent nonlinearity cannot be ignored.