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Node Analysis for AC Circuits01:14

Node Analysis for AC Circuits

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Consider an angioplasty system featuring a catheter equipped with a turbine, a critical tool for removing plaque deposits from coronary arteries. This intricate medical device operates using a circuit model reminiscent of a dual-node RLC circuit powered by a current-controlled voltage source.
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Nodal Analysis01:10

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Nodal analysis is a fundamental method in electrical engineering used to simplify the process of circuit analysis. This method revolves around the concept of using node voltages as the primary variables for circuit analysis. The objective is to determine the voltage at each node in a circuit, which can then be used to find other quantities of interest, such as currents through specific components.
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Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.
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Properties of the Root Locus01:05

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The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
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Construction of Root Locus01:15

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The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Radix-4 CORDIC algorithm based low-latency and hardware efficient VLSI architecture for Nth root and Nth power

Ankur Changela1, Yogesh Kumar2, Marcin Woźniak3

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A novel radix-4 hyperbolic COordinate Rotion DIgital Computer (CORDIC) architecture offers reduced hardware utilization and improved error performance for fixed-point root and power computations compared to radix-2 methods.

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Area of Science:

  • Digital Signal Processing
  • VLSI Architecture Design
  • Computer Arithmetic

Background:

  • Existing methods for fixed-point root and power computation often rely on radix-2 COordinate Rotion DIgital Computer (CORDIC) algorithms.
  • Radix-2 CORDIC algorithms suffer from high computation latency, posing a challenge for efficient hardware implementation.
  • The complexity of radix-4 CORDIC, while offering faster convergence, is a barrier due to intricate logic and scale factor management.

Purpose of the Study:

  • To propose a low-complexity VLSI architecture for computing the root and power of fixed-point numbers using a radix-4 hyperbolic CORDIC.
  • To address the hardware complexity and computational challenges associated with radix-4 CORDIC algorithms.
  • To improve hardware utilization and error performance compared to existing radix-2 CORDIC-based approaches.

Main Methods:

  • A modified radix-4 hyperbolic vectoring (R4HV) CORDIC is used for logarithm computation with simplified input-dependent rotation criteria.
  • Radix-4 linear vectoring (R4LV) CORDIC is employed for division operations.
  • A modified scaling-free radix-4 hyperbolic rotation (R4HR) CORDIC is utilized for exponential computation, with pre-computed scale factors and scaling-free rotations.

Main Results:

  • The proposed modified R4HV CORDIC simplifies angle selection criteria, reducing hardware complexity.
  • The R4HR CORDIC achieves reduced complexity by pre-computing scale factors and using scaling-free rotations.
  • Hardware analysis indicates superior hardware utilization compared to recent methods, with FPGA implementation showing a 20% reduction in hardware usage and better error performance.

Conclusions:

  • The proposed low-complexity VLSI architecture based on modified radix-4 hyperbolic CORDIC effectively computes root and power functions for fixed-point numbers.
  • The architectural modifications significantly reduce hardware complexity and improve performance metrics.
  • The implemented Virtex-6 FPGA solution demonstrates practical advantages in terms of hardware efficiency and accuracy over radix-2 CORDIC methods.