A 16-bit CORDIC rotator for high-performance wireless LAN

In this paper we propose a novel 16-bit low power CORDIC rotator that is used for high-speed wireless LAN. The algorithm converges to the final target angle by adaptively selecting appropriate iteration steps while keeping the scale factor virtually constant. The VLSI architecture of the proposed design eliminates the entire arithmetic hardware in the angle approximation datapath and reduces the number of iterations by 50% on an average. The cell area of the processor is 0.7 mm2 and it dissipates 7 mW power at 20 MHz frequency

New virtually scaling free adaptive CORDIC rotator

In this article we propose a novel CORDIC rotator algorithm that eliminates the problems of scale factor compensation and limited range of convergence associated with the classical CORDIC algorithm. In our scheme, depending on the target angle or the initial coordinate of the vector, a scaling by 1 or 1/?2 is needed that can be realised with minimal hardware. The proposed CORDIC rotator adaptively selects appropriate iteration steps and converges to the final result by executing 50% less number of iterations on an average compared to that required for the classical CORDIC. Unlike classical CORDIC, the final value of the scale factor is completely independent of number of executed iterations. Based on the proposed algorithm, a 16-bit pipelined CORDIC rotator implementation has been described. The silicon area of the fabricated pipelined CORDIC rotator core is 2.73 mm2. This is equivalent to 38 k inverter gates in IHP in-house 0.25 ?m BiCMOS technology. The average dynamic power consumption of the fabricated CORDIC rotator is 17 mW @ 2.5 V supply and 20Msps throughput. Currently, this CORDIC rotator is used as a part of the baseband processor for a project that aims to design a single-chip wireless modem compliant with IEEE 802.11a and Hiperlan/2

Direct kinematics solution architectures for industrial robot manipulators: Bit-serial versus parallel

A Very Large Scale Integration (VLSI) architecture for robot direct kinematic computation suitable for industrial robot manipulators was investigated. The Denavit-Hartenberg transformations are reviewed to exploit a proper processing element, namely an augmented CORDIC. Specifically, two distinct implementations are elaborated on, such as the bit-serial and parallel. Performance of each scheme is analyzed with respect to the time to compute one location of the end-effector of a 6-links manipulator, and the number of transistors required

CORDICのハードウェア構成及び応用に関する研究

電気通信大学201

A study and comparison of COordinate Rotation DIgital Computer (CORDIC) architectures

Most of the digital signal processing applications performs operations like multiplication, addition, square-root calculation, solving linear equations etc. The physical implementation of these operations consumes a lot of hardware and, software implementation consumes large memory. Even if they are implemented in hardware, they do not provide high speed, and due to this reason, even today the software implementation dominates hardware. For realizing operations from basic to very complex ones with less hardware, a Co-ordinate Rotation Digital Computer (CORDIC) proves beneficial. It is capable of performing mathematical operations right from addition to highly complex functions with the help of arithmetic unit and shifters only. This paper gives a brief overview of various existing CORDIC architectures, their working principle, application domain and a comparison of these architectures. Different designs are available as per the target, i.e. high accuracy and precision, low area, low latency, hardware efficient, low power, reconfigurability, etc. that can be used as per the application in which the architecture needs to be employed

The implementation and applications of multiple-valued logic

Multiple-Valued Logic (MVL) takes two major forms. Multiple-valued circuits can implement the logic directly by using multiple-valued signals, or the logic can be implemented indirectly with binary circuits, by using more than one binary signal to represent a single multiple-valued signal. Techniques such as carry-save addition can be viewed as indirectly implemented MVL. Both direct and indirect techniques have been shown in the past to provide advantages over conventional arithmetic and logic techniques in algorithms required widely in computing for applications such as image and signal processing. It is possible to implement basic MVL building blocks at the transistor level. However, these circuits are difficult to design due to their non binary nature. In the design stage they are more like analogue circuits than binary circuits. Current integrated circuit technologies are biased towards binary circuitry. However, in spite of this, there is potential for power and area savings from MVL circuits, especially in technologies such as BiCMOS. This thesis shows that the use of voltage mode MVL will, in general not provide bandwidth increases on circuit buses because the buses become slower as the number of signal levels increases. Current mode MVL circuits however do have potential to reduce power and area requirements of arithmetic circuitry. The design of transistor level circuits is investigated in terms of a modern production technology. A novel methodology for the design of current mode MVL circuits is developed. The methodology is based upon the novel concept of the use of non-linear current encoding of signals, providing the opportunity for the efficient design of many previously unimplemented circuits in current mode MVL. This methodology is used to design a useful set of basic MVL building blocks, and fabrication results are reported. The creation of libraries of MVL circuits is also discussed. The CORDIC algorithm for two dimensional vector rotation is examined in detail as an example for indirect MVL implementation. The algorithm is extended to a set of three dimensional vector rotators using conventional arithmetic, redundant radix four arithmetic, and Taylor's series expansions. These algorithms can be used for two dimensional vector rotations in which no scale factor corrections are needed. The new algorithms are compared in terms of basic VLSI criteria against previously reported algorithms. A pipelined version of the redundant arithmetic algorithm is floorplanned and partially laid out to give indications of wiring overheads, and layout densities. An indirectly implemented MVL algorithm such as the CORDIC algorithm described in this thesis would clearly benefit from direct implementation in MVL

An approach to the application of shift-and-add algorithms on engineering and industrial processes

Different kinds of algorithms can be chosen so as to compute elementary functions. Among all of them, it is worthwhile mentioning the shift-and-add algorithms due to the fact that they have been specifically designed to be very simple and to save computer resources. In fact, almost the only operations usually involved with these methods are additions and shifts, which can be easily and efficiently performed by a digital processor. Shift-and-add algorithms allow fairly good precision with low cost iterations. The most famous algorithm belonging to this type is CORDIC. CORDIC has the capability of approximating a wide variety of functions with only the help of a slight change in their iterations. In this paper, we will analyze the requirements of some engineering and industrial problems in terms of type of operands and functions to approximate. Then, we will propose the application of shift-and-add algorithms based on CORDIC to these problems. We will make a comparison between the different methods applied in terms of the precision of the results and the number of iterations required.This research was supported by the Conselleria de Educacion of the Valencia Region Government under grant number GV/2011/043

An on-line approach for evaluating trigonometric functions

This thesis investigates the evaluation of trigonometric functions based on an on-line arithmetic approach. On-line algorithms have been developed to evaluate the sine and cosine functions. Error analysis and heuristics are carried out to arrive at a minimal error algorithm based on the series expansion of the sine and cosine function. A logical design based on the algorithm is presented where the unit is designed as a set of basic modules. A detailed bit slice design of each module is also presented. A simulator was designed as an experimental tool for synthesis of the on-line algorithms, and a tool for performance evaluation

Design and Implementation of FPGA based linear All Digital Phase-Locked Loop for Signal Processing Applications

This project presents a linear all-digital phase locked loop based on FPGA. In this ADPLL the phase detection system is realized by generating an analytic signal using a compact implementation of Hilbert transform and then simply computing the instantaneous phase using CORDIC algorithm in vectoring mode of operation. A 16-bit pipelined CORDIC algorithm is employed in order to obtain the phase information of the signal. All the components used in this phase detection system are realized as digital discrete time components. This design does not involve any class of multipliers thus reducing the complexity of the design. The loop filter of the ADPLL has been designed using PI controller which has a low pass behavior and is used to discard the higher order harmonics of the error signal. The CORDIC algorithm in its rotation mode of operation is used to compute sinusoidal values for the DDS. The ADPLL model has been implemented using Xilinx ISE 12.3 and ModelSim PE Student Edition 10.1a. The ADPLL model describes a novel method of implementation of CORDIC algorithm for the DDS system. This ADPLL model basically used for synchronization of closed loop RF control signals in a heavy ion particle accelerator can be implemented even in an ASIC which can be seen with a more general use for many a applications in the daily life