The document describes the Mismatch Noise Cancellation (MNC) architecture. The key components of the MNC architecture are:
1. A pseudo-random number generator that generates random binary sequences.
2. A mismatch estimation block that estimates mismatches.
3. A noise cancellation block that corrects the effects of mismatches.
4. Synchronization elements that synchronize data flow.
The document proposes a low power, high speed parallel architecture for cyclic convolution based on the Fermat Number Transform (FNT). It introduces techniques like Code Conversion without Addition (CCWA) and Butterfly Operation without Addition (BOWA) to perform FNT and inverse FNT without additions except for the final stages. This avoids modulo 2n+1 carry save additions to reduce power and delay. Modulo 2n+1 Partial Products Multipliers are used for pointwise multiplications to further improve efficiency. Simulation results show the proposed 4-2 compressor architecture achieves lower power compared to existing designs.
Comparative Study of Low Power Low Area Bypass Multipliers for Signal Process...IJERA Editor
This document presents a comparative study of low power, low area bypass multipliers that are well-suited for digital signal processing applications. It analyzes Braun multipliers, row bypassing, column bypassing, and a proposed mixed bypassing technique. Simulation results on an FPGA show the mixed bypassing multiplier has the lowest power and area requirements compared to the other techniques. Specifically, it uses the fewest slices and LUTs. Therefore, the mixed bypassing multiplier is concluded to be an effective design for low power, low cost digital signal processing applications.
Implementation of Stronger S-Box for Advanced Encryption Standardtheijes
This document describes the implementation of a stronger S-box for the Advanced Encryption Standard (AES) using combinational logic. It presents a two-stage pipelined combinational logic based S-box that has smaller area and higher throughput compared to traditional ROM-based implementations. The S-box construction methodology decomposes arithmetic in GF(28) fields into lower order GF(2^2) and GF(2) fields. Equations for addition, squaring, multiplication and inversion in these composite fields are derived. Simulation results show encryption and decryption working as intended. Synthesis results indicate lower device utilization compared to ROM implementations.
This document summarizes research on improving the performance of multiplier and accumulator (MAC) circuits used in digital signal processing. It presents four architectures for carry-select adders (CSLA) that can be used in MACs: 1) a regular CSLA, 2) a CSLA that replaces full adders with binary-to-excess converters (BEC) to reduce area, 3) a CSLA that uses D-latches to store intermediate values and reduce the number of adders, and 4) a modified CSLA architecture. The document analyzes the delay and area of each group of bits for the different CSLA architectures. It finds that BEC and D-latch based C
Low cost high-performance vlsi architecture for montgomery modular multiplica...Ratnakar Varun
This document discusses VLSI implementation of Montgomery modular multiplication for cryptographic applications. It proposes a configurable carry-save adder architecture to reduce the number of clock cycles needed for Montgomery multiplication. The architecture can perform either one three-input carry-save addition or two serial two-input carry-save additions. It also discusses the Advanced Encryption Standard (AES) algorithm for encryption and decryption. AES is based on substitution-permutation networks and involves key expansion, initial/final rounds, and intermediate rounds of sub bytes, shift rows, mix columns and add round key transformations.
The document provides guitar chord progressions and instructions for an intro, verse, pre-chorus, chorus, bridge, and outro section of a song. It includes tab notation for two guitar parts throughout most sections. The intro is played twice before moving to the verse. The pre-chorus and chorus are each played twice, followed by a bridge with minimal guitar accompaniment. The chorus is then repeated four times before concluding with a final guitar progression.
Joint Compensation of CIM3 and I/Q Imbalance in the Up-conversion Mixer with ...Ealwan Lee
This document discusses a technique for jointly compensating for third-order intermodulation distortion (CIM3) and I/Q imbalance in an up-conversion mixer using a single skew matrix. It presents a simplified model showing that CIM3 can be modeled with two coefficients similar to the I/Q imbalance model. The technique allows for joint compensation of CIM3 and I/Q imbalance with a single matrix, providing an effective way to meet stringent emission requirements without the need for SAW filters. It also describes how the existing I/Q imbalance estimation method can be extended to estimate the CIM3 coefficients. Numerical results demonstrate that the technique can compensate initial CIM3 levels as high as -45dBc to within the -
1. A block diagram is a pictorial representation of a system that shows the relationship between inputs and outputs of the entire system.
2. Block diagrams can represent physical systems and use symbols like summing points, gains, and transfer functions.
3. Reduction techniques can be used to simplify block diagrams, such as combining blocks in series or parallel or eliminating feedback loops.
The document proposes a low power, high speed parallel architecture for cyclic convolution based on the Fermat Number Transform (FNT). It introduces techniques like Code Conversion without Addition (CCWA) and Butterfly Operation without Addition (BOWA) to perform FNT and inverse FNT without additions except for the final stages. This avoids modulo 2n+1 carry save additions to reduce power and delay. Modulo 2n+1 Partial Products Multipliers are used for pointwise multiplications to further improve efficiency. Simulation results show the proposed 4-2 compressor architecture achieves lower power compared to existing designs.
Comparative Study of Low Power Low Area Bypass Multipliers for Signal Process...IJERA Editor
This document presents a comparative study of low power, low area bypass multipliers that are well-suited for digital signal processing applications. It analyzes Braun multipliers, row bypassing, column bypassing, and a proposed mixed bypassing technique. Simulation results on an FPGA show the mixed bypassing multiplier has the lowest power and area requirements compared to the other techniques. Specifically, it uses the fewest slices and LUTs. Therefore, the mixed bypassing multiplier is concluded to be an effective design for low power, low cost digital signal processing applications.
Implementation of Stronger S-Box for Advanced Encryption Standardtheijes
This document describes the implementation of a stronger S-box for the Advanced Encryption Standard (AES) using combinational logic. It presents a two-stage pipelined combinational logic based S-box that has smaller area and higher throughput compared to traditional ROM-based implementations. The S-box construction methodology decomposes arithmetic in GF(28) fields into lower order GF(2^2) and GF(2) fields. Equations for addition, squaring, multiplication and inversion in these composite fields are derived. Simulation results show encryption and decryption working as intended. Synthesis results indicate lower device utilization compared to ROM implementations.
This document summarizes research on improving the performance of multiplier and accumulator (MAC) circuits used in digital signal processing. It presents four architectures for carry-select adders (CSLA) that can be used in MACs: 1) a regular CSLA, 2) a CSLA that replaces full adders with binary-to-excess converters (BEC) to reduce area, 3) a CSLA that uses D-latches to store intermediate values and reduce the number of adders, and 4) a modified CSLA architecture. The document analyzes the delay and area of each group of bits for the different CSLA architectures. It finds that BEC and D-latch based C
Low cost high-performance vlsi architecture for montgomery modular multiplica...Ratnakar Varun
This document discusses VLSI implementation of Montgomery modular multiplication for cryptographic applications. It proposes a configurable carry-save adder architecture to reduce the number of clock cycles needed for Montgomery multiplication. The architecture can perform either one three-input carry-save addition or two serial two-input carry-save additions. It also discusses the Advanced Encryption Standard (AES) algorithm for encryption and decryption. AES is based on substitution-permutation networks and involves key expansion, initial/final rounds, and intermediate rounds of sub bytes, shift rows, mix columns and add round key transformations.
The document provides guitar chord progressions and instructions for an intro, verse, pre-chorus, chorus, bridge, and outro section of a song. It includes tab notation for two guitar parts throughout most sections. The intro is played twice before moving to the verse. The pre-chorus and chorus are each played twice, followed by a bridge with minimal guitar accompaniment. The chorus is then repeated four times before concluding with a final guitar progression.
Joint Compensation of CIM3 and I/Q Imbalance in the Up-conversion Mixer with ...Ealwan Lee
This document discusses a technique for jointly compensating for third-order intermodulation distortion (CIM3) and I/Q imbalance in an up-conversion mixer using a single skew matrix. It presents a simplified model showing that CIM3 can be modeled with two coefficients similar to the I/Q imbalance model. The technique allows for joint compensation of CIM3 and I/Q imbalance with a single matrix, providing an effective way to meet stringent emission requirements without the need for SAW filters. It also describes how the existing I/Q imbalance estimation method can be extended to estimate the CIM3 coefficients. Numerical results demonstrate that the technique can compensate initial CIM3 levels as high as -45dBc to within the -
1. A block diagram is a pictorial representation of a system that shows the relationship between inputs and outputs of the entire system.
2. Block diagrams can represent physical systems and use symbols like summing points, gains, and transfer functions.
3. Reduction techniques can be used to simplify block diagrams, such as combining blocks in series or parallel or eliminating feedback loops.
A High Speed Wallace Tree Multiplier Using Modified Booth Algorithm for Fast ...Kumar Goud
Abstract— Designing multipliers that are of high-speed, low power, and regular in layout are of substantial research interest. Speed of the multiplier can be increased by reducing the generated partial products. Many attempts have been made to reduce the number of partial products generated in a multiplication process; one of them is Wallace tree multiplier. Wallace Tree CSA structures have been used to sum the partial products in reduced time. In this paper Wallace tree construction is investigated and evaluated. Speed of traditional Wallace tree multiplier can be improved by using compressor techniques. In this paper Wallace tree is constructed by traditional method and with the help of compressor techniques such as 4:2 compressor, 5:2 compressor, 6:2 compressor, 7:2 compressor. Therefore, minimizing the number of half adders used in a multiplier reduction will reduce the complexity.
Index Terms—Component, formatting, style, styling, insert. (key words)
The document describes a proposed approach to modify the modified Booth multiplier to generate a more regular partial product array. The conventional MBE generates an irregular array due to an extra partial product bit at the least significant bit position of each row. The proposed approach incorporates this extra bit into the sign extension bits of the first row, reducing the number of rows from n/2+1 to n/2. It generates the partial product bits and new sign extension bits using simple logic gates, minimizing overhead. Experimental results show the proposed MBE multipliers achieve significant improvements in area, delay, and power compared to conventional MBE multipliers due to the more regular array enabling a smaller, faster reduction tree.
This document describes the design of a 16-bit, 3-input adder using two different strategies: a wait strategy and a speculative/divide-and-conquer (DAC) strategy. The wait strategy uses a divide-and-conquer tree of 5-bit full adders as the basic building block. The DAC strategy speculatively calculates potential outputs in parallel for subsets of bits and then selects the correct outputs using multiplexers once the carry bits are known. Both strategies were implemented and tested for area and delay, with the DAC strategy showing around a 26.6% reduction in worst-case propagation delay over the wait strategy.
this presentation will help u with understanding basic elements of the bloc diagram and how to reduce multi loop block diagram with some suitable numerical example.
The document provides example problems and solutions for mathematical modeling and analysis of control systems. It includes the following examples:
1) It derives the transfer function C(s)/R(s) for a system represented by a block diagram, obtaining the simplified closed-loop transfer function.
2) It models a simplified automobile suspension system as a mass-spring-damper system and derives the transfer function between the input and output displacements.
3) It obtains the transfer function Y(s)/U(s) for another simplified suspension system represented by a diagram relating displacements and forces.
4) It derives the state-space representation for a mechanical system represented by equations relating positions, velocities and
This document describes a project to design a sequential circuit to calculate the remainder (modulo-3) of an n-bit number A. The circuit uses a divide-and-conquer approach with multiple finite state machines (FSMs) running in parallel. A 128-bit shift register sequentially feeds bits to the FSMs. A 7-bit counter generates signals to stop the FSMs after processing all bits. The FSM outputs are combined using additional logic to produce the final remainder. The design aims to calculate the remainder in n/4 clock cycles, faster than the n cycles of a single FSM.
Power Systems Engineering - Matlab programs for Power system Simulation Lab -...Mathankumar S
This MATLAB code calculates line constants and impedances for single and double circuit transmission lines. It inputs parameters like conductor spacing, diameter, and distances between conductors and calculates the series inductance L and shunt capacitance C per unit length. It also forms the bus admittance matrix Ybus for a power system network and calculates real and reactive power flows and losses for a two-bus system.
The document describes the principles and implementation of an array multiplier. It discusses how array multipliers generate partial products simultaneously using parallel logic, making them faster than serial multipliers. A 4x4 bit array multiplier is implemented in Verilog using AND gates and adders, and its functionality is verified through simulation. While array multipliers require more gates and area than serial multipliers, their performance can be increased using pipelining. The document concludes that array multiplication is well-suited for applications requiring high speed.
MATLAB programs Power System Simulation lab (Electrical Engineer)Mathankumar S
The document contains MATLAB code for calculating line constants (inductance L and capacitance C) for overhead transmission lines with different configurations (single-circuit, single-circuit with multiple subconductors, and double-circuit). It requests user input of various line parameters and geometric mean distances and then calculates L and C values. Additional code calculates the network bus admittance matrix and transmission line losses.
The document discusses frequency response and Bode plots. It begins by defining the sinusoidal transfer function and frequency response. The frequency response consists of the magnitude and phase functions of the transfer function. Bode plots graphically display the magnitude and phase functions versus frequency on logarithmic scales. The document then provides procedures for constructing Bode plots, including determining individual component responses, combining them, and reading off gain and phase margins. Examples are given to demonstrate the procedures.
The document provides examples of microcontroller system design, including buses, data transfer, general purpose input/output (GPIO), and timers. It describes tristate and multiplexer-based bus structures, synchronous and asynchronous data transfer methods, GPIO hardware and programming models, and basic timer operations like event counting and rate generation. Radial and daisy-chain bus arbitration techniques are also explained.
A high performance fir filter architecture for fixed and reconfigurable appli...Ieee Xpert
A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications
This document discusses system design methodologies including finite state machines (FSMs), register transfer level (RTL) design using algorithmic state machine (ASM) charts and the datapath and controller design approach. It provides examples of modeling styles for FSMs and ASM charts in Verilog. Specifically, it describes modeling a pattern detector FSM and implementing the Booth multiplication algorithm using an ASM chart, which is then transformed into a datapath and controller architecture.
This document describes the design of different types of parallel multipliers using low power techniques on a 0.18um technology node. It discusses Braun multipliers, row-bypassing multipliers, and column-bypassing multipliers. The multipliers are implemented using both conventional methods and the Gate-Diffusion-Input (GDI) technique. Simulation results show that implementing the multipliers using GDI reduces transistor counts and power consumption compared to conventional implementations. The 4x4 Braun multiplier implemented with GDI uses 136 transistors and consumes 3mW of power, providing significant improvements over the conventional implementation.
This document discusses system compensation in control systems. It begins with an introduction to compensation design and the different types of compensators, including phase lead, phase lag, and phase lead-lag compensation. It describes how compensators are used to alter the frequency response of a system to meet performance requirements like steady-state error, bandwidth, and phase margin. Examples are provided of designing phase lead and phase lag compensators to compensate sample systems and satisfy given stability and performance criteria. The document provides guidance on determining appropriate compensator parameters.
High performance pipelined architecture of elliptic curve scalar multiplicati...Ieee Xpert
High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m)
This document discusses time-domain analysis and design of control systems through block diagrams. It defines key terms like plant, controller, feedback, and transfer functions. It describes how to represent systems using block diagrams and rules for simplifying block diagrams, including combining blocks in series and parallel and eliminating feedback loops. Examples are provided to demonstrate reducing complex block diagrams to standard forms and handling multiple-input systems using superposition.
1. Block diagrams can be used to model both simple and complex systems, and consist of multiple blocks connected to represent the system's functioning.
2. It is often necessary to reduce block diagrams by combining or rearranging blocks for easier analysis and calculation of the transfer function.
3. Common block diagram reduction techniques include combining blocks in cascade or parallel, moving summing or pickoff points, eliminating feedback loops, and swapping summing points.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Imprecise computing is an attractive model for digital processing at nano metric scales. Inexact computing is particularly interesting for computer arithmetic designs. This work deals about the design and analysis of two new inaccurate 4-2 compressors for utilization in a multiplier. These designs rely on different features of compression, such that imprecision in computation is measured by the error rate and the so-called normalized error distance can meet with respect to circuit-based figures of merit of a design in terms of number of transistors, delay and power consumption. The proposed approximate compressors are proposed and analyzed in Dadda multiplier. Extensive simulation results are provided and an application of the approximate multipliers to image processing is presented. The results proposed designs shows that reduced power dissipation, delay and transistor count.
Implementation of FinFET technology based low power 4×4 Wallace tree multipli...TELKOMNIKA JOURNAL
Many systems, including digital signal processors, finite impulse response (FIR) filters, application-specific integrated circuits, and microprocessors, use multipliers. The demand for low power multipliers is gradually rising day by day in the current technological trend. In this study, we describe a 4×4 Wallace multiplier based on a carry select adder (CSA) that uses less power and has a better power delay product than existing multipliers. HSPICE tool at 16 nm technology is used to simulate the results. In comparison to the traditional CSA-based multiplier, which has a power consumption of 1.7 µW and power delay product (PDP) of 57.3 fJ, the results demonstrate that the Wallace multiplier design employing CSA with first zero finding logic (FZF) logic has the lowest power consumption of 1.4 µW and PDP of 27.5 fJ.
This document discusses the design of finite impulse response (FIR) filters using multiple constant multiplication/accumulation (MCMA) technique to reduce hardware resources and cost. It proposes using truncated multipliers in the MCMA module to remove unnecessary partial product bits without affecting output precision. The filter coefficients are quantized with unequal word lengths using non-uniform quantization to minimize bit widths and reduce hardware cost while maintaining frequency response specifications. Simulation results show that direct-form FIR filters using the proposed truncated MCMA technique achieve lower area and power consumption than transposed-form implementations.
A High Speed Wallace Tree Multiplier Using Modified Booth Algorithm for Fast ...Kumar Goud
Abstract— Designing multipliers that are of high-speed, low power, and regular in layout are of substantial research interest. Speed of the multiplier can be increased by reducing the generated partial products. Many attempts have been made to reduce the number of partial products generated in a multiplication process; one of them is Wallace tree multiplier. Wallace Tree CSA structures have been used to sum the partial products in reduced time. In this paper Wallace tree construction is investigated and evaluated. Speed of traditional Wallace tree multiplier can be improved by using compressor techniques. In this paper Wallace tree is constructed by traditional method and with the help of compressor techniques such as 4:2 compressor, 5:2 compressor, 6:2 compressor, 7:2 compressor. Therefore, minimizing the number of half adders used in a multiplier reduction will reduce the complexity.
Index Terms—Component, formatting, style, styling, insert. (key words)
The document describes a proposed approach to modify the modified Booth multiplier to generate a more regular partial product array. The conventional MBE generates an irregular array due to an extra partial product bit at the least significant bit position of each row. The proposed approach incorporates this extra bit into the sign extension bits of the first row, reducing the number of rows from n/2+1 to n/2. It generates the partial product bits and new sign extension bits using simple logic gates, minimizing overhead. Experimental results show the proposed MBE multipliers achieve significant improvements in area, delay, and power compared to conventional MBE multipliers due to the more regular array enabling a smaller, faster reduction tree.
This document describes the design of a 16-bit, 3-input adder using two different strategies: a wait strategy and a speculative/divide-and-conquer (DAC) strategy. The wait strategy uses a divide-and-conquer tree of 5-bit full adders as the basic building block. The DAC strategy speculatively calculates potential outputs in parallel for subsets of bits and then selects the correct outputs using multiplexers once the carry bits are known. Both strategies were implemented and tested for area and delay, with the DAC strategy showing around a 26.6% reduction in worst-case propagation delay over the wait strategy.
this presentation will help u with understanding basic elements of the bloc diagram and how to reduce multi loop block diagram with some suitable numerical example.
The document provides example problems and solutions for mathematical modeling and analysis of control systems. It includes the following examples:
1) It derives the transfer function C(s)/R(s) for a system represented by a block diagram, obtaining the simplified closed-loop transfer function.
2) It models a simplified automobile suspension system as a mass-spring-damper system and derives the transfer function between the input and output displacements.
3) It obtains the transfer function Y(s)/U(s) for another simplified suspension system represented by a diagram relating displacements and forces.
4) It derives the state-space representation for a mechanical system represented by equations relating positions, velocities and
This document describes a project to design a sequential circuit to calculate the remainder (modulo-3) of an n-bit number A. The circuit uses a divide-and-conquer approach with multiple finite state machines (FSMs) running in parallel. A 128-bit shift register sequentially feeds bits to the FSMs. A 7-bit counter generates signals to stop the FSMs after processing all bits. The FSM outputs are combined using additional logic to produce the final remainder. The design aims to calculate the remainder in n/4 clock cycles, faster than the n cycles of a single FSM.
Power Systems Engineering - Matlab programs for Power system Simulation Lab -...Mathankumar S
This MATLAB code calculates line constants and impedances for single and double circuit transmission lines. It inputs parameters like conductor spacing, diameter, and distances between conductors and calculates the series inductance L and shunt capacitance C per unit length. It also forms the bus admittance matrix Ybus for a power system network and calculates real and reactive power flows and losses for a two-bus system.
The document describes the principles and implementation of an array multiplier. It discusses how array multipliers generate partial products simultaneously using parallel logic, making them faster than serial multipliers. A 4x4 bit array multiplier is implemented in Verilog using AND gates and adders, and its functionality is verified through simulation. While array multipliers require more gates and area than serial multipliers, their performance can be increased using pipelining. The document concludes that array multiplication is well-suited for applications requiring high speed.
MATLAB programs Power System Simulation lab (Electrical Engineer)Mathankumar S
The document contains MATLAB code for calculating line constants (inductance L and capacitance C) for overhead transmission lines with different configurations (single-circuit, single-circuit with multiple subconductors, and double-circuit). It requests user input of various line parameters and geometric mean distances and then calculates L and C values. Additional code calculates the network bus admittance matrix and transmission line losses.
The document discusses frequency response and Bode plots. It begins by defining the sinusoidal transfer function and frequency response. The frequency response consists of the magnitude and phase functions of the transfer function. Bode plots graphically display the magnitude and phase functions versus frequency on logarithmic scales. The document then provides procedures for constructing Bode plots, including determining individual component responses, combining them, and reading off gain and phase margins. Examples are given to demonstrate the procedures.
The document provides examples of microcontroller system design, including buses, data transfer, general purpose input/output (GPIO), and timers. It describes tristate and multiplexer-based bus structures, synchronous and asynchronous data transfer methods, GPIO hardware and programming models, and basic timer operations like event counting and rate generation. Radial and daisy-chain bus arbitration techniques are also explained.
A high performance fir filter architecture for fixed and reconfigurable appli...Ieee Xpert
A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications A high performance fir filter architecture for fixed and reconfigurable applications
This document discusses system design methodologies including finite state machines (FSMs), register transfer level (RTL) design using algorithmic state machine (ASM) charts and the datapath and controller design approach. It provides examples of modeling styles for FSMs and ASM charts in Verilog. Specifically, it describes modeling a pattern detector FSM and implementing the Booth multiplication algorithm using an ASM chart, which is then transformed into a datapath and controller architecture.
This document describes the design of different types of parallel multipliers using low power techniques on a 0.18um technology node. It discusses Braun multipliers, row-bypassing multipliers, and column-bypassing multipliers. The multipliers are implemented using both conventional methods and the Gate-Diffusion-Input (GDI) technique. Simulation results show that implementing the multipliers using GDI reduces transistor counts and power consumption compared to conventional implementations. The 4x4 Braun multiplier implemented with GDI uses 136 transistors and consumes 3mW of power, providing significant improvements over the conventional implementation.
This document discusses system compensation in control systems. It begins with an introduction to compensation design and the different types of compensators, including phase lead, phase lag, and phase lead-lag compensation. It describes how compensators are used to alter the frequency response of a system to meet performance requirements like steady-state error, bandwidth, and phase margin. Examples are provided of designing phase lead and phase lag compensators to compensate sample systems and satisfy given stability and performance criteria. The document provides guidance on determining appropriate compensator parameters.
High performance pipelined architecture of elliptic curve scalar multiplicati...Ieee Xpert
High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m) High performance pipelined architecture of elliptic curve scalar multiplication over gf(2m)
This document discusses time-domain analysis and design of control systems through block diagrams. It defines key terms like plant, controller, feedback, and transfer functions. It describes how to represent systems using block diagrams and rules for simplifying block diagrams, including combining blocks in series and parallel and eliminating feedback loops. Examples are provided to demonstrate reducing complex block diagrams to standard forms and handling multiple-input systems using superposition.
1. Block diagrams can be used to model both simple and complex systems, and consist of multiple blocks connected to represent the system's functioning.
2. It is often necessary to reduce block diagrams by combining or rearranging blocks for easier analysis and calculation of the transfer function.
3. Common block diagram reduction techniques include combining blocks in cascade or parallel, moving summing or pickoff points, eliminating feedback loops, and swapping summing points.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Imprecise computing is an attractive model for digital processing at nano metric scales. Inexact computing is particularly interesting for computer arithmetic designs. This work deals about the design and analysis of two new inaccurate 4-2 compressors for utilization in a multiplier. These designs rely on different features of compression, such that imprecision in computation is measured by the error rate and the so-called normalized error distance can meet with respect to circuit-based figures of merit of a design in terms of number of transistors, delay and power consumption. The proposed approximate compressors are proposed and analyzed in Dadda multiplier. Extensive simulation results are provided and an application of the approximate multipliers to image processing is presented. The results proposed designs shows that reduced power dissipation, delay and transistor count.
Implementation of FinFET technology based low power 4×4 Wallace tree multipli...TELKOMNIKA JOURNAL
Many systems, including digital signal processors, finite impulse response (FIR) filters, application-specific integrated circuits, and microprocessors, use multipliers. The demand for low power multipliers is gradually rising day by day in the current technological trend. In this study, we describe a 4×4 Wallace multiplier based on a carry select adder (CSA) that uses less power and has a better power delay product than existing multipliers. HSPICE tool at 16 nm technology is used to simulate the results. In comparison to the traditional CSA-based multiplier, which has a power consumption of 1.7 µW and power delay product (PDP) of 57.3 fJ, the results demonstrate that the Wallace multiplier design employing CSA with first zero finding logic (FZF) logic has the lowest power consumption of 1.4 µW and PDP of 27.5 fJ.
This document discusses the design of finite impulse response (FIR) filters using multiple constant multiplication/accumulation (MCMA) technique to reduce hardware resources and cost. It proposes using truncated multipliers in the MCMA module to remove unnecessary partial product bits without affecting output precision. The filter coefficients are quantized with unequal word lengths using non-uniform quantization to minimize bit widths and reduce hardware cost while maintaining frequency response specifications. Simulation results show that direct-form FIR filters using the proposed truncated MCMA technique achieve lower area and power consumption than transposed-form implementations.
This document describes a low power pipelined FFT processor architecture based on the Radix-4 single delay commutator (R4SDC) algorithm. It implements and compares 16, 64, and 256-point FFT architectures using conventional R4SDC, a complex multiplier, and a multiplier-less architecture based on common subexpression technique. For the 16-point FFT, an ordered R4SDC architecture is proposed that reorders coefficients and inputs to minimize switching activity and reduce power consumption compared to the conventional design. Simulation results show the area and power requirements of the different architectural implementations.
Development of Digital Controller for DC-DC Buck ConverterIJPEDS-IAES
This paper presents a design & implementation of 3P3Z (3-pole 3-zero)
digital controller based on DSC (Digital Signal Controller) for low voltage
synchronous Buck Converter. The proposed control involves one voltage
control loop. Analog Type-3 controller is designed for Buck Converter using
standard frequency response techniques.Type-3 analog controller transforms
to 3P3Z controller in discrete domain.Matlab/Simulink model of the Buck
Converter with digital controller is developed. Simualtion results for steady
Keyword: state response and load transient response is tested using the model.
This document summarizes research on improving the performance of multiplier and accumulator (MAC) circuits used in digital signal processing. It describes the traditional ripple carry adder and its limitations. It then introduces several optimizations to the carry select adder (CSLA) circuit to reduce area and power consumption, including using a binary to excess-1 converter to replace full adders with carry inputs of 1, and using D-latches to store intermediate results and pipeline the computation. Simulation and synthesis results on Xilinx FPGA tools show that these CSLA optimizations can achieve lower delay, area and power compared to traditional ripple carry and regular CSLA designs.
DESIGN OF RADIX-8 BOOTH MULTIPLIER USING KOGGESTONE ADDER FOR HIGH SPEED ARIT...eeiej_journal
This paper presents the design and implementation of radix-8 booth Multiplier .The number of partial
products are reduced to n/2 in radix-4We can reduce the number of partial products even further to n/3 by
using a higher radix-8 in the multiplier encoding, thereby obtaining a simpler CSA tree .This implies less
delay and a smaller area size .Since this multiplication operation is for both signed and unsigned
numbers,cost of the system can also be reduced.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a methodology for designing low error fixed width adaptive multipliers. It begins by discussing Baugh-Wooley multiplication, which produces a 2n-bit output from n-bit inputs. For digital signal processing applications, only an n-bit output is required. Direct truncation introduces errors. The methodology proposes using a generalized index and binary thresholding to derive an error-compensation bias to reduce truncation errors. It defines different types of binary thresholding and analyzes statistics to determine average bias values. The proposed fixed width multiplier is intended to have better error performance than other existing multiplier structures.
A Configurable and Low Power Hard-Decision Viterbi Decoder in VLSI ArchitectureIRJET Journal
This document describes a configurable and low power VLSI architecture for a hard-decision Viterbi decoder. It proposes a design that can be configured for different numbers of traceback steps (N) by adjusting traceback parameters without major modifications to the register transfer level design. The design aims to consume low power. It was synthesized in Xilinx and showed good results for operational speed and area consumption when tested for N=32 and N=64 traceback steps. Viterbi decoding is an important error correction technique that involves convolutional encoding, transmission with potential errors, and decoding using the Viterbi algorithm. Low power is a priority for Viterbi decoders due to their power consumption.
Design and Implementation of 8 Bit Multiplier Using M.G.D.I. TechniqueIJMER
In this paper we have implemented Radix 8 High Speed Low Power Binary Multiplier using
Modified Gate Diffusion Input(M.G.D.I) technique. Here we have used “Urdhva-tiryakbhyam”(
Vertically and crosswise ) Algorithm because as compared to other multiplication algorithms it shows
less computation and less complexity since it reduces the total number of partial products to half of it.
This multiplier at gate level can be design using any technique such as CMOS, PTL and TG but design
with new MGDI technique gives far better result in terms of area, switching delay and power
dissipation. The radix 8 High Speed Low Power Pipelined Multiplier is designed with MGDI technique
in DSCH 3.5 and layout generated in Microwind tool. The Simulation is done using 0.12μm technology
at 1.2 v supply voltage and results are compared with conventional CMOS technique. Simulation result
shows great improvement in terms of area, switching delay and power dissipation.
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A comparative study of different multiplier designsHoopeer Hoopeer
This document compares four different multiplier designs from the perspectives of power consumption, delay, and area usage. It finds that a carry save adder (CSA) multiplier achieves the lowest power consumption of 0.198mW and delay of 6psec, making it suitable for low-power applications. A modified Booth encoder (MBE) multiplier requires the smallest area of 4030μm2. In general, the four multiplier designs show tradeoffs between power, speed, and area depending on the specific implementation and modification techniques used.
The document describes a proposed low power, high speed multiplier circuit designed using a technique called New Vedic VLSI. The multiplier uses a Vedic multiplication method to generate partial products faster. An addition section with a carry look ahead adder is used to sum the partial products, providing faster operation than a ripple carry adder. Simulation results showed the proposed design consumed 41.868 μw of power over 10ns, compared to 65.4 μw for a design using a ripple carry adder, for a 23.592 μw power reduction. The high speed, low power multiplier design is suitable for applications like digital signal processors that require efficient multiplication.
Harmonic Mitigation Method for the DC-AC Converter in a Single Phase SystemIJTET Journal
This document summarizes a research paper that proposes a harmonic mitigation method for a DC-AC converter without using a low pass filter. Specifically, it suggests using sine wave modulation of the converter along with injection of specific harmonics calculated using Fourier analysis to cancel out existing harmonics. A proportional-resonant integral controller is also used to eliminate any DC offset. Simulation results show the total harmonic distortion is reduced to 11.15% using this approach, avoiding the need for an output filter. The proposed method continuously monitors and mitigates harmonics in the output to improve power quality.
Effective Area and Power Reduction for Low-Voltage CMOS Image Sensor Based Ap...IJTET Journal
1) The document presents a novel 45nm CMOS image sensor with reduced area and power consumption. It uses a single inverter for time-to-threshold pulse width modulation that can operate under low supply voltage.
2) The proposed 45nm design reduces area through a two-transistor pixel structure and reduces power to 3.7uW from 36uW in the 130nm design. It also allows operation at a lower 0.8V supply voltage.
3) Simulation results show the 45nm design produces the same 8-bit image quality as the 130nm design but with reduced area and power, making it suitable for portable imaging applications.
IRJET- Wallace Tree Multiplier using MFA CountersIRJET Journal
The document proposes a new design for 7-bit to 3-bit counters that uses multiplexer-based full adders (MFAs) to reduce delay and power consumption compared to existing symmetric stacking counter designs. It presents the design of an MFA-based 7:3 counter that replaces the XOR gates in conventional full adders with multiplexers to minimize critical path delay. This MFA counter is then implemented and tested in a Wallace tree multiplier architecture. Simulation results show the MFA 7:3 counter achieves lower delay of 7.981ns and uses fewer logic resources compared to a symmetric stacking 7:3 counter. Overall, integrating the proposed MFA counters into the Wallace tree multiplier reduces its delay and power consumption
Implementation of Low Power and Area Efficient Carry Select Adderinventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Design and Implementation of Low-Power and Area-Efficient 64 bit CSLA using VHDLIJSRD
All processor consisting ALU and adder plays important role for design of ALU. Design of low area and power efficient adder helps to reduce power consumption and area of any processor. Now a day’s major area of research in VLSI system is design of area, high speed and low power data path logic systems. In digital adders, the speed of addition is restricted by the time necessary to send a carry signal through the adder. The area and power consumption is reduced by modifying regular CSLA architecture. The proposed architecture is developed with the help of a simple ripple carry adder (RCA) and gate-level architecture. It consists of single RCA which improves the performance of the proposed designs then the regular designs in terms of power consumption and area.
Design and Implementation of 8 Bit Multiplier Using M.G.D.I. TechniqueIJMER
In this paper we have implemented Radix 8 High Speed Low Power Binary Multiplier using
Modified Gate Diffusion Input(M.G.D.I) technique. Here we have used “Urdhva-tiryakbhyam”(
Vertically and crosswise ) Algorithm because as compared to other multiplication algorithms it shows
less computation and less complexity since it reduces the total number of partial products to half of it.
This multiplier at gate level can be design using any technique such as CMOS, PTL and TG but design
with new MGDI technique gives far better result in terms of area, switching delay and power
dissipation. The radix 8 High Speed Low Power Pipelined Multiplier is designed with MGDI technique
in DSCH 3.5 and layout generated in Microwind tool. The Simulation is done using 0.12μm technology
at 1.2 v supply voltage and results are compared with conventional CMOS technique. Simulation result
shows great improvement in terms of area, switching delay and power dissipation.
This document describes a speed-up technique for a Windows image scalar algorithm. It involves detecting when an output pixel generation cycle will be immediately followed by an input pixel consumption cycle. In this case, the cycles can be merged to improve performance. Specifically:
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2. The Mismatch Noise Cancellation(MNC) Top Level
To the third stage
of the Pipelined
ADC
MNC Top Level
Clock1
Gama1[1:0]
Gama2[1:0]
Gama12[1:0]
PRN1_0
RawOut_PN[11:0]
RawOut_Corr[11:0]
Clock2
Reset
En_Shuffle
OV_P
OV_M
PRN1_1
PRN1_2
PRN2_0
PRN2_1
PRN2_2
PRN3_0
PRN3_1
PRN3_2
To the first stage
of the Pipelined
ADC
To the second stage
of the Pipelined
ADC
From the first stage
of the Pipelined ADC
From the first stage
of the Pipelined ADC
The output of the
rest of the pipeline after
The output of the pipeline
after Mismatch noise
cancellation
Figure 1: Top level of the MNC
architecture
3. The MNC Architecture
X1_EST[15:0]X2_EST[15:0]X3_EST[15:0]qvoffset[??:0]
MNC mismatch Estimation
Clock1/2Gama1[1:0]Gama2[1:0]Gama12[1:0] PN1PN2PN3Dither
RawOut_PN[11:0]
Clock1/2Reset
RawOut_Corr[11:0]
RawOut_PN[11:0]Gama1[1:0]Gama2[1:0]Gama12[2:0]PN1PN2PN3X1[15:0]X2[15:0]X3[15:0]qvoffset
MNC Noise Cancellation
Reset
En_Shuffle
Clock2
Clock1
PN1_1PN1_2PN1_3PN2_1PN2_2PN2_3PN3_1PN3_2PN3_3
Pseudo Random Generator
Dither[10:0]
PN1_ECPN2_ECPN3_EC Gama2_EC Gama1_ECGama12_EC
OV_P OV_M
PN_DELAY_EQUALIZER_EC Gama_Delay_Equalizer_EC
MNCTOPLEVEL
PN1PN2PN3
PN_DLY_EQ_EEGama_DLY_EQ_EE
Figure 2: The component block of the MNC architecture
4. Components of the Mismatch Noise Cancellation
Figure 1, and Figure 2 illustrates the top level of the MNS architecture and the component of the
architecture respectively.
The main components of the MNC Architecture are the following blocks/components:
1- Pseudo Random Generator
This block generates random binary sequences for use by the rest of the components in the ADC
pipeline and the rest of the MNC blocks
2- Mismatch Estimation
This block is responsible for the estimation of the mismatches.
3- Noise Cancellation
This block is responsible for correcting the effect of the mismatches.
5. 4- Synchronization Elements
Synchronization and delay elements to synchronize the MNC circuit to the rest of the pipeline, as
well as synchronizing the data flow within the MNC architecture.
6. I- Pseudo Random Generator
The Random Number Generator is implemented as an Linear Feedback Shift Register(LFSR) type II,
with one output fed-back to many points, i.e. taps across the LFSR
Reset
En_Shuffle
Clock2
Clock1
PN1_1
PN1_2
PN1_3
PN2_1
PN2_2
PN2_3
PN3_1
PN3_2
PN3_3
Pseudo Random Generator
Dither[10:0]
7. TYPE-II LFSR
Type-II LFSR
This Linear Feedback shift register(LFSR) topology used in the MNC architecture has a generator
polynomial of degree 31 and produces a maximal lenght binary sequence of length (2^31 - 1).
b0b1
b2b3b4b5b6bn-1 bn-2
+ + +
0
9. The MNC Noise Cancellation architectuer is pipelined to meet the system clock requirement and the throughput of the ADC. The
Noise Cancellation must maintain the same throughput as that of the ADC, since its operation corrects the output of the ADC each
cycle.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
ECX2 PN2 X2 γ2••=
ECX3 PN3 X3 γ3••=
ECX12 PN1 PN2 X2 γ12•••=
ECX13 PN1 PN3 X3 γ12•••=
ECXSUM ECX1 ECX2 ECX3 ECX12 ECX13+ + + +=
RawOutDAC RawOutPN ECX1 ECX2 ECX3 ECX12 ECX13+ + + +( ) 2
m2 1–( )
•–=
MismatchTerm PN1 X1• PN2 X2• PN3 X3• PN1 PN2 X2•• PN1 PN3 X3••+–+ +=
10. (8)
(9)
The signal flow graph for the computations shown in (1) through (9) are illustrated in Figure 3.
TotCorrecfactor 1 MismatchTerm–=
RawOutCorrect RawOutDAC TotCorrecfactor•=
12. Arithmetic Operations used in the Noise Cancellation architecture
Table 1: The list of operations used in the MNC noise cancellation architecture.
Operation Symbol Definition
Scaling Scale a 2’s complement number, and corresponds to mul-
tiplication or division by a power of 2 integer. The way
scaling is implemented in this architecture, has no hard-
ware cost.
Sign Extenstion Sign Extends a 2’s complement number. For 2’s comple-
ment variables, the sign extension does not change the
value of the variable.
Addition Adder, adds the values of 2’s complement numbers.
Subtraction Subtracter, subtracts 2’s complement numbers
Simple multiplication This multiplication is done using logic and not a full
parallel multiplier.
Rounding This operations performs rounding to nearest on a 2’s
complement value.
scale
SXT
+
-
*
Round
13. The list of operations used in the MNC noise cancellation blocks are shwon in Table 1.
Parallel multiplication Full parallel multiplier.
Carry Save Adder The carry save adder reduces the problem of adding three
numbers into that of adding just two numbers and per-
forms this reduction operation within a time delay inde-
pendent of the word size.
Operation Symbol Definition
*
∑
14. Architectural innovations and contributions
1- The use of Extended Precision without sacrificing area nor speed.
The architecture presented here employs an innovative approach for the increase of the precision of the architecture without sacrific-
ing the area and delay. This approach makes use of a bit true C-level model for the architecture that allows us to have in-depth
insight into all the intermediate variables and their upper and lower ranges. This approach have allowed us to use precision equivalent
to 19-bits of precision, while only having 16 physical bits. This amounts to the increase of the precision of computations by a factor of
8.
To represent a signed fixed point number in 2’s complement format, we use the following representation as in (10):
(10)
This notation, presents a number that has wordsize, . The binary-point bit position within the fixed-point word is and the
“t” signifies the fact that this signed number is represented in 2’s complement format. The real value of a fixed-point number repre-
sented in (10), is shown in (11).
(11)
The binary-point bit position within the fixedpoint word decided the precision with wich the fixed point can represent real numbers.
For the Mismatch Noise Cancellation, the inputs to the computation have three variables that require high precision. These variables,
X1, X2 and X3 represent some linear combinations of the capacitance mismatches in a pipeline stage of the ADC.
S wsize bp t >, ,<
wsize bp
2
bp–
bwsize 1–– 2
wsize 1–
⋅ bi 2
i
⋅
i 0=
wsize 2–
∑+
•
15. The fixed-point representation shown in Table 2 illustrates the format S<16,15,t>. This format has a precision of and the
corresponding value range .
Insight into the range of values of the capacitance mismatches in a typical submicron CMOS or BICMOS process enables us to extend
the precision of the computation up to
Table 2: 2’s complement representation of a fixed point fraction reprsented by wsize of 16-bits.
Table 3: 2’s complement representation of a fixed point fration represented by wsize of 16-bits and extended precision.
Format Precision Range Pictorial representation
S<16,15,t>
Format Precision Range Pictorial representation
S<16,19,t>
P 2 15–=
1– V≤ 1<
P 2 15–= 1– V≤ 1<
b0b1b2b3b13b14b15 b12
bp = 15
P 2 19–= 0.0625– V≤ 0.0625<
b0b1b2b3b13b14b15 b12
bp = 19
16. 2- Performing Tree-Height reduction on the Signal Flow graph to minimize the delay through additions or subtrac-
tions trees.
We can identify two segments in the signal flow graph for the MNC noise cancellation computation that can we can use the properties of the
addition computation to reduce the delay of those segments of the data flow graphs. First the computation in Equation (5), corresponds to the
signal flow graph segment shown in Figure 4
As can be seen in Figure 5, we can re-arrange the computation tree (this segment of the data flow graph). Mathematically those two computa-
tions are equivalent. However, the computation in Figure 5 less delay, since there is only 3 adders on the critical path, as opposed to four for the
computation in Figure 4.
+
+
+
ECX2
ECX3
ECX12
ECX1+
ECX13
ECXSUM
Figure 4: Computation of the variable ECXSUM prior to the application of Tree-Height Reduction.
17. + +
+
+
ECX1 ECX12 ECX13
ECXSUM
ECX2 ECX3
Figure 5: Computation of the variable ECXSUM after the application of Tree-Height Reduction. The critical
path through the transformed computation tree has one adder delay less compared to the one without Tree height
redcution optimization.
-
+
+
PN1*X1
PN2*X2
PN1*PN3*X3
PN1*PN2*X2+
PN3*X3
MismatchTerm
-+
Figure 6: Computation of the variable MismatchTerm prior to the application of Tree-Height Reduction.
18. + -
+
+
PN1*X1 PN1*PN3*X3 PN1*PN2*X2
Mismatch_Term
PN2*X2 PN3*X3
-
+
Figure 7: Computation of the variable Mismatch_Term after the application of Tree-Height Reduction. The
critical path through the transformed computation tree has one adder delay less compared to the one without
Tree height redcution optimization.
19. 3- Identification of the suitable arithmetic operator that can benefit from Carry Save Transformations.
Making use of the carry save Adders architectures to reduce the area and delay of different addition/subtraction trees.
To have an additional impact(in addition to the tree height reduction) on the addition tree segments shown in Figure 4 and Figure 6,
carry save transformation can be used to further reduce the delay.
The idea of carry save transformation is to reduce the addition of 3 numbers to that of just two numbers, and to achieve this reduction in
constant time, that is to say, that the delay of the transformation is independent of the word size.
Mathematically the carry save transformation accepts three n-bit numbers, such as x,y and z in Figure 8, and produces two output
numbers u, and v, such that:
(12)
∑
Figure 8: Symbol for Carry Save Adder
x y z
u v
x y z+ + u v+=
20. (13)
(14)
This is for i=0,1,2,...,n-1. Bit is being zero.
Since there is no carry involved in this computation one could compute the values of and for all values of “i” in parallel. This
allows execution in constant time, independent of the bit-width of the operands. Both the parity and majority function can be imple-
mented by simple logic similar in cost and delay to that of a full adder.
The computation for ECXSUM, illustrated in Figure 4, is transformed using carry save addition and the result of the transofrmation is
illustrated in Figure 9.
Similarly in Figure 10, the computation for Mismatch term is illustrated after the carry save transformation.
ui parity xi yi zi, ,( )=
vi 1+ majority xi yi zi, ,( )=
v0
vi 1+ ui
21. ∑
∑
∑
ECX1 ECX13 ECX12
ECX3 ECX2
+
Figure 9: The Computation of ECXSUM after the Carry Save Adder Transformation.
23. 4- Reducing the number of full multipliers in the architecture to just one multiplier.
Careful investigation of the ranges of values for the variables within the signal flow graph, we managed to remove all the unnecessary
multipliers from the implementation and replacing those with much simpler(smaller area) and faster logic to implement the multiplica-
tion operation. The multiplication operations suitable for such replacement are those who are actually multiplying two variables with
wide descriptancy in the bit-width.
*
PN1 * X1[S<16,19,t>]
ECX1[S<16,19,t>]
γ1 [S<2,0,t>]
Figure 11: ECX1 computation using simplified logic. The area required is about 28% of the area of a full multiplier
that perform the same operation, and the delay is about 45% of the delay required for a full multiplier.
*
PN1 * X1[S<16,19,t>]
ECX1[S<16,19,t>]
γ1 [S<2,0,t>]
Replace the multiplier with simplified equivalent logic
results in reduction in both area and delay
24. 5- Using a single Binary Random Number Generator to generate all the binary Random numbers as well as
the dither signal.
This was possible by developing a bit-true C-model for the Random number generator and extrapolating the cross correlation informa-
tion. The cross correlation information verified the possibility of having same random number generator produce several random bina-
rysequences as well as the dither signal. Moreover, creating a simulation enviornment that made the verification of the C-model versus
the hardware model possible.
6- Fixed point optimization
Thefixed point algorithm is designed such that issues of overflow and quantization does not affect the signal processing of the algo-
rithm. Optimizing the sign format, the word length at various internal points (i.e. internal variables) within the signal flow graph enables
us to tailor the hardware to the required computations such that we do not use excessive hardware. Extensive C-Level simulation as
well as VHDL simulationare performed to insure the proper operation of the hardware under fixed point condition as well as optimizing
the hardware in order for it not to sacrifice any signal to quantization noise ratio.
Figure 12 illustrates an abstraction of the verification methodology used to enable the fixed point optimizations used in this architec-
ture.
25. RTL SimulationC-Level Simulation
PN1_X1_VHDPN1_X1_C Compare
PN2_X2_VHDPN2_X2_C Compare
PN3_X3_VHDPN3_X3_C Compare
ECX1_VHDLECX1_C Compare
ECX2_VHDLECX2_C Compare
ECX12_VHDLECX12_C Compare
ecxSUM_VHDecxSUM_C Compare
Figure 12: Verification methodology for fixed point optimization of internal variables.
26. Noise Cancellation Archtiecture
In this section we illustrate the computation of the different segments of the signal flow graph for the MNC noise cancellation.
This section makes use of the operators defined in Table 1.
(15)
In performing these computations illustrated in Figure 13, we replace the multipliers with faster and smaller logic than when using full
multipliers.
Similar optimizations are performed for the following multiplications illustrated in Figure 14, Figure 15, Figure 16, and Figure 17.
ECX1 PN1 X1 γ1••=
*PN1 * X1[S<16,19,t>]
ECX1[S<16,19,t>]
γ1
PN1 [S<2,0,t>] X1[S<16,19,t>]
[S<2,0,t>]
*
Figure 13: computation of PN1*X1 and ECX1
31. Noise Cancellation Archtiecture(Continued)
(20)
(21)
MismatchTerm PN1 X1• PN2 X2• PN3 X3• PN1 PN2 X2•• PN1 PN3 X3••+–+ +=
TotCorrecfactor 1 MismatchTerm–=
+ -
+
+
PN1*X1[S<16,19,t>] PN1*PN3*X3[S<16,19,t>] PN1*PN2*X2[S<16,19,t>]
Mismatch_Term[S[17,19,t>]
SXT
SE1<17,19,t>
SXT
PN2*X2[S<16,19,t>]
SE1<17,19,t>
SXT
PN3*X3[S<16,19,t>]
SXT
-
+
Integer = 1
scale
-
SXT
SE4<21,19,t>]SE<21,19,t>
Round
-
S<21,19,t>
S<17,15,t>
Tot_Correc_factor
SXT
SE1<17,19,t>
SE1<17,19,t>
SE1<17,19,t>
Figure 18: Computation of the Total_Correc_factor, detailed implementation transformation such as the carry
save transformation is not shown.
32. Noise Cancellation Archtiecture(Continued)
(22)RawOutCorrect RawOutDAC TotCorrecfactor•=
*
RawOutDAC[S<13,0,t>]
RawOut_Corr[S<12,0,t>]
Tot_Correc_factor[SE1<17,15,t>]
Round
RawOut_Corr_int[SE3<30,15,t>]
Figure 19: Computing the final output RawOut_Corr after MNC noise cancellation. This is the
only point in the signal flow graph that we use a full parallel multilier.
Full parallel
pipelined multiplier
33. The output of the MNC is finally combined with the output of the first stage of the pipelined ADC to form the final 14-bit output of the
pipelined analog to digital converter. This is illustrated in Figure 20.
First ADC Pipeline Stage The rest of the Pipeline stages(Pipe Stages 2,3,4,5,6)
Digital Error Correction
MNC TOP LEVEL Delay Stages
MNC ON/OFF
RawOut_Corr[11:0]
RawOut_PN[11:0]
Digital Error Correction (final stage)
offon
PN1_1
PN1_2
PN1_3
Delay Stages
2’s Complement
2’s Complement
2’s Complement
2’s Complement
3
12
123
14
Output of the first stage
Final output of the ADC
gama1
gama2
gama12
Figure 20: The MNC architecture as it is used in the 14-bit ADC pipeline to cancenll the mismatch noise
34. MNC Mismatch Estimation
The MNC mismatch Estimation block is illustrated in Figure 21. The binary random sequences PN1, PN2, and PN3 are inputs as well
as the “Dither” input are outputs from the Random Generator block after proper delay equalization.
The inputs (Gama1), and (Gama2) are from the analog ADC. The MNC mismatch estimation block, generates The estimated
values for the variables X1, X2, X3 and qvoffset. All these variables are used by the MNC noise cancellation block to correct the out-
put of the ADC for mismach noise. Figure 22 illustrates the block diagram of the MNC estimation logic.
X1_EST[15:0]<
X2_EST[15:0]
X3_EST[15:0]
qvoffset[10:0]
MNC Mismatch Estimation
Clock 1/2
Gama1[1:0]
Gama2[1:0]
PN1
PN2
PN3
Dither
Figure 21: MNC mismatch Estimation
γ1 γ2
35. MNC Mismatch Estimation Architecture
Dither generator
+
RawOut_PN
RawOut_PN_Dither
1 when > 1024
-1 when < -1024
0 otherwise
RawOut_PN_Quant
* * *PN3
PN1
PN2
V1
Averager
qvoffset_Ave
if γ1= 1 if γ1= -1
Sum_Gama1 = Sum_Gama1 - V1Sum_Gama1 = Sum_Gama1 + V1
Count1_Sum = Count1_Sum + 1
V2
if γ2= 1 if γ2= -1
Sum_Gama2 = Sum_Gama2- V2Sum_Gama2 = Sum_Gama2 + V2
Count2_Sum = Count2_Sum + 1
V3
if γ3= 1 if γ3= -1
Sum_Gama3 = Sum_Gama3 - V3Sum_Gama3= Sum_Gama3 + V3
Count3_Sum = Count3_Sum + 1
if count1_Sum = 2^n
X1_Ave = Sum_Gama1 / Count1_Sum X2_Ave = Sum_Gama2 / Count2_Sum X3_Ave = Sum_Gama3 / Count3_Sum
if count2_Sum = 2^n if count3_Sum = 2^n
Average(X1) Average(X2) Average(X3)
Figure 22: Block diagram of the MNC mismatchestimation
36. The computed average values for X1, X2, X3 and qvoffset are to be scaled and rounded before it is fed to the MNC noise cancellation
block.
The computation of the average value is done keeping in mind that we want to reduce the complexity of the hardware. We divide the
accumulated values for X1, X2, X3, qvoffset with a number that is a power of 2.
Due to the statistical nature of this computation, the accumulation process tends to take a large number of cycles before the average
values of the computed mismatched become stable and converge to within a reasonable error band to the correct values.
Figure 23 illustrates the behavior of the MNC estimation block as we increase the number of cycles used for averaging the values to be
estimated. It is evident that as the number of cycles reaches a certain point, the error in the estimation of the mismatches decreases to
within an error band of around +/- 10%. The percentage error in estimating the mismatches is illustrated in Figure 24. The results of
such simulations is used for guiding the choice of the number of cycles that is needed to get a more or less some good separation of
the cross correlation between the different contributers to the mismatch (namely X1, X2, X3 which represent the mismatches of the
capacitance).
Finally rounding and scaling is performed on these average values, and they are used as input to the MNC mismatch cancellation.
37. Figure 23: Simulation of the convergence behavior of the MNC estimation versus the number of cycles used for
averaging.
38. Figure 24: Percentage error of the mismatch estimation versus the number of cycles used for
averaging
39. FFT Comparison
Graph(I)
Graph(II)
Graph(III)
Figure 25: FFT comparison for the following cases: (I) Double precision C-level simulations, (II) Hardware
simulation, (III) Double-precision C-simulation followed by rounding.
40. Table 4: Comparison of the simulation result for MNC algorithm.
Graph(I), in Figure 25 illustrates the FFT of the output of the ADC when The Error Correction/Cancellation is per-
formed using C-simulation with double precision.
Graph(II) in Figure 25 illustrates the FFT of the output of the ADC when the The Error Correction/Cancellation is performed
using the architecture described here (simulated by VHDL), and the se
Graph(III) in Figure 25 illustrates the FFT of the output of the ADC when the The Error Correction/Cancellation is per-
formed C-simulation, however the correction result is rounded before it is added to the pipeline output to corre-
sponding to the real ADC resolution.
It is evident from comparing the result of the hardware simulation and the C-simulation with rounding, that the results obtained from
the hardware is within 1 dB of that obtained from the C-simulation with rounding.
From C Simulation, IDEAL case
Graph(I)
From VHDL/Hardware
Simulation
Graph(II)
From C Simulation with Rounding
Graph(III)
sqnr = 85.0130 dB sqnr = 81.5997 dB sqnr = 82.5849 dB