Analog multipliers are used for frequency conversion and are critical components in modern radio frequency (RF) systems. RF systems must process analog signals with a wide dynamic range at high frequencies. A mixer converts RF power at one frequency into power at another frequency to make signal processing easier and also inexpensive. A fundamental reason for frequency conversion is to allow amplification of the received signal at a frequency other than the RF, or the audio, frequency. This paper deals with two such multipliers using MOSFETs which can be used in communication systems. They were designed and implemented using 0.5 micron CMOS process. The two multipliers were characterized for power consumption, linearity, noise and harmonic distortion. The initial circuit simulated is a basic Gilbert cell whose gain is fairly high but shows more power consumption and high total harmonic distortion. Our paper aims in reducing both power consumption and total harmonic distortion. The second multiplier is a new architecture that consumes 43.07 percent less power and shows 22.69 percent less total harmonic distortion when compared to the basic Gilbert cell. The common centroid layouts of both the circuits have also been developed.
- The document discusses various techniques for designing fast complex logic gates in VLSI circuits.
- Two transistor sizing techniques are presented: progressive transistor sizing and transistor ordering to reduce signal delay.
- Alternative logic structures, buffer insertion, and reducing voltage swing are additional techniques described.
- The concept of logical effort is introduced as a way to optimize logic paths for speed based on the topology rather than transistor sizing.
Logic Level Techniques for Power Reduction GargiKhanna1
This document discusses various logic level techniques for low power VLSI design, including:
- Gate reorganization techniques like combining gates to reduce switching activity.
- Signal gating to block propagation of unwanted signals using AND/OR gates or latches.
- Logic encoding methods like gray code counting to reduce bit transitions.
- State machine encoding to lower expected bit transitions in the state register and outputs.
- Precomputation logic that disables inputs to combinational logic when output is invariant, reducing switching activity at the cost of increased area.
Fault Simulation (Testing of VLSI Design)Usha Mehta
This document provides an overview of fault simulation for testing VLSI designs. It discusses:
- The major steps of fault simulation including generating random patterns, simulating the fault-free circuit output, inserting faults, and simulating the faulty circuit output.
- Types of circuit simulators including event-driven, cycle-based, and compiled code simulators.
- Techniques for gate evaluation in simulators like truth tables, input scanning, and input counting.
- The goals of fault simulation as measuring test pattern effectiveness, guiding test pattern generation, and generating fault dictionaries.
Comparator circuits compare two input voltages and produce a logic output signal that is high or low depending on which input is larger. Real comparators do not have an abrupt transition and have very high voltage gain in the transition region. Comparators are often used as interfaces between analog and digital circuits by converting analog signals to logic levels. Open-collector outputs are useful for this by producing either 0V or the supply voltage at their outputs. Schmitt triggers, which are comparators with positive feedback, are commonly used as they introduce hysteresis which helps eliminate unwanted output transitions from noise.
This document discusses small-signal modeling of MOSFETs. It introduces small-signal modeling as a way to linearize circuits by considering only small amplitude signals. It then presents the low-frequency small-signal model of a MOSFET, including terms like transconductance and output conductance. Finally, it discusses the high-frequency model, noting the need to account for parasitic capacitances between terminals at high frequencies. Diagrams of the complete low-frequency and high-frequency small-signal MOSFET models are provided.
The document discusses asynchronous sequential circuits. It covers the analysis and design of these circuits including:
- The differences between asynchronous and synchronous sequential circuits. Asynchronous circuits use unclocked memory elements and inputs can change states at any time.
- The steps to analyze fundamental mode asynchronous circuits including constructing state, transition, and output tables from the next state and output equations.
- Techniques for designing asynchronous circuits including developing a primitive flow table from requirements, reducing states using methods like merger graphs, assigning states to avoid races, and realizing the circuit with logic elements.
A register is a group of flip-flops that can store multiple bits of data. There are four types of shift registers: serial-in serial-out (SISO), serial-in parallel-out (SIPO), parallel-in serial-out (PISO), and parallel-in parallel-out (PIPO). Shift registers allow data to move between flip-flops on each clock pulse. Ring counters and Johnson counters are examples of shift register counters that produce repeating output sequences.
- The document discusses various techniques for designing fast complex logic gates in VLSI circuits.
- Two transistor sizing techniques are presented: progressive transistor sizing and transistor ordering to reduce signal delay.
- Alternative logic structures, buffer insertion, and reducing voltage swing are additional techniques described.
- The concept of logical effort is introduced as a way to optimize logic paths for speed based on the topology rather than transistor sizing.
Logic Level Techniques for Power Reduction GargiKhanna1
This document discusses various logic level techniques for low power VLSI design, including:
- Gate reorganization techniques like combining gates to reduce switching activity.
- Signal gating to block propagation of unwanted signals using AND/OR gates or latches.
- Logic encoding methods like gray code counting to reduce bit transitions.
- State machine encoding to lower expected bit transitions in the state register and outputs.
- Precomputation logic that disables inputs to combinational logic when output is invariant, reducing switching activity at the cost of increased area.
Fault Simulation (Testing of VLSI Design)Usha Mehta
This document provides an overview of fault simulation for testing VLSI designs. It discusses:
- The major steps of fault simulation including generating random patterns, simulating the fault-free circuit output, inserting faults, and simulating the faulty circuit output.
- Types of circuit simulators including event-driven, cycle-based, and compiled code simulators.
- Techniques for gate evaluation in simulators like truth tables, input scanning, and input counting.
- The goals of fault simulation as measuring test pattern effectiveness, guiding test pattern generation, and generating fault dictionaries.
Comparator circuits compare two input voltages and produce a logic output signal that is high or low depending on which input is larger. Real comparators do not have an abrupt transition and have very high voltage gain in the transition region. Comparators are often used as interfaces between analog and digital circuits by converting analog signals to logic levels. Open-collector outputs are useful for this by producing either 0V or the supply voltage at their outputs. Schmitt triggers, which are comparators with positive feedback, are commonly used as they introduce hysteresis which helps eliminate unwanted output transitions from noise.
This document discusses small-signal modeling of MOSFETs. It introduces small-signal modeling as a way to linearize circuits by considering only small amplitude signals. It then presents the low-frequency small-signal model of a MOSFET, including terms like transconductance and output conductance. Finally, it discusses the high-frequency model, noting the need to account for parasitic capacitances between terminals at high frequencies. Diagrams of the complete low-frequency and high-frequency small-signal MOSFET models are provided.
The document discusses asynchronous sequential circuits. It covers the analysis and design of these circuits including:
- The differences between asynchronous and synchronous sequential circuits. Asynchronous circuits use unclocked memory elements and inputs can change states at any time.
- The steps to analyze fundamental mode asynchronous circuits including constructing state, transition, and output tables from the next state and output equations.
- Techniques for designing asynchronous circuits including developing a primitive flow table from requirements, reducing states using methods like merger graphs, assigning states to avoid races, and realizing the circuit with logic elements.
A register is a group of flip-flops that can store multiple bits of data. There are four types of shift registers: serial-in serial-out (SISO), serial-in parallel-out (SIPO), parallel-in serial-out (PISO), and parallel-in parallel-out (PIPO). Shift registers allow data to move between flip-flops on each clock pulse. Ring counters and Johnson counters are examples of shift register counters that produce repeating output sequences.
The document discusses latches and flip-flops. It describes how a latch stores a data value and is non-volatile, while a flip-flop is built from two back-to-back latches clocked on opposite phases. Various latch and flip-flop circuit designs are presented, including pass transistor, transmission gate, buffered input/output, and master-slave designs. Features like enables, resets, and sets are also discussed along with their synchronous and asynchronous implementations in flip-flops. Different flip-flop circuit styles are covered such as transmission gate, complementary CMOS, precharge, and self-gating designs.
Introduction to Built In Self Test (BIST).pdfFEMILAECE
Built-in self-test (BIST) is a technique that uses on-chip circuitry to test other parts of the chip. It involves a pseudo-random sequence generator (PRSG) to produce input signals and a signature analyzer to observe outputs. A PRSG is typically a linear feedback shift register (LFSR) that cycles through a pseudo-random sequence. A signature analyzer receives outputs and XORs them to produce a syndrome signature that is compared to a correct signature to determine if the circuit passed the test. BIST provides advantages like lower cost and better fault coverage compared to external testing. However, it requires additional silicon area and the on-chip test circuitry could also fail.
Flipflops JK T SR D All FlipFlop SlidesSid Rehmani
Flipflops JK T SR D All FlipFlop Slides. Uploaded by SidRehmani.
Jk flip flop presentation, T flip flop presentation, D flip flop presentation, D flip flop presentation.
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The document discusses a Phase Locked Loop (PLL). It describes PLL as a circuit that synchronizes an output signal generated by an oscillator to match the frequency and phase of a reference input signal. The key functional blocks of a PLL are a phase detector, low pass filter, and voltage controlled oscillator (VCO). The phase detector compares the input and feedback frequencies and provides an error signal. The low pass filter removes noise and the VCO generates the output frequency controlled by the error signal voltage. A PLL goes through free running, capture, and phase locked stages of operation. Applications of PLL include frequency modulation/demodulation and signal synchronization.
Latch and flip flop circuits are used to store digital information. A latch can store a bit as long as power is applied, while a flip flop uses feedback to store a bit even after inputs change. There are different types of flip flops like SR, JK, D and T flip flops that store bits based on their input conditions and clock signal. Flip flops are edge triggered which means they change state only on rising or falling edge of the clock signal. This provides synchronization between logic and memory in digital circuits.
Msp430 assembly language instructions &addressing modesHarsha herle
The document discusses MSP430 assembly language. It covers topics like MSP430 data storage in registers, double operand instructions, single operand instructions, jump instructions, and emulated instructions. Examples of various instructions like ADD, SUB, BIC, MOV, CALL etc. are provided. It also discusses MSP430 memory structure and explains that words are only stored at even addresses with the low byte at the even address and high byte at the next odd address.
This document discusses several methods for designing sequential circuits, including state tables, state assignment, and deriving flip-flop input equations. It then provides examples of implementing sequential circuits using ROMs, PLAs, CPLDs, and FPGAs. Specifically, it designs a comparator circuit and code converter as examples of iterative and sequential circuits. It also discusses implementing a parallel adder and shift register using an FPGA.
The document discusses different types of flip-flops including RS NAND and NOR flip-flops, and covers the basics of sequential logic circuits. It defines level-triggered and edge-triggered clock inputs for flip-flops and compares asynchronous and synchronous clocked flip-flops. The timing diagrams show how positive and negative edge triggering determines when the output of a flip-flop changes state in response to clock pulses and input signals.
The document summarizes operational transconductance amplifiers (OTAs). It discusses how OTAs work as voltage controlled current sources and two-quadrant multipliers. The ideal OTA has infinite input impedance and converts the differential input voltage to a controlled current output. Real OTAs use circuitry to process input voltages over a wide range and produce a relatively output-independent current. Bipolar OTAs use a differential transistor pair to convert the input voltage difference to output current. Additional circuitry like input diode linearization can improve characteristics but reduces maximum transconductance.
A combinational circuit is a logic circuit whose output is solely determined by the present input. It has no internal memory and its output depends only on the current inputs. A half adder is a basic combinational circuit that adds two single bits and produces a sum and carry output. A full adder adds three bits and produces a sum and carry like the half adder. Other combinational circuits discussed include half and full subtractors, decoders, encoders, and priority encoders.
This document provides an overview of different digital logic families. It begins by introducing logic gates and integrated circuits. It then classifies logic families as either bipolar or unipolar, and lists examples of each. Key specifications of digital ICs are defined, including propagation delay, fan-in/fan-out, input/output logic levels, and noise margin. Transistor-transistor logic (TTL) and complementary metal-oxide-semiconductor (CMOS) circuits are described. The TTL NAND gate uses multiple emitter transistors while the CMOS NAND gate uses both P-channel and N-channel MOSFETs. Emitter-coupled logic (ECL) provides the fastest
The document discusses design for testability (DFT) techniques. It explains that DFT is important for testing integrated circuits due to unavoidable manufacturing defects. DFT aims to increase testability by making internal nodes more controllable and observable. Common DFT techniques mentioned include adding scan chains, which allow testing at speed by launching test vectors from a shift register. Stuck-at fault and transition fault models are discussed as well as methods for detecting these faults including launch-on-capture and launch-on-shift. Fault equivalence and collapsing techniques are also summarized.
This document discusses limitations of traditional serial scan design for testing integrated circuits and proposes an alternative called Random Access Scan (RAS). RAS addresses three key limitations of serial scan: 1) test data volume, 2) test application time, and 3) test power. In RAS, flip-flops act as addressable memory elements during test mode, reducing time to set and observe flip-flop states compared to serial scan. While RAS requires more gates and test pins than serial scan, it significantly reduces switching activity and power consumption during testing.
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
This document discusses transmission impairment, which refers to degradation of signals as they travel through transmission media. There are three main causes of transmission impairment: 1) attenuation, which is the loss of signal energy as it passes through a medium, 2) distortion, which is a change in the signal's form or shape, such as different frequency components arriving at different times, and 3) noise, which adds unwanted signals from sources like thermal effects, interference, or crosstalk between wires. Attenuation is measured in decibels and can be compensated for using amplifiers, while signal to noise ratio (SNR) measures the quality of a transmission system by comparing the signal strength to the noise power.
This document summarizes different types of semiconductor memories. DRAM uses a capacitor and transistor to store data as charge. SRAM uses a 6 transistor latch. Mask ROM is one-time programmable. EPROM and EEPROM can be reprogrammed using ultraviolet rays or electrical pulses. FRAM uses a ferroelectric capacitor. Memory cells are arranged in a grid and accessed using row and column decoders. The document then describes the operation of DRAM, SRAM, flash memory, and NAND flash memory cells.
The document discusses the steps in the logic synthesis process from RTL to optimized gate-level netlist. It includes:
1) RTL description is converted to an internal representation
2) Logic is optimized to remove redundancy
3) Technology mapping implements the representation using cells from a technology library
The document also discusses floor planning, which determines routing areas by placing blocks/macros, and placement which places standard cells in rows to minimize area and interconnect cost.
The document is about CMOS logic design. It covers topics such as logic values and encoding bits in digital systems, logic gates and families, MOS transistors, CMOS inverters and their electrical characteristics. It discusses power consumption analysis of CMOS circuits including static and dynamic power. It also covers pull-up and pull-down networks, DC analysis of CMOS inverters, beta ratio, switching characteristics of inverters and examples of CMOS logic gates like inverters, NAND, NOR, buffers and AND/OR gates.
The document discusses digital circuits including combinational and sequential circuits. It describes various combinational logic circuits such as half adders, full adders, comparators, multiplexers, encoders, decoders. It also discusses sequential circuits and how they employ memory elements. Arithmetic circuits, binary adders, subtractors, and BCD to 7-segment decoders are explained in detail through diagrams and examples.
Design and implementation of analog multipliers with IC'sheyaci
This document discusses the design and implementation of analog multipliers and integrated circuits. It describes how analog multipliers are used for frequency conversion in radio frequency systems. It then explains the basic principles of analog multipliers and mixers, how they multiply input signals and translate frequencies. The document outlines different mixer definitions and equations. It also discusses important parameters for analog multipliers like conversion gain and noise figure. Furthermore, it presents the Gilbert cell mixer and its mathematics, and how operational transconductance amplifiers can be used to realize a multiplier. Finally, it provides examples of applications for multiplier ICs like voltage multiplication, division, squaring and frequency doubling, demonstrating these using the AD633 analog multiplier chip.
A current injection folded switch mixer for direct conversionIAEME Publication
1) The document discusses a current injection folded-switch mixer (CI-FSM) for direct conversion receivers in wireless applications.
2) CI-FSM is proposed to increase the conversion gain and reduce the noise figure of a folded switch mixer further. For comparison, a folded switch mixer (FSM) and CI-FSM are implemented in a 180nm CMOS process.
3) Simulation results show that the CI-FSM achieves a conversion gain higher by 2dB and noise figure lower by 1.0dB compared to the FSM, while maintaining similar linearity, at the cost of increased area.
The document discusses latches and flip-flops. It describes how a latch stores a data value and is non-volatile, while a flip-flop is built from two back-to-back latches clocked on opposite phases. Various latch and flip-flop circuit designs are presented, including pass transistor, transmission gate, buffered input/output, and master-slave designs. Features like enables, resets, and sets are also discussed along with their synchronous and asynchronous implementations in flip-flops. Different flip-flop circuit styles are covered such as transmission gate, complementary CMOS, precharge, and self-gating designs.
Introduction to Built In Self Test (BIST).pdfFEMILAECE
Built-in self-test (BIST) is a technique that uses on-chip circuitry to test other parts of the chip. It involves a pseudo-random sequence generator (PRSG) to produce input signals and a signature analyzer to observe outputs. A PRSG is typically a linear feedback shift register (LFSR) that cycles through a pseudo-random sequence. A signature analyzer receives outputs and XORs them to produce a syndrome signature that is compared to a correct signature to determine if the circuit passed the test. BIST provides advantages like lower cost and better fault coverage compared to external testing. However, it requires additional silicon area and the on-chip test circuitry could also fail.
Flipflops JK T SR D All FlipFlop SlidesSid Rehmani
Flipflops JK T SR D All FlipFlop Slides. Uploaded by SidRehmani.
Jk flip flop presentation, T flip flop presentation, D flip flop presentation, D flip flop presentation.
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facebook.com/RjSidRehmani
The document discusses a Phase Locked Loop (PLL). It describes PLL as a circuit that synchronizes an output signal generated by an oscillator to match the frequency and phase of a reference input signal. The key functional blocks of a PLL are a phase detector, low pass filter, and voltage controlled oscillator (VCO). The phase detector compares the input and feedback frequencies and provides an error signal. The low pass filter removes noise and the VCO generates the output frequency controlled by the error signal voltage. A PLL goes through free running, capture, and phase locked stages of operation. Applications of PLL include frequency modulation/demodulation and signal synchronization.
Latch and flip flop circuits are used to store digital information. A latch can store a bit as long as power is applied, while a flip flop uses feedback to store a bit even after inputs change. There are different types of flip flops like SR, JK, D and T flip flops that store bits based on their input conditions and clock signal. Flip flops are edge triggered which means they change state only on rising or falling edge of the clock signal. This provides synchronization between logic and memory in digital circuits.
Msp430 assembly language instructions &addressing modesHarsha herle
The document discusses MSP430 assembly language. It covers topics like MSP430 data storage in registers, double operand instructions, single operand instructions, jump instructions, and emulated instructions. Examples of various instructions like ADD, SUB, BIC, MOV, CALL etc. are provided. It also discusses MSP430 memory structure and explains that words are only stored at even addresses with the low byte at the even address and high byte at the next odd address.
This document discusses several methods for designing sequential circuits, including state tables, state assignment, and deriving flip-flop input equations. It then provides examples of implementing sequential circuits using ROMs, PLAs, CPLDs, and FPGAs. Specifically, it designs a comparator circuit and code converter as examples of iterative and sequential circuits. It also discusses implementing a parallel adder and shift register using an FPGA.
The document discusses different types of flip-flops including RS NAND and NOR flip-flops, and covers the basics of sequential logic circuits. It defines level-triggered and edge-triggered clock inputs for flip-flops and compares asynchronous and synchronous clocked flip-flops. The timing diagrams show how positive and negative edge triggering determines when the output of a flip-flop changes state in response to clock pulses and input signals.
The document summarizes operational transconductance amplifiers (OTAs). It discusses how OTAs work as voltage controlled current sources and two-quadrant multipliers. The ideal OTA has infinite input impedance and converts the differential input voltage to a controlled current output. Real OTAs use circuitry to process input voltages over a wide range and produce a relatively output-independent current. Bipolar OTAs use a differential transistor pair to convert the input voltage difference to output current. Additional circuitry like input diode linearization can improve characteristics but reduces maximum transconductance.
A combinational circuit is a logic circuit whose output is solely determined by the present input. It has no internal memory and its output depends only on the current inputs. A half adder is a basic combinational circuit that adds two single bits and produces a sum and carry output. A full adder adds three bits and produces a sum and carry like the half adder. Other combinational circuits discussed include half and full subtractors, decoders, encoders, and priority encoders.
This document provides an overview of different digital logic families. It begins by introducing logic gates and integrated circuits. It then classifies logic families as either bipolar or unipolar, and lists examples of each. Key specifications of digital ICs are defined, including propagation delay, fan-in/fan-out, input/output logic levels, and noise margin. Transistor-transistor logic (TTL) and complementary metal-oxide-semiconductor (CMOS) circuits are described. The TTL NAND gate uses multiple emitter transistors while the CMOS NAND gate uses both P-channel and N-channel MOSFETs. Emitter-coupled logic (ECL) provides the fastest
The document discusses design for testability (DFT) techniques. It explains that DFT is important for testing integrated circuits due to unavoidable manufacturing defects. DFT aims to increase testability by making internal nodes more controllable and observable. Common DFT techniques mentioned include adding scan chains, which allow testing at speed by launching test vectors from a shift register. Stuck-at fault and transition fault models are discussed as well as methods for detecting these faults including launch-on-capture and launch-on-shift. Fault equivalence and collapsing techniques are also summarized.
This document discusses limitations of traditional serial scan design for testing integrated circuits and proposes an alternative called Random Access Scan (RAS). RAS addresses three key limitations of serial scan: 1) test data volume, 2) test application time, and 3) test power. In RAS, flip-flops act as addressable memory elements during test mode, reducing time to set and observe flip-flop states compared to serial scan. While RAS requires more gates and test pins than serial scan, it significantly reduces switching activity and power consumption during testing.
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
This document discusses transmission impairment, which refers to degradation of signals as they travel through transmission media. There are three main causes of transmission impairment: 1) attenuation, which is the loss of signal energy as it passes through a medium, 2) distortion, which is a change in the signal's form or shape, such as different frequency components arriving at different times, and 3) noise, which adds unwanted signals from sources like thermal effects, interference, or crosstalk between wires. Attenuation is measured in decibels and can be compensated for using amplifiers, while signal to noise ratio (SNR) measures the quality of a transmission system by comparing the signal strength to the noise power.
This document summarizes different types of semiconductor memories. DRAM uses a capacitor and transistor to store data as charge. SRAM uses a 6 transistor latch. Mask ROM is one-time programmable. EPROM and EEPROM can be reprogrammed using ultraviolet rays or electrical pulses. FRAM uses a ferroelectric capacitor. Memory cells are arranged in a grid and accessed using row and column decoders. The document then describes the operation of DRAM, SRAM, flash memory, and NAND flash memory cells.
The document discusses the steps in the logic synthesis process from RTL to optimized gate-level netlist. It includes:
1) RTL description is converted to an internal representation
2) Logic is optimized to remove redundancy
3) Technology mapping implements the representation using cells from a technology library
The document also discusses floor planning, which determines routing areas by placing blocks/macros, and placement which places standard cells in rows to minimize area and interconnect cost.
The document is about CMOS logic design. It covers topics such as logic values and encoding bits in digital systems, logic gates and families, MOS transistors, CMOS inverters and their electrical characteristics. It discusses power consumption analysis of CMOS circuits including static and dynamic power. It also covers pull-up and pull-down networks, DC analysis of CMOS inverters, beta ratio, switching characteristics of inverters and examples of CMOS logic gates like inverters, NAND, NOR, buffers and AND/OR gates.
The document discusses digital circuits including combinational and sequential circuits. It describes various combinational logic circuits such as half adders, full adders, comparators, multiplexers, encoders, decoders. It also discusses sequential circuits and how they employ memory elements. Arithmetic circuits, binary adders, subtractors, and BCD to 7-segment decoders are explained in detail through diagrams and examples.
Design and implementation of analog multipliers with IC'sheyaci
This document discusses the design and implementation of analog multipliers and integrated circuits. It describes how analog multipliers are used for frequency conversion in radio frequency systems. It then explains the basic principles of analog multipliers and mixers, how they multiply input signals and translate frequencies. The document outlines different mixer definitions and equations. It also discusses important parameters for analog multipliers like conversion gain and noise figure. Furthermore, it presents the Gilbert cell mixer and its mathematics, and how operational transconductance amplifiers can be used to realize a multiplier. Finally, it provides examples of applications for multiplier ICs like voltage multiplication, division, squaring and frequency doubling, demonstrating these using the AD633 analog multiplier chip.
A current injection folded switch mixer for direct conversionIAEME Publication
1) The document discusses a current injection folded-switch mixer (CI-FSM) for direct conversion receivers in wireless applications.
2) CI-FSM is proposed to increase the conversion gain and reduce the noise figure of a folded switch mixer further. For comparison, a folded switch mixer (FSM) and CI-FSM are implemented in a 180nm CMOS process.
3) Simulation results show that the CI-FSM achieves a conversion gain higher by 2dB and noise figure lower by 1.0dB compared to the FSM, while maintaining similar linearity, at the cost of increased area.
A current injection folded switch mixer for direct conversionIAEME Publication
The document describes a proposed Dynamic Current Injection Folded-Switch Mixer (CI-FSM) for direct conversion receivers.
1) CI-FSM combines a folded switch mixer topology with a dynamic current injection technique to improve conversion gain and reduce noise figure compared to a standard folded switch mixer.
2) Simulation results show the CI-FSM achieves over 2dB higher conversion gain and around 1dB lower noise figure than the folded switch mixer.
3) The CI-FSM maintains similar linearity as the folded switch mixer while increasing circuit area due to added inductors used for current injection.
Negative resistance amplifier circuit using GaAsFET modelled single MESFETTELKOMNIKA JOURNAL
Negative resistance devices have attracted much attention in the wireless communication industry because of their low cost, better performance, high speed, and reduced power requirements. Although negative resistance circuits are non-linear circuits, they are associated with distortion, which may either be amplitude-to-amplitude distortion or amplitude-to-phase distortion. In this paper, a unique way of realizing a negative resistance amplifier is proposed using a single metal-semiconductor field-effect transistor (MESFET). Intermodulation distortion test (IMD) is performed to evaluate the characteristic response of the negative resistance circuit amplifier to different bias voltages using the harmonic balance (HB) of the advanced designed software (ADS 2016). The results obtained are compared to those of a conventional distributed amplifier. The findings of this study showed that the negative resistance amplifier spreads over a wider frequency output with reduced power requirements while the conventional distributed amplifier has a direct current (DC) offset with output voltage of 32.34 dBm.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Study and implementation of comparator in cmos 50 nm technologyeSAT Journals
Abstract This paper describes the comparator circuits used in FLASH Analog to digital converter (ADC). The performance of FLASH ADC is greatly influenced by the choice of comparator. In this paper, first a single ended “Threshold Inverter Quantizer” (TIQ) is presented. The TIQ comparator is based on a CMOS inverter cell, in which voltage transfer characteristics (VTC) are changed by systematic transistor sizing. However, TIQ comparator is very sensitive to power supply noise. Another comparator circuit presented in this paper is “Two stage open loop comparator”. It is implemented in 50 nm CMOS Technology. Pre-simulation of comparator is done in LT-Spice and post layout simulation is done in Microwind 3.1. Keywords: CMOS, Comparator, TIQ (Threshold Inverter Quantizer), LT-Spice.
Wavelet Based Fault Detection, Classification in Transmission System with TCS...IJERA Editor
This paper presents simulation results of the application of distance relays for the protection of transmission systems employing flexible alternating current transmission controllers such as Thyristor Controlled Series Capacitor (TCSC). The complete digital simulation of TCSC within a transmission system is performed in the MATLAB/Simulink environment using the Power System Block set (PSB). This paper presents an efficient method based on wavelet transforms both fault detection and classification which is almost independent of fault impedance, fault location and fault inception angle of transmission line fault currents with FACTS controllers.
An operational amplifier with recycling folded cascode topology and adaptive ...VLSICS Design
This paper presents a highly adaptive operational amplifier with high gain, high bandwidth, high speed
and low power consumption. By adopting the recycling folded cascode topology along with an adaptivebiasing
circuit, this design achieves high performance in terms of gain-bandwidth product (GBW) and slew
rate (SR). This single stage op-amp has been designed in 0.18μm technology with a power supply of 1.8V
and a 5pF load. The simulation results show that the amplifier achieved a GBW of 335.5MHz, Unity Gain
Bandwidth of 247.1MHz and a slew rate of 92.8V/μs.
Modeling of a Microwave Amplifier Operating around 11 GHz for Radar Applicati...IJECEIAES
The low noise amplifier is one of the basic functional blocks in communication systems. The main interest of the LNA at the input of the analog processing chain is to amplify the signal without adding significant noise. In this work, we have modeled a LNA for radar reception systems operating around 11 GHz, using the technique of impedance transformations with Smith chart utility. The type of transistor used is: the transistor HEMT AFP02N2-00 of Alpha Industries®. The results show that the modeled amplifier has a gain greater than 20 dB, a noise figure less than 2 dB, input and output reflection coefficients lower than -20 dB and unconditional stability.
Conducted electromagnetic interference mitigation in super-lift Luo-converte...IJECEIAES
In this article, a digital chaotic pulse width modulation (DCPWM)-dependent electromagnetic interference (EMI) noise attenuating procedure has been implemented. With the aid of a field programmable gate array (FPGA), a randomized carrier frequency modulation with a fixed duty cycle has been generated through chaotic carrier frequency, and this process is called DCPWM. Conducted EMI suppression is achieved in a 200 kHz, 40 W elementary positive output super lift Luo (EPOSLL) converter using the DCPWM technique. The results are compared and validated with periodic PWM over DCPWM in simulation and hardware with electromagnetic compatibility (EMC) standards. Besides, 9 dBV (2.81 V) of conducted EMI noise has been minimized in the DCPWM approach against periodic pulse width modulation method for the EPOSLL converter in electric vehicles applications.
Codec Scheme for Power Optimization in VLSI InterconnectsIJEEE
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DESIGN AND IMPLEMENTATION OF ANALOG MULTIPLIER WITH IMPROVED LINEARITY
1. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
DOI : 10.5121/vlsic.2012.3508 93
DESIGN AND IMPLEMENTATION OF ANALOG
MULTIPLIER WITH IMPROVED LINEARITY
Nandini A.S1
, Sowmya Madhavan2
and Dr Chirag Sharma3
1
Department of Electronics and Communication Engineering, Nitte Meenakshi Institute
of Technology, Yelahanka, Bangalore- 560064
nandini.sreenivas@rediffmail.com
2
Department of Electronics and Communication Engineering, Nitte Meenakshi Institute
of Technology, Yelahanka, Bangalore- 560064
shuba.sow2004@gmail.com
3
Department of Electronics and Communication Engineering, Nitte Meenakshi Institute
of Technology, Yelahanka, Bangalore- 560064
chirag.nmit@gmail.com
ABSTRACT
Analog multipliers are used for frequency conversion and are critical components in modern radio
frequency (RF) systems. RF systems must process analog signals with a wide dynamic range at high
frequencies. A mixer converts RF power at one frequency into power at another frequency to make signal
processing easier and also inexpensive. A fundamental reason for frequency conversion is to allow
amplification of the received signal at a frequency other than the RF, or the audio, frequency. This paper
deals with two such multipliers using MOSFETs which can be used in communication systems. They were
designed and implemented using 0.5 micron CMOS process. The two multipliers were characterized for
power consumption, linearity, noise and harmonic distortion. The initial circuit simulated is a basic Gilbert
cell whose gain is fairly high but shows more power consumption and high total harmonic distortion. Our
paper aims in reducing both power consumption and total harmonic distortion. The second multiplier is a
new architecture that consumes 43.07 percent less power and shows 22.69 percent less total harmonic
distortion when compared to the basic Gilbert cell. The common centroid layouts of both the circuits have
also been developed.
KEYWORDS
Multiplier, Gilbert cell, Noise spectral density, Total Harmonic Distortion, Transconductance
1. INTRODUCTION
An Analog multiplier is a device having two input ports and an output port. The signal at the
output is the product of the two input signals. If both input and output signals are voltages, the
transfer characteristic is the product of the two voltages divided by a scaling factor, K, which has
the dimension of voltage as shown in Figure 1 [1].
Figure 1. Basic Analog multiplier
2. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
94
Mixer is a device used to mix two input signals and deliver an output voltage at frequencies equal
to the difference or sum of the input frequencies. Any nonlinear device can do the job of mixing
or modulation, but it often needs a frequency selection network which is normally composed as a
LC network. Hence a mixer needs at least one non-linearity, such as multiplication or squaring, in
its transfer function. Every analog multiplier can effectively used as a mixer, but the inverse does
not hold [2].
There is a lot of similarity between multiplier and mixer, but the main difference between them is
that in frequency multiplier only one signal is implied while in mixer we need two signals as
source. The similarity is that, in both of them, we drive circuits to nonlinear region to produce the
harmonic of input signal in multiplier and to produce the intermodulation of input signals in
mixer. That is, in a mixer, there is a sum and difference of the input frequencies due to the non-
linearity of a device.
2. MIXER DEFINITIONS
Mixers are non-linear devices used in systems to translate one frequency to another. All mixer
types work on the principle that a large Local Oscillator (LO) RF drive will cause
switching/modulating the incoming Radio Frequency (RF) to the Intermediate Frequency (IF) [3].
The multiplication process begins by taking two signals:
a = Asin(ω1.t + φ1 ) and signal b = Bsin(ω2.t + φ2 ) (1)
The resulting multiplied signal will be:
a.b = AB sin(ω1.t + φ1 ). sin(ω2.t + φ2 ) (2)
This can be multiplied out thus:
Using the trigonometric identity
sinAsinB = -½[cos(A+B)-cos(A-B)] (3)
Where A = (ω1.t + φ1 ) and B = (ω2.t + φ2 )
= -AB/2 [cos((ω1.t +φ1 )+(ω2.t + φ2 ))
- cos((ω1.t + φ1 )-(ω2.t + φ2 ))] (4)
= -AB/2 [cos((ω1 + ω2 )t + (φ1+ φ2 ))
- cos((ω1 - φ1 )t - (φ1- φ2 ))] (5)
= -AB/2 [cos((ω1 + ω2 )t + (φ1+ φ2 )) - cos((ω1 – ω2 )t - (φ1- φ2 ))]
The following parameters are important for an analog multiplier.
(1) Conversion Gain: This is the ratio in dB between the IF signal which is the difference
frequency between the RF and LO signals and the RF signal.
(2) Noise Figure: Noise figure is defined as the ratio of SNR(Signal to Noise Ratio) at the IF port
to the SNR of the RF port.
3. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
95
3. GILBERT CELL MIXER
The basic idea of multiplier implementation is illustrated in Figure 2 [4]. Two signals V1(t) and
V2(t) are applied to a non linear device, which can be characterized by a higher order polynomial
function. This polynomial function generates the terms like V1² (t), V2² (t), V1³ (t), V2³ (t), V1²
(t)*V2(t) and many others besides the desired V1(t).V2(t). Then it is required to cancel the
undesired components. This is accomplished by a cancellation circuit configuration.
A multiplier could be realized using programmable transconductance components. Consider the
conceptual transconductance amplifier of Figure 3(a), where the output current is simply given by
i0 = Gm1v1 (6)
Figure 2. Basic idea of multiplier.
where
Gm1 = Gm1 (Ibias1) (7)
For a bipolar transconductor, Gm1 becomes
Gm1 = Ibias1/(2.Vt ) (8)
Where Vt is the thermal voltage (kT/q).
Next, a small signal is added to the bias current as shown in Figure 3(b). The second input signal
v2(t)can be converted into a current, i2(t) = Gm2v2(t), as illustrated in Figure 3(c).
Then, the output current yields
i0(t) = Gm1v1 =
t
mbias
v
tvGI
2
)(221 +
. V1(t) (9)
i0(t) = )(
22
)()(
1
1212
tv
v
I
v
tvtvG
t
bias
t
m
+
=
t
bias
tt
bias
v
tvI
vv
tvtvI
2
)(
2.2
)()( 11212
+ (10)
or
i0(t) = )()()( 12211 tvktvtvk + (11)
Thus, i0(t) represents the multiplication of two signals v1(t) and v2(t) and an unwanted component
k2v1(t) [4]. This component can be eliminated as shown in Figure 3(d). Better cancellation is
achieved when the third transconductor (Gm2) becomes a fully differential transconductor, and v1
and v2 are fully differential inputs as illustrated in Figure 3(e).
i0(t) = )()(2 211 tvtvk (12)
4. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
96
This is the basic operation principle of a Gilbert cell [5], [6]. Operational transconductance
amplifier (OTA)-based implementations are reported in [8]–[9]. The connection to the Gilbert cell
can be seen by substituting the transconductors in Figure 3(e) by bipolar junction transistor (BJT)
differential pairs.
As the digital technology dominates in modern electronics, analog circuits are required to share
the same standard CMOS process for low-cost fabrication. Thus, the popular BJT Gilbert Cell is
not suitable in a standard digital process, and designers must address low power supply voltage
requirements. One problem that circuit designers often encounter is how to select the best
multiplier architecture for their applications. Unfortunately, designers who propose multipliers in
the literature often do not make reference to or comparison to other multipliers. This lack of
comparison causes the same basic multiplier architectures to be, from time to time, reported as
“new” architectures. The transconductance multipliers are classified into eight types. They can be
categorized into two groups based on its MOS operating region, linear and saturation. It should be
emphasized that the fundamental multiplier circuit topology for many of the multipliers is the
same [4].
4. CIRCUIT TOPOLOGIES
Differential pairs reveals two important aspects of their operations: (1) the small – signal gain of
the circuit is a function of the tail current and (2) the two transistors in a differential pair provides
a simple means of steering the tail current to one of two destinations. By combining these two
properties, we can develop a versatile building block.
Figure 3. Multiplication operation using programmable transconductor
5. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
97
Suppose we wish to construct a differential pair whose gain is varied by a control voltage. This
can be accomplished as depicted in Figure 4(a), where the control voltage defines the tail current
and hence the gain. In this topology, the voltage gain varies from zero to a maximum value given
by voltage headroom limitations and device dimensions. This circuit is a simple example of a
“variable – gain amplifier” (VGA) [10]. VGAs find application in systems where the signal
amplitude may experience large variations and hence requires inverse changes in the gain.
Now suppose we seek an amplifier whose gain can be continuously varied from a negative value
to a positive value. For that we consider two differential pairs that amplify the input by opposite
gains Figure 4(b). We now have
Vout1/Vin = -gmRD (13)
and Vout2/Vin = +gmRD (14)
where gm denotes the transconductance of each transistor in equilibrium. If I1 and I2 vary in
opposite directions, then we have two gain values inout vv /1 and inout vv /2 which vary in
opposite directions.
We can combine Vout1 and Vout2 into a single output as shown in Fig 5(a) then the two voltages
can be summed, producing
Vout = Vout1 + Vout2 = inin VAVA .. 21 + (15)
Where A1 and A2 are controlled by Vcont1 and Vcont2 respectively.
Since 211 DDDDout IRIRV −= (16)
342 DDDDout IRIRV −= (17)
We have,
).()( 324121 DDDDDDoutout IIRIIRVV +−+=+ (18)
Thus, rather than add Vout1 and Vout2, we can short the corresponding drain terminals to sum the
currents and subsequently generate the output voltage. If I1 =0 then Vout = gmRDVin and if I2 =0,
then Vout = -gmRDVin. For I1 = I2 the gain drops to zero. In the circuit of Figure 5(b), Vcont1 and
Vcont2 must vary I1 and I2 in opposite directions such that the gain of the amplifier changes
monotonically [10]. For a large 21 contcont vv − all of the tail current is steered to one of
Figure 4. (a) Simple VGA. (b) two stages providing opposite gains.
6. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
98
the top differential pairs and the gain from Vin to Vout is at its most positive or most negative
value. For Vcont1 = Vcont2, the gain is zero. For simplicity, we redraw the circuit as shown in Fig
5(d) which is called as “Gilbert cell”. The idea is to convert the input voltage to current by means
of M5 and M6 and route the current through M1 –M4 to the output nodes. If the voltage given to
M1 and M3 is positive, then only M1 and M2 are on.
inDmout VRgV 6,5= (19)
Similarly if the voltage given to M4 and M2 is negative then only M3 and M4 are on.
inDmout VRgV 6,5−= (20)
Table 1. Specifications for Multiplier Design
VDD = 5V Noise spectral
density <1µV/Rt
Conversion gain
> 10dB
Power < 1mW Frequency of
operation
>100MHz
Dynamic Range
> 100dB
Figure 5. (a) Summation of the output voltages of two amplifiers, (b) summation in the current
domain, (c) use of M5- M6 to control the gain, (d) Gilbert cell
7. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
99
The Gilbert cell shown in Figure 6 includes two resistive loads and eight NMOS transistors,
where all are working in saturation region. There are two differential inputs given to the circuit.
Input in1 and in2 is a differential square signal and in3 and in4 is a differential sine signal. The
current source provides current to bias the circuit and in this top most four transistor works as
switch, the signal fed in the lower part of the circuit is multiplied by the signal fed into the
transistors M1-M4 and the output obtained is a differential output. This circuit is characterized
with respect to parameters shown in Table 1 and the result is compared with the result of circuit
shown in Figure 7 after characterizing it with respect to the same parameters.
Figure 6. Basic Gilbert cell
Figure 7. Fully differential four quadrant multiplier
8. International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.5, October 2012
100
Table 2. Circuit Elements
Parameter Name Basic Gilbert cell
Fully Differential four
quadrant multiplier
R1
R2
Ibias
Device Name
M1
M2
M3
M4
M5
M6
M7
70k
70k
14µ A
W/L
4
4
4
4
8
8
16
70k
70k
-
W/L
8
8
8
8
8
8
8
M8 4 8
5. SIMULATION RESULTS AND
PART A: The simulation results for the basic multiplier are discussed next. Each parameter is
numbered for clarity of the overall characterization.
1. Transient analysis for the basic multiplier which is in figure 6 is done. The output is as shown
in figure 8.
Figure 8.Transient Analysis of the Basic Gilbert cell multiplier
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The multiplier output from the simulation result in figure 8 is 1.55v.
This approximately equals to the output value got from equation 19.
Hence Conversion Gain = 20 log (vout/vin) (21)
= 23.80dB
2. Dynamic range = 20 log (vmax/vmin) (22)
= 187.23dB
Where vmax and vmin are maximum and minimum values of voltages given to test the output
of the multiplier.
3. Noise spectral density N0 is the noise power per unit of bandwidth; that is, it is the power
spectral density of the noise which has a dimension of power/frequency.
Figure 9. Noise spectral density of basic Gilbert cell multiplier
From figure 9, the noise spectral density is 36ηv/Rt.
4. The power consumption of the circuit is 325µW.
5. Total Harmonic Distortion, or THD is an amplifier or pre-amplifier specification that
compares the output signal of the amplifier with the input signal and measures the level
differences in harmonic frequencies between the two. The difference is called total harmonic
distortion. The maximum THD in percentage is 40.75% for an input voltage of 1.5V. The THD
plot is as shown in the Figure 10.
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Figure 10. THD plot of basic Gilbert cell multiplier
PART B: The simulation results for the fully Differential four quadrant multiplier are discussed
next. Each parameter is numbered for clarity of the overall characterization.
1. Transient analysis for the fully differential four quadrant multiplier is as shown in Figure 11.
Figure 11. Fully Differential four quadrant multiplier
The fully differential four quadrant multiplier output is 0.65v.
The conversion gain = 20 log (vout/vin) = 16.25dB.
2. Dynamic range = 20 log (vmax/vmin)
= 195.56dB
Where vmax and vmin are maximum and minimum values of voltages given to test the output
of the multiplier.
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3. The Noise spectral density is 590ηv/Rt for the fully differential multiplier as shown in figure
12.
Figure 12. Noise spectral density of Fully Differential multiplier
4. Power consumption of the Fully Differential multiplier is 185µW.
5. The maximum Total Harmonic Distortion in percentage is 18.06% for an input voltage of
1.5V. The THD plot is as shown in the Figure 13.
Figure 13. THD plot of Fully Differential four quadrant multiplier
Comparison of the results of Basic Gilbert cell multiplier and Fully differential four
quadrant multiplier is given in the Table 3.
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Table 3. Comparison of The Two Multipliers
This shows that the fully differential four quadrant multiplier is more linear and has less power
consumption as compared to basic Gilbert cell multiplier.
PART C: Comparison plots for power consumption and THD
1. The power consumption for the Basic Gilbert cell multiplier and fully differential four
quadrant multiplier are compared and is as shown in Figure 14.
Figure 14. Comparison graph of power consumption of figures (6) and (7).
2. The total harmonic distortion for the Basic Gilbert cell multiplier and fully differential
four quadrant multiplier are compared and is as shown in the Figure 15.
Parameter Name
Basic Gilbert cell
multiplier
Fully Differential four
quadrant multiplier
Supply Voltage
Conversion gain
Dynamic range
Noise spectral
density
Frequency of
operation
5V
24.17dB
187.23dB
36 ηV/Rt
>100MHz
5V
16.25dB
195.56dB
590 ηV/Rt
>100MHz
Power consumption 325µW 185µW
Total harmonic
distortion for
1.5volt
40.75% 18.06%
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The goal of this work is to come with a multiplier architecture suitable for spread spectrum time
domain reflectometry (SSTDR) [7]. SSTDR requires a multiplier with wide linear range and low
power consumption. Fig 15 shows that fully differential four quadrant multiplier is much linear
compared to Gilbert cell multiplier.
5. LAYOUTS
Layouts are drawn for the Basic Gilbert cell multiplier both with IO padframe and without IO
padframe. In basic Gilbert cell multiplier, common centroid and fingering have been used and the
layout is as shown in Figure 16.
Figure 15. Comparison graph of THD of figures (6) and (7).
Figure 16. Common centroid layout of Basic Gilbert multiplier
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106
Area without IO pad = L * W
= 66.6µm * 43.2µm = 2877.12µm2
Basic Gilbert cell multiplier layout with IO pad frame is as shown in Figure 17.
Figure 17. Basic Gilbert multiplier with IO padframe
Area with IO padframe = 1498.5µm * 1498.5µm
Fully differential four quadrant multiplier layout without IO pad frame is as shown in Figure 18.
Figure 18. Common centroid layout of Fully differential four quadrant multiplier
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107
Area without IO pad = L * W
= 72.6µm * 43.2µm = 3158.1µm2
Fully differential four quadrant multiplier layout with IO pad frame is as shown in Figure 19.
Figure 19. Fully differential four quadrant circuit with IO pad
For fully differential four quadrant multiplier, area with IO padframe is same as for the circuit
shown in Figure 17.
6. CONCLUSIONS
In this work new multiplier architecture was compared to the widely used Gilbert cell multiplier.
The goal of this work was to find a multiplier architecture with a wider linear range and lower
power consumption. The Total Harmonic Distortion for the basic Gilbert cell multiplier and the
fully differential four quadrant multiplier are 40.75% and 18.06% respectively. The power
consumption for the basic Gilbert cell multiplier and the fully differential four quadrant multiplier
are 325µW and 185µW respectively. Hence the proposed fully differential architecture has a
lower Total Harmonic Distortion and power consumption than a Gilbert cell multiplier without
much increase in chip area. Hence the fully differential four quadrant multiplier is better suited
for SSTDR system compared to widely used Gilbert cell multiplier.
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Authors
Nandini A S was born on 4th
November, 1987 in Bangalore. Nandini A S completed
her Bachelor of Engineering in Telecommunication Engineering from Vivekananda
Institute of Technology, Bangalore, Karnataka, India in 2009 and currently pursuing
Master of Technology from Nitte Meenakshi Institute of Technology, Bangalore,
Karnataka, India in VLSI Design and Embedded Systems.
Sowmya Madhavan was born on 26th
May, 1983 in Bangalore. Sowmya Madhavan
completed her Bachelor of Engineering in Telecommunication Engineering from
Vivekananda Institute of Technology, Bangalore, Karnataka, India in 2001 and Master
of Technology from AMC College of Engineering, Bangalore, Karnataka, India in
digital electronics and communication. She is currently pursuing her PhD under
Visvesvaraya Institute of Technology in low power VLSI design.
Chirag R. Sharma was born on 1st
November, 1979. Chirag R Sharma received the
B.E. degree in electrical engineering from the Maharaja Sayajirao University, Baroda,
India, in 2001, and the M.S. degree in electrical and computer engineering from Utah
State University, Logan, in 2003. He also received the Ph.D. degree in electrical
engineering at the University of Utah, Salt Lake City in 2009.His current research
interests are analog and mixed-signal CMOS circuit design, CMOS sensors, and
reflectometry techniques for locating intermittent faults on aircraft wiring.