Embodiment and Optimization of Logical Comparator in Practical Application

In digital system, especially in the process of computer data processing and operation, logical comparator is essential. This paper analyzes the performance of the logical comparator and its influence on the actual circuit by combining the image of the digital circuit, and puts forward the factors to be considered when designing the logical comparator based on the above. Based on the basic working rules of the logic gate, the advantages and disadvantages of the constructed logical comparator are analyzed, and several methods of optimizing the logical comparator are introduced in combination with practical cases. As a key component of digital circuit, logical comparator has been widely used in many fields. By understanding the principles and applications of logical comparators, designers and researchers can effectively utilize these circuits to meet the requirements of various digital systems. In the future, the accelerated development of artificial intelligence and mechanization industries will improve the efficiency of the entire logic circuit and digital systems and even electronic products.


INTRODUCTION
With the gradual development of digital systems, the application of deep learning technology to the field of electronic design automation (EDA) has become a hot topic, and electronic products such as computers increasingly rely on logic circuits based on gate structures [1].Especially in the process of computer data processing and operation, logical comparator is essential.
This paper aims to introduce the comprehensive performance of the logical comparator from the basic definition to the actual application scenario.First, the definition and practical functions of the logical value circuit are visualized by combining the image of the digital circuit, and the performance of the logical comparator and its influence on the actual circuit are analyzed by focusing on the two typical and important indicators, response time and delay.Based on the above understanding and the influence factors of the logical comparator itself, this paper puts forward the factors that need to be considered when designing the logical comparator to ensure the normal operation of the digital circuit.As gate structure is the important basic structure of logical comparator, the following content briefly introduces some basic operation rules of logic gate and focuses on analyzing the advantages and disadvantages of logical comparator built based on these logic gates.Furthermore, several methods to optimize the logical comparator are specifically introduced based on actual cases.Finally, the importance and operating principle of the logical comparator are analyzed with practical examples in the three most widely used scenarios: digitalto-analog conversion, sensor interface and measurement system, digital communication, and data processing.
By understanding the principles and applications of logical comparators, engineers and researchers can make more informed decisions in the design and utilization of these important digital circuit components, thereby promoting the development of digital system-related industrialization and the updated iteration of related electronic product applications.

LOGICAL COMPARATOR 2.1 Definition and Function of Logical Comparator
Logic comparators play a crucial role in flash memory, pipelined and successive approximation register (SAR) ADCs, which can compare multiple input signals and produce logical outputs based on their relative relationships [2].A typical configuration of a logical comparator circuit comprises two signal inputs and one output, as shown in the Figure 1 below.However, it is important to note that a functional comparator can have multiple inputs and outputs, depending on the specific  1 to present all the combined results of the logic circuit where a comparator is located.The universality of logic comparator and its important significance in electronic design make it an indispensable tool for efficient information processing and control in modern technology.To evaluate the performance of a logical comparator, two key parameters are considered: response time and latency.

Performance Parameters and Metrics of Logical Comparator
time refers to the duration required for the output signal of the logical comparator to change when the input signal changes, representing the speed at which the logical comparator responds to the change in the input value.This is an important performance for evaluating logical comparators.For example, in 2005, when using asynchronous control to improve the logic comparator, the researchers mentioned in the evaluation that it can reduce the average response time of the chip to 82% of the worst response time of 23.37ns [3].This shows that the fast response time can realize the real-time decision of logic comparator and efficient signal processing, and improve the reliability and function of the circuit.
Delay, another important parameter for evaluating the performance of a logical comparator, quantifies the time interval between a change in the input signal and a corresponding change in the output signal.Similar to response time, it represents the processing speed of the logical value comparator.In 1965, when designing and analyzing the test results of an eight-bit adder, scientists found that the average carry delay time of each stage of the adder was 3/4 nanosecond [4].It shows that delay has been accepted as a necessary condition for evaluating a logical comparator at a very early stage.A shorter latency is ideal because it minimizes the delay between input changes and output responses, facilitating faster system operation.Long delays can lead to delays in subsequent stages of the circuit, potentially affecting the overall performance and timing requirements of the electronic system.

Design Considerations for Logical Comparator
In the logical comparator design process, apart from the two mentioned evaluation parameters, several operational factors require careful consideration.These factors include bias voltage, inverse feedback noise, linearity, supply voltage, speed, common mode voltage, delay, and power consumption.The main objective of the design is to strike a proper trade-off among these factors [2].By carefully considering these factors, designers can more reasonably design the logic comparator to meet the requirements of the intended application.

IMPLEMENTING COMPARATORS THROUGH LOGIC CIRCUITS 3.1 Basic Principles and Functions of Logic Gates
A logic gate is an electronic component that performs basic logical operations on signals from one or more binary inputs and generates a binary output based on a predefined truth table.The most used logic gates include AND, OR, NOT, NAND, NOR, and XOR gates.Each gate has a specific function and behavior, and the fundamentals and functions of these logic gates implement the building blocks of a logical comparator.For example, an NAND gate, as a general logic gate, has a low output (0) if the inputs are high ( 1) and a high output (1) if at least one of the inputs is low (0).This result is presented in Table 2.
The following is the formula for the NAND gate: The corresponding truth table and formula can clearly reflect the operation rules of a basic logic gate, and the function of the logic comparator composed of logic gates can also be understood through the truth table and formula.

Methods of Implementing Comparators
Using Logic Gates

Comparator Design
Based on a Single Logic Gate.It is a common way to construct a logic comparator using a single logic gate.For example, the logic control module of the successive approximation analog-to-digital converter is mainly composed of a 16-bit counter, and not gate, and delay module.This makes it outstanding advantages of simple structure, high precision, low power consumption, small area, etc., and makes it widely used in portable instruments, pen input quantizers, industrial control and data signal collectors [5].A logic comparator composed of a single logic gate can be implemented simply and directly and requires relatively few components.And because only one logic gate is required, its chip area and component cost are low.Therefore, for applications with a small number of comparators, a comparator consisting of a single logic gate may be sufficient.However, the accuracy of the comparator composed of a single logic gate is limited by its own gate delay and threshold, and may not be suitable for high-precision comparison requirements.Moreover, due to the propagation delay of a single logic gate, its response speed may be slow, which is not suitable for high-speed comparison requirements.In some cases, transient or steady-state instability may also occur due to the non-ideal properties of the gate.

Comparator Design
Based on Multiple Logic Gates.By utilizing different combinations of multiple logic gates, designers can create efficient and reliable logic comparators that accurately compare logical values in digital systems.First, its well-designed circuit structure allows for higher precision comparison functions.Moreover, by optimizing the circuit structure and using high-speed logic gates, the comparator composed of multiple logic gates can achieve faster response time.The cooperation of multiple logic gates can also improve the stability of the comparator to some extent.But at the same time, comparator circuits built with multiple logic gates are often more complex, and their design and layout can be more difficult.Due to the need for multiple logic gates, its chip area and component cost are high, and it also needs to be considered for power-sensitive applications.

Optimization of Logical Comparators
To improve the performance and efficiency of a logical comparator, several optimization techniques can be employed.By applying these technologies, designers can improve response time, reduce latency, and optimize power consumption.Here are some common ways to optimize a logical comparator.
Choosing the right comparator type can be optimized to a large extent first.There are many types of logical comparators to choose from, such as simple comparators, Flash comparators, differential comparators, and so on.According to the application requirements, choosing the most suitable type can improve the optimization in terms of performance and power consumption.
Optimizing the threshold, which is the decision level of the comparator in response to the input signal, can also improve the performance and stability of the logical comparator.For example, a threshold selection acceleration algorithm based on genetic optimization proposed in 2003 can reduce the amount of computation by about 30% compared with the traditional genetic optimization threshold selection method, so as to achieve the purpose of optimizing threshold voltage setting [6].It can accurately determine the level of the input signal or the relationship with the reference signal under different working conditions, and meet the requirements of higher precision in some comparator applications.
As one of the main objectives of optimizing logic comparators, minimizing propagation delay directly affects the overall speed of the system.In general, it is a common approach to manually exploit the parallel comparison architecture by employing multiple levels in a parallel comparator, where each level performs a partial comparison.By distributing the comparison tasks in multiple stages, the parallel comparison mode can significantly reduce the propagation delay of the comparator.However, advances and changes in algorithms can reduce the propagation delay of the comparator in more precise details.In 2006, a greedy algorithm was proposed to minimize the maximum propagation delay for multisource multi-summary line topologies under the RLC delay model [7].This algorithm can effectively reduce the critical bus delay in deep submicron technology, which is a representative of low power technology.At the same time, it minimizes the maximum delay by inserting the signal repeater in the critical path and adjusting its size, which is very effective for reducing the overall propagation delay of the comparator and improving the system speed.
The structure and low-power design of logic comparator, along with the emergence of new technology, also have a great impact on its optimization.Back in 2011, a folding structure was developed for the differential input of a comparator.This structure involved converting the input voltage into a current using transistors, which was then compared to the original static working current to generate the comparator's voltage output [8].The key feature of this circuit was the utilization of the Wilson current mirror to determine the DC operating point.By transforming the low threshold voltage comparison into a current comparison, the need for a DC bias circuit for the common source and common gate device, typical in the input stage of traditional folding voltage comparators, was eliminated.As a result, this design exhibited excellent accuracy and dynamic response characteristics.In 2018, a SFG+DFG all-optical numerical comparator based on PPLN waveguide uses a new logic signal processing technology, which can not only complete the corresponding logic function, but also ensure the transmission quality of the signal, on this basis, the application of PPLN waveguide in all-optical logic signal processing is expanded [9].In 2020, a 10bit successively approximation analog-to-digital converter based on CMOS 90 nm process using time domain comparator converts the voltage signal into time signal by using differential multistage voltage control delay line, and obtains the comparator result by identifying the phase difference through the phase discriminator, reducing the influence of common-mode migration on the comparator and static power consumption [10].At the same time, the circuit adopts a partially monotonic voltage conversion process of capacitor array, which effectively reduces the total capacitance and power consumption of capacitor array.
Adding a preamplifier or gain is also a way to improve the comparator's performance.Adding a pre-amplifier or gain circuit to the input can increase the amplitude of the input signal, thereby improving the response speed of the comparator.As mentioned above, the innovative design of FIA architecture is also aimed at improving the gain of the preamplifier.The pre-amplifier circuit is given a positive feedback signal, and the innovative comparator circuit is designed and built.After simulation, the innovative gain comparator is better than the original circuit design in terms of power consumption, offset and gain, which can be improved by more than 30 times in terms of gain, or 16% in terms of offset performance [10].
In addition, advanced circuit design techniques can improve the comparator's operating speed and reduce power consumption.The digital logic circuit of the memristor has the characteristics of no volatility and small area, and is an important substitute for the transistor logic circuit.The design idea of gate level logic circuit based on memristor ratio logic (MRL) is presented, and the required comparator circuit is realized by gate level logic circuit.Simulation and theoretical analysis validate the proposed design with higher speed and lower power consumption compared to CMOS equivalent circuits [11].
Considering the above methods, the performance of the logical comparator can be optimized according to the specific application requirements, so that it can perform better in different application scenarios.

APPLICATIONS OF COMPARATORS
Logical comparators have widespread applications in various fields.This section highlights three important scenarios where these comparators play a crucial role: analog-to-digital conversion, sensor interfaces and measurement systems, and digital communication and data processing.Real-world examples are provided to illustrate the practical utilization of logical comparators in these areas.

Analog-to-Digital Conversion
In analog-to-digital conversion, logical comparators are employed to convert continuous analog signals into discrete digital representations.For instance, in audio systems, a comparator is utilized to convert the audio waveform into a digital signal that can be processed and stored in digital audio formats.In 2020, logical comparators were used in the design of analog-to-digital converters based on 18nm FinFET technology to overcome the shortcomings associated with CMOS technology, such as channel length, power consumption, delay and transistor area [12].

Sensor Interfaces and Measurement Systems
Logical comparators are also integral to sensor interfaces and measurement systems.For example, in temperature sensors, comparators compare the analog voltage output from the sensor with a reference voltage, generating a logic high or low output based on whether the temperature is above or below a set threshold.In a logic circuit designed in 2016, the single-ended output swing of the comparator is -7.73V at 25℃, -7.63V at 500 ℃, the supply voltage is -15 V and the comparator consumes 585 mW at 25℃.The divider consisting of two latches displays a relatively constant output voltage swing over a wide temperature range.The output voltage swing is 7.62V at 25 °C and 7.32V at 500 °C.It implements a fully integrated master-slave coupled logic (ECL) comparator and can act as a temperature sensor [13].This facilitates precise temperature monitoring and control in various applications.

Digital Communication and Data Processing
In the domain of digital communication and data processing, logical comparators play a key role in error detection and correction.As the low-power two-stage dynamic latch comparator, which is composed of dynamic latch and pre-amplifier stage, is used in mixed-signal system, it works fast and has low power consumption [14].Moreover, in data processing applications, comparators assist in bitwise operations, such as equality checks, leading to efficient data manipulation and decision-making [15].
These examples illustrate the practical significance of logical comparators in different applications.Their ability to compare signals and generate logical outputs enables accurate measurements, reliable data processing, and efficient communication systems.As technology advances, the demand for high-speed and high-accuracy comparators continues to grow, fueling innovation in this field and expanding the range of applications where logical comparators can be effectively employed.

CONCLUSION
In conclusion, logical comparators are an essential part of digital systems, providing the ability to compare input signals and generate logical outputs.This paper provides a comprehensive introduction to logical comparator covering its definition, functions, design considerations, implementation, performance parameters, optimization techniques and application scenarios.As a key component of digital circuit, logical comparator has been widely used in a wide range of fields.Designers and researchers can effectively utilize these circuits to meet the requirements of various digital systems by understanding the principles and applications of logical comparators and the knowledge and insights presented in this paper will help to effectively design and utilize logical comparators to develop efficient and reliable digital systems.
In the future, artificial intelligence, and mechanization industry to accelerate iteration, if the use of machine learning methods instead of manual screening and calculation of different optimization schemes of comparison logical comparator, will greatly reduce the response time and delay of logical comparator, so as to improve the entire logic circuit and digital systems and even electronic products work efficiency.This requires the introduction of the calculation formula and code for its optimization rule from the aspect of algorithm and artificial intelligence, and the mechanical design and production of the chip.

Figure 1 :
Figure 1: Logic circuit of NOR gate (Photo/Picture credit: Original)

Table 1 :
Truth table of NOR gate By analyzing the relationship between the input signals, the logic comparator can determine whether the output signal should be set to a logic high or logic low level.Different combinations of input signals will get their respective output signals, and usually use a truth table such as Table

Table 2 :
Truth table about the NAND gate