Key Insights
The Japan Analog IC Market is poised for robust growth, projected to reach an estimated $6.78 billion in 2025, with a healthy Compound Annual Growth Rate (CAGR) of 4.62% through the forecast period of 2025-2033. This expansion is fueled by the relentless demand for advanced electronic devices across various sectors. Key drivers include the burgeoning automotive industry's need for sophisticated infotainment systems and advanced driver-assistance systems (ADAS), which rely heavily on high-performance analog ICs for signal processing and control. Furthermore, the growing adoption of smart home devices and the increasing complexity of consumer electronics, particularly in audio/video applications and digital cameras, are significantly boosting the demand for general-purpose and application-specific analog integrated circuits. The industrial sector's push towards automation and the Internet of Things (IoT) is also a critical growth stimulant, requiring robust analog solutions for sensing, power management, and communication.
Japan Analog IC Market Market Size (In Billion)
While the market shows strong upward momentum, certain restraints could influence the pace of growth. Intense competition among established players like Infineon Technologies AG, Rohm Semiconductor, and Texas Instruments Incorporated, alongside emerging innovators, necessitates continuous product development and cost optimization. Fluctuations in raw material prices and global supply chain disruptions also present potential challenges. However, the inherent demand for improved performance, miniaturization, and energy efficiency in electronic components, coupled with Japan's strong technological foundation and innovation capabilities, is expected to outweigh these restraints. The market's segmentation reveals a significant role for both general-purpose ICs, such as power management and signal conversion ICs, and application-specific ICs catering to the dynamic consumer, automotive, communication, and computer industries, all contributing to a vibrant and evolving market landscape.
Japan Analog IC Market Company Market Share
Japan Analog IC Market: Comprehensive Analysis and Future Outlook (2019-2033)
This in-depth report delivers a detailed analysis of the Japan Analog Integrated Circuit (IC) market, encompassing its structure, dynamics, growth trends, product landscape, and future outlook. Focusing on key segments like General-purpose ICs and Application-specific ICs, including crucial sub-segments like Power Management ICs, Automotive ICs, and Communication ICs, this report provides actionable insights for stakeholders. With a study period spanning from 2019 to 2033, including historical, base, and forecast periods, the report leverages high-traffic keywords such as "Japan Analog IC Market," "Automotive Analog IC," "Power Management IC Japan," "Semiconductor Market Japan," and "Industrial Analog ICs" to maximize search engine visibility and attract industry professionals. We explore market concentration, technological innovation drivers, regulatory frameworks, competitive product substitutes, end-user demographics, and M&A trends, offering quantitative insights and qualitative factors. Furthermore, the report dissects dominant regions, countries, or segments, highlights product innovations, and identifies key drivers, barriers, challenges, and emerging opportunities. A comprehensive overview of key players and notable milestones, including recent industry developments from Spinnaker Systems Inc. & Xiphera Ltd. and Tower Semiconductor & Cadence Design Systems Inc., provides a complete picture of the market's evolution.
Japan Analog IC Market Market Dynamics & Structure
The Japan Analog IC market is characterized by a moderate to high market concentration, with a few dominant global players and several specialized domestic manufacturers vying for market share. Technological innovation is a primary driver, fueled by Japan's strong legacy in advanced electronics manufacturing and its commitment to research and development, particularly in areas like automotive and industrial automation. Stringent regulatory frameworks, while ensuring quality and safety, can also present barriers to entry for new technologies. Competitive product substitutes exist, primarily from integrated solutions or digital alternatives, but the inherent advantages of analog circuits in signal processing, power management, and interfacing ensure their continued demand. End-user demographics are shifting, with a growing demand from the automotive sector for advanced driver-assistance systems (ADAS) and electric vehicle (EV) components, and from the industrial sector for automation and IoT applications. Mergers and acquisition (M&A) trends are observed as companies seek to consolidate portfolios, expand technological capabilities, and gain market access.
- Market Concentration: Dominated by global leaders and key domestic players.
- Technological Innovation: Driven by R&D in automotive, industrial, and communication sectors.
- Regulatory Frameworks: Adherence to strict quality and safety standards.
- Competitive Landscape: Analog ICs maintain edge over digital alternatives in specific applications.
- End-User Demand: Strong growth in Automotive, Industrial, and Communication segments.
- M&A Activities: Strategic acquisitions to enhance product offerings and market reach.
Japan Analog IC Market Growth Trends & Insights
The Japan Analog IC market is poised for significant market size evolution, driven by Japan's robust industrial base and its leadership in advanced technologies. The adoption rates for sophisticated analog solutions are accelerating, particularly in sectors embracing digital transformation and automation. Technological disruptions, such as advancements in AI, IoT, and 5G, are creating new demands for high-performance analog components, including power management ICs, signal converters, and interface ICs. Shifts in consumer behavior, emphasizing smarter devices, connected homes, and personalized experiences, indirectly fuel the demand for underlying analog technologies that enable these functionalities. The market's trajectory is further shaped by government initiatives promoting technological advancement and manufacturing competitiveness. From a historical perspective, the market has demonstrated resilience and consistent growth, a trend expected to continue.
The market penetration of advanced analog ICs is steadily increasing across various applications. For instance, in the automotive sector, the transition towards autonomous driving and electrified powertrains necessitates a greater number of complex analog ICs for sensor fusion, battery management, and motor control. The industrial segment, driven by Industry 4.0 initiatives, requires high-precision analog components for automation, robotics, and sophisticated monitoring systems. The communication sector, with the ongoing rollout of 5G and the expansion of wireless communication technologies, is a consistent demand generator for analog ICs like RF components and signal conditioners.
Furthermore, the trend towards miniaturization and increased power efficiency in electronic devices is a critical factor influencing growth. Analog IC manufacturers are continuously innovating to deliver smaller form-factor solutions with lower power consumption, catering to the evolving needs of portable electronics and battery-operated devices. The integration of analog and digital functionalities within System-on-Chip (SoC) designs also presents opportunities, requiring advanced analog blocks to interface with digital cores.
The compound annual growth rate (CAGR) for the Japan Analog IC market is projected to be robust, reflecting sustained demand across key end-use industries. This growth is underpinned by the country's commitment to innovation and its position as a global hub for high-technology manufacturing. The increasing complexity of electronic systems demands specialized analog solutions, ensuring a sustained need for high-performance and reliable components. The report estimates the market to reach XX billion units by 2033, indicating a substantial expansion from its current size. The base year of 2025 is estimated to reach XX billion units.
Dominant Regions, Countries, or Segments in Japan Analog IC Market
Within the Japan Analog IC market, the Application-specific IC (ASIC) segment, particularly those designed for the Automotive and Industrial and Others applications, are the primary growth engines. The automotive sector's rapid adoption of advanced driver-assistance systems (ADAS), electric vehicles (EVs), and next-generation infotainment systems is a significant catalyst. This surge demands specialized analog ICs for sensor signal conditioning, power management, motor control, and robust connectivity. The Japanese automotive industry's global leadership and its focus on safety and efficiency directly translate to a higher demand for high-performance analog solutions.
The Industrial and Others segment, encompassing automation, robotics, IoT devices, and advanced manufacturing equipment, also plays a crucial role in market dominance. Japan's strong industrial manufacturing base, coupled with its commitment to Industry 4.0 principles, fuels the demand for precision analog ICs that enable sophisticated control systems, data acquisition, and machine-to-machine communication. This includes a wide array of applications such as industrial power supplies, programmable logic controllers (PLCs), and smart sensors.
The Communication segment, with its sub-segments like Cellphone and Infrastructure, continues to be a substantial contributor, driven by the ongoing rollout of 5G networks and the proliferation of connected devices. However, the pace of innovation and upgrade cycles in communication might be more dynamic compared to the sustained, foundational demand from automotive and industrial sectors.
Within General-purpose ICs, Power Management ICs are consistently in high demand across all application segments due to the increasing need for energy efficiency and battery longevity in electronic devices. Interface ICs also remain critical for seamless data transfer and communication between different components and systems.
- Automotive Segment: Dominant due to the demand for ADAS, EVs, and advanced infotainment.
- Market Share: Estimated to hold the largest share, projected at XX% in 2025.
- Growth Potential: High, driven by technological advancements in autonomous driving and electrification.
- Key Drivers: Government incentives for EVs, increasing safety regulations, and consumer demand for advanced features.
- Industrial and Others Segment: Significant growth driven by Industry 4.0 and IoT adoption.
- Market Share: Expected to be the second-largest segment, with XX% in 2025.
- Growth Potential: Strong, fueled by automation, smart manufacturing, and smart city initiatives.
- Key Drivers: Need for precision control, data acquisition, and efficient energy management in industrial settings.
- Communication Segment: Consistent demand from 5G deployment and wireless technologies.
- Market Share: Substantial contribution, projected at XX% in 2025.
- Growth Potential: Steady, influenced by network upgrades and the expansion of IoT.
- Key Drivers: High-speed data transmission requirements and the growth of connected devices.
- General-purpose ICs (Power Management ICs): Ubiquitous demand across all sectors for energy efficiency.
- Market Share: Critical enabler across segments, estimated at XX% of general-purpose ICs.
- Growth Potential: Evergreen, driven by power-sensitive applications.
- Key Drivers: Demand for longer battery life, reduced energy consumption, and efficient power delivery.
Japan Analog IC Market Product Landscape
The Japan Analog IC market is characterized by continuous product innovation focused on enhanced performance, miniaturization, and power efficiency. Key product developments include highly integrated Power Management ICs (PMICs) for mobile devices and automotive systems, advanced Signal Conversion ICs for high-speed data acquisition and processing, and sophisticated Interface ICs enabling seamless communication in complex systems. Amplifiers/Comparators are being refined for higher precision and lower noise in sensitive applications like medical devices and test equipment. The ASIC segment sees a surge in application-specific solutions for Infotainment in automotive, short-range wireless communication, and specialized Industrial control systems. Unique selling propositions revolve around superior analog performance, reliability in harsh environments, and tailored functionalities for niche applications. Technological advancements are pushing the boundaries of semiconductor technology to achieve higher bandwidth, lower latency, and improved signal integrity.
Key Drivers, Barriers & Challenges in Japan Analog IC Market
Key Drivers:
The Japan Analog IC market is propelled by several key drivers. The relentless pursuit of technological advancement in sectors like automotive, industrial automation, and telecommunications is a primary force. Government initiatives supporting digital transformation and Industry 4.0 adoption further fuel demand. The increasing complexity and interconnectedness of electronic devices necessitate sophisticated analog components for power management, signal conditioning, and interfacing. High R&D investment by Japanese semiconductor companies ensures a steady stream of innovative products.
Barriers & Challenges:
Despite strong drivers, the market faces several challenges. Supply chain disruptions, particularly in raw materials and specialized manufacturing processes, can impact production and lead times, as seen in recent global semiconductor shortages. Intense global competition from established players and emerging manufacturers presents a constant pressure on pricing and market share. High development costs for cutting-edge analog technologies and the long design cycles for some applications can act as barriers. Additionally, the increasing complexity of global trade regulations and geopolitical factors can introduce uncertainties. Ensuring consistent quality and reliability in the face of rapidly evolving technological demands remains a critical challenge.
Emerging Opportunities in Japan Analog IC Market
Emerging opportunities in the Japan Analog IC market lie in the burgeoning Internet of Things (IoT) ecosystem, requiring specialized analog ICs for sensor integration, low-power communication, and efficient power management in a vast array of connected devices. The advancement of artificial intelligence (AI) and machine learning is creating demand for analog front-ends and specialized processing units for edge AI applications. The continued growth of the electric vehicle (EV) market presents significant opportunities for advanced battery management systems, motor control ICs, and charging infrastructure components. Furthermore, the increasing focus on sustainability and energy efficiency across industries is driving demand for highly optimized power management solutions.
Growth Accelerators in the Japan Analog IC Market Industry
Long-term growth in the Japan Analog IC market will be significantly accelerated by breakthroughs in analog design methodologies and materials science, enabling higher performance and novel functionalities. Strategic partnerships between semiconductor manufacturers, system integrators, and end-users are crucial for co-developing solutions tailored to specific market needs. Government support and incentives for research, development, and domestic manufacturing of advanced semiconductors will further bolster the industry. The expansion of 5G and future communication technologies will continue to be a key growth driver, creating demand for high-frequency analog components. Moreover, the increasing adoption of advanced automation and robotics in various industries will sustain the demand for precise and reliable analog control systems.
Key Players Shaping the Japan Analog IC Market Market
- Infineon Technologies AG
- Rohm Semiconductor
- Microchip Technology Inc
- NXP Semiconductors NV
- Analog Devices KK (Analog Devices Inc )
- Mitsubishi Electric Corporation
- Skyworks Solutions Inc
- STMicroelectronics
- Renesas Electronics Corporation
- Texas Instruments Incorporated
Notable Milestones in Japan Analog IC Market Sector
- February 2023: Spinnaker Systems Inc. and Xiphera Ltd. collaborated to develop and deploy hardware-based security for ASICs and FPGAs, establishing a co-marketing, sales, product delivery, and customer support program for the Japanese semiconductor sector. This partnership enables the offering of Xiphera's comprehensive cryptographic IP cores.
- July 2022: Tower Semiconductor and Cadence Design Systems Inc. partnered to accelerate automotive and mobile IC development, aiming to provide customers with a faster design cycle and comprehensive design verification for advanced automotive IC product development.
In-Depth Japan Analog IC Market Market Outlook
The future market potential for the Japan Analog IC market is exceptionally strong, driven by sustained innovation and the increasing integration of analog components across diverse technologies. The report forecasts continued robust growth, with an estimated market size of XX billion units by 2033. Strategic opportunities lie in capitalizing on the demand from the rapidly evolving automotive sector, particularly for EVs and autonomous driving technologies. The industrial automation and IoT segments also present a vast and growing landscape for analog solutions. Advancements in post-quantum cryptography, as demonstrated by the Spinnaker Systems and Xiphera collaboration, highlight the forward-looking nature of the market and its commitment to future-proofing technologies. The ongoing synergy between analog and digital domains will continue to drive the development of integrated solutions, further solidifying the indispensable role of analog ICs in the technological advancements of Japan and the global market.
Japan Analog IC Market Segmentation
-
1. Type
-
1.1. General-purpose IC
- 1.1.1. Interface
- 1.1.2. Power Management
- 1.1.3. Signal Conversion
- 1.1.4. Amplifiers/Comparators (Signal Conditioning)
-
1.2. Application-specific IC
-
1.2.1. Consumer
- 1.2.1.1. Audio/Video
- 1.2.1.2. Digital Still Camera and Camcorder
- 1.2.1.3. Other Consumers
-
1.2.2. Automotive
- 1.2.2.1. Infotainment
- 1.2.2.2. Other Infotainment
-
1.2.3. Communication
- 1.2.3.1. Cellphone
- 1.2.3.2. Infrastructure
- 1.2.3.3. Wired Communication
- 1.2.3.4. Short Range
- 1.2.3.5. Other Wireless
-
1.2.4. Computer
- 1.2.4.1. Computer System and Display
- 1.2.4.2. Computer Periphery
- 1.2.4.3. Storage
- 1.2.4.4. Other Computers
- 1.2.5. Industrial and Others
-
1.2.1. Consumer
-
1.1. General-purpose IC
Japan Analog IC Market Segmentation By Geography
- 1. Japan
Japan Analog IC Market Regional Market Share
Geographic Coverage of Japan Analog IC Market
Japan Analog IC Market REPORT HIGHLIGHTS
| Aspects | Details |
|---|---|
| Study Period | 2020-2034 |
| Base Year | 2025 |
| Estimated Year | 2026 |
| Forecast Period | 2026-2034 |
| Historical Period | 2020-2025 |
| Growth Rate | CAGR of 4.62% from 2020-2034 |
| Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Methodology
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Introduction
- 3. Market Dynamics
- 3.1. Introduction
- 3.2. Market Drivers
- 3.2.1 Rising Penetration of Smartphones
- 3.2.2 Feature Phones
- 3.2.3 and Tablets
- 3.3. Market Restrains
- 3.3.1. Increasing Design Complexity of Analog IC; Requirement of Skilled Workforce
- 3.4. Market Trends
- 3.4.1. General Purpose IC (Power Management) Sub-segment is Expected to Hold a Considerable Share
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.2. Supply/Value Chain
- 4.3. PESTEL analysis
- 4.4. Market Entropy
- 4.5. Patent/Trademark Analysis
- 5. Japan Analog IC Market Analysis, Insights and Forecast, 2020-2032
- 5.1. Market Analysis, Insights and Forecast - by Type
- 5.1.1. General-purpose IC
- 5.1.1.1. Interface
- 5.1.1.2. Power Management
- 5.1.1.3. Signal Conversion
- 5.1.1.4. Amplifiers/Comparators (Signal Conditioning)
- 5.1.2. Application-specific IC
- 5.1.2.1. Consumer
- 5.1.2.1.1. Audio/Video
- 5.1.2.1.2. Digital Still Camera and Camcorder
- 5.1.2.1.3. Other Consumers
- 5.1.2.2. Automotive
- 5.1.2.2.1. Infotainment
- 5.1.2.2.2. Other Infotainment
- 5.1.2.3. Communication
- 5.1.2.3.1. Cellphone
- 5.1.2.3.2. Infrastructure
- 5.1.2.3.3. Wired Communication
- 5.1.2.3.4. Short Range
- 5.1.2.3.5. Other Wireless
- 5.1.2.4. Computer
- 5.1.2.4.1. Computer System and Display
- 5.1.2.4.2. Computer Periphery
- 5.1.2.4.3. Storage
- 5.1.2.4.4. Other Computers
- 5.1.2.5. Industrial and Others
- 5.1.2.1. Consumer
- 5.1.1. General-purpose IC
- 5.2. Market Analysis, Insights and Forecast - by Region
- 5.2.1. Japan
- 5.1. Market Analysis, Insights and Forecast - by Type
- 6. Competitive Analysis
- 6.1. Market Share Analysis 2025
- 6.2. Company Profiles
- 6.2.1 Infineon Technologies AG
- 6.2.1.1. Overview
- 6.2.1.2. Products
- 6.2.1.3. SWOT Analysis
- 6.2.1.4. Recent Developments
- 6.2.1.5. Financials (Based on Availability)
- 6.2.2 Rohm Semiconductor
- 6.2.2.1. Overview
- 6.2.2.2. Products
- 6.2.2.3. SWOT Analysis
- 6.2.2.4. Recent Developments
- 6.2.2.5. Financials (Based on Availability)
- 6.2.3 Microchip Technology Inc
- 6.2.3.1. Overview
- 6.2.3.2. Products
- 6.2.3.3. SWOT Analysis
- 6.2.3.4. Recent Developments
- 6.2.3.5. Financials (Based on Availability)
- 6.2.4 NXP Semiconductors NV
- 6.2.4.1. Overview
- 6.2.4.2. Products
- 6.2.4.3. SWOT Analysis
- 6.2.4.4. Recent Developments
- 6.2.4.5. Financials (Based on Availability)
- 6.2.5 Analog Devices KK (Analog Devices Inc )
- 6.2.5.1. Overview
- 6.2.5.2. Products
- 6.2.5.3. SWOT Analysis
- 6.2.5.4. Recent Developments
- 6.2.5.5. Financials (Based on Availability)
- 6.2.6 Mitsubishi Electric Corporation
- 6.2.6.1. Overview
- 6.2.6.2. Products
- 6.2.6.3. SWOT Analysis
- 6.2.6.4. Recent Developments
- 6.2.6.5. Financials (Based on Availability)
- 6.2.7 Skyworks Solutions Inc
- 6.2.7.1. Overview
- 6.2.7.2. Products
- 6.2.7.3. SWOT Analysis
- 6.2.7.4. Recent Developments
- 6.2.7.5. Financials (Based on Availability)
- 6.2.8 STMicroelectronics
- 6.2.8.1. Overview
- 6.2.8.2. Products
- 6.2.8.3. SWOT Analysis
- 6.2.8.4. Recent Developments
- 6.2.8.5. Financials (Based on Availability)
- 6.2.9 Renesas Electronics Corporation
- 6.2.9.1. Overview
- 6.2.9.2. Products
- 6.2.9.3. SWOT Analysis
- 6.2.9.4. Recent Developments
- 6.2.9.5. Financials (Based on Availability)
- 6.2.10 Texas Instruments Incorporated
- 6.2.10.1. Overview
- 6.2.10.2. Products
- 6.2.10.3. SWOT Analysis
- 6.2.10.4. Recent Developments
- 6.2.10.5. Financials (Based on Availability)
- 6.2.1 Infineon Technologies AG
List of Figures
- Figure 1: Japan Analog IC Market Revenue Breakdown (billion, %) by Product 2025 & 2033
- Figure 2: Japan Analog IC Market Share (%) by Company 2025
List of Tables
- Table 1: Japan Analog IC Market Revenue billion Forecast, by Type 2020 & 2033
- Table 2: Japan Analog IC Market Revenue billion Forecast, by Region 2020 & 2033
- Table 3: Japan Analog IC Market Revenue billion Forecast, by Type 2020 & 2033
- Table 4: Japan Analog IC Market Revenue billion Forecast, by Country 2020 & 2033
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the Japan Analog IC Market?
The projected CAGR is approximately 4.62%.
2. Which companies are prominent players in the Japan Analog IC Market?
Key companies in the market include Infineon Technologies AG, Rohm Semiconductor, Microchip Technology Inc, NXP Semiconductors NV, Analog Devices KK (Analog Devices Inc ), Mitsubishi Electric Corporation, Skyworks Solutions Inc, STMicroelectronics, Renesas Electronics Corporation, Texas Instruments Incorporated.
3. What are the main segments of the Japan Analog IC Market?
The market segments include Type.
4. Can you provide details about the market size?
The market size is estimated to be USD 6.78 billion as of 2022.
5. What are some drivers contributing to market growth?
Rising Penetration of Smartphones. Feature Phones. and Tablets.
6. What are the notable trends driving market growth?
General Purpose IC (Power Management) Sub-segment is Expected to Hold a Considerable Share.
7. Are there any restraints impacting market growth?
Increasing Design Complexity of Analog IC; Requirement of Skilled Workforce.
8. Can you provide examples of recent developments in the market?
February 2023 - Spinnaker Systems Inc., a Japanese supplier and distributor of semiconductor intellectual property (SIP) and EDA tools, and Xiphera Ltd developed and deployed hardware-based security for ASICs and FPGAs and have begun working together. As a result of the cooperation, a co-marketing, sales, product delivery, and customer support program is now available for the Japanese semiconductor sector. Through their partnership, Xiphera and Spinnaker are able to offer the full range of cryptographic IP cores from Xiphera for ASIC and FPGA circuits, including hash algorithms, symmetric and asymmetric ciphers, a True Random Number Generator, full protocol implementations for TLS and MACsec, and the recently launched xQlave product family of post-quantum cryptographic algorithms for defense against attacks from quantum computers.
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 3800, USD 4500, and USD 5800 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in billion.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "Japan Analog IC Market," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the Japan Analog IC Market report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
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Methodology
Step 1 - Identification of Relevant Samples Size from Population Database
Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)
Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations
Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence