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1530671

射頻 (RF) 功率半導體的全球市場預測（截至 2030 年）：按組件、材料、功率範圍、應用和地區進行分析

Radio Frequency (RF) Power Semiconductor Market Forecasts to 2030 - Global Analysis By Component (Power Amplifiers, Passives, Switches, Transistors, Diodes, Duplexers and Other Components), Material, Power Range, Application and By Geography
出版日期: | 出版商: Stratistics Market Research Consulting | 英文 200+ Pages | 商品交期: 2-3個工作天內

價格

2024年全球射頻（RF）功率半導體市場規模為195.7億美元，預計在預測期內將以10.5%的複合年成長率成長，到2030年達到302.1億美元。

射頻 (RF) 功率半導體是專門設計用於有效放大和傳輸高頻訊號的元件。這些半導體針對高功率運行進行了最佳化，頻率通常為數百兆赫茲到數吉赫。射頻功率半導體透過提供必要的放大和傳輸功能來最大限度地減少損耗和干擾並確保遠距可靠的訊號傳播，在現代無線通訊系統中發揮至關重要的作用。

愛立信預計，2018 年第一季智慧型手機訂閱量將達到 15.75 億美元，位居亞太地區（不包括中國和印度）之首。這種滲透率正在推動射頻設備製造商開發高效能射頻濾波器，以滿足智慧型手機和平板電腦OEM的需求。

無線通訊需求不斷成長

射頻功率半導體對於提高資料傳輸速度、擴大網路覆蓋範圍和支援新通訊標準至關重要。這種需求正在推動氮化鎵 (GaN) 和碳化矽 (SiC) 等半導體技術的創新，以提高效率和功率處理能力。隨著通訊的不斷發展，射頻功率半導體在滿足現代無線網路的性能需求並推動市場成長方面發揮關鍵作用。

技術挑戰和可靠性問題

射頻功率半導體面臨的技術挑戰包括溫度控管、在各種條件下保持效率以及確保長期可靠性。這些因素導致新產品的開發成本更高，上市時間更長。可靠性問題，例如由於壓力或劣化而導致的設備故障，會削弱客戶的信心並增加維護成本。因此，這些挑戰可能會阻止潛在的採用者，並減緩射頻功率半導體技術的市場需求和創新。

加強鼓勵採用可再生能源解決方案的政策

隨著太陽能和風能等再生能源來源需要先進的射頻功率半導體用於逆變器和電網整合，需求將激增。這些半導體可實現更高的功率轉換效率和可靠性，對於有效利用可再生能源至關重要。監管支持促進半導體技術創新，提高性能並降低成本。因此，促進可再生能源採用的政策透過催化該領域的需求和技術進步，直接推動射頻功率半導體市場的成長。

初始投資和開發成本高

射頻功率半導體的初始投資和開發成本較高，這是由於複雜的製造流程、GaN和SiC等專用材料以及嚴格的品質標準所造成的。這些成本阻礙了新進入者和小型企業進入市場，限制了競爭和創新。因此，價格居高不下，阻礙了廣泛的市場需求，因為與傳統的半導體解決方案相比，通訊和汽車行業等潛在用戶可能會發現初始投資過高。

COVID-19 的影響

COVID-19 大流行擾亂了供應鏈、推遲了計劃並影響了通訊和汽車等行業的需求，從而對射頻 (RF) 功率半導體市場產生了重大影響。儘管最初遇到了挫折，但由於向通訊技術的轉變以及醫療設備中對射頻功率元件的需求增加，市場已表現出彈性。復甦工作的重點是適應新常態並加速各產業的數位轉型。

高功率細分市場預計將在預測期內成為最大的細分市場

高功率領域預計將出現良好的成長。高功率範圍射頻功率半導體元件是通訊和雷達系統中的關鍵組件，通常在 1 GHz 以上的頻率下運作。這些半導體可實現高效的功率放大，這對於遠距傳輸和接收高頻訊號至關重要。這些半導體旨在以最小的損耗和產生的熱量處理高功率水平，這使得它們在需要可靠、高性能射頻功率處理能力的應用中至關重要。

預計家用電器領域在預測期內複合年成長率最高

預計家用電器領域在預測期內將出現最高的複合年成長率。射頻功率半導體是消費性電子產品中的重要元件，可實現射頻訊號的高效傳輸和接收。它應用於智慧型手機、Wi-Fi路由器、智慧型家電等設備中，實現高可靠的無線通訊。這些半導體旨在以最小的損耗處理高頻訊號，從而提高日常消費性電子應用中無線設備的性能和範圍。

佔比最大的地區：

由於通訊基礎設施的擴張和無線技術的日益採用，預計亞太地區在預測期內將佔據最大的市場佔有率。中國、日本和韓國等主要國家在行動通訊、雷達系統和工業應用中對射頻功率放大器和電晶體的強勁需求引領市場。該地區受益於強大的製造基礎和先進的技術，促進了主要企業之間的競爭動態。這一成長機會得到了對 5G 網路和物聯網連接的持續投資的支持，為亞太地區的射頻功率半導體製造商創造了更多機會。

複合年成長率最高的地區：

由於通訊、家用電器和汽車行業的需求增加，預計北美在預測期內將經歷最高的複合年成長率。主要企業專注於技術進步，以提高射頻功率半導體的效率和性能。該市場的特點是競爭格局激烈，主要企業投資於創新解決方案的研發。對無線通訊技術的監管支援也有助於市場擴張。總體而言，隨著技術格局和產業需求的不斷發展，北美射頻功率半導體市場展現了未來性。

提供免費客製化：

訂閱此報告的客戶可以存取以下免費自訂選項之一：

  • 公司簡介
    • 其他市場公司的綜合分析（最多 3 家公司）
    • 主要企業SWOT分析（最多3家企業）
  • 區域分割
    • 根據客戶興趣對主要國家的市場估計、預測和複合年成長率（註：基於可行性檢查）
  • 競爭基準化分析
    • 根據產品系列、地理分佈和策略聯盟對主要企業基準化分析

目錄

第1章執行摘要

第2章 前言

  • 概述
  • 相關利益者
  • 調查範圍
  • 調查方法
    • 資料探勘
    • 資料分析
    • 資料檢驗
    • 研究途徑
  • 研究資訊來源
    • 主要研究資訊來源
    • 二次研究資訊來源
    • 先決條件

第3章市場趨勢分析

  • 促進因素
  • 抑制因素
  • 機會
  • 威脅
  • 應用分析
  • 新興市場
  • COVID-19 的影響

第4章波特五力分析

  • 供應商的議價能力
  • 買方議價能力
  • 替代品的威脅
  • 新進入者的威脅
  • 競爭公司之間的敵對關係

第5章全球射頻 (RF) 功率半導體市場：依組成部分

  • 功率放大器
  • 被動的
  • 轉變
  • 電晶體
  • 二極體
  • 雙工器
  • 其他部分

第6章全球射頻 (RF) 功率半導體市場：依材料分類

  • 氮化鎵（GaN）
  • 砷化鎵 (GaAs)
  • 矽（Si）
  • 矽鍺 (SiGe)
  • 其他材料

第7章全球射頻 (RF) 功率半導體市場：依功率範圍

  • 低功率
  • 中型功率
  • 高功率

第8章全球射頻 (RF) 功率半導體市場：依應用分類

  • 家電
  • 通訊
  • 航太/國防
  • 車
  • 醫療設備
  • 工業/科學
  • 其他用途

第 9 章全球射頻 (RF) 功率半導體市場：按地區

  • 北美洲
    • 美國
    • 加拿大
    • 墨西哥
  • 歐洲
    • 德國
    • 英國
    • 義大利
    • 法國
    • 西班牙
    • 其他歐洲國家
  • 亞太地區
    • 日本
    • 中國
    • 印度
    • 澳洲
    • 紐西蘭
    • 韓國
    • 其他亞太地區
  • 南美洲
    • 阿根廷
    • 巴西
    • 智利
    • 南美洲其他地區
  • 中東/非洲
    • 沙烏地阿拉伯
    • 阿拉伯聯合大公國
    • 卡達
    • 南非
    • 其他中東/非洲

第10章 主要進展

  • 合約、夥伴關係、協作和合資企業
  • 收購和合併
  • 新產品發布
  • 業務拓展
  • 其他關鍵策略

第11章 公司概況

  • Mitsubishi Electric Corporation
  • Texas Instruments
  • Infineon Technologies
  • NXP Semiconductors
  • Skyworks Solutions
  • MACOM Technology Solutions
  • STMicroelectronics
  • RFHIC Corporation
  • Renesas Electronics Corporation
  • II-VI Incorporated
  • Maxim Integrated
  • Efficient Power Conversion Corporation
  • Cree Inc.
  • Qorvo
  • Broadcom Inc.
  • Ampleon
Product Code: SMRC26783

According to Stratistics MRC, the Global Radio Frequency (RF) Power Semiconductor Market is accounted for $19.57 billion in 2024 and is expected to reach $30.21 billion by 2030 growing at a CAGR of 10.5% during the forecast period. Radio Frequency (RF) Power Semiconductor devices are specialized components designed to amplify and transmit high-frequency signals efficiently. These semiconductors are optimized for high-power operation at frequencies typically ranging from hundreds of megahertz to several gigahertz. RF power semiconductors play a crucial role in modern wireless communication systems by providing the necessary amplification and transmission capabilities to ensure reliable signal propagation over long distances with minimal loss and interference.

According to Ericsson, the estimated number of smartphone subscription is maximum in Asia-Pacific (excluding China and India) with USD 1575 million in Q1 2018. This adoption rate will drive RF device manufacturers to develop high-performance RF filters that can cater to the needs of smartphone and tablet OEMs.

Market Dynamics:

Driver:

Growing demand for wireless communication

RF power semiconductors are essential in enabling higher data transfer rates, extending network coverage, and supporting new communication standards. This demand fuels innovation in semiconductor technologies like gallium nitride (GaN) and silicon carbide (SiC), which offer enhanced efficiency and power handling capabilities. As telecommunications continue to evolve, RF power semiconductors play a crucial role in meeting the performance demands of modern wireless networks, driving market growth.

Restraint:

Technological challenges and reliability concerns

Technological challenges in RF Power Semiconductors include heat management, maintaining efficiency across varying conditions, and ensuring long-term reliability. These factors can lead to higher development costs and longer time-to-market for new products. Reliability concerns, such as device failure under stress or aging, undermine customer confidence and increase maintenance costs. As a result, these challenges can deter potential adopters, slowing market demand and innovation in RF Power Semiconductor technologies.

Opportunity:

Mounting policies promoting the adoption of renewable energy solutions

As renewable energy sources like solar and wind require advanced RF power semiconductors for inverters and grid integration, demand surges. These semiconductors enable higher efficiency and reliability in power conversion, crucial for harnessing renewable energy effectively. Regulatory support encourages innovation in semiconductor technology, enhancing performance and lowering costs. Thus, policies fostering renewable energy adoption directly propel the growth of RF Power Semiconductor markets by catalyzing demand and technological advancements in the sector.

Threat:

High initial investment and development costs

High initial investment and development costs in RF power semiconductor arise due to complex manufacturing processes, specialized materials like GaN and SiC, and stringent quality standards. These costs deter new entrants and smaller firms from entering the market, limiting competition and innovation. Consequently, prices remain high, hampering broader market demand as potential users, such as telecommunications and automotive sectors, may find the initial investment prohibitive compared to conventional semiconductor solutions.

Covid-19 Impact

The covid-19 pandemic significantly affected the radio frequency (RF) power semiconductor market by disrupting supply chains, delaying projects, and impacting demand across industries like telecommunications and automotive. Despite initial setbacks, the market showed resilience with a shift towards remote communication technologies and increased demand for RF power components in healthcare devices. Recovery efforts focused on adapting to new norms and accelerating digital transformation in various sectors.

The high power segment is expected to be the largest during the forecast period

The high power segment is estimated to have a lucrative growth. High power range radio frequency power semiconductor devices are critical components in telecommunications and radar systems, operating at frequencies typically above 1 GHz. These semiconductors enable efficient power amplification, essential for transmitting and receiving high-frequency signals over long distances. They are designed to handle high power levels with minimal loss and heat generation, making them indispensable in applications demanding reliable and high-performance RF power handling capabilities.

The consumer electronics segment is expected to have the highest CAGR during the forecast period

The consumer electronics segment is anticipated to witness the highest CAGR growth during the forecast period. RF power semiconductors are crucial components in consumer electronics, enabling efficient transmission and reception of radio frequency signals. They are used in devices like smart phones, Wi-Fi routers, and smart home appliances to ensure reliable wireless communication. These semiconductors are designed to handle high-frequency signals with minimal loss, enhancing the performance and range of wireless devices in everyday consumer applications.

Region with largest share:

Asia Pacific is projected to hold the largest market share during the forecast period due to expanding telecommunications infrastructure and increasing adoption of wireless technologies. Key countries like China, Japan, and South Korea are leading the market with robust demand for RF power amplifiers and transistors in mobile communications, radar systems, and industrial applications. The region benefits from a strong manufacturing base and technological advancements, fostering competitive dynamics among key players. This growth is supported by ongoing investments in 5G networks and IoT connectivity, driving further opportunities for RF power semiconductor manufacturers in Asia-Pacific.

Region with highest CAGR:

North America is projected to have the highest CAGR over the forecast period, owing to increasing demand across telecommunications, consumer electronics, and automotive sectors. Key players are focusing on technological advancements to enhance efficiency and performance of RF power semiconductors. The market is characterized by a competitive landscape with prominent companies investing in research and development for innovative solutions. Regulatory support for wireless communication technologies also contributes to market expansion. Overall, the North American RF Power Semiconductor market shows promise amidst evolving technological landscapes and industry demands.

Key players in the market

Some of the key players profiled in the Radio Frequency (RF) Power Semiconductor Market include Mitsubishi Electric Corporation, Texas Instruments, Infineon Technologies, NXP Semiconductors, Skyworks Solutions, MACOM Technology Solutions, STMicroelectronics, RFHIC Corporation, Renesas Electronics Corporation, II-VI Incorporated, Maxim Integrated, Efficient Power Conversion Corporation, Cree Inc., Qorvo, Broadcom Inc. and Ampleon.

Key Developments:

In February 2024, Mitsubishi Electric Corporation announced that it will begin shipping samples of its new 6.5W silicon radio-frequency (RF) high-power metal-oxide semiconductor field-effect transistor (MOSFET) for use in RF high-power amplifiers of commercial handheld two-way radios. The model, which achieves an industry-leading 6.5W output power from a 3.6V single-cell lithium-ion battery, is expected to extend the range and reduce the power consumption of commercial radio equipment.

In June 2023, NXP Semiconductors N.V. of Eindhoven, The Netherlands has launched a family of top-side-cooled RF amplifier modules, based on a packaging innovation designed to enable thinner and lighter radios for 5G infrastructure. These smaller base stations can be more easily and cost-effectively installed, and blend more discretely into their environment.

Components Covered:

  • Power Amplifiers
  • Passives
  • Switches
  • Transistors
  • Diodes
  • Duplexers
  • Other Components

Materials Covered:

  • Gallium Nitride (GaN)
  • Gallium Arsenide (GaAs)
  • Silicon (Si)
  • Silicon Germanium (SiGe)
  • Other Materials

Power Ranges Covered:

  • Low Power
  • Medium Power
  • High Power

Applications Covered:

  • Consumer Electronics
  • Telecommunications
  • Aerospace & Defense
  • Automotive
  • Medical Equipment
  • Industrial & Scientific
  • Other Applications

Regions Covered:

  • North America
    • US
    • Canada
    • Mexico
  • Europe
    • Germany
    • UK
    • Italy
    • France
    • Spain
    • Rest of Europe
  • Asia Pacific
    • Japan
    • China
    • India
    • Australia
    • New Zealand
    • South Korea
    • Rest of Asia Pacific
  • South America
    • Argentina
    • Brazil
    • Chile
    • Rest of South America
  • Middle East & Africa
    • Saudi Arabia
    • UAE
    • Qatar
    • South Africa
    • Rest of Middle East & Africa

What our report offers:

  • Market share assessments for the regional and country-level segments
  • Strategic recommendations for the new entrants
  • Covers Market data for the years 2022, 2023, 2024, 2026, and 2030
  • Market Trends (Drivers, Constraints, Opportunities, Threats, Challenges, Investment Opportunities, and recommendations)
  • Strategic recommendations in key business segments based on the market estimations
  • Competitive landscaping mapping the key common trends
  • Company profiling with detailed strategies, financials, and recent developments
  • Supply chain trends mapping the latest technological advancements

Free Customization Offerings:

All the customers of this report will be entitled to receive one of the following free customization options:

  • Company Profiling
    • Comprehensive profiling of additional market players (up to 3)
    • SWOT Analysis of key players (up to 3)
  • Regional Segmentation
    • Market estimations, Forecasts and CAGR of any prominent country as per the client's interest (Note: Depends on feasibility check)
  • Competitive Benchmarking
    • Benchmarking of key players based on product portfolio, geographical presence, and strategic alliances

Table of Contents

1 Executive Summary

2 Preface

  • 2.1 Abstract
  • 2.2 Stake Holders
  • 2.3 Research Scope
  • 2.4 Research Methodology
    • 2.4.1 Data Mining
    • 2.4.2 Data Analysis
    • 2.4.3 Data Validation
    • 2.4.4 Research Approach
  • 2.5 Research Sources
    • 2.5.1 Primary Research Sources
    • 2.5.2 Secondary Research Sources
    • 2.5.3 Assumptions

3 Market Trend Analysis

  • 3.1 Introduction
  • 3.2 Drivers
  • 3.3 Restraints
  • 3.4 Opportunities
  • 3.5 Threats
  • 3.6 Application Analysis
  • 3.7 Emerging Markets
  • 3.8 Impact of Covid-19

4 Porters Five Force Analysis

  • 4.1 Bargaining power of suppliers
  • 4.2 Bargaining power of buyers
  • 4.3 Threat of substitutes
  • 4.4 Threat of new entrants
  • 4.5 Competitive rivalry

5 Global Radio Frequency (RF) Power Semiconductor Market, By Component

  • 5.1 Introduction
  • 5.2 Power Amplifiers
  • 5.3 Passives
  • 5.4 Switches
  • 5.5 Transistors
  • 5.6 Diodes
  • 5.7 Duplexers
  • 5.8 Other Components

6 Global Radio Frequency (RF) Power Semiconductor Market, By Material

  • 6.1 Introduction
  • 6.2 Gallium Nitride (GaN)
  • 6.3 Gallium Arsenide (GaAs)
  • 6.4 Silicon (Si)
  • 6.5 Silicon Germanium (SiGe)
  • 6.6 Other Materials

7 Global Radio Frequency (RF) Power Semiconductor Market, By Power Range

  • 7.1 Introduction
  • 7.2 Low Power
  • 7.3 Medium Power
  • 7.4 High Power

8 Global Radio Frequency (RF) Power Semiconductor Market, By Application

  • 8.1 Introduction
  • 8.2 Consumer Electronics
  • 8.3 Telecommunications
  • 8.4 Aerospace & Defense
  • 8.5 Automotive
  • 8.6 Medical Equipment
  • 8.7 Industrial & Scientific
  • 8.8 Other Applications

9 Global Radio Frequency (RF) Power Semiconductor Market, By Geography

  • 9.1 Introduction
  • 9.2 North America
    • 9.2.1 US
    • 9.2.2 Canada
    • 9.2.3 Mexico
  • 9.3 Europe
    • 9.3.1 Germany
    • 9.3.2 UK
    • 9.3.3 Italy
    • 9.3.4 France
    • 9.3.5 Spain
    • 9.3.6 Rest of Europe
  • 9.4 Asia Pacific
    • 9.4.1 Japan
    • 9.4.2 China
    • 9.4.3 India
    • 9.4.4 Australia
    • 9.4.5 New Zealand
    • 9.4.6 South Korea
    • 9.4.7 Rest of Asia Pacific
  • 9.5 South America
    • 9.5.1 Argentina
    • 9.5.2 Brazil
    • 9.5.3 Chile
    • 9.5.4 Rest of South America
  • 9.6 Middle East & Africa
    • 9.6.1 Saudi Arabia
    • 9.6.2 UAE
    • 9.6.3 Qatar
    • 9.6.4 South Africa
    • 9.6.5 Rest of Middle East & Africa

10 Key Developments

  • 10.1 Agreements, Partnerships, Collaborations and Joint Ventures
  • 10.2 Acquisitions & Mergers
  • 10.3 New Product Launch
  • 10.4 Expansions
  • 10.5 Other Key Strategies

11 Company Profiling

  • 11.1 Mitsubishi Electric Corporation
  • 11.2 Texas Instruments
  • 11.3 Infineon Technologies
  • 11.4 NXP Semiconductors
  • 11.5 Skyworks Solutions
  • 11.6 MACOM Technology Solutions
  • 11.7 STMicroelectronics
  • 11.8 RFHIC Corporation
  • 11.9 Renesas Electronics Corporation
  • 11.10 II-VI Incorporated
  • 11.11 Maxim Integrated
  • 11.12 Efficient Power Conversion Corporation
  • 11.13 Cree Inc.
  • 11.14 Qorvo
  • 11.15 Broadcom Inc.
  • 11.16 Ampleon

List of Tables

  • Table 1 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Region (2022-2030) ($MN)
  • Table 2 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Component (2022-2030) ($MN)
  • Table 3 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Power Amplifiers (2022-2030) ($MN)
  • Table 4 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Passives (2022-2030) ($MN)
  • Table 5 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Switches (2022-2030) ($MN)
  • Table 6 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Transistors (2022-2030) ($MN)
  • Table 7 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Diodes (2022-2030) ($MN)
  • Table 8 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Duplexers (2022-2030) ($MN)
  • Table 9 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Other Components (2022-2030) ($MN)
  • Table 10 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Material (2022-2030) ($MN)
  • Table 11 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Gallium Nitride (GaN) (2022-2030) ($MN)
  • Table 12 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Gallium Arsenide (GaAs) (2022-2030) ($MN)
  • Table 13 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Silicon (Si) (2022-2030) ($MN)
  • Table 14 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Silicon Germanium (SiGe) (2022-2030) ($MN)
  • Table 15 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Other Materials (2022-2030) ($MN)
  • Table 16 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Power Range (2022-2030) ($MN)
  • Table 17 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Low Power (2022-2030) ($MN)
  • Table 18 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Medium Power (2022-2030) ($MN)
  • Table 19 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By High Power (2022-2030) ($MN)
  • Table 20 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Application (2022-2030) ($MN)
  • Table 21 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Consumer Electronics (2022-2030) ($MN)
  • Table 22 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Telecommunications (2022-2030) ($MN)
  • Table 23 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Aerospace & Defense (2022-2030) ($MN)
  • Table 24 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Automotive (2022-2030) ($MN)
  • Table 25 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Medical Equipment (2022-2030) ($MN)
  • Table 26 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Industrial & Scientific (2022-2030) ($MN)
  • Table 27 Global Radio Frequency (RF) Power Semiconductor Market Outlook, By Other Applications (2022-2030) ($MN)

Note: Tables for North America, Europe, APAC, South America, and Middle East & Africa Regions are also represented in the same manner as above.