EEWeb Pulse - Issue 60

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1 Visit www.eeweb.com INTERVIEW PULSE EEWeb.com Issue 60 August 21, 2012 Marcus Ryle Founder Line 6 Electrical Engineering Community EEWeb

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Interview with Marcus Ryle - Founder of Line 6; Sonic Benefits of Digital Wireless Microphones; Programming with Low-Cost JTAG Tools - Part 1; Automating Op Amp Selection Flow for On Line Design Tools; RTZ - Return to Zero Comic

Transcript of EEWeb Pulse - Issue 60

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1Visit www.eeweb.com

EEWeb PULSE INTERVIEW

PULSEEEWeb.com

Issue 60August 21, 2012

Marcus RyleFounderLine 6

Electrical Engineering Community

EEW

eb

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ExpertsExchanging IdeasEvery Day.VISIT DIGIKEY.COM/TECHXCHANGE TODAY!

Digi-Key is an authorized distributor for all supplier partners. New products added daily. © 2012 Digi-Key Corporation, 701 Brooks Ave. South, Thief River Falls, MN 56701, USA

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EEWeb PULSE TABLE OF CONTENTS

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Marcus Ryle LINE 6

Interview with Marcus Ryle - Founder of Line 6

How Line 6’s digital technology brings a number of advantages to the world of wireless microphones.

Overcoming one of the biggest limitations when programming your board: the high cost of tools.

Considerations for optimizing an op-amp selection to a non-inverting design requirement.

Tools - Part 1

RTZ - Return to Zero Comic

Automating Op Amp Selection Flow for On Line Design ToolsBY MICHAEL STEFFES WITH INTERSIL

Programming with Low-Cost JTAG

Featured Products

Sonic Benefits of Digital Wireless MicrophonesBY MARCUS RYLE

BY PAUL CLARKE WITH EBM-PAPST

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Line 6

MarcusRyle

Tell us a little bit about your background. How did you get into engineering?I’ve had an interest in technology since as long as I can remember, which was instilled by my father who was an early software pioneer as well as a hardware engineer and all around entrepreneur. He was involved in designing the computer systems for the Saturn 5 rockets and was a pioneer in fault-tolerant computing systems. He encouraged me at an early age when he saw my interest in taking things apart and trying to figure things out. I also had

a strong interest in music from a very early age. My mother’s family has a musical background, and she encouraged me to study piano, which I started at age seven. My beginning engineering education was largely self-taught due to my interest in music and technology. When I was 12, I bought my first analog synthesizer and proceeded to take it apart, in hopes of making it do things it wasn’t designed to do. My dad was also an early adopter in the home computing market, so he bought one of the early versions of the Apple II which

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EEWeb PULSE INTERVIEW gave me the opportunity to start playing around with programming as well. Computers, electronics and progressive rock music were my primary interests as a kid, but these were not subjects readily available in high school in the 1970s, so I ended up leaving high school at the age of 16. I went on to attend Cal State University, Dominguez Hills, where I did not complete a degree, but took a bunch of classes to fill in the gaps that naturally occur when you are self-taught – some physics, a bit of analog and digital electronics courses, microcontrollers and a few different software classes. I also spent most of my time in the school’s recording studio and synthesizer lab. When I was 19 Tom Oberheim came to visit the lab and offered me a job at Oberheim Electronics, which was a U.S. synthesizer company.

What kind of work did you do at Oberheim Electronics?Oberheim was really the perfect combination of my interests—music, electronics, synthesizers, etc. They were a relatively small company at the time—in fact, there were really only two main engineers, Tom Oberheim and Jim Cooper. I had the advantage in starting that job of not knowing what I didn’t know, which can be great for learning as you go. I took on the task of designing a digital sequencer as my first project, which was difficult because at the time there was no standard protocol for communication in musical devices i.e. MIDI. These were the early days of digitally-controlled analog synthesizers. The devices being made had analog circuitry for sound generation, but all of the voltage control was being derived under software control from a microcontroller so that you could make these devices programmable. The notion of a digital sequencer

was to record what notes someone played, rather than recording the audio itself, so that you could replay them back directly on the synthesizer—a common idea today. Since it was a small company, they gave me the latitude to learn as I went. They were using Zilog Z80 controllers at the time, so I read a book and started coding!

Do you have any notable stories from your time at Oberheim?At that time, we didn’t have any real development tools for writing code. What we had was a General Automation computer with a simple text editor for writing assembly code, and a cross-assembler that could spit out machine code for a Z80. That could then be downloaded to an EPROM Programmer, burned into a chip, which was plugged into the target system and when you turned it on, you found out if it worked—there were no emulators, no trace buffers, no way of debugging your code. As difficult as that sounds, there was actually an advantage in that it taught you to be extremely disciplined in planning your code and writing your code, because if you just put it in an EPROM and stuck it in your hardware and nothing happened, the only way to track down the problem was to go back and look at your source code and figure out what you did wrong. That was a really great learning experience for me in terms of software. On the hardware side, there was also the fun of hand-drawing schematics and laying out circuit boards with tape—the good old-fashioned way—and just trying to understand how things worked.

What did you do after working at Oberheim?I was at Oberheim for almost five years and it was a really important

part of my education. It also taught me, without me realizing, that my main strengths were systems engineering and the role of product marketing in product development—recognizing my marketing abilities and how that really drove the product development. The technology is just a means to an end. You have to really know what problem you are trying to solve for the user and that the product your developing will be meaningful and not just a potential technological marvel. With that education, myself and another engineer at Oberheim, Michel Doidic, as well as my wife, Susan Wolf, decided to start a company called Fast Forward Designs. The basic premise was to work more on music technology, and we had the notion that if we could be design consultants and develop products for other companies, then we’d have the opportunity to have a more diverse range of technology and products. We started in 1985, quickly got some clients in the industry, and developed a large number of products for some of the manufacturers of musical instrument technology at the time like Dynacord, Alesis and Digidesign, among others. We focused on developing products for other companies for the first 10 years of our company, and during that time we were fortunate enough to be a part of developing products that became quite successful in our industry like the ADAT, which was the first affordable digital multi-track tape recorder, as well as a variety of effects processors, drum machines, sound cards, etc. Our business model was really quite simple; we’d receive a royalty for the products that we helped develop, and this would assure our clients that we were highly motivated to develop products that were going to be successful in the marketplace

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We have regularly scheduled jams and

we’ve got a large performance venue in our headquarters with a big stage so that our employees can see the

musical experience from product creation

to performance on a regular basis.

because the more successful they were, the more successful we were. This grew to the point where we were generating enough income from our royalty stream that around 1994, we started exploring what products we might want to start developing for ourselves. We were able to do self-funded research because of the number of products we had in the marketplace. At that time, we saw that guitar players were really getting a raw deal when it came to the evolution of technology. By 1994, keyboard players could get just about any sound they wanted at the touch of a button and producers in recording studios and home project studios were now abundant with technology, software plug-ins and sound processing. In many aspects of music production and creation, technology was opening huge opportunities, but guitar players were still relying on needing a wide collection of different guitars, effects pedals, and vacuum-tube

guitar amps in order to get a wide range of sound. At the time, the power of DSPs were getting to the point where there could be enough power to create software models of how an electric guitar sounded processed through a tube guitar amp.. That research is what led to the first digital modeling guitar amp in 1996, and our new brand, Line 6, was born.

Did Line 6 turn out to be pretty successful?Yes, we were very pleased! We seemed to hit on a nerve of an unmet need in the marketplace that guitar players definitely wanted to have the flexibility and power that digital modeling could provide. There were certainly plenty of detractors as well. It fundamentally became another analog to digital transition like in many other industries, so you could say that our first digital modeling amp in 1996 was a little bit like the early digital cameras. The advantages were obvious to

some—not having to develop film, being able to digitally manipulate pictures, e-mail pictures, etc—but the resolution of those early cameras wasn’t up to the resolution of film and analog cameras. Today, digital cameras are the standard, and the resolution available is very impressive. We did manage to make our first product the best we could with the given technology at the time. That first generation of guitar amps, we sold about 20,000 units and managed to get a good footing at the start of this new brand and technology. We were also awarded a patent on digital modeling guitar amplifiers, which was our first Line 6 patent. From there, we decided that we’d like to accelerate our development and continue to expand the products we were making, so we decided to raise venture capital. In 1997, we brought in Sutter Hill Ventures as a partner, and later added Redpoint Ventures.. We’ve continued to grow ever since.

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EEWeb PULSE INTERVIEW How big is the company now?

Today, we have over 280 employees worldwide, we bring in over $90 million in sales per year, and we have six different locations that we operate out of, including our main headquarters in Calabasas, California.

What are some of the more exciting products that you guys make today?

For the first decade of Line 6, we focused our attention on bringing new technology to guitar players and we managed to come from being a start-up with new digital technology to becoming the number one guitar amp maker in the world. As DSP processors became more powerful, we’ve been able to evolve that line considerably over the years and build on our understanding of how to model the subtle nuances of analog circuits that can have a big impact on the tone. We’ve expanded beyond modeling amps and effects to modeling the actual guitar itself, with our James Tyler Variax; James Tyler is a guitar luthier who has created several incredible instrument designs, which is not our area of expertise, and we’ve married his instrument designs with our technology so that you can have a collection of over two dozen guitars built into a single instrument. We’ve modeled body resonance, the placement and magnetic aperture of pickups, and can even do alternate tunings in real-time. Many guitar players end up using many different guitars while on tour just because they want them tuned to different tunings for different songs, and now they can do all that in one guitar. So there’s a wide range of products we make for the guitar player and more recently, we’ve done innovations broadening into other areas as well. We have a new line of digital audio

wireless microphones and wireless guitar products for musicians and audio professionals. We’ve most recently brought new technology innovations to the world of live sound in general—we now have a line of what we consider the world’s most versatile loudspeakers for musicians, StageSource, which have digital processing, networking and intelligence built in so that it can be configured for a number of different applications as well as being scaled for different size venues. We also have a new digital mixer called StageScape, which is a shift in how to mix sound live by using a visual interface and a tremendous amount of DSP power to give you a lot of flexibility and newfound ease in how you would mix your live performance. It’s just another new frontier, much like the early days of guitar, where we felt that technology could be used to bring really great benefits to the musician. Even though there have been other digital mixers before, they largely follow the same paradigm as analog mixing boards that have been used for many decades and require the musician to have a solid understanding of audio engineering in order to get the sound they are looking for. With our approach, great sound should be accessible to everyone.

As you are hiring new employees for your team, what are some of things you like to look for in engineers?

Mainly, we are looking for people who share a passion for wanting to create transformational products for musicians, products that really enable creativity and expression. For many of the engineers working here, that really becomes a true win-win. Life can just be that much more enjoyable if you are passionate

about the projects you are a working on. Although it’s not a requirement, virtually all of our engineers here are musicians. They actually use the gear we make, so they really feel a direct connection to the artists and professionals that use our products as well. By having an engineer who can actually directly relate to and understand the musician’s needs, besides developing products, they can play an active role in contributing to the concepts and the solutions of how we can best meet their needs. In some other companies you have a marketing department siloed from an engineering department, where you end up with someone just telling you what to build. We prefer that there be a much more collaborative environment where technical people and marketing people contribute together to what the future of music making might be.

It’s a neat culture. We have regularly scheduled jams and we’ve got a large performance venue in our headquarters with a big stage so that our employees can see the musical experience from product creation to performance on a regular basis. ■

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To request a free evaluation board go to:

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Voice Coil Motor Driver ICMagnaChip Semiconductor Corporation (“MagnaChip”) announced that it has unveiled a Voice Coil Motor (VCM) driver IC (MAP1011) to support the autofocus function found in mobile phone and tablet PC cameras. The MAP1011 VCM driver also uses wafer level chip scale packaging (WLCSP) enhancing low-power operation and reducing standby power consumption. In addition, WLCSP provides user flexibility allowing mobile phone and tablet PC camera module developers a broad choice of product options based only on input and standby voltage criteria. For more information, please click here.

Ultra Compact Inductors for SmartphonesMurata Manufacturing Co., Ltd. announced that it has now commercialized chip inductors with an inductance of 270 nH — the largest in the industry for the 0603 size. These inductors are optimal for use in high-frequency circuits in smartphones, mobile phones and other small mobile devices. Among our ultracompact 0603-size (0.6 × 0.3 × 0.3mm) film-type high-frequency chip inductors,*1 in addition to the previously available 0.6-120 nH products, we have increased the inductance so that our lineup now includes products that are compatible with inductances from 150-270 nH (LQP03TN_02 series). For more information, please click here.

Solutions for Automotive HVAC ControlFreescale Semiconductor introduced two automotive heating, ventilation and air conditioning (HVAC) reference control solutions that provide comprehensive, production-ready hardware and software enablement designed to speed up development cycles and reduce overall R&D costs for OEMs and Tier 1 suppliers. The two reference solutions are low-power, inexpensive, multi-functional and scalable and can be tailored for a customer’s unique 12V or 24V automotive HVAC system requirements. The reference solutions integrate Freescale S12G and S12HY 16-bit microcontrollers (MCUs) and MC33905, MC33932 and MC33937 analog devices, along with key motor control algorithms. For more information, please click here.

Low-Energy Backlight LED DriversIntersil Corporation announced the newest family of backlight LED drivers that can operate from the low input voltage of a single cell Li-ion battery. The ISL9769x series features ultra-low quiescent current and high efficiency required to maximize battery life in the latest generation of smartphones, tablets and Ultrabook/notebook PCs. With a minimum input voltage of just 2.4V, and quiescent current of only 0.8mA, the new ISL97692/3/4A series of LED drivers makes the most of the limited capacity of Li-Ion batteries in portable devices. For more information, please click here.

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Radio Interference

Anyone familiar with a traditional FM radio has experienced many types of interference artifacts. When two radio stations are close together in frequency, it is sometimes possible to hear a combination of both at the same time. Or when manually tuning a radio to a frequency that is not broadcasting, noise can be heard as a result of the spurious electromagnetic waves that are always around us.

In analog wireless microphones, any interference that causes audio artifacts can disrupt a performance. Causes of interference include obstructions (people, walls, equipment), radio wave reflections

(causing multiple paths of the signal to be received), and TV channels.

Any interference that alters the reception of the audio modulation of the carrier can produce unwanted audio artifacts. One way that analog wireless attempts to reduce spurious radio waves from being turned into audio is the use of a pilot tone and a squelch circuit.

The squelch circuit’s main purpose is to mute (“squelch”) the audio output when the transmitter’s signal is not being received. Without this, the receiver would output high amplitude noise due to the random radio waves it is receiving. But when the transmitter signal is being

received, the system needs some method to attempt to differentiate the wanted signal from any interfering signal. One method is to have the transmitter always transmit a pilot tone along with the audio. This tone is usually at a very high audio frequency, and is filtered out before the audio is output from the receiver. If the receiver does not see the pilot tone at the expected level, then the squelch circuit is turned on to mute the audio. Since modulated tones can be created due to interference, spurious audio is still able to pass through the system in certain circumstances.

Digital wireless microphones, like all digital transmission systems,

DigitalWireless

Sonic Benefits of

by Marcus Ryle

Microphones

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rely on data being “correct”, that is, a zero is always a zero, and a one is always a one. However, noise or interference on the signal will not have an impact on the receiver’s interpretation of the data unless it is significant enough to make the data unreadable. When an analog audio signal has noise or interference, the result becomes audible because it is combined with the intended audio waveform, as shown in Figure 1.

When a digital signal has noise or interference up to a certain level, the data can still be properly interpreted as ones and zeroes without any alteration in the audio, as shown in Figure 2.

Diversity

The term “true diversity” is often used to describe a feature of many analog wireless systems that utilize two antennas and two receiver circuits. Since the two antennas are spaced apart, they pick up the RF signal relative to their respective location. When the signal at one antenna is weak (due to an obstruction or multipath interference), the signal at the other antenna may not be as affected. These wireless systems have circuitry that selects the audio signal from the receiver that has the stronger signal. Switching noise is encountered, but is usually low enough to not be disruptive (Figure 3).

Digital systems use a similar approach to this type of diversity (also known as “spatial” diversity). Two antennas and two receiver circuits are used, but instead of switching the audio, the digital data from both receivers is compared and the one with the fewest errors detected is used. Since the data is received and buffered on both receivers, the decision of which data to use can happen continuously and without any interruption of audio from the switchover.

An additional diversity that Line 6 Digital Wireless systems provide is Frequency Diversity. Frequency

diversity utilizes multiple RF carrier frequencies to carry different parts of the audio data. This significantly reduces the impact of other RF signals, since the interference is not likely to be present on all of the frequencies being used.

The result of the error detection, frequency diversity, and data coding properties of digital wireless allow Line 6 2.4 GHz wireless systems to operate in heavily congested RF environments without the necessity of a clear channel while ensuring that the only audio that will ever be passed through the receiver is the intended audio from the transmitter.

Choosing a Channel

In many analog wireless systems, each uniquely selectable frequency is called a “channel”. This terminology can be misleading, since most of these channels typically cannot be used at the same time. Analog wireless frequencies need to be spaced apart, typically by at least 1MHz, in order for them to operate with minimal interference. But selectable channel frequencies on many devices can be spaced as close as 25kHz from each other. Fine resolution of tuning is provided in order to make it more likely to find frequencies that have minimal interference. Due to the space needed between simultaneously

Figure 1

Figure 2

The low and high signals (zeroes and ones) can still be read without any audible artifacts.

Significant radio interference can impact a digital receiver’s ability to correctly interpret the zeroes and ones. But digital has the advantage of being able to include additional information to help the receiver know if the data is correct. This is called error detection, and is commonly used in most digital storage or communication systems. This is usually performed by adding additional data to each packet of information that can be mathematically checked to validate the whole packet of data as being good or bad.

Figure 3

DigitalWireless

Sonic Benefits of

by Marcus Ryle

Microphones

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operating channels, the number of actual usable channels is about ten times less than the number of frequencies that are selectable.

In digital wireless systems operating in the ISM bands, all channels are always available. This is because there are no competing high powered transmitters permitted in this space. The total number of channels selectable is the number of channels that can be used simultaneously. Additionally, ISM bands such as 2.4GHz are usable throughout the world regardless of the local TV channel assignments.

Dynamic Range

The typical dynamic range of an unprocessed audio signal transmitted via FM is about 50dB. This is because the audio dynamic range is directly proportional to the amount of frequency modulation that can be applied to the carrier, and the amount of modulation is limited so it won’t overlap into adjacent frequency bands.

In order to achieve 100dB of dynamic

range, which is considered to be a minimum for high quality audio, an analog wireless microphone compresses 100dB of input dynamic range by a ratio of 2:1 in order to have it fit within 50dB. This compression is achieved by using a “VGA”, or Variable Gain Amplifier, with its gain being adjusted as a function of the average signal level being input. Louder signals are reduced in level, and/or softer signals are increased in level, so that the overall dynamic range is smaller.

On the receiver side, expansion is required, again using a VGA, in order to attempt to restore the original dynamic range. In this case, louder signals are made louder, and or softer signals are made softer, such that the original dynamic range is restored. The combination of these two processes is known as “companding” (a combination of compressing and expanding).

Unfortunately, companding does create some sonic artifacts. Depending on the time constants used to analyze the signal level and

“decide” on the gain the VGA is set to, gain changes can become audible, creating a sound often called “breathing”. This can be heard most obviously when a loud transient sound occurs, causing the VGA gain to quickly reduce level to compress the signal. After the transient has passed, the VGA gain is gradually returned to “normal”, during which time any other sound or noise can be heard to increase in volume, or breathe. Additionally, the expander on the receiver has no knowledge of the original input signal, so its ability to restore the original dynamic range is dependent on the manufacturer’s accuracy of matching the time constants and gain control between the transmitter and receiver (Figure 4).

Additionally, the dynamic range of the original audio signal can exceed 100dB. In order to accommodate this, the transmitter usually has a user adjustment for level control. If a singer is clipping the input, then the transmitter’s signal level must be adjusted downward, and the receiver’s level must be

Figure 4 Figure 5

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proportionally adjusted upward to maintain unity gain. Typical FM transmitters will also include an additional audio processing section called a “limiter”. This function prevents an overload condition of the audio signal which can cause distortion. The limiter also prevents “overmodulation” (excessive frequency deviation) of the RF signal. Overmodulation results in the RF signal deviation exceeding the bandwidth of the receiver, resulting in additional distortion. The limiter prevents the audio signal from exceeding a preset maximum level.

Dynamic range in analog systems is further reduced in high frequen-cies due to a technique called Pre-emphasis/De-emphasis. Pre-em-phasis is the act of boosting high frequencies in the audio band and De-emphasis is the act of cutting high frequencies in the audio band. These methods are used to improve

signal to noise during transmission. The boosted high frequencies pro-duce a larger deviation of the RF carrier thus creating a larger signal compared to the existing RF noise floor. Once the signal is received, the De-emphasis reduces the high frequencies, also reducing noise in the process.

The result is a reduction in the residual noise present in analog FM wireless systems, but at the cost of reduced dynamic range in higher frequencies due to the higher gain of these frequencies at the transmitter.

Digital wireless systems are able to transmit the digital audio signal without any compression or limiting, or Pre-emphasis/De-emphasis. It also can accommodate a wider input dynamic range, eliminating the need for level controls. The result is that the input signal is accurately reproduced at the receiving end (Figure 5).

Frequency Response

The frequency response of an analog wireless system is limited at both the low and the high end. On the low end, it is necessary to roll off frequencies that would interfere with the companding circuitry. For example, a frequency of 20Hz is slow enough to cause the gain to change with each cycle of the waveform. Therefore, low frequencies are filtered out. The high frequencies are limited by the constraints of analog FM technology, which typically cannot produce frequencies above 15kHz. The following graph shows the wireless frequency response of two popular brands (Figure 6).

The high frequency response of a digital wireless system is a function of the sample rate, and not any aspects of the RF transmission.

Also, since there is no compander, the low frequencies do not need to be rolled off. As a result, a digital wireless system can transmit signals flat between 10Hz and 20kHz (Figure 7).

These graphs represent the frequency response of the wireless systems, independent of the microphone element frequency response. Each microphone has its own tonal response, which can determine the character of its sound. If a wireless system has a flat frequency response, it allows the characteristics of the microphone’s response to remain unaltered.

Summary

Line 6’s digital technology brings a number of advantages to the world of wireless microphones. By overcoming the limitations of analog systems, wireless can now be used with all the reliability, ease, and sonic benefits of a wired microphone. ■

Figure 6

Figure 7

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Meet the Experts

Design Issues for Systems That Use LCD Panels

M2M Development

Development Ecosystem and Services

Customer Feedback

Expert Panel: The Auto Industry Speaks

Expert Panel: The Future of Auto Software/System Development

Model-based Development

Simulation: Expert Insights into Modelling Microcontrollers

Automotive

Cost Effective HIL for Rapid Prototyping

Virtual HIL test/ISO 2626 using Processor Models

Introduction to Velocity Lab

Infotainment & Instrumentation Solutions

QuantiPhi for RL78: The Fastest Path from Idea to Implementation

Simulation: Moving Development into the Virtual World

Active Safety SolutionsGraphic System Design Considerations

Insights into MCU & Mixed Signal Design

Automotive Quality/Failure Analysis

Working with AUTOSAR

Trends in Automotive Communication

Improve a Product’s User Experience with Model-based UI Design

Intelligent Power Devices

Mastering Functional Safety and ISO 26262

Advanced SOC for Telematics and Infotainment

MICON Racing – Qualify using QuantiPhi for RL78

Using Processor Models for Software Development and Validation

HEV/EV Traction Motor Control Lab

Computing Architecture

Renesas Next-generation Microcontroller and Microprocessor Technology Roadmap

Microcontroller Solutions Enabling a Greener Society

The Core Difference: When the Core Matters

RH850 & RL78: Introducing the Next Generation of Microcontollers for Automotive Applications

Benchmarking using EEMBC

Optimizing Performance of RX-based Applications

Connectivity

Industrial Ethernet

Instant Connectivity for the “Internet of Things”

PLM-1 Modem

Renesas Connecting through 802.15.4 Radio

CMX TCP-IP

LibUSB: Create a Solution Without the Class Struggle

CAN In a Day: Using the RX CAN API

IR and Bluetooth Connectivity Using the RL78

Development Tools

Getting Started with Renesas Development Tools

Introduction to e2studio, The New Eclipse-based IDE from Renesas

Getting the most out of the Renesas Demonstration Kits (RDKs)

Trends in Embedded Software Development

High-performance Compiler Solutions for Renesas MCUs

Getting the Most Out of the GNU Toolchain

Getting Started with e2studio, The New Eclipse-based IDE from Renesas

Introduction to the RX Arduino

Using Embedded Tools for I2C, SPI, and USB Debugging and Develop-ment on the Renesas RX63N RDK

Seeing Inside your Target at Run-time with µC/Probe

Advanced Debugging with the RX600

Migration from HEW to Eclipse

Migration from Cube Suite to Eclipse

Using Software Building Blocks for Faster Time-to-market

VectorCAST Tools: A Complete Test Environment for Safety-critical Applications

Using a Renesas Code-generation Tool for RL78 Devices

e2studio Advanced Topics

Advanced Debugging on RX with IAR Embedded Workbench

Security

NFC Ecosystem and Solutions

Hardware Roots of Trust – A Foundation for Security

Security Solutions for the Automotive Industry

Security Solutions Part 1: Javacard Applet Development Training

Security Solutions Lab 2: Secure Host Firmware Upgrade using BoardID Secure Solution

Human Machine Interface

Audio Solutions on the RX MCU Family

Capacitive Touch Based User Interfaces and Hardware-based Solutions

Enhance Embedded Designs with Low-cost TFT LCD Solutions

Embedded Vision: Creating “Machines that See”

Driving E Ink Displays

Direct-drive LCD

Using Altia to Design a GUI and Deploy it on Renesas SH7269

Extreme Makeover with the RX600: Adding Touch/Graphics to Your Product

Direct-drive LCD Software Integration for the RX62N/RX63N

Incorporating a Capacitive Touch Interface into Your Design

Industrial Controls GUI Application Using emWin

Display

Flat Panel Displays: LCD Technologies and Trends

Flat Panel Displays: Touch Panel Technologies and Integration

Flat Panel Displays: Beyond the Basics

Flat Panel Displays: How to Over-come High Ambient Light Conditions

Flat Panel Displays: Exploring a 2D/3D Solution

Flat Panel Displays: Advanced Technology TrendsM2M and Cloud Solutions

Energy-efficient Communications with Wi-Fi

Adding Wi-Fi to Embedded Applications

Wireless Connectivity for Embedded Systems

M2M: How to Create Revenue- generating Services and Applications

Wireless SensorsWireless TransceiversM2M: Cloud Connectivity with RX and Exosite

Power

IGBT vs. Mosfet: Which Device to Select?

How to Make Your House Smarter

Digital Power: Design and Architectural Trade-offs

Increasing the Performance of PFC and LED Driver IC Applications

Optical Isolation, SSR Switching, and Ambient Light Sensing in MCU-based Applications

IGBTs for HEV/EV

Motor Control

Power Factor Correction: Why and How?

Sensorless Vector Control and Implementation: Why and How

Know your Precise Position with RX600 MCUs

Field-oriented Control Using a 16-bit Low-power MCU

Operating Systems

Using ThreadX and IAR Embedded Workbench on the RX Processor

Introduction to RoweBots’ Ultra Tiny Linux™ RTOS

Embedding USB: Implementation Challenges and Limitations

FreeRTOS Lecture

Rapid Development on the Renesas RX63N RDK using µEZ® and FreeRTOS

Introduction to Python

Software Development with an Open Source Real-time Operating System

HTML5 HMI Development with QNX

Developing Next-gen Automotive User Interface using EB GUIDE 5.3 w/Windows Embedded Automotive 7 and Renesas R-Car H1

Getting Started with Micriµm’s µC/OS-III Kernel

Embedding TCP/IP: Working Through uC/TCP-IP Usage

Introduction to the .NET Micro Framework

System Design Technologies

Are all Batteries Created Equal?

A/D Converter Fundamentals

Designing Modern Medical Systems

Digital Filtering on a MCU

Infinite Runtime: Energy Harvesting with Renesas MCUs

Moving from 8-bit to 32-bit MCUs

Battery Management

ADC Resolution: Myth and Reality

Exploring the Safety Features of the RX210

Low-power Design

Increase the Dynamic Range and Precision of Digital Filters Using a FPU

RL78 Project Configuration Tips

RX Project Configuration Tips

Sensor Fundamentals

Extreme Low-power Design: Tools, Design Techniques and Implementation

Creating Virtual EEPROM on Renesas MCUs

Implementing Bootloaders on Renesas MCUs

Designing Energy Harvesting Applications with the RL78

Portable Instrumentation Applications with the RL78

Embedded Systems Bootcamp

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16 EEWeb | Electrical Engineering Community

There is a growing interest in FPGA and CPLD design and with that, the development kits are getting cheaper and cheaper. However, one of the restrictions for some has been the cost of tools when it comes to programming your boards. There are a number of top companies out there all pushing their own chips, IDEs and JTAG programmers. These are not cheap, so I want to look at how this can be resolved or avoided.

JTAG has been around for a while and is a standard used by FPGA as well as microprocessor manufacturers. It has many very useful functions apart from programming. There are options like performing board level testing or programming of devices i.e. onboard flash. It’s also a great debug tool, but this and the other functions come at a price. In most cases if you need this level of functionality then you can afford the tools because of the type of work you’re doing. But people on a budget like small start-ups or hobbyists don’t have the money.

The JTAG protocol is quite simple to follow and is a lot like an SPI but, there is a clock, device select and a data-

in and -out line. This is clearly a simple protocol that a small microcontroller could use, so why not use one to program it with too? The solution therefore is a system that allows you to take your program and convert it into a language that a simple micro can use. This solution comes in the form of an SVF file format. This is a format that is generated by the big leading manufacturers (once you have turned it on in the IDE). SVF is a human readable format that explains or tells a device how to toggle the clock, select the data lines as well as check returned data.

Xilinx has taken the file format one step further. There is a popular application note called XAPP058 that not only explains how to design your own JTAG programmer, but also supplies a working application ready to drop in your target, add a few tweaks and is ready to go. I will explore this more in Part 2 of this article.

If you’re not a big fan of building it yourself, then you could use one of the (X)SVF players that are available on the internet. Notable is the Bus Pirate from Dangerous

Tools

ProgrammingWith Low-Cost

JTAGJ

Paul Cla

rke

Electronics

Desig

n

Engineer

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Prototypes. Originally designed as a tool to sniff, monitor, inject or bus protocols like SPI, its open platform has meant that the ‘community’ has developed an XSVF player. This allows a user to convert an SVF file format to XSVF with the tools supplied. The board, which is a very good price, can then be easily re-programmed as a JTAG programmer. You then simply run the right command from your computer and the file is uploaded to the Bus Pirate via USB which then carries out the required toggling of the JTAG lines.

So the path to programming a device with a JTAG interface need not be expensive or difficult. In the next part, I’ll look at just how easy it is to implement this in hardware too.

About the AuthorDigital Electronics Engineer with strong software skills in assembly and C for embedded systems. At ebm-papst I’m developing embedded electronics for thermal management control solutions for the air movement industry. These controllers monitor environmental inputs like Temperature, Humidity and Pressure and then control the speed of our fans based on various profiles. Our controls also interface with other systems over RS232/485 or TCP/IP as well as a host of other user or control interfaces. ■

Tools

ProgrammingWith Low-Cost

JTAGJ

Paul Cla

rke

Electronics

Desig

n

Engineer

TMS

TCK

TDI TDO

Device

1TMS

TCK

TDI TDO

Device

2TMS

TCK

TDI TDO

Device

3

TMS

TCK

TDI

TDO

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Single or Multiple Cell Li-ion Battery Powered 4-Channel and 6-Channel LED DriversISL97692, ISL97693, ISL97694AThe ISL97692, ISL97693, ISL97694A are Intersil’s highly integrated 4- and 6-channel LED drivers for display backlighting . These parts maximize battery life by featuring only 1mA quiescent current, and by operating down to 2.4V input voltage, with no need for higher voltage supplies.The ISL97692 has 4 channels and provides 8-bit PWM dimming with adjustable dimming frequency up to 30kHz. The ISL97693 has 6 channels with Direct PWM dimming control. The ISL97694A has 6 channels and provides 8-, 10-, or 12-bit PWM dimming with adjustable dimming frequency up to 30kHz, 7.5kHz, or 1.875kHz, respectively, controlled with I2C or PWM input. ISL97692 and ISL97694A feature phase shifting that may be enabled optionally, with a phase delay between channels optimized for the number of active channels. In ISL97694A, phase shifting can multiply the effective dimming frequency by 6 allowing above-audio PWM dimming with 10-bit dimming resolution.

The ISL97692/3/4A employ adaptive boost architecture, which keeps the headroom voltage as low as possible to maximize battery life while allowing ultra low dimming duty cycle as low as 0.005% at 100Hz dimming frequency in Direct PWM mode.

The ISL97692/3/4A incorporate extensive protection functions including string open and short circuit detections, OVP, and OTP.

The ISL97692/3 are offered in the 16 Ld 3mmx3mm TQFN package and ISL97694A is offered in the 20 Ld 3mmx4mm TQFN package. All parts operate in ambient temperature range of -40°C to +85°C.

Features• 2.4V Minimum Input Voltage, No Need for Higher Voltage

Supplies

• 4 Channels, up to 40mA Each (ISL97692) or 6 Channels, up to 30mA Each (ISL97693/4A)

• 90% Efficient at 6P5S, 3.7V and 20mA (ISL97693/4A)• Low 0.8mA Quiescent Current

• PWM Dimming Control with Internally Generated Clock

- 8-bit Resolution with Adjustable Dimming Frequency up to 30kHz (ISL97692/4A)

- 12-bit Resolution with Adjustable Dimming Frequency up to 1.875kHz (ISL97694A)

- Optional Automatic Channel Phase Shift (ISL97692/4A)- Linear Dimming from 0.025%~100% up to 5kHz or

0.4%~100% up to 30kHz (ISL97692/4A)• Direct PWM Dimming with 0.005% Minimum Duty Cycle at

100Hz• ±2.5% Output Current Matching

• Adjustable Switching Frequency from 400kHz to 1.5MHz

Applications• Tablet, Notebook PC and Smart Phone Displays LED

Backlighting

Related Literature (Coming Soon)• AN1733 “ISL97694A Evaluation Board User Guide”

• AN1734 “ISL97693 Evaluation Board User Guide”

• AN1735 “ISL97692 Evaluation Board User Guide”

FIGURE 1. ISL97694A TYPICAL APPLICATION DIAGRAM FIGURE 2. ULTRA LOW PWM DIMMING LINEARITY

FSW

FPWM

AGND

OVP

VIN

SDA/PWMI

ISET

COMP

SCL

D1

CH1

CH2

CH3

CH4

PGND

LX

VIN: 2.4V~5.5V VOUT: 24.5V, 6 x 20mA

CH5

CH6

L1

10µH

12k15nF

10

1µF

4.7µF4.7µF

470k

23.7k

143k

291k

53k

100pF

2.2nFISL97694A

4.7µF

EN

0.0001

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10INPUT DIMMING DUTY CYCLE (%)

ILED

(mA

)

fPWM: 200Hz

fPWM: 100Hz

July 19, 2012FN7839.2

Intersil (and design) is a registered trademark of Intersil Americas Inc. Copyright Intersil Americas Inc. 2012All Rights Reserved. All other trademarks mentioned are the property of their respective owners.

Get the Datasheet and Order Samples

http://www.intersil.com

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laudantium, totam rem aperiam,

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dicta sunt explicabo. Nemo enim ipsam

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qui ratione voluptatem sequi nesciunt. Neque porro

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Michael SteffesIntersil - Sr. Applications Manager

AutomatingOp AmpSelectionFlow forOn LineDesign Tool

The “Many-to-One” Mapping Problem in Applying Op Amps to Signal Processing Needs

The op amp is so ubiquitous and flexible it can be a daunting task to come away from any design feeling like it has been “optimized” to the device. Most decisions become a series of overlapping performance coverage type decisions at what cost in power and price? Almost always, a range of devices will meet the requirements. For instance, a requirement at some gain for a 100kHz

signal path can be met by a device that exactly provides the 100kHz target – but also by many devices faster than this. For any particular set of design requirements, there will probably be several devices that can provide a design of interest.

One proven approach is exemplified using the Intersil online op amp tools in 4 steps as follows:

1. Request some basic design goals for the signal path. For the non-inverting tool (ref.1), these were gain, minimum signal bandwidth, and some options on the input network.

2. Apply a few constraints to the implementation. The most important is always the desired total supply voltage available to power the device. The Intersil tool supports a 1.8V to 40V range where moving through that sweeps a wide range of process technologies. This is the total supply voltage across the device where the initial assumption is that +/- ½ of that value will be used in a bipolar supply design. The next most important constraint is the desired maximum output swing which will feed into the slew rate and I/O headroom check.

Automating a flow into a semi-expert system requires a combination of parametric analysis and some judgment on required design issues and margins. This breaks the selection flow into a set of “must have” op amp characteristics, 2nd order parasitic considerations, and then a ranking by closeness of fit with enough parametric data to anticipate a range of solutions. The non-inverting op amp application is perhaps the simplest but even here there are enough pitfalls to warrant moderate analysis. The amplifier screening flows for a recently released (late 2011) online non-inverting op amp design tool will be described here with examples.

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Michael SteffesIntersil - Sr. Applications Manager

AutomatingOp AmpSelectionFlow forOn LineDesign Tool

3. From these basic requirements, all devices in the tool are screened for ones that just aren’t going to be applicable. For instance, a 30V supply design (+/-15V) isn’t going to be able to use a single supply +5V type device. Then, the more sophisticated bandwidth and slew rate screens are applied.

4. From the screened down list of candidate devices, use the desired signal path performance targets to rank by minimum to maximum overkill to the requirements. Typically, this then tends to rank the devices in roughly ascending speed and supply current.

This should get a good first pass at looking for candidate solutions. The sorted list of acceptable devices is shown with a small set of secondary parameters that might lead one to be more attractive than others. Things like supply current, input noise voltage, and list price might be very important to the specific application but not a make or break performance parameter on other designs. This approach is more than just a parametric sorting tool commonly found on vendor websites. It is also doing some intermediate calculations to anticipate issues sometimes overlooked in the design process. Built into the selection flows are some assumed component element value design algorithms.

Screening Op Amps for the Required Performance Targets

The simplest screening of course rejects devices that cannot operate at the desired supply voltage. Then it rejects devices that cannot support the maximum required I/O voltage swing. This is an I/O headroom check where most of the time the output will be the dominant limit – except perhaps for a gain of 1 design target. Given a maximum output Vpp, the implied maximum input Vpp is just that divided by the gain. These will be the same for a gain of 1 design. Often, just asking for a little bit of gain (say 1.3V/V) can eliminate input range issues quickly for non-RR input devices. The Intersil tool guardbands this headroom calculation by 10% to anticipate some tolerancing on the supplies and device headroom. More interesting are the bandwidth and slew rate checks.

From the specific gain and desired minimum bandwidth, a set of simple calculations can determine if a device can meet those. These are slightly different calculations between a Voltage Feedback Amplifier (VFA) and a Current Feedback Amplifier (CFA) type device. Underlying this estimated bandwidth at some gain is an overriding goal to deliver at most a modestly peaked

frequency response. Allowing significant peaking in the response is certainly possible and useful in some cases. But more often it leads to un-anticipated overshoot, much higher integrated noise, and quite a lot more part to part variation in response shape. The nominal target response is an approximate Butterworth response and more often overcompensated. While simple algorithms are used to estimate a device bandwidth over a continuum of gains, good macromodels will include numerous parasitics that will likely introduce some deviation from predicted bandwidth due to the phase margin changing over gain setting.

While it is very common to suggest specific bandwidth control techniques in a non-inverting stage, this tool just delivers an approximate bandwidth > than the minimum target. If desired, one of 3 simple RC bandwidth setting techniques can then be applied as described in the Appendix B of ref. 2. (a warning! – putting a cap across the feedback resistor to set the signal bandwidth is probably the least effective of the 3 choices and hazards more 2nd order baggage).

To anticipate part to part and temperature variation, the actual target bandwidth is increased to 1.3X the user entered value. Then, for a VFA device –

1. A check is made that the desired gain is not below the minimum operating gain. Asking for a gain of 1 and then applying a non-unity gain stable device would not be such a good idea.

2. Then, a simple Gain Bandwidth Product (GBP) divided by the gain check that it is > target is made. If so, that test gets checked off as passing for that device.

Estimating the Achievable Bandwidth for a CFA Op Amp

For a CFA device, the process is a bit more involved. Up to a certain gain, the feedback resistor can be adjusted to hold an approximately constant bandwidth (Butterworth is usually the target for a CFA nominal frequency response). Continuing up in gain, the Rf + Rg sum will eventually get so low as to load the output so heavily it will start to ‘bandlimit.’ That is not well controlled so the approach here is to solve for a maximum constant bandwidth gain based on this loading issue, (which will be adjusting the Rf down as the gain increases), then start increasing the Rf linearly above that maximum gain and then estimate the resulting closed loop bandwidth as it comes down with increasing gain and Rf for the CFA.

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22 EEWeb | Electrical Engineering Community

Underlying this CFA bandwidth check is the approximate constant bandwidth relationship of Equation 1. Every CFA has a total feedback transimpedance that will hold about the same loop gain crossover and hence closed loop bandwidth. For the non-inverting case, this feedback transimpedance is the sum of the feedback resistor and the product of the open loop output impedance looking into the inverting node times the “noise gain”(ref.3). The “noise gain” in this simple non-inverting circuit is just the target signal gain. In eq. 1, Zopt is the nominal target feedback impedance and then the other terms can be controlled to hit that number over gain. Ri is the open loop inverting input resistance. The higher this is, the less “gain bandwidth independence” a CFA will have and the more quickly Rf will need to come down to hold constant bandwidth.

Where a is defined in Eq. 4.

Ref 1. Resistor settings vs. gain and estimated F-3dB for the EL5165

As the target gain goes up, the same Zopt may be achieved by adjusting the Rf value down as shown in Eq. 2. This simple model eventually predicts a negative Rf as Av increases so it is only useful up to a point.

The key here is to know the Zopt and Ri for each CFA device. This is sometimes specified but more often can be backed out of the recommended Rf vs gain data in the device data sheet. CFA data sheets are usually constructed with bandwidth response curves stepped up in gain holding approximately the same response shape by adjusting the feedback R value.

Eventually, this first order adjustment breaks down and the bandwidth decreases due to loading. A very approximate estimate of this is to assign a maximum % of linear output current available that can be spent in the Rf + Rg feedback load. This is done in the Intersil non-inverting design tool (ref. 1) for the maximum available peak swing on nominal supplies and letting 20% of the linear output current go back into the feedback path. This gives a minimum Rf +Rg = Zmin limit. Combining that with eq. 2 will give an Avmax through a quadratic solution. An approximate maximum signal gain over which Eq. 2 may be used is shown as Eq. 3.

Once the desired Av exceeds this for a particular candidate solution, the target feedback impedance is increased in the same ratio as target gain to Avmax given by Eq. 5.

Putting this new target feedback transimpedance into Eq. 2 will give an Rf value and then of course the desired gain will give the Rg value.

Stepping the gain from 1 to 10 using a low power, wideband, CFA like the EL5165 (ref. 4) will illustrate the approach. The required parameters for this 5mA quiescent current device are

Zopt = 900Ω

Ri = 200Ω

The EL5165 linear output current is estimated at 154mA. With its specified +/-4.1V swing on +/-5V supplies, spending 20% of that in the feedback network sets Zmin = 133ohms.

Putting these numbers into Eq. 3 will give a maximum gain to hold constant bandwidth = 4.0V/V. Above that gain, the Rf will be increased using Eq. 5 to get a scaled up target feedback transimpedance then Eq. 2 to solve for Rf. Table 1 shows the resulting resistor values using a 1% value snap, estimated BW, and then simulation bandwidth from Ref. 1.

GainV/V

RfOhms

RgOhms

EstimatedBandwidth

(MHz)

SimulationBandwidth

(MHz)

456401402395323269229193165148

370370370370296247211185164148

open49915033.230.930.129.428.72828

698499301100124150174200226249

12345678910

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This is showing that we would expect about a constant 370Mhz bandwidth up through a gain of 4, then it will start stepping down as the Rf is increased from that point forward. The other approach would be to hold a fixed feedback load as the gain increases (at Zmin). This shifts the Rg value down from the values shown in Table 1 which often exposes a secondary bandlimiting issue related to the input buffer response. Figure 1 shows the simulation schematic generated for the gain of 2 target from Ref. 1.

Figure 2 shows the resulting small signal response shapes for the values of table 1. This is a normalized plot at 0dB to more easily see the range of F-3dB vs.

gain. Gain of 1 is often more peaked than expected while gains from 2 to 4 are tightly clustered around 400Mhz showing the constant bandwidth feature of the CFA over some gain range. The slight peaking in the response extended the bandwidth slightly over the expected 370Mhz. Then, as the Rf goes up with gain above 4, the bandwidth steps down in an approximate proportionate fashion.

For each CFA device in the Intersil non-inverting design tool, an estimate of closed loop bandwidth at the desired gain is made using this approach then compared to the 1.3X guardbanded minimum target bandwidth to accept or reject the device as a possible solution.

Figure 1: Gain of +2 non-inverting gain design using the EL5165

Figure 2: EL5165 simulated response shapes over gain using the values of Table 1

5V

5V

20Ω

499Ω

499Ω

1.00 kΩ

EL5165

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V3

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No

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Ga

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Frequency (Hz)

3

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1

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-2

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-4

-5

-6

-7

-8

-9

1

2

3

4

5

6

7

8

9

10

1.E+06 1.E+07 1.E+08 1.E+09

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24 EEWeb | Electrical Engineering Community

Every op amp has some physical limit to the maximum output dV/dT it can support before it goes into a slew limited mode of operation. While this might be acceptable in some applications, it is assumed here that this nonlinear mode of operation should be avoided if possible. This estimated slew rate requirement breaks into either a time domain or frequency domain application consideration. For an assumed step response type application, the output peak dV/dT will normally be a combination of the input edge rate and the response shape of the amplifier. One approach is to use the target bandwidth as an implied estimate on the source signal. Using the estimated solution bandwidth where that can be far beyond the desired bandwidth can lead to a much higher implied slew rate requirement. A good estimate for the peak slew rate from 2nd order frequency response may be derived (ref. 5) as Eq. 6.

the specified maximum Vpp and Fmax defaults to ½ the target F-3dB.

Continuing the EL5165 example, and specifying a 100Mhz minimum bandwidth target with 2.5V maximum output swing, and first checking the reported step response amplifier slew rate requirement, delivers a 1335V/μsec minimum target (2X the result of Eq. 6). Switching to an SFDR design, with the default maximum 50MHz signal at 2.5V maximum output and the default 60 to 69dBc SFDR target, yields a much higher 3333V/μsec minimum target. The signal itself will be asking for 392V/μsec peak dV/dT from Eq. 7. To get into the mid 60dBc SFDR region requires an approximate 10X slew rate margin in the device. These are both below the available 4500V/μsec slew rate for the EL5165 so it still shows enough design margin for either the step or SFDR oriented requirement.

To eliminate these very approximate slew rate requirement estimates from consideration, going to a very low maximum operating frequency in the SFDR mode and targeting only the 40->49dBc range will drop the estimated target significantly. For instance, changing this constraint to be applied at a 10Mhz maximum signal frequency and this lowest SFDR range delivers an 800V/μsec screening target. Doing this will often expand the range of possible op amp solutions significantly.

Summary and Conclusions

Any designer that has tried to “optimize” an op amp selection to a non-inverting design requirement discovers quickly the multiple layers of consideration. Issues like operating supply voltage and staying out of I/O clipping issues are simple while estimating a slew rate requirement and design margin gets into both calculations and judgment calls. Some of the details in the selection flow for an online automated design tool have been described here. The overriding aim has been to build in enough, but not too much, design margin into the recommended solution amplifiers to handle part to part, temperature, and supply variation. Adequate flexibility was built into the design flows to allow users to override some of the design margin estimates from the default design assumptions.

About the Author

With 27 years of involvement in high speed amplifier design, applications, and marketing, Michael Steffes has introduced over 80 products spanning five companies while publishing more than 40 technical articles. His current focus is on high efficiency high speed ADC interfaces, DSL/PLC line interface solutions, and online design tool development. ■

This is the peak dV/dT for a 2nd order step response – basically solving the maximum derivative of the time waveform. As the poles become more complex, giving rise to more overshoot and peaking in the frequency response, the F-3dB of the response will also be increasing – It is that part of Eq. 6 that captures the increasing peak dV/dT for an overshooting step response.

Just putting the target F-3dB into this equation is definitely a rough approximation. The specified nominal slew rate on most amplifiers has a significant tolerance over supply and temperature. To anticipate that in volume production, the Intersil tool then multiplies the result of Eq. 6 by 2X to build in some guardband to the design target.

For frequency domain oriented applications, the slew rate requirements come in more through a targeted SFDR requirement to some maximum frequency. This becomes a 2 step calculation of a maximum single tone dV/dT for the maximum entered output Vpp at some maximum frequency < than the specified F-3dB. The default frequency for this calculation is ½ the designer entered F-3dB but can be overridden to higher or lower frequencies. This maximum dV/dT for the physical output signal (given in Eq. 7) is then guardbanded by an exponential multiplier related to the target SFDR (Ref.6).

Slew Rate Considerations in Screening Op Amps

Eq. 7 is assuming a sinusoidal swing where Vpeak is ½

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