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Telos Enabling Ultra-Low Power Wireless Research

Telos:Enabling Ultra-Low Power Wireless Research

Joseph Polastre,Robert Szewczyk,and David Culler

Computer Science Department

University of California,Berkeley

Berkeley,CA94720

{polastre,szewczyk,culler}@https://www.sodocs.net/doc/89223698.html,

Abstract—We present Telos,an ultra low power wireless sensor module (“mote”)for research and experimentation.Telos is the latest in a line of motes developed by UC Berkeley to enable wireless sensor network (WSN)research.It is a new mote design built from scratch based on expe-riences with previous mote generations.Telos’new design consists of three major goals to enable experimentation:minimal power consumption,easy to use,and increased software and hardware robustness.We discuss how hardware components are selected and integrated in order to achieve these https://www.sodocs.net/doc/89223698.html,ing a Texas Instruments MSP430microcontroller,Chipcon IEEE802.15.4-compliant radio,and USB,Telos’power pro?le is almost one-tenth the consumption of previous mote platforms while providing greater performance and throughput.It eliminates programming and support boards,while enabling experimentation with WSNs in both lab, testbed,and deployment settings.

I.I NTRODUCTION

Wireless sensor networks are ideally suited for long-lived appli-cations deployed at large densities for low cost.Unfortunately,the current WSN platforms built from commercial off-the-shelf(COTS) components have a lifetime of no more than two years,communicate through non-standard interfaces,are expensive,and are dif?cult to use for experimentation,development,testing,and deployment.

In this paper,we introduce the design of Telos,the latest wireless sensor device,

or“mote”,from the University of California,Berkeley. Telos(shown in Figure1)is a new design to further research in sensor networks with three major goals:lower power operation than previous mote generations,easy to use,and robustness for experimentation and deployment.The Telos design is based on the following low duty cycle principle:the node is asleep for the majority of the time, wakes up quickly on an event,processes,and returns to sleep.For the lowest power consumption,the standby current and wakeup time (time to transition from sleep to active mode)must be minimized[1] since the the active portion of a sensor network application is typically extremely small[2].Telos offers more than just low power operation through its integrated design.Integration of programming, communication,storage,and sensing allows researchers to utilize more functionality and develop more robust systems.

II.R ELATED W ORK

The lineage of current platforms can be traced back to a number of devices called“COTS motes”built by the SmartDust project and shown in Figure2.These devices were built to approximate the capabilities of an envisioned SmartDust node with off the shelf components[3].These designs used a small8-bit microcontrollers(4 to8kB of?ash,512bytes of RAM);a simple radio(OOK modulation at4kbps)and integrated sensors(magnetometers,accelerometers, temperature,pressure,etc).Later designs(weC[4],and Ren′e) exposed a custom sensor interface and allowed for the possibility of remote reprogramming.

Mica[5],released in2001,was carefully designed to serve as a general purpose platform for WSN https://www.sodocs.net/doc/89223698.html,pared with preceding designs,it offered more memory(4kB of RAM and128kB of?ash),extensive sensor interfaces(8analog lines,several digital IO Fig.1.Telos ultra-low power wireless module(“mote”)with IEEE802.15.4 wireless transceiver.

channels,dedicated serial busses),and a very?exible radio interface. Mica used the RFM TR1000and simple modulation techniques.The radio’s primitive interfaces allowed low power operation and quick turn-on times.The unbuffered,bit-level radio interface connected to several IO pins,interrupts,and an SPI bus on the main microcon-troller;the bus timing was controlled by the CPU clock.Researchers implemented a number of schemes for radio wakeup,low power asynchronous communications,fairly high bandwidth protocols(40 kHz physical layer),and precise time synchronization(to within a1 bit time).

Mica was useful for development,but unsuitable for deployments. The boost converter provided a stable voltage but used excess quies-cent current.The radio communication range was short and relatively unreliable.The extensive I/O connector was not robust to variations in temperature[6].Mica2,the follow on to the Mica platform,corrected many shortcomings:the boost converter was discarded,and the MCU was replaced with the ATmega128.This lowered the Mica2standby current to about17μA,while waking up the system takes up to4ms if using the external crystal.The radio transceiver was replaced with the Chipcon CC1000offering tunable frequencies from300to900MHz and FSK modulation resilient to noise.The radio exposed a byte-level interface and timing interrupts.Although more resilient,the Mica2 had higher energy per bit and an order of magnitude higher wakeup time.Despite these shortcomings,Mica2and the smaller Mica2Dot are the de facto standard research platforms in WSN research(16 of21papers in SenSys2004used Mica2for evaluation).MicaZ[7] continues the evolution of the Mica family:it replaces the CC1000 radio with a CC2420,an IEEE802.15.4compatible radio.

A single chip mote implementation called Spec[8]resulted from analyzing the Mica platform.Just5mm2in size,Spec uses a number of dedicated hardware accelerators to perform programmable start

Fig.2.The family of Berkeley motes preceeding Telos and their capabilities

symbol detection,bit serialization,and encryption.A simple FSK radio uses a number of unusual structures(e.g.digital frequency-lock-loops)to reduce startup times and active power,while still providing the frequency agility and improved resistance to noise.The CPU has been optimized to reduce the cost of context switching. Spec’s performance is over1000times better than Mica in many applications.Unlike the Mica family,Spec is fully integrated and offers limited interface?exibility.Since it is a research project,it is unlikely to become available in quantities to the research community. Spec provides signi?cant advantages in power consumption due to its integrated design and hardware accelerators.The Telos design parallels that of Spec–instead of integrating the design into silicon, Telos uses COTS components with hardware accelerators to build a power ef?cient system that does not sacri?ce performance.

III.T ELOS P LATFORM

We discuss the design and implementation of Telos,including the intuition behind hardware selection.We offer an analysis of Telos and existing devices and provide a discussion of research enabled by the Telos platform.

The Telos platform is the result of over12months of research and development by two full-time graduate students,and numerous collaborator,at the University of California,Berkeley.Telos is a completely new design based off experiences from using previous mote generations designed by former graduate students at Berkeley and researchers at other institutions(Intel,ETH Zurich,etc...).We discuss how we achieve the three major goals for Telos:ultra-low power operation,easy to use,and robust hardware and software implementation.

A.Technological Trends

Since the Mica2mote was released in2002,a number of new mi-crocontrollers have been introduced offering lower power consump-tion,more on-chip peripherals,and various RAM and?ash sizes. Our low power principle focuses on reducing the sleep current and wakeup time of our system.Figure4summarizes the microcontroller improvements over time.

For Telos,we chose the MSP430microcontroller after evaluating existing products from Atmel,Motorola,and Microchip.Figure4 shows that the MSP430has the lowest power consumption in sleep and active modes.The microcontroller operates down to1.8V.Low voltages are important for extracting all of the energy out of a power source–e.g.,AA batteries have a cut-off voltage of0.9V.If two batteries are used in series,the system cut-off voltage is1.8V, exactly the same as the minimum required voltage for the MSP430.In contrast,the ATmega128MCU(Mica family)will only run down to 2.7V,leaving almost50%of the AA batteries unused.The MSP430 also has the fastest wakeup time of any microcontroller;transitioning from standby(1μA)to active mode(8MHz)in no more than6μs. The MSP430has a DMA controller to reduce load from the MCU core,lower power consumption,and increase performance.

The trend is to keep RAM and Flash sizes constant(shown in Figure4)while adding additional hardware accelerator modules. The MSP430provides us with the largest on-chip RAM buffer (10kB),useful for on-chip signal https://www.sodocs.net/doc/89223698.html,rger RAM buffers enable more sophisticated applications–for example,Mat′e[9]can use extended RAM to support more execution contexts and larger program images;TinyDB[10]uses larger RAM storage for in-network aggregation and data table https://www.sodocs.net/doc/89223698.html,rger?ash storage, although useful for large applications,has not been the limiting factor in developing WSN applications to date.

There are two distinct types of low power,low data rate radios: narrowband and wideband radios as shown in Figure3.Many narrow-band radios provide very fast startup times since they are clocked by the MCU but have simple modulation schemes,no spreading codes, and are not robust to noise.Wideband radios must wait for high speed oscillators to start.Enhanced modulation schemes found in wideband radios,such as spread spectrum(DSSS)and phase shift keying(O-QPSK),provide signal robustness to noise and interfer-ence.Narrowband radios typically operate at lower frequencies and lower data rates;wideband radios typically operate in the2.4GHz band and provide higher data rates.To pick the most applicable radio,we must evaluate the impact of noise,?exibility available to the end application,ease of communication with other devices,power

Type Narrowband Wideband

Vendor RFM Chipcon Chipcon Nordic Chipcon Motorola Zeevo Part no.TR1000CC1000CC2400nRF2401CC2420MC13191/92ZV4002 Max Data rate(kbps)115.276.810001000250250723.2 RX power(mA) 3.89.62418(25)19.737(42)65

TX power(mA/dBm)12/1.516.5/1019/013/017.4/034(30)/065/0 Powerdown power(μA)11 1.50.411140 Turn on time(ms)0.022 1.1330.5820* Modulation OOK/ASK FSK FSK,GFSK GFSK DSSS-O-QPSK DSSS-O-QPSK FHSS-GFSK Packet detection no no programmable yes yes yes yes Address decoding no no no yes yes yes yes Encryption support no no no no128-bit AES no128-bit SC Error detection no no yes yes yes yes yes Error correction no no no no yes yes yes Acknowledgments no no no no yes yes yes Interface bit byte packet/byte packet/byte packet/byte packet/byte packet Buffering(bytes)no132********yes* Time-sync bit SFD/byte SFD/packet packet SFD SFD Bluetooth Localization RSSI RSSI RSSI no RSSI/LQI RSSI/LQI RSSI

*Manufacturer’s documentation does not include additional information.

Fig.3.Capabilities of current COTS radios suitable for WSNs,their features,and power pro?le.

Manufacturer Device RAM Flash Active Sleep Release

(kB)(kB)(mA)(μA) Atmel AT90LS85350.585151998

Mega12841288202001

Mega165/325/645464 2.522004 General PIC0.0250.51911975

Instruments

Microchip PIC Modern4128 2.212002

Intel40044-bit0.625430N/A1971

80518-bit Classic0.5323051995

805116-bit11645101996 Philips80C5116-bit2601532000

Motorola HC050.532 6.6901988

HC0823281001993

HCS08460 6.512003 Texas TSS4004-bit0.0311*******

Instruments MSP430F14x16-bit260 1.512000

MSP430F16x16-bit1048212004 Atmel AT91ARM Thumb2561024381602004

Intel XScale PXA27X256N/A395742004 Fig.4.Microcontroller history:The main table contains traditional micro-controllers;the bottom two devices are32-bit microprocessors presented for comparison.

consumption,startup times,and available data bandwidth.Figure3 provides a summary of common radio features.No single radio in Figure3is globally optimal;instead a radio must be chosen based on application requirements.

For Telos,we chose to use the new IEEE802.15.4standard.By using a standardized radio,Telos can communicate with any number of devices sharing the same physical layer,including devices from other vendors.The primary factor in selecting a radio technology was the desire experiment with the new IEEE802.15.4wireless technology.Telos uses the Chipcon CC2420radio in the2.4GHz band,a wideband radio with O-QPSK modulation with DSSS at 250kbps.The higher data rate allows shorter active periods further reducing energy consumption.The radio crystal used on Telos was carefully chosen to be a low-ESR16MHz crystal;low resistance is essential for minimizing the startup time of the crystal(and thus minimizing wasted energy),The Telos crystal yields a580μs startup time,almost300μs lower than the minimum advertised startup time by Chipcon.

Since IEEE802.15.4radio interfaces are packet-based,we lose considerable?exibility in software for controlling the radio’s oper-ation.The CC2420provides a number of hardware accelerators to achieve better performance.These include encryption and authenti-cation,packet handling support,auto acknowledgments,and address decoding.Since hardware accelerators are embedded in the radio instead of the microcontroller,the accelerators may not be used as general purpose functions.For example,a data buffer may be encrypted and stored in?ash,however since it is not being sent over the radio,the radio’s hardware encryption module cannot be used. Other downsides include auto acknowledgment support–when this feature is used,packets not addressed to the local node are discarded by hardware preventing services from overhearing messages useful for link estimation and routing.

B.Integrated Design

Instead of using separate pluggable modules to create a full sensor node,Telos integrates programming,computation,communication, and sensing onto a single device.The integrated design provides an easy to use mote with increased robustness.

Telos uses an internal2.4GHz Planar Inverted Folded Antenna (PIFA)built into the printed circuit board and tuned to match the radio circuitry.An optional SMA coax connection may be used instead of the internal antenna.Integration of the antenna lowers the overall cost of the mote since no expensive external antennae are needed. Telos is programmed(either with the bootstrap loader or JTAG) through on-board USB that also provides https://www.sodocs.net/doc/89223698.html,B was chosen since it is a standardized protocol that interfaces well with current PCs.On-board USB is extremely easy to use and has lowered development time compared to non-standard mote interfaces. Telos has a user button,reset button,and16-pin IDC expansion header.The user and reset button signals are exported via the header so the physical user-interface may be located on support hardware. The reset button may be retasked as a non-maskable interrupt allowing it to be used as a power button instead.By exporting I2C and UART over the expansion header,I/O bus expanders can be used to attach as many connections as are found on legacy“Mica-style”sensor boards[11].

Inside the Telos,it is the?rst mote to include hardware write-protection for external storage.When plugged into a USB port,the write protection is disabled and the?rst segment of the external ?ash may be written.When running on batteries(without USB),the segment is write protected.Hardware write protection is essential for systems that may be reprogrammed wirelessly–since a known good program image may be stored in the write protected?ash,there is always a fallback mechanism to a usable mote.

Each hardware“sub-circuit”is isolated;power to the circuit can be turned on or off independently of the rest of the platform.This

Distance (ft)

P a c k e t Y i e l d (%)

Distance (ft)

A v e r a g e L Q I

Distance (ft)

R S S I (d B m )

Fig.5.Packet yield (left ),link quality indicator (LQI,center ),and received signal strength (RSSI,right )outdoors with the Telos mote and internal antenna.The results are averaged over 10receivers co-located.From 75-110feet,a dip in the terrain yields more erratic readings and wider variation in RSSI.

isolation provides a degree of robustness–in the event of a failure,faulty modules can be disabled to minimize their impact on the system.The motivation for this design comes from the experience with real-world sensor networks on Great Duck Island (GDI)[12],[6].On GDI,one of the main predictors of node failure was the existence of a failed sensor.Since the failure can be recognized in software,the ability to cut power to that section of the board may have saved the system as a whole.

Since the IEEE 802.15.4protocol has a 64-bit addressing scheme,we have included a 48-bit silicon serial identi?cation chip.The id,combined with a manufacturer’s IEEE Organizationally Unique Identi?er (OUI)stored in write protected ?ash,provides the user with a valid,unique 64-bit MAC address.The MAC address is useful for system and network diagnostics,as well as absolute node identi?cation.C.Analysis

Our analysis of the Telos platform focuses on the platform’s power consumption and the features that further research in sensor networks.The power consumption of a sensor module is not just the microcontroller and/or radio,but also the auxiliary components and their quiescent current.The power consumption of the Telos mote for various operations compared to the existing Mica2and MicaZ platforms is shown in Figure 6.

Telos features a lower power ?ash and microcontroller than Mica2(Atmel with CC1000radio)and MicaZ (Atmel with CC2420radio).Due to Telos’integrated design,3μA additional current in sleep state is sacri?ced to switches and buffers that protect current from ?owing backward into disconnected components,speci?cally the USB circuitry.Despite this sacri?ce,the overall power consumption of a sampling cycle (wakeup,sample,transmit,and sleep)is lower than existing platforms.The power consumption is the total time the mote is active multiplied by the current consumption during that time.Since Telos has lower current consumption,lower startup time,and lower operating voltage for the entire mote,it can achieve longer lifetimes than previous designs.At a 1%duty cycle,Telos can last for almost 3years.For comparison,the lifetime of the Mica2mote is 1.5years and the MicaZ mote is 1year [1].

Lower power consumption does not imply that Telos has less func-tionality.Powerful microprocessor modules are now being integrated into embedded microcontrollers.Telos features a DMA controller that operates while the MCU core is sleeping.The DMA permits applications to sample from the ADC,output a voltage on the DAC,

Operation

Telos Mica2MicaZ Minimum V oltage

1.8V

2.7V 2.7V Mote Standby (RTC on) 5.1μA 19.0μA 27.0μA MCU Idle (DCO on)54.5μA

3.2mA 3.2mA MCU Active

1.8mA 8.0mA 8.0mA MCU +Radio RX

21.8mA 15.1mA 23.3mA MCU +Radio TX (0dBm)19.5mA 25.4mA 21.0mA MCU +Flash Read 4.1mA 9.4mA 9.4mA MCU +Flash Write 15.1mA

21.6mA 21.6mA MCU Wakeup 6μs 180μs 180μs Radio Wakeup

580μs

1800μs

860μs

Fig.6.Measured current consumption of Telos compared to Mica2and MicaZ motes

or transfer data to and from the radio without interrupting the MCU.DMA is traditionally used to increase performance,but in the case of low power embedded systems,the DMA controller actually lowers the duty cycle by permitting the MCU core to remain asleep longer and service less interrupts.The performance enhancements of DMA permit up to 200ksamples/sec ADC sampling,compared to a max-imum of 10ksamples/sec on MCUs without DMA (some powerful MCUs can achieve as high as 70ksamples/sec,but no interrupt-based method on current MCUs can achieve 200ksamples/sec).The lower sampling rate is caused by the overhead of context switching due to interrupts after each ADC conversation.Telos also has built-in brown-out reset,supply voltage supervisor,and interrupt driven sensors to maximize the sleeping time of the mote.

For communications,IEEE 802.15.4radios provide applications with information about the incoming signal.Telos’on-board antenna provides a mostly omnidirectional pattern 1.We tested the effect of distance on received signal strength (RSSI),packet success rate,and link quality (LQI).LQI is a metric introduced in 802.15.4that measures the error in the incoming modulation of successfully received packets (packets that pass CRC check).We placed 10receivers at the same location and 1node transmitting at 0dBm at a distance d ,all located 4”above the ground outdoors.We averaged the results over all receivers.Figure 5shows the average packet success,LQI,and RSSI for Telos using the internal antenna.The LQI provided by the radio closely maps to the packet success rate as shown in Figure 5.The RSSI follows an exponential decrease while the packet success rate is high;after 60feet,the signal is noisier and decreases to the minimum sensitivity of the transceiver.The small variance in RSSI among receivers and the correlation between LQI and packet

1More

microbenchmarks including radio and antenna impedance matching

can be found in the Telos datasheet [13].

success rate provides additional information not previously available to network services such as multihop networking and localization. The consequence of using a higher speed radio is that it may saturate the MCU’s processing capabilities when the channel is fully loaded.We ran experiments on a30node Telos network to measure the effective bandwidth.A single Telos node is able to source approximately1/2of the full data bandwidth of the channel, or125kbps.When all30nodes transmit as quickly as possible, Telos is limited to an average reception rate of150kbps.Our current implementation is interrupt driven;however we intend to increase performance by using the DMA controller to directly transfer data from the radio,reduce the number of interrupt context switches,and reduce the number of receive buffer over?ow events.

D.Enabling Research

To support current research efforts,Telos integrates a number of features that create more robust systems.Deluge[14]is an epidemic code-propagation protocol used in BNP[15]to reprogram the net-work wirelessly.In the event that a faulty code image renders the node unusable,a halted node may be reset via the watchdog timer or a button(referred to as a“Golden Gesture”).Telos will automatically reload the microcontroller’s code?ash with the hardware protected golden image.

The golden gesture can be performed through a number of se-quences.Since Telos features a“User Button”for external user input, a combination of pressing the reset and user buttons may be required to boot to the golden image.The user button may serve other user programmable services thereby providing a method for physical input to be received at the mote when radio commands are not an option (such as during physical deployment).

Due to Telos’low wake up times,the mote is automatically put to sleep when there is no active processing.By automatically entering the lowest power mode when idle,Telos has a lower operating power pro?le.The low power pro?le also makes Telos attractive for rechargeable designs,including solar and vibration harvesting. Since Telos operates down to1.8V,super-capacitor designs are now possible(many super-capacitors operate at a maximum of2.5V,lower than the minimum operating voltage of previous motes).Since the sleep current and wakeup times are lower,harvested energy may be stored quicker and be used for more operations.

Finally,Telos lowers the barrier of entry for using WSNs.By using USB on every mote,any Telos may operate as an experimental device on a lab bench,a gateway to a PC or higher functionality device,or as a node in a large testbed.In the lab or classroom, USB provides an easy and robust way to interface,program,and experiment with motes.As a gateway,no programming or interface board is required and any node may act as the gateway.Finally,off-the-shelf USB products are a low cost method for deploying testbeds with a back-channel link.Back-channels are important for developing algorithms on the motes while being able to debug their state and operation without relying on the wireless transceiver.Most testbeds with back-channel links are created using long runs of Ethernet.The infrastructure cost of a60-node Telos testbed is approximately$1,000 ($600in cabling,$400in USB hubs).For longer cable runs,a Linksys Ethernet to USB device may be purchased for$79and includes2 USB ports.A networked testbed with Linksys devices is an additional $2,400.In contrast,a60-node Mica2testbed costs almost$21,000 in infrastructure hardware alone($349per Mica2Ethernet adapter as of February2005).E.Software Implications

There is a huge impact on the software when creating a new hardware platform.TinyOS[16]is a componentized operating system suitable for research in wireless embedded systems.The composition of components and whole program analysis allows researchers to work on the system at any level(e.g.,the details of link protocols up to the application semantics).Since the MSP430is a different architecture than the microcontrollers commonly used in TinyOS,we were forced to rethink hardware abstraction for embedded systems. An opportunity was created by Telos to redesign the existing TinyOS 1.1.x interfaces to create effective abstractions that take advantage of the powerful hardware features of the MSP430microcontroller. We developed a three-tier architecture to provide a hardware independent abstraction regardless of microcontroller or radio.The design is described in detail by Handziski et.al.[17].We chose to expose the primitives of the hardware,such as register access and module?ags,through a hardware presentation layer(HPL).

A platform-dependent hardware abstraction layer(HAL)exposes hardware module functionality so that the full power of the hardware may be used.The HAL includes getting data from the ADC, setting a hardware Timer,or writing to external?ash.The hardware independent layer(HIL)exposes a subset of a platform’s capabilities that are available to system services.The HPL/HAL/HIL model is implemented in TinyOS for the TI MSP430microcontrollers and has been adopted as the basic architecture for hardware abstraction by the TinyOS2.0Working Group.

On top of the HAL/HPL/HIL abstraction,we built a platform-independent radio stack(link protocol and physical layer access)for the CC2420transceiver.Each platform using the CC2420implements a set of components that provide register access to the radio;the radio stack then acts as a library that uses these primitives to the control the radio.Our CC2420implementation operates on Telos,MicaZ, iMote2,and Chipcon CC2420EB platforms.Since these platforms all share the same physical layer,TinyOS enables cross-platform communication and research on hybrid networks.

IV.C ONCLUSION

We have presented the design and implementation of Telos,the latest generation in a family of motes from UC Berkeley.We showed that Telos is the lowest power mote to date.Telos includes numerous enhancements that enable research in wireless sensor networks while making the devices easier to use and lowering the per-module cost. Other features,like hardware write protection and radio signal stabil-ity,closely map to current research.Researchers may experiment with the new IEEE802.15.4standard and use existing work in TinyOS. Additional?exibility allows software to con?gure or disable hardware modules.Telos is a robust module with lower power consumption yet greater performance than existing designs.

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学生: 科目: 数 学 教师: 刘美玲 一、二次函数和特殊多边形形状 二、二次函数和特殊多边形面积 三、函数动点引起的最值问题 四、常考点汇总 1、两点间的距离公式:()()22B A B A x x y y AB -+-= 2、中点坐标:线段AB 的中点C 的坐标为:??? ??++22 B A B A y y x x , 直线11b x k y +=(01≠k )与22b x k y +=(02≠k )的位置关系: (1)两直线平行?21k k =且21b b ≠ (2)两直线相交?21k k ≠ (3)两直线重合?21k k =且21b b = (4)两直线垂直?121-=k k 3、一元二次方程有整数根问题,解题步骤如下: ① 用?和参数的其他要求确定参数的取值范围; ② 解方程,求出方程的根;(两种形式:分式、二次根式) ③ 分析求解:若是分式,分母是分子的因数;若是二次根式,被开方式是完全平方式。 例:关于x 的一元二次方程()0122 2 =-m x m x ++有两个整数根,5<m 且m 为整数,求m 的值。 4、二次函数与x 轴的交点为整数点问题。(方法同上) 例:若抛物线()3132 +++=x m mx y 与x 轴交于两个不同的整数点,且m 为正整数,试确定 此抛物线的解析式。 课 题 函数的综合压轴题型归类 教学目标 1、 要学会利用特殊图形的性质去分析二次函数与特殊图形的关系 2、 掌握特殊图形面积的各种求法 重点、难点 1、 利用图形的性质找点 2、 分解图形求面积 教学内容

5、方程总有固定根问题,可以通过解方程的方法求出该固定根。举例如下: 已知关于x 的方程2 3(1)230mx m x m --+-=(m 为实数),求证:无论m 为何值,方程总有一个固定的根。 解:当0=m 时,1=x ; 当0≠m 时,()032 ≥-=?m ,()m m x 213?±-= ,m x 3 21-=、12=x ; 综上所述:无论m 为何值,方程总有一个固定的根是1。 6、函数过固定点问题,举例如下: 已知抛物线22 -+-=m mx x y (m 是常数),求证:不论m 为何值,该抛物线总经过一个固定的点,并求出固定点的坐标。 解:把原解析式变形为关于m 的方程()x m x y -=+-122 ; ∴ ???=-=+-0 1 02 2x x y ,解得:???=-=1 1 x y ; ∴ 抛物线总经过一个固定的点(1,-1)。 (题目要求等价于:关于m 的方程()x m x y -=+-122 不论m 为何值,方程恒成立) 小结.. :关于x 的方程b ax =有无数解????==0 b a 7、路径最值问题(待定的点所在的直线就是对称轴) (1)如图,直线1l 、2l ,点A 在2l 上,分别在1l 、2l 上确定两点M 、N ,使得MN AM +之和最小。 (2)如图,直线1l 、2l 相交,两个固定点A 、B ,分别在1l 、2l 上确定两点M 、N ,使得 AN MN BM ++之和最小。

MAX4666EPE中文资料

For free samples & the latest literature: https://www.sodocs.net/doc/89223698.html,, or phone 1-800-998-8800.For small orders, phone 1-800-835-8769. General Description The MAX4664/MAX4665/MAX4666 quad analog switch-es feature 5?max on-resistance. On-resistance is matched between switches to 0.5?max and is flat (0.5?max) over the specified signal range. Each switch can handle Rail-to-Rail ?analog signals. The off-leakage cur-rent is only 5nA max at +85°C. These analog switches are ideal in low-distortion applications and are the pre-ferred solution over mechanical relays in automatic test equipment or in applications where current switching is required. They have low power requirements, require less board space, and are more reliable than mechanical relays. The MAX4664 has four normally closed (NC) switches,the MAX4665 has four normally open (NO) switches, and the MAX4666 has two NC and two NO switches that guarantee break-before-make switching times. These switches operate from a single +4.5V to +36V supply or from dual ±4.5V to ±20V supplies. All digital inputs have +0.8V and +2.4V logic thresholds, ensuring TTL/CMOS-logic compatibility when using ±15V sup-plies or a single +12V supply. Applications Reed Relay Replacement PBX, PABX Systems Test Equipment Audio-Signal Routing Communication Systems Avionics Features o Low On-Resistance (5?max) o Guaranteed R ON Match Between Channels (0.5?max)o Guaranteed R ON Flatness over Specified Signal Range (0.5?max)o Guaranteed Break-Before-Make (MAX4666)o Rail-to-Rail Signal Handling o Guaranteed ESD Protection > 2kV per Method 3015.7o +4.5V to +36V Single-Supply Operation ±4.5V to ±20V Dual-Supply Operation o TTL/CMOS-Compatible Control Inputs MAX4664/MAX4665/MAX4666 5?, Quad, SPST, CMOS Analog Switches ________________________________________________________________Maxim Integrated Products 1 Pin Configurations/Functional Diagrams/Truth Tables 19-1504; Rev 0; 7/99 Ordering Information continued at end of data sheet. Ordering Information Rail-to-Rail is a registered trademark of Nippon Motorola, Ltd.

PB常用函数

PB常用函数日期时间类函数 日期时间类函数的功能如下: Date:把日期转换为Date类型。 Time:把时间转换为Time类型。 Day:日期值。 Month:月值。 Year:年值。 DayName:星期几。 DayNumber:一周中的第几天。 DaysAfer:两个日期之间所差的天数。 SecondsAfer:两个时间之间所差的秒数。 Hour:小时。 Minute:分钟。 Second:秒。 Now:系统当前时间。 Today:系统日期和时间。 RelativeDate:指定日期前后的天数值。 RelativeTime:指定时间的前后时间值。 数值计算类函数 数值计算类函数主要的作用就是对数据进行计算,功能如下:Abs:返回数据的绝对值。 Max:求输入的最大值。 Min:求输入的最小值。 Ceiling:返回整数,小数会自动向上进位。 Int:返回整数,小数会自动向下退位。 Round:对数据进行四舍五入操作。 Truncate:删除掉小数点后若干位。 Cos:求余弦值。 Sin:求正弦值。 Tan:求正切值。 Exp:以e为底,输入值为次方的乘方值。 Sqrt:求平方根。 Fact:求阶乘。 Log:求自然对数。 LogTen:求以10为底的对数。 Mod:求余数。 Pi:求与PI的乘积。 Rand:返回1与输入值之间的一个伪随机数。 字符串类函数 字符串类函数的功能如下。 Fill:建立一个指定长度的字符串。 Lower:转换为小写字母。

Upper:转换为大写字母。 WordCap:首写字母大写,其他小写。 Space:由指定字符个数组成的空格字符串。 Left:从字符串左边开始指定字符串。 Right:从字符串右边开始指定字符串。 LeftTrim:删除字符串左边的空格。 RightTrim:删除字符串右边的空格。 Trim:删除左右两边的空格。 Len:返回字符串长度。 Match:判断是否有指定模式的字符。 Mid:取子字符串。 Replace:用指定字符替换另外一个字符串。 String:将数据转换为指定格式的字符串。 信息类函数 信息类函数可以获取数据窗口中的一些信息,函数的功能如下: CurrentRow:获取数据窗口的焦点的行数。 Page:获取当前记录的页数。 PageAcross:获取当前水平方向的页面。 PageCount:获取总页数。 RowHeight:获得记录的高度。 Describe:获取数据窗口对象的属性值。 IsRowModified:获取记录是否修改过,如果修改过返回True。 IsRowNew:获取是否新插入数据,如果插入返回True。 IsSelected:获取记录是否被选中,选中返True。 PageCountAcross:获取水平方向总页面。 RowCount:获取主缓冲区的总记录数。 统计类函数 统计类函数主要是用来对数据库中的数据进行统计操作,统计函数功能如下: Avg:计算字段的平均数,例如Avg(id)。 Max:计算字段的最大值,例如Max(id)。 Min:计算字段的最小值,例如Min(id)。 Median:计算字段的中间值。 Count:计算表或字段的记录数,例如Count(*)。 Frist:返回第一条记录。 Last:返回最后一条记录。 交叉表函数 只能在交叉列表风格的数据窗口中的细节区使用交叉表函数,交叉表的函数功能如下:CrosstabVag:计算字段数据的平均数。 CrosstabCount:计算字段数据的记录数。 CrosstabMax:计算字段数据的最大值。 CrosstabMin:计算字段数据的最小值。 数据类型转换与检查函数 数据类型转换与检查函数用于定义数据窗口的过滤条件、有效性检查和数据类型转换,数据类型转换与检查函数的功能如下:

云管理平台解决方案

随着云计算在企业内应用,大多数企业都认识到了云计算的的重要性,因为它可以实现资源分配的灵活性、可伸缩性并且提高了服务器的利用率,降低了企业的成本。但是随着企业信息化程度的越来越高、信息系统支持的业务越来越复杂,管理的难度也越来越大,所以就需要选择一个合理的解决方案来支撑企业信息系统的管理和发展。 云管理平台最重要的两个特质在于管理云资源和提供云服务。即通过构建基础架构资源池(IaaS)、搭建企业级应用、开发、数据平台(PaaS),以及通过SOA架构整合服务(SaaS)来实现全服务周期的一站式服务,构建多层级、全方位的云资源管理体系。那么有没有合适的云管理平台解决方案可以推荐呢? SmartOps作为新一代多云管理平台,经过6年多的持续研发和实际运营,已经逐渐走向成熟,能通过单一入口广泛支持腾讯云、阿里云、华为云、AWS等超大规模公有云的统一监控、资源编排、资产管理、成本管理、DevOps 等管理功能,同时也支持私有云和物理裸机环境的统一纳管。SmartOps平台具有统一门户、CMDB配置

数据库、IT服务管理、运维自动化和监控告警等主要模块,支持客户自助在线处理订单、付款销账、申报问题、管理维护等商务运营流程,而且对客户的管理、交付、技术支持也都完全在平台上运行,这极大提升了整体运营效率并大幅降低成本,业务交付速度更快、自动化程度更高、成本更具竞争力、用户体验更佳。 同时,SmartOps正在构建适应业务创新发展的云管理平台,实现从服务中提炼普惠性的服务方案,并构建软件化、工具化、自动化的快速上线对外提供服务的通道。SmartOps不仅是一个云管平台,也是一个面向企业用户的服务迭代的创新平台,一切有利于企业用户数字化发展的个性化服务,都有可能在普遍落地后实现技术服务产品化、工具化的再输出。不仅如此,下一步,SmartOps还将融入更多的价值,包括借助人工智能的技术,面向企业用户领导决策提供参考价值。借助平台化的管理工具,为企业财务人员提供有价值的成本参

云课堂解决方案

创新管理价值,引导教学未来——云课堂解决方案 一、概述 随着计算机教育的发展,计算机机房在各中小学已经相当普及,这些计算机资源在很大程度上提高了课题的教学效果。同时,随着机房规模的不断扩大,学校需要管理和维护的各种计算机硬件和软件资源也越来越多,而中小学维护力量相对薄弱,如何科学有效地对这些教育资源进行管理已成为各中小学面临的一个难点管理维护问题:很少中小学有专门的机房管理人员,机房维护专业性要求高,工作量大 使用体验问题:PC使用时间一长,运行速度变慢,故障变多 投资保护问题:PC更新换代较快,投资得不到保障 节能环保问题:机房耗电量大,废弃电脑会产生大量电子垃圾 二、方案简介 RCC(Ruijie Cloud Class)云课堂是根据不断整合和优化校园机房设备的工作思路,结合普教广大学校的实际情况编制的新一代计算机教室建设方案。每间教室只需一台云课堂主机设备,便可获得几十台性能超越普通PC机的虚拟机,这些虚拟机通过网络交付给云课堂终端,学生便可体验生动的云桌面环境。云课堂可按照课程提供丰富多彩的教学系统镜像,将云技术和教育场景紧密结合,实现教学集中化,管理智能化,维护简单化,将计算机教室带入云的时代。 三、方案特性 简管理

云课堂采用全新的集中管理技术管理学校所有计算机教室,管理员在云课堂集中管理平台RCC Center中根据教学课程的不同应用软件制作课程镜像, 同步给教室中的云课堂主机设备,老师上课时可根据课程安排一键选择镜像从而随时获得想要的教学环境。 管理员也不用再为记录繁杂的命令而烦恼,云课堂提供全图形控制管理界面,无论虚拟机制作,编辑,还原都只需轻轻一按。云课堂的管理模式可彻底解决机房中常见大量软件安装导致系统臃肿、软件冲突,病毒侵入、教学、考试场景切换工作量大等难题,还可省去Ghost或还原卡的繁杂设置。全校的计算机教室设备监控和软件维护在办公室中即可轻松实现,效率比PC管理提高9倍! 促教学 云课堂三大关键技术,全面提升虚拟机性能,可令终端启动和课程切换加速,教学软件运行更快,并且可以全面控制学生用机行为,杜绝上课开小差的情况发生。 智能镜像加速技术 - 所有定制好的系统镜像会由云课堂主机自动优化,在该技术的支持下,60个虚拟机启动时间只需短短几分钟,同时还提供老师在上课过程中可随时切换学生操作系统的选择,从而轻易改变教学环境,演绎云技术带给传统教学的优化和创新实践。 多级Cache缓存技术 - 实现镜像启动加速、IO加速,使云桌面启动和应用程序运行速度大幅度提升,用户体验远高于市面上其他产品。在该技术帮助下,教师常用教学课件,专用软件启动、运行速度比同配置物理机提升200%,大幅提升用机体验,让学生畅游”云海”,领略“飞”一般的感受! 多媒体教学管理软件防卸载技术–云课堂终端内嵌多媒体教学管理程序,且学生不可见。老师在使用该软件教学时,不会再出现学生因卸载或关闭管理程序而脱离教师的管理现象,大大加强对学生上课行为的控制力度,严肃课堂纪律,教学质量得以保证。 易获得 云课堂是包括课堂主机,课堂终端,多媒体教学管理软件和课堂集中管理平台在内的一套端到端的整体解决方案。其部署过程极其简单,仅需将云课堂主机和云课堂终端相连,在云课堂主机上做一次课程配置,一间全新的计算机教室即建设完成。因省去逐台PC分区设置和系统同传等过程,效率上可提高3小时以上。 同时云课堂终端功耗极低,普通教室不需强电改造即可转型为云课堂,加快校园IT信息化建设的同时,打造绿色校园 更环保 每台云课堂终端设备平均功耗20w,是传统PC机的1/12。且整个终端机身使用一体化设计,无风扇、硬盘等易损元件,寿命比PC机延长20%以上。节省开支的同时大大减少电子垃圾,响应国家倡导的绿色节能号召,创造舒适、低能耗的绿色校园环境。

max3485esa中文资料

General Description The MAX3483, MAX3485, MAX3486, MAX3488, MAX3490, and MAX3491 are 3.3V , low-power transceivers for RS-485 and RS-422 communication. Each part contains one driver and one receiver. The MAX3483 and MAX3488 feature slew-rate-limited drivers that minimize EMI and reduce reflections caused by improperly terminated cables, allowing error-free data transmission at data rates up to 250kbps. The partially slew-rate-limited MAX3486 transmits up to 2.5Mbps. The MAX3485, MAX3490, and MAX3491 transmit at up to 10Mbps. Drivers are short-circuit current-limited and are protected against excessive power dissipation by thermal shutdown circuitry that places the driver outputs into a high-imped- ance state. The receiver input has a fail-safe feature that guarantees a logic-high output if both inputs are open circuit. The MAX3488, MAX3490, and MAX3491 feature full- duplex communication, while the MAX3483, MAX3485, and MAX3486 are designed for half-duplex communication.Applications ●Low-Power RS-485/RS-422 Transceivers ●Telecommunications ●Transceivers for EMI-Sensitive Applications ●Industrial-Control Local Area Networks Features ●Operate from a Single 3.3V Supply—No Charge Pump!●Interoperable with +5V Logic ●8ns Max Skew (MAX3485/MAX3490/MAX3491)●Slew-Rate Limited for Errorless Data Transmission (MAX3483/MAX3488)●2nA Low-Current Shutdown Mode (MAX3483/MAX3485/MAX3486/MAX3491)●-7V to +12V Common-Mode Input Voltage Range ●Allows up to 32 Transceivers on the Bus ●Full-Duplex and Half-Duplex Versions Available ●Industry Standard 75176 Pinout (MAX3483/MAX3485/MAX3486)●Current-Limiting and Thermal Shutdown for Driver Overload Protection 19-0333; Rev 1; 5/19 Ordering Information continued at end of data sheet. *Contact factory for for dice specifications. PART TEMP . RANGE PIN-PACKAGE MAX3483CPA 0°C to +70°C 8 Plastic DIP MAX3483CSA 0°C to +70°C 8 SO MAX3483C/D 0°C to +70°C Dice*MAX3483EPA -40°C to +85°C 8 Plastic DIP MAX3483ESA -40°C to +85°C 8 SO MAX3485CPA 0°C to +70°C 8 Plastic DIP MAX3485CSA 0°C to +70°C 8 SO MAX3485C/D 0°C to +70°C Dice*MAX3485EPA -40°C to +85°C 8 Plastic DIP MAX3485ESA -40°C to +85°C 8 SO PART NUMBER GUARANTEED DATA RATE (Mbps)SUPPLY VOLTAGE (V)HALF/FULL DUPLEX SLEW-RATE LIMITED DRIVER/RECEIVER ENABLE SHUTDOWN CURRENT (nA)PIN COUNT MAX3483 0.25 3.0 to 3.6Half Yes Yes 28MAX3485 10Half No No 28MAX3486 2.5Half Yes Yes 28MAX3488 0.25Half Yes Yes —8MAX3490 10Half No No —8MAX349110Half No Yes 214MAX3483/MAX3485/MAX3486/MAX3488/MAX3490/MAX3491 Selection Table Ordering Information 找电子元器件上宇航军工

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