OPT05_4E
ARTISAN TECHNOLOGY GROUP 用户指南说明书
Getting StartedGB1400 Pattern Generator and Error DetectorFeatures•Test digital data transmission up to 1400 Mb/s•Set Data Rate with 1 kHz resolution•Vary Clock and Data timing with 5 pSresolution•Phase-Synchronous Clock and Data EdgeTracking•Up to 1-Mbit custom data pattern memory•Measure Eye-Width at Specific BERAutomatically•Auto-Synchronization Rx/Tx Lock-up•Front panel or computer control operationThe GB1400 is a general-purpose 1400 Mb/s bit error rate tester (BERT) built tomeet the exacting standards of design engineers who need to verify andcharacterize high-speed serial data transmission circuits, interfaces and systems.While primarily a lab instrument, the GB1400’s compact design, full computerprogrammability and relatively light weight also enable it to serve inmanufacturing ATE and field test applications.The quality of a digital link depends on many factors, but everything comesdown to the issue of whether the circuit exhibits a satisfactory BER (bit errorrate) and has sufficient margin to function under stress conditions.The GB1400 has all of the features you expect in a general-purpose BERT, andsome you expect only in more expensive instruments, such automated eye-widthmeasurements at a specified BER, and the ability to accept an external real-timedata stream for bit error testing. Also, the GB1400 has options to add advancedfeatures, such as Burst Mode (which also extends external clock range down to150 kb/s), and a 1-Mbit programmable pattern memory option.Getting StartedSymmetrical, Low-Jitter Output WaveformsThe GB1400 generates low-jitter, symmetrical waveforms over its entireoperating frequency range. The clock and data ports provide both true andinverted output signals. The instrument can drive single-ended or differentialECL inputs.ApplicationsThe GB1400 is focused on the research, design, and manufacturing oftelecommunication components, modules, or links operating at data rates to1400 Mb/s. It is frequently employed in testing and development well under thistop speed rating, where sharp clock and data waveforms are especially desired, orwhere additional frequency range is thought to be needed in the future.Sample Applications•Development of Gigabit LAN/Data Comm Devices:•High-Speed Fibre Channel, Ethernet•Digital Video (MPEG, SDV, HDDV)•Wideband Satellite Data Links•SONET/SDH Network Devices up to OC-12e/STM4e•High-speed GaAs/ECL/E/O device testing•Test Clock Recovery Circuits•Parallel-to-Serial Analysis with Tektronix MB100•Testing of High Speed Fibre Channel links up to 1,063 Mb/s•Gigabit Ethernet at 1,250 Mb/s.•Testing of high-speed Optical Busses (Opto Bus, Opto Bahn) at 800 Mb/s perchannel.•Satellite system testing and TDMA (Burst Mode) at 400, 800 Mb/s•GaAs, ECL and optical component testingPRBS Or User-Defined Test PatternsThe GB1400 can generate pseudo-random bit sequences (PRBS) up to 223−1 bitsand others up to 1-Mbit in length, via user-programmable patterns. Patterns canbe created locally using setup menus or externally by using a workstation or PC.A PC Windows based Pattern Editor software package comes with the 1-MbitMemory Option. Externally created patterns can be downloaded via the GPIB orRS-232 port. All user patterns are saved in battery-backed RAM.Getting StartedAdjustable Inputs For Maximum FlexibilityThe clock and data ports on the GB1400 Error Detector accept both true and inverted inputs. Single-ended or differential signals can be internally terminated. Input data delay is adjustable over a 4 ns range to accommodate different clock and data signal path delays.Auto Search For Easy SetupAuto search greatly simplifies the Error Detector setup. The GB1400 Error Detector automatically synchronizes to the incoming signal by 1) Setting the input data decision voltage to its optimum value; 2) Adjusting input data delay for an optimum clock/data phase relationship; 3) Selecting the correct PRBS test pattern; and 4) selecting the correct pattern polarity (normal or inverted).It synchronizes with any pattern sourced by a gigaBERT Pattern Generator. It can perform a bit-by-bit comparison of an external data stream via the Reference Data input. Thus the GB1400 can perform bit error analysis on any data pattern with a known good reference pattern.Powerful Analysis And Reporting FunctionsThe GB1400 performs a full-rate, bit-by-bit analysis of the received signal. Bit error results are then used to calculate three bit error rate (BER) measures. Total BER is calculated from the last power-on or reset. Window BER is calculated over a sliding window specified in terms of time (1 second to 24 hours) or bits (18- to 116-bits). Test BER is calculated from the start of the current test. A hard copy of all test results can be generated locally by connecting a printer to the parallel printer port or GPIB or RS-232 port. Reports may be printed when an error is detected, at the end of test intervals, or both.Front Panel Or Automated OperationThe GB1400 provides easy operation augmented by set-up store and recall. Clear, concise LCD displays of setup and results make it easy to use. The 1 Megabit memory option for both the Pattern Generator and the Error Detector is sufficient for storing and outputting complex data such as SONET frames, ATM cells, MPEG digital video, etc, allowing designers to simulate “live” traffic. The GB1400 Pattern Generator and Error Detector can be controlled via the GPIB or RS-232 interface ports. The gigaBERT remote command set includes commands for all setup menus and front panel selections. The status of front panel indicators and test results can be remotely accessed.Burst ModeBURST mode, allows for operation with non-continuous external clocks. Use of BURST mode requires ECL-level signals with a minimum rate during the burst of 150 kHz. This is an option to the GB1400. See a write-up on Burst Mode at the end of the Functional Overview section of Chapter 2.Getting StartedOrdering InformationgigaBERT GB14001400 Mb/s BERT Generator and Detector. Not available in Europe.Includes: Power Cord, Manual.Opt. 02 - 75 Ohm Both Sets.Opt. 05 - BURST Mode Both Sets.Opt. 07 - Positive ECL (Pattern Generator Only).Opt. 08 - 1-Mbit RAM WORD Both Sets & PC Pattern Editor Software.Opt. 2M - Rack Mounts - 2 rackmount kitsOpt. A3 - Australian 240 V, 50 Hz.gB1400T1400 Mb/s BERT Pattern Generator.Opt. 02 - 75 Ohm Pattern Generator Only.Opt. 05 - BURST Mode Pattern Generator Only.Opt. 07 - Positive ECL Pattern Generator OnlyOpt. 08 - 1-Mbit RAM WORD, Generator Only, w/ PC Pattern Edit softwareOpt. 1M - Rack Mount.Opt. A3 - Australian 240 V, 50 Hz.gB1400R1400 Mb/s BERT Error Detector.Opt. 02 - 75 Ohm Error Detector Only.Opt. 05 - BURST Mode Error Detector Only.Opt. 08 - 1-Mbit RAM WORD, Detector Only w/ PC Pattern Edit SoftwareOpt. 1M - Rack Mount.Opt. A3 - Australian 240 V, 50 HzGetting StartedGB Comparison Feature GB660/CSA907ATx and RxGB700Tx and RxGB1400Tx and RxTransmitter Frequency rangeInternal Clock SourceExternal ClockExternal Clock w/Burst Mode1150 kHz to 700 MHz150 kHz to 700 MHz150 kHz to 700 MHz150 kHz to 705 MHz150 kHz to 705 MHz150 kHz to 705 MHz1 MHz to 1400 MHz1 MHz to 1400 MHz150 kHz to 1400 MHzFreq Resolution (InternalClock)1 kHz 1 kHz 1 kHz (was 10 kHz)Clock /DataOutput Amplitude500mV to 2.0 V500mV to 2.0 V500mV to 2.0 VClock/Data Output Offset -2.0V to +1.8 V-2.0V to +1.8 V-2.0V to +1.0 V-2.0V to +1.8 V withPECL opt.Clock/Data ThresholdResolution50 mV steps50 mV steps50 mV steps Std. Programmable Memory16 bits128 Kbits16 bitsOptional Memory128 Kbits none 1 MbitPRBS Patterns (2n-1)7,15,17,20,237,15,17,20,237,15,17,20,23 Burst Mode (External ClkOnly)Standard Feature Standard Feature Optional Feature ReceiverFrequency range w/Burst Mode1150 kHz to 705 MHz150 kHz to 705 MHz150 kHz to 705 MHz150 kHz to 705 MHz1 MHz to 1400 MHz150 kHz to 1400 MHzBurst Mode (Ext Clk Only)Standard Feature Standard Feature Optional Feature Clock/Data Input levels (max)500 mV to 6.0 V p-p500 mV to 6.0 V p-p500 mV to 2.0 V p-p Clock Input Threshold-3.00 to +4.5 V-3.00 to +4.5 V Fixed threshold levels Data Input Threshold-3.00 to +4.5 V-3.00 to +4.5 V-1.5V to 1.0 VClock/Data ThresholdResolution50 mV steps50 mV steps50 mV stepsClock/Data Input Terminations GND, AC, -2V, +3V GND, AC, -2V, +3V GND, AC, -2VSingle-Ended operation Automatic selection Automatic selection Requires externalcable2Clk/Data Delay Range / Resolution ±4 ns in 100 pSsteps±4 ns in 20 pS steps±4 ns in 5 pS stepsNote 1 Burst mode operation requires ECL levels and is DC coupledNote 2 Single-ended operation requires ext. cable connection from rear panel DATA THRESHOLD SMAGetting StartedGB1400 Instrument Configurations - Standard and Burst OptionGB1400 instruments are sold with and without the BURST option. To determine if the burst option is installed in a GB1400, press the F1 key several times until you get to the UTIL menu. Then select the OPTION menu. The OPTIONS menu will tell you if the Burst option is installed in the unit. External indications of the BURST option are unique labels for both transmitter and receiver. See a write-up on Burst Mode at the end of the Functional Overview section of Chapter 2.GB1400 with no Burst Option Standard instrument configurationAll standard configuration GB1400 Generators (TX) (no burst option) have an AC coupled external clock input. All standard configuration GB1400 Analyzers (RX) (no burst option) have AC coupled paths in the receiver clock input circuitry.GB1400 with Burst OptionWhen the BURST option is installed in the GB1400, the AC coupled paths in both transmitter and receiver are eliminated. This will also change several specifications listed in the table below. External clock inputs to the GB1400 transmitter must be ECL levels when the BURST option is installed. Clock inputs into the GB1400 receiver must be ECL levels and are terminated into 50 Ohms to -2V.GB1400 Clock Signals for Standard and Burst and InstrumentsStandard Burst (Option)GB1400 TXExternal Clock Input50 Ohm, 2V max50 Ohm to -2V ECLGB1400 RXClock Input50 Ohm, 2.0V max50 Ohm ECL LevelsGetting StartedInitial Self-Check ProcedureYou may perform the following procedure as an initial self-check of yourGB1400 Generator and Analyzer. It is also a useful introduction to the basicfeatures and operation of the GB1400.The fan openings of the GB1400 needs 2-inches of clearance for properventilation.Procedure1.Make sure both the Generator and Analyzer are equipped with the properfuse.2.Make sure that the Generator and Analyzer rear-panel power switchesare ON, and that their front-panel power switches are in the STBYposition.3.Plug both instruments into grounded (three-conductor) AC power outlets.4.Connect a 50-Ohm SMA cable from the Generator CLOCK output to theAnalyzer CLOCK input.5.Connect a 50-Ohm SMA cable from the Generator DATA output to theAnalyzer DATA input.6.Connect a 50-Ohm SMA cable from the Analyzer rear panel DATATHRESHOLD output to the Analyzer DATA BAR input (required forsingle-ended data inputs).7.Power the Generator while pressing and holding its VIEW ANGLE,MSB 1 and (PATTERN) CLEAR keys simultaneously. Release the keyafter the message Default Settings appears in the display. Repeat thisprocedure with the Analyzer. This will force both the Generator andAnalyzer to power up using factory default settings.8.Set up the Generator clock and data outputs using controls in theOUTPUT box as follows:Set this parameter…to this value… using this procedure.DATA amplitude. 2 volts Press the DATA key.Press AMPLITUDE up/down keys untildata amplitude is set to 2.00V.DATA baseline offset-1 volt Press BASELINE OFFSET up/down keysuntil data baseline offset is set to -1.00V.CLOCK amplitude 2 volts Press CLOCK.Press AMPLITUDE up/down keys untilclock amplitude is set to 2.00V.CLOCK baseline offset-1 volt Press BASELINE OFFSET up/down keysuntil clock baseline OFFSET is set to -1.00V.Getting Started9.Set Generator pattern to a 223-1 bit PRBS using controls in thePATTERN box as follows:a.Press PRBS.b.Press the pattern up/down keys until PATTERN is set to PN 23.10.Verify that the Generator error rate generator is off. If the LED in theerror inject RATE key is on, then press RATE one or more times until itturns off.11.Verify that the Analyzer auto-search function is enabled. If the LED inthe AUTO SEARCH key is off, then press AUTO SEARCH one time toturn it on. At this point, verify that the green LOCK LED in theAnalyzer SYNC box is on.12.Zero all Analyzer error counts by pressing CLEAR in the ERRORDETECTION group.13.Reset all Analyzer history LEDs by pressing CLEAR in the ERRORHISTORY group.14.Verify GB1400 Analyzer can detect errors by pressing the Generatorerror inject SINGLE key several times. Verify that the Number of Errorscount displayed by the Analyzer increments each time the GeneratorSINGLE key is pressed.In effect you are now performing a bit error rate test on the test cables connectingthe GB1400 Generator and Analyzer. In an actual BER test, GB1400 Generatorclock and data outputs would be connected to inputs on a "device under test"(DUT) while GB1400 Analyzer inputs would be connected to outputs on theDUT.。
TCL王牌彩电通病
TCL电源采用STR6708/9A、热端待机三极管用D667的机器，开机指示灯一直闪烁，开不了机的。
用全新D1273替换D667，即可修复3430R待机状态交流声大在Q842的B极接一只1UF/50V电容到地AT2575S 1.冷机开机电源有唧唧响声 R807由4.7KΩ//6W改为3.9KΩ1/6W TCL近年采用TD A16846的TCL王牌彩电电源的，在雷击后极易坏。
一般TD A16846外围零件不坏。
换后即三洋机心丢失亮度信号（鬼影）重新抄写存储器即可TC LD系列电源的R812 0.22欧电阻变质，光栅虽亮度变化比如21--25寸+B整流二极管（RU3)容易击穿，造成电源停振，用RU4代换即可。
TC L2976S不定时停机，一般是行推动变压器内部热开路引起，更换即可非利浦机心水平亮线场块8351及45V供电电阻33欧损坏非利普机心指示灯闪不开机更换视放级的TCL2976S,2966机型无论Tv或Av状态,图像上下抖动,多为X701(Y/C分离,316K)烂,换新即可用T DA16846的TC L王牌彩电电源的，如果电源管坏，请查一下+B的整流管，整流管短路，电源管一定是坏的。
TC L2976S不定时停机另一原因:503F2行震荡晶体不良TCL2510G 场块易开焊造成开机困难彩条干扰。
TC L2502C出现不开机一般是行推动F422有问题用C4554代换即可行推动变压器及+B滤波电感虚焊是TC L机的通病。
TCL2511C不能自动和手动搜台，换新存储器。
TC L电视机2968Z、2969Z声音问题刚开机时声音特小而且发闷，10-30分钟后正常更换两个236540中周（原机为大磁芯）微调整后正常D系列彩色时有时无，但在NTSC制式下正常如碰到此故障是由于总线控制的梳状滤波器被打开。
各种型号碳粉对应通用机型对照表
品名编号型号适用机型 RMB/KGFC220/230PC3/5/7/11/25/745/795/ FC220/310/530/770/230/330/902/E16/21/31 A15/30 55NPG-1 NPG-4/5NP 3100 /1215 /1015 /3030/3020/3200/1318/3050/3325/4080/60253825/4050/6030/1218/1510/2020/2120/6020/201055NP1010 NP 1010 57 NPG-13 NP6035/623055 NPG-6/7/8 NP6000/7000/8000/6650/6150/8530/6080/6150Ⅱ/7050/7550/8070/5060/8570/858055 NPG-3/12 NP6050/6550/6250/608555 NPG-10/14/3NP6050/6045/6030/6545/6551/6560/60356230/55GP-605GP-605 GP1/555/55055 NGP-26/25/20GP330/335/405/GR2/355/315/210/215/220/225/ IR2270/IR3570/IR457058NGP-16IR5000/IR600055 NGP-18 IR2200/IR2210/IR2220/IR2800/IR3300 55NGP-19 NGP-1 IR8500/105/105+/9070 IR550/600/7200 GP605/555/550 55 NGP-20IR-155/165/1600/1600N/1610/200/2000/2010/2200/2800/33055NGP-21 IR1510 55NGP-25IR2230/2270/2830/2870/3570/4570GP215/40555NGP-26 IR3530/3570/4570 55NGP-27 IR5570/6570 55佳能CANONNGP-28 IR2016 55GR121XR1027/1025/1038/5025/5026/5416/5421/1017/1035/5615/5618/551865V330 V250/330/228/250/258/338/388/5320/5322 65V400V455/500/555/5340/5343/5350656R343 5008/5240/5260/5280/50096R359 5370/5309/5310 施乐XEROX6R737/333 XC351/355/356/520/540/560无品名 编号 型号 适用机型106R00280 W315/320/415/420/518/412 65 6R914 XD102/100/103/104/105/125/130/15565 106R445/647416/421无施乐 XEROXF440/469 ABLE1321/3321/1180/3180/1250/1251/13501351/ 1405/1406/DC250/350/400/251/351/220/DC230/265ST/332/340/420/432/440/505/600605/705/755 65SF125/126 SF1016/1018/1020/1116/11865126ST/216ST SF2116/2118/2020/2120/2016/2018/2021/2022/2027 65230ST/240ST SF2025/2030/2530/2040/2540/2035/2040/2050/2052 65SF7370 SF7370/7800/7850/7300 65 SF850 SF8850/8570/9550/8100 65AR-200TD AR160/161/200/205/162/163/201/206/207 68AR201/203ST M160/2821/1818/AR215/235/275/255 162 163 165 201 205 206 209 1820 2616 2618 2620 27182818 2820 2918 68AR270/271ST M208/236/276 68AL100TD AL1000/1200/1220/1240/1250/1000/1001/1010/1020/1200/ 1241/1250/1251/1340/1451/1551/1820/1818 68AR-153ST AR158/250/255/280/285/286/335/336/337/405/407/507/151/155686R914 XD100/102/103/104/125/130/155 68AR5030 AR5130/5122/5230/5020/5320/5030/5230 无AR450/451ST M350/450/280/310U/M300/M420U 无AR330/400ST AR250/280/285/286/366/337/405/407/336 无AR500ST AR501/505/507 无夏普SHARPSD2060SD2060/3062TYPE-410/420FT4418/4220/4215/4221/4525/4415/4222/442258FT5010/4800 FT4420/4430/4470/4480/4490/4495/5010/5560/4530 58 TYPE-450I TF4022/4027/5035/5535/5632/5832/5640/5840/5627/4527F 58 FT4000 FT4000/4020/4030/4035/4040/4060/4065/4085 58FT1305 FT4015/4018/4615/4621/3813 58理光RICOHFT610FT6035/6050/6645/6655/6665/58TYPE610FT4500/5500/6500/7650/665/6650/7660/7670/5550/5570/ 6550/7070/Aficio550/650/551/700/1055无FT5010 FT4430/4480/4490/4495/470058 889511 FT3300/3320无1270D Aficio1250D/1013/1515/1515M 651140D Aficio1015/1018/1220D/1115P/1113/1012 651230D Aficio2015/2018/mp1610L/2020D/MP1000/2000/1610/ 2015L/2018D/1800/2000SP65221OD Aficio2210/270/220/250/200 65 2220D Aficio1022/1027/2022/2027/2032/3025/3030 653200D Aficio340/345/350/355/450/455/400/500/649/850/1055 700/551/1045/1035 653210D Aficio2035/2045/3200D 653205D Aficio1030/1045/1035/320D/3205D 65AF6210D Aficio1060/1075/2051/2060/2075/5500/6500/7500 65 理光RICOH5305D/5200D 5100DAficio551/5305D/550/650/700/1055/6550Imajio5550/5570/6500/7070/1060无T-1710C T1710 2050 2310 2500 2540 1650 60 T-1550C T1560 1550 1580 156860T-2060C T2860 2040 2060 2068 2870 2878 60T-3560CT3560 3570 4560 4570 206060T-85P BD1310 3810 391060 DP-5580 DP5570 6570 8070 4580 5560 6560 E55 E65 E80 T-1600C E-168 168S 163 203 230 169 208 258 259 16 160 60T-2500CE20 25 200 250 20960 T-3500C/3520C E-358 458 288 45 35 28/350 450 352 452 65 E550 E550 650 81065 T1640C 163 165 203 166 167 206 207 23765BD5540BD5540 6550 6555 7550 SD5540 7650 7560 766065东芝TOSHIBAT-6560 BD 5560 6560无 7320/6225/7261Lanier 7320 7328 722870雷立LANIER53555355 5365 5480 7345 7335 7328 7228 7216无名称 编号 型号 适用机型MT-ⅡEP 4230 4232 4233 4250 3170 4300 1232 450 470 49058 MT101A0 1080 1051 1070 1081 58 MT102AEP1052 1083 1085 201058MT104A EP1054 10851084 58MT201A EP2050 58MT202A EP2080 58MT204AEP2030 3000 3010 58MT401AEP3050 405058MT501A EP 58MT601A EP6000 5000 58MT602A EP6001 5050 600058 MT105A/106ADI180 181 152 183 183S 1611 2011 181165 MT302A DI200 250 251 350 351 251F 65 TN114162 180 210 7516 752165MT502A DI450 550 470 65MT603A DI520 620 65 K-1212 1015 1212 2120 1218 2020 1216 2223 58K-20282028 4045 3035 4145 3135 3240 3340 233058 TN101KKM7075 7085 7165 7155 7216 7020 7255 7030 70357130 7218 7220 65 美能达MINOLTA 柯卡尼KONICAU7050KM7118 7050 7060 7150 7160 7055 7065 7020 70407033 7145 71355 M9000 M9000 9100 8210 8010 8110 65 联想LENOVOM9215M9215 9218 9325 933265DC-AO DC211 2137037090011 DC 1560 1860 2060 2360 2050 25501670 1755 70 TK418 410 411 KM 1620 1650 2020 2050 2550 2520 2030 165 100 1500 85370AB001KM 2530 3530 4030 3035 4035 5035 6330 3070 553085 DC1855 DC1555 1605 1656 1657 1685 1855 215570 KM1525 KM1525 1530 2070 150570 京瓷美达KYOCERA MITAKM5230AI 2310 3010 4040 5050 1505 1510 1810 4230 523070FP16801670 1680 2080 7117 7121 TA1960 TF15 FP 7713 7715 7115 7113 60FQ-TK05/10 FP 7718 7722 7818 7824 7830 7728 60TU10C DP1510 1212 2120 1216 2223 1810 2010 65 DQ-TU10J-PB DP1820 1515 1570 1870 1510 1520 182070DQ-TUJ5K-PK DP1515 70DQ-TU15EDP1500 3010 2310 2330 3030 2310 3510 4510 6010 802070DP6530 DP8130FQ-TK20FP 7728 7735 7830 7835 无 松下PANASONICDQ-TU18EDP2000 2500 3000 无 震旦AURORA165 AD 165 158 159 259 309 359 40970打印机型号SERIESCOMMODITYNAMETYPE3906FHP5L/6L/1100/3100 /3150CanonAX/FX-3/460/465/66055CB388/488A HP1008/1005/1006/1505/1522/1120 70Q2613A/2624A HP1320/1300/2015/3005/1150/ 55 C7115A HP1000/1200/1220/1020/1010/2400/3050/3300 5592274AHP4L/4P/4ML/4MP/4LCCanonFX-2/PX/HX/430/P90/L50055C3903FHP5P/6P/5MP/6MPCanonFX-1/VX/LX/CX/430/430W/55Q2610A/4096A/C5949HP2100/N/M/SE/TN/XI/2200/4VC/4000/5000/4100/4300/4050CanonEX/SX/BX/TX/P27055C4127AX/C8061AHP4VC/4V/4MV/4000/4100/5000/8000/8100/4050/CanonBX/JX/304/309/P380/52X/62X55C4129XHP4000/5000/5100/CanonWX/NX/2460/P170/660055L-380 Canon FAXL-250/L-380，FX-3 5592298AHP4/4M/4+/4M+/5/5M/5NCanon EX/20/860/554092AHP1100/3200/1200/3100Canon22X/800/810/55C3909A/C4182 5SI/NX/3SI/4SI/8000/8100/8150 55 Q2612HP1010/1012/1015/1020/3015/3020/1220/2400/3050/55EP25 LBP1210/2900/3200 Canon 55EP22 LBPAX/440/460/660/465/210/310/Canon 55EPA LBP200/250/280/300/350/360/380 Canon 55Q1338A/1339A/5942A/Q7516AHP 4200/4300/4250/4350/5200 55CB388A P1007/1008 70 CB435A P1005/1006 70惠普/佳能HP/CANONCB436A M1120/1120N/1522N/1505/1505N XML-1210D 1210/1220M/1250/1430/1010/1610/1740 65 ML-1710D/D3 1510/1710/1610/1750/1520/1740/1640/2430/1630 65ML-4500D ML4500/4600/4300/5000A/5100A 65ML-5100D SF5100/5100P/530/535e/ML808/SF5000/5109 655112 SCX5112/5312F/4500 655800SF5800/5800P 65 ML-6060D6ML6060s/6160/1430/1440/1450/1451/1650/1651/4016658000 ML8000/8500 65 SF-503 SF503/508X SCX5312D6 5112/5312/4100/4016/4116/421655 113R00455 XEROXP8E/P8EX/385/3115/3110/3116/3120/ 3121/3130 X ML-1610D2 1610/1615无 三星SAMSUNGML-2010D1 2010/2015/4521/4321 无 10S0150C E210/ E310/312/322/1850/215 65 522E520/522/62065 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TYPE REMARKLBP5100 （BLACK）Canon2040/460/2160/660/LBP5100/5000/5360/5300320LBP5100 （CYAN）Canon2040/460/2160/660/LBP5100/5000/5360/5300LBP5100 （MAGENTA）Canon2040/460/2160/660/LBP5100/5000/5360/5300CANONLBP5100 （YELLOW）Canon2040/460/2160/660/LBP5100/5000/5360/5300HP-2600 （BLACK）HP1500/2500/2600/5500/4550/4600/8500/8550/3550/370/CM1215/1015/1017320HP-2600 （CYAN）HP1500/2500/2600/5500/4550/4600/8500/ 8550/3550/3700/ CM1215/1015/1017HP2600 （MAGENTA）HP1500/2500/2600/5500/4550/4600/8500/ 8550/3550/3700/ CM1215/1015/1017HPHP-2600 （YELLOW）HP1500/2500/2600/5500/4550/4600/8500/ 8550/3550/3700/ CM1215/1015/1017C900/C1900 （BLACK）C900/C1900/C1000/C2000/C8000/C8200/C8500/C8600320C900/C1900 （CYAN）C900/C1900/C1000/C2000/C8000/C8200/C8500/C8600C900/C1900 （MAGENTA）C900/C1900/C1000/C2000/C8000/C8200/C8500/C8600EPSONC900/C1900 （YELLOW）C900/C1900/C1000/C2000/C8000/C8200/C8500/C8600Minolta2500 （BLACK）Minolta330/2/DP/2200/2300/6100/2400/2500W/2530320Minolta2500 （CYAN）Minolta330/2/DP/2200/2300/6100/2400/2500W/2530Minolta2500 （MAGENTA）Minolta330/2/DP/2200/2300/6100/2400/2500W/2530MINOLTAMinolta2500 （YELLOW）Minolta330/2/DP/2200/2300/6100/2400/2500W/2530SERIES COMMODITYNAMEN.W. TYPEREMARK Xerox-620（BLACK）Xerox-620/625/2006/3310/4CR/410/831/7700/7750/C525/C1100/ 380 Xerox-620（CYAN）Xerox-620/625/2006/3310/4CR/410/831/7700/7750/C525/C1100/Xerox-620（MAGENTA）Xerox-620/625/2006/3310/4CR/410/831/7700/7750/C525/C1100/XEROXXerox-620 （YELLOW）Xerox-620/625/2006/3310/4CR/410/831/7700/7750/C525/C1100/CLP300（BLACK）CLP300/315/500/600/5100 360CLP300（CYAN）CLP300/315/500/600/5100CLP300 （MAGENTA）CLP300/315/500/600/5100SAMSUNGCLP300（YELLOW）CLP300/315/500/600/51003800（BLACK）1500/1600/2000/2200/4100/3800 3203800（CYAN）1500/1600/2000/2200/4100/38003800 （MAGENTA）1500/1600/2000/2200/4100/3800RICOH3800（YELLOW）1500/1600/2000/2200/4100/3800C8000（BLACK）5116/8500C/1800/7500/5500 380C8000（CYAN）5116/8500C/1800/7500/5500C8000 （YELLOW）5116/8500C/1800/7500/5500LENOVOC8000（BLACK）5116/8500C/1800/7500/5500SERIES COMMODITYNAMEN.W.TYPE REMARKC720（BLACK）C720/SC1275/C710/C510/C1200/C910/C912/T620/T622/W812/E320380C720（CYAN）C720/SC1275/C710/C510/C1200/C910/C912/T620/T622/W812/E320C720（MAGENTA）C720/SC1275/C710/C510/C1200/C910/C912/T620/T622/W812/E320LEXMARKC720 （YELLOW）C720/SC1275/C710/C510/C1200/C910/ C912/T620/T622/W812/E3203100（BLACK）3100/5100/5200/5300/7300/9300/9500 3603100（CYAN）3100/5100/5200/5300/7300/9300/95003100 （MAGENTA）3100/5100/5200/5300/7300/9300/9500OKI3100（YELLOW）3100/5100/5200/5300/7300/9300/9500 彩色复印机系列SERIES COMMODITYNAMEN.W.TYPE REMARK ARC350（BLACK）ARC150/330/350 360ARC350（CYAN）ARC150/330/350ARC350（MAGENTA）ARC150/330/350SHARPARC350（YELLOW）ARC150/330/350SERIES COMMODITYNAMEN.W. 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TYPEREMARK DC1250（BLACK）DC-4/DC-6/DC1250/DC2060/DC1255/DC2045/DC3525/DC5750/DC5760/5790/DC6060320DC1250（CYAN）DC-4/DC-6/DC1250/DC2060/DC1255/DC2045/DC3525/DC5750/DC5760/5790/DC6060 DC1250（MAGENTA）DC-4/DC-6/DC1250/DC2060/DC1255/DC2045/DC3525/DC5750/DC5760/5790/DC6060 DC1250（YELLOW）DC-4/DC-6/DC1250/DC2060/DC1255/DC2045/DC3525/DC5750/DC5760/5790/DC6060 DC400（BLACK）DC400/450/500/600 320DC400（CYAN）DC400/450/500/600DC400（MAGENTA）DC400/450/500/600XEROXDC400（YELLOW）DC400/450/500/600TN310（BLACK）BzC350/351/450/200/252/203/353 360TN310（CYAN）BzC350/351/450/200/252/203/353TN310（MAGENTA）BzC350/351/450/200/252/203/353TN310（YELLOW）BzC350/351/450/200/252/203/353TN611（BLACK）BzC550/451/650/5500/500 360TN611（CYAN）BzC550/451/650/5500/500TN611 （MAGENTA）BzC550/451/650/5500/500 360KONIKAMINOLTATN611（YELLOW）BzC550/451/650/5500/500SERIES COMMODITYNAMEN.W. TYPEREMARK 6020（BLACK）Kx-mc6020 3806020（CYAN）Kx-mc60206020（MAGENTA）Kx-mc60206020（YELLOW）Kx-mc6020323（BLACK）DCP323/213/262/322/354/264/263/264 360323（CYAN）DCP323/213/262/322/354/264/263/264323（MAGENTA）DCP323/213/262/322/354/264/263/264PANASONIC323（YELLOW）DCP323/213/262/322/354/264/263/2643500C （BLACK）E-STUDIO281C/2330C/2500C/4520C/351C/3500C/3510C/3530C/2830C/451C3603500C （CYAN）E-STUDIO281C/2330C/2500C/4520C/351C/ 3500C/3510C/3530C/2830C/451C3500C （MAGENTA）E-STUDIO281C/2330C/2500C/4520C/351C/ 3500C/3510C/3530C/2830C/451CTOSHIBA3500C （YELLOW）E-STUDIO281C/2330C/2500C/4520C/351C/ 3500C/3510C/3530C/2830C/451C2238C（BLACK）2238C/MPC2500/MPC4500 3602238C（CYAN）2238CMPC2500/MPC45002238C （MAGENTA）2238CMPC2500/MPC4500RICOH2238C（YELLOW）2238CMPC2500/MPC4500。
长虹CH 16机芯介绍及总线调试方法及代表机型总线数-12页文档资料
长虹CH 16机芯介绍及总线调试方法及代表机型总线数-、机芯介绍长虹CH-16机芯是长虹公司2019年引进菲利浦公司超级芯片--TDA9370开发的一种电视机芯。
该机芯的电视小信号处理、CPU、TV/AV切换开关，波段切换开关等电路都集成在一块芯片TDA9370内部。
使电路结构更加流畅。
外部调试点无乎为零。
大大地提高了整机的可靠性，也使维修更加方便，广泛装配21、25、29、34英寸电视机。
二、适用机型长虹的CH-16机芯的电视机，最初都用"SF"来代表"CH-16"机芯。
主要机型有：SF2115、SF2198、SF2139、SF2598、SF2515、SF2915、SF2998、SF3498F、HY29S86、PF2198、PF2598、PF2998、SF2939等三、CH-16机芯彩电I 2C总线系统的调整方法(1)进入维修状的方法将本机音量减至最小，使用K16型遥控器(K16C、K16D、K16H)或K3型遥控器(K3A、K3D、K3E等)，按住静音键不放，此时荧光屏上出现红色的"静音X"字样。
紧接着按本机键中的"菜单键"，屏幕上出现红色的"S"字符，表示本机已经进入维修状态。
(注有时按本机面板控制键中的"菜单键"有时需要多停留几秒钟)。
(2)选项与调整进入"S"状态以后，按压遥控器或本机节目选择键可选择所需调整的项目。
按压遥控器或本机音量键调整总线数据。
(3)调试完毕，遥控关机，即可退出"S"状态，并自动关机。
(一)小屏幕机芯总线数据参考机型有SF2198、SF2139、PF2198等21英寸小屏幕电视机项目释义数据(十六进制)预置范围备注OPT1选项1 FC 0-FF功能选择，不能随意更改OPT2选项2 6C 0-FF同上OPT3选项3 F2 0-FF同上OPT4选项4 4E 0-FF同上AVG 20 0-3F VS场线性23 0-3F SC 15 0-3F 5VA 50Hz场幅23 0-3F5VSH 50Hz帧中心16 0-3F 5HS 50Hz行中心1A 0-3F 50V字符中心位置37 0-3F RCUT红截止1F 0-3F GCUT绿截止1F 0-3F RDRV红激励20 0-3F GDRV绿激励20 0-3F BDRV兰激励20 0-3F AGC AGC设定14 0-3F音量00音量最小25 0-3F可影响声音的变化音量25通常音量35 0-3F亮度50通常亮度1C 0-3F亮度99最高亮度设置3F 0-3F对比度50对比度适中值20 0-3F对对度99最大对比度设置3F 0-3F色饱和99最大色饱和度3F 0-3F YDEL亮度信号延迟0D 0-0F CL彩色预置09 0-0F PODE模式选择10 0-1F(二)SF3498总线数据表项目释义数据(十六进制)预置范围备注OP1选项1 FE 0-FF功能性选选择OP2选项2 48 0-FF同上OP3选项3 C6 0-FF同上AVG 28 0-3F VX00 19 0-3F VS场线性23 0-3F SC帧线性20 0-3F 5VA 50Hz场幅19 0-3F 5VSH 50Hz场中心23 0-3F 5HA行幅2A 0-3F 5HS 50Hz行中心20 0-3F 5EW枕校1F 0-3F 50V字符上下位置3F 0-3F HP行补偿2C 0-3F TC四角补偿20 0-3F VCP帧补偿30 0-3F BCP 2B 0-3F HB 20 0-3F RCUT 红截止21 0-3F GCUT绿截止24 0-3F RDRV红驱动15 0-3F GDRV绿驱动18 0-3F BDRV兰驱动20 0-3F AGC AGC设定16 0-3F VOL音量28 0-3F 音量00最小音量39 0-3F可影响声音变化音量25中间音量3C 0-3F亮度50通常亮度设置1F 0-33可影响整机亮度亮度99最高亮度设置33 0-3F对比度50通常对比度0C 0-3F对比度99最大对比度3F 0-3F彩色99色饱和度最大3F 0-3F可能引起无彩IF0 20 0-3F YDEL亮度延迟00 0-0F CL对比度预置0B 0-0F PODE模式选择10 0-1F CH-16机芯概述及检修提示CH-16机芯是在菲利浦公司研究开发的超大规模集成电路TDA9370的基础上开发的另一种电视机芯。
ProductTypeList-optiMOS(20-250V)
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IPB009N03L G IPB011N04L G IPB011N04N G IPB016N06L3 G IPB017N06N3 G IPB019N08N3 G IPB020N04N G IPB025N10N3 G IPB030N08N3 GIPB036N12N3 G IPB065N15N3 G IPB010N06NIPB014N06NSPD07N20 GIPD031N06L3 G IPD034N06N3 G IPD035N06L3 G IPD036N04L GIPD038N06N3 G IPD048N06L3 G IPD053N08N3 G SPD50N03S2L-06 G SPD30N03S2L-07 G IPD068N10N3 G SPD50N03S2-07 GIPD082N10N3 G IPD088N06N3 G IPD096N08N3 G SPD30N03S2L-10 G IPD127N06L GIPD135N08N3 G IPD160N04L GIPD170N04N GIPD200N15N3 G SPD30N03S2L-20 G IPD220N06L3 G IPD25CN10N GIPD250N06N3 G IPD33CN10N GIPD350N06L GIPD640N06L G IPD78CN10N G IPD800N06N G IPD122N10N3 G IPD180N10N3 G IPD110N12N3 G IPD031N03L G IPD040N03L G IPD050N03L G IPD060N03L G IPD075N03L G IPD090N03L G IPD320N20N3 G IPD600N25N3 G IPD530N15N3 G IPD105N03L G IPD135N03L GIPD025N06N IPD053N06N IPI023NE7N3 G IPI034NE7N3 G IPI052NE7N3 G IPI126N10N3 G IPI180N10N3 G IPI041N12N3 G IPI076N12N3 G IPI147N12N3 G IPI045N10N3 G IPI086N10N3 G IPI030N10N3 G IPI04CN10N G IPI072N10N3 G IPI26CN10N G IPI35CN10N 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7pin (TO-2637pin)in production/dgdl/IPB019N08N3_Rev2.3.pdf?f olderId=db3a304313b8b5a60113cee8763b02d7&fileId=db 3a30431add1d95011ae87fdf90569f D2PAK 7pin (TO-2637pin)in production/dgdl/IPB020N04N_rev1.3.pdf?fol derId=db3a304313b8b5a60113cee8763b02d7&fileId=db3 a30431936bc4b0119382c70a859ed D2PAK 7pin (TO-2637pin)in production/dgdl/IPB025N10N3+G_Rev2.03.p df?folderId=db3a304313b8b5a60113cee8763b02d7&fileId =db3a30431ce5fb52011d1ab1d9d51349D2PAK 7pin (TO-2637pin)in production/dgdl/IPB030N08N3_Rev2.3.pdf?f olderId=db3a304313b8b5a60113cee8763b02d7&fileId=db 3a30431add1d95011ae88a47a856b1D2PAK 7pin (TO-2637pin)in productiondf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30431ce5fb52011d1ed1fd3915e07pin)/dgdl/IPB036N12N3+G_Rev2.2.pd f?folderId=db3a304313b8b5a60113cee8763b02d7&fileId= db3a304323b87bc20123c7030ed51f56D2PAK 7pin (TO-2637pin)in production/dgdl/IPB065N15N3+G_Rev2.1.pd f?folderId=db3a304326623792012669f6bee2224b&fileId= db3a30432662379201266a0379d1225c D2PAK 7pin 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/dgdl/IPP_I_B041N12N3_Rev2.2.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30432239cccd0122a75b86467ca4I2PAK (TO-262)in production /dgdl/IPP_I076N12N3+G_Rev2.3.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30432239cccd0122a77a83ab7cd4I2PAK (TO-262)in production /dgdl/IPP_I_B147N12N3+G_Rev2.6.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30432239cccd0122a79a30f57d01I2PAK (TO-262)in production /dgdl/IPP045N10N3+G_Rev2.5.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30431ce5fb52011d1e8b0cc31586I2PAK (TO-262)in production /dgdl/IPP086N10N3+G_Rev2.5.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30431ce5fb52011d1ac5c8fa1358I2PAK (TO-262)in production /dgdl/IPP030N10N3+G_Rev2%5B1%5D.1.pdf?folderId=db3a304313b8b5a60113cee8763b02d7&fileId=db3a30432313ff5e0123939fdbcf03c9/dgdl/IPP04CN10N_Rev1.4.pdf?foI2PAK (TO-262)not for new design 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一类耦合非线性薛定谔方程组的求解
第３８卷第１期２０２４年１月兰州文理学院学报(自然科学版)J o u r n a l o fL a n z h o uU n i v e r s i t y ofA r t s a n dS c i e n c e (N a t u r a l S c i e n c e s )V o l ．３８N o ．１J a n ．２０２４收稿日期:２０２３Ｇ０５Ｇ１５基金项目:国家自然科学基金项目(１１７６１０４４)作者简介:仁世杰(１９９５Ｇ),男,甘肃庄浪人,助教,硕士,研究方向为孤立子理论及其应用．E Ｇm a i l :４８７４５０３９５＠q q．c o m．㊀㊀文章编号:２０９５Ｇ６９９１(２０２４)０１Ｇ００３９Ｇ０５一类耦合非线性薛定谔方程组的求解仁世杰１,李永军２,张㊀娟３(１．兰州城市学院信息工程学院,甘肃兰州７３００７０;２．兰州城市学院电子工程学院,甘肃兰州７３００７０;３．宁夏师范学院数学与计算机科学学院,宁夏固原７５６０００)摘要:在可积条件c (t )＝(γ２(t ))２＝１(C １t ＋C ２)２,γ１(t )＝γ２(t )＝１C １t ＋C ２ìîíïïïï下,利用特殊变换法和S i n e Ｇc o s i n e 方法,得到了双芯光纤变系数线性耦合薛定谔方程组i ∂∂t u (x ,t )＋i ∂∂x u (x ,t )－∂２∂t ２u (x ,t )＋γ１(t )u (x ,t )２u (x ,t )＋㊀㊀c (t )v (x ,t )＝０,i ∂∂t v (x ,t )＋i ∂∂x v (x ,t )－∂２∂t ２v (x ,t )＋γ２(t )v (x ,t )２v (x ,t )＋㊀㊀c (t )u (x ,t )＝０ìîíïïïïïï的精确解．其中:C i (i ＝１,２)是常数;γi (t )(i ＝１,２)是第i 个纤芯的非线性参数;c (t )是两个纤芯之间的线性耦合参数．关键词:双芯光纤;线性耦合;薛定谔方程;可积;S i n e Ｇc o s i n e 方法中图分类号:O １７５．２９㊀㊀㊀文献标志码:AS o l v i n g aC l a s s o fC o u p l e dN o n l i n e a r S c h r öd i n g e rE qu a t i o n s R E N S h i Ｇj i e １,L IY o n g Ｇju n ２,Z HA N GJ u a n ３(１．S c h o o l o f I n f o r m a t i o nE n g i n e e r i n g ,L a n z h o uC i t y U n i v e r s i t y,L a n z h o u７３００７０,C h i n a ;２．S c h o o l o fE l e c t r o n i cE n g i n e e r i n g ,L a n z h o uC i t y U n i v e r s i t y,L a n z h o u７３００７０,C h i n a ;３．S c h o o l o fM a t h e m a t i c s a n dC o m p u t e r S c i e n c e ,N i n g x i aN o r m a lU n i v e r s i t y,G u y u a n７５６０００,N i n gx i a ,C h i n a )A b s t r a c t :I n t h i s p a p e r ,t h e e x a c t s o l u t i o n s o f t h e l i n e a r l y c o u p l e d n o n l i n e a r S c h r öd i n g e r E qu a Ｇt i o n G r o u p i ∂∂t u (x ,t )＋i ∂∂x u (x ,t )－∂２∂t ２u (x ,t )＋γ１(t )u (x ,t )２u (x ,t )＋㊀㊀c (t )v (x ,t )＝０i ∂∂t v (x ,t )＋i ∂∂x v (x ,t )－∂２∂t ２v (x ,t )＋γ２(t )v (x ,t )２v (x ,t )＋㊀㊀c (t )u (x ,t )＝０ìîíïïïïïïïïw i t h v a r i a b l e c o e f f i c i e n t s o f t w o Ｇc o r e f i b e r a r e c a l c u l a t e db y s p e c i a l t r a n s f o r m a t i o nm e t h o d a n dm e t h o du n Ｇd e r i n t e g r a b l e c o n d i t i o n c (t )＝(γ２(t ))２＝１(C １t ＋C ２)２γ１(t )＝γ２(t )＝１C １t ＋C ２ìîíïïïïa m o n g wh i c h C i (i ＝１,２)i s t h e c o n Ｇs t a n t ,γi (t )i s t h e n o n l i n e a r p a r a m e t e r s o f t h e i Ｇt h c o r e a n d c (t )i s t h e l i n e a r c o u p l i n g p a r a m e Ｇt e r sb e t w e e n t h e t w o c o r e s ．K e y wo r d s :t w o Ｇc o r e f i b e r ;l i n e a r c o u p l i n g ;S c h r öd i n g e r e q u a t i o n ;i n t e g r a b l e ;S i n e Ｇc o s i n em e t h o d 0㊀引言双芯光纤耦合方程是一类数学与物理领域研究的热点方程,它描述了光纤中光孤子是光波在传播过程中色散效应与非线性压缩效应相平衡的结果．因为光孤立子通信具有高码率㊁长距离和大容量的优点,可以构成超高速传输系统,所以光孤立子及其在通信中的应用研究具有重要的研究价值．文献[１]研究了变系数线性耦合的非线性薛定谔方程组:i ∂∂t u (x ,t )＋i ∂∂x β１１u (x ,t )－㊀β１２２∂２∂t ２u (x ,t )＋γ１(t )u (x ,t )２㊀u (x ,t )＋c v (x ,t )＋δa u (x ,t )＝０,i ∂∂t v (x ,t )＋i ∂∂x β２１v (x ,t )－㊀β２２２(t )∂２∂t２v (x ,t )＋γ２(t )v (x ,t )２㊀v (x ,t )＋c (t )u (x ,t )－δav (x ,t )＝０．ìîíïïïïïïïïïïïïïï(１)其中:βj １(j ＝１,２)是第j 个纤芯的群速度参数;βj ２(j ＝１,２)是第j 个纤芯的色散参数;γi (i ＝１,２)是非线性参数;c 是两个纤芯之间的线性耦合参数;δa 是两个纤芯的相速度参数．对于方程组(１),文献[１]针对非线性定向耦合器中光学明孤子的相互作用动力学进行了广泛的数值研究,考虑群速度失配,相速度失配,以及群速度色散和有效模面积的差异等因素的影响,主要使用数值方法研究了在均匀白躁声形式下的谐波无穷小扰动作用下亮孤子的稳定性．求解此类方程学有以下方法:I S T 方法[２Ｇ３],齐次平衡法[４Ｇ５],B äc k l u n d 变换方法[６Ｇ７],S i n e Ｇc o s i n e 方法[８Ｇ９]等．本文研究的是变系数的线性耦合非线性薛定谔方程组,方程组为i ∂∂t u (x ,t )＋i ∂∂x u (x ,t )－∂２∂t ２u (x ,t )＋㊀γ１(t )u (x ,t )２u (x ,t )＋㊀c (t )v (x ,t )＝０,i ∂∂t v (x ,t )＋i ∂∂x v (x ,t )－∂２∂t ２v (x ,t )＋㊀γ２(t )v (x ,t )２v (x ,t )＋㊀c (t )u (x ,t )＝０．ìîíïïïïïïïïïïïï(２)通过P a i n l e v é检验,得到当非线性参数和耦合参数满足:c (t )＝(γ２(t ))２＝１(C １t ＋C ２)２,γ１(t )＝γ２(t )＝１C １t ＋C ２ìîíïïïï(３)时,方程组(２)是P a i n l e v é可积的．本文在条件(３)基础上,首先利用S i n e Ｇc o s i n e 方法求解方程组的特殊精确解,然后选取满足方程的特定参数,并给出图像,所涉及的计算均由M a pl e 完成．1㊀预备知识S i n e Ｇc o s i n e 方法是求解非线性数学物理方程的有效方法,主要用于可积系统的求解．本节简单地介绍S i n e Ｇc o s i n e 方法．考虑非线性偏微分方程组i ∂∂T U (X ,T )－α∂２∂X ２U (X ,T )＋㊀㊀βU (X ,T )２U (X ,T )＋㊀㊀μV (X ,T )＝０,i ∂∂T V (X ,T )－α∂２∂X ２V (X ,T )＋㊀㊀βV (X ,T )２V (X ,T )＋㊀㊀μU (X ,T )＝０．ìîíïïïïïïïïïïïï(４)假设方程组(４)的解具有如下形式:U (X ,T )＝r １(X ,T )e i (ωT ＋k X ),V (X ,T )＝r ２(X ,T )e i (ωT ＋k X )．{(５)将(５)代入方程组(４),得－α∂２∂X２r １(X ,T )＋i ∂∂T r １(X ,T )－㊀㊀２i αk ∂２∂X２r １(X ,T )＋β(r １(X ,T ))３＋㊀㊀(αk ２－ω)r １(X ,T )＋μr ２(X ,T )＝０,－α∂２∂X ２r ２(X ,T )＋i ∂∂T r ２(X ,T )－㊀㊀２i αk ∂２∂X ２r ２(X ,T )＋β(r ２(X ,T ))３＋㊀㊀(αk ２－ω)r ２(X ,T )＋μr １(X ,T )＝０．ìîíïïïïïïïïïïïïïï(６)分离(６)中实部和虚部,则式(６)等价于虚部为０:式(７),实部为０:式(８)．０４㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀兰州文理学院学报(自然科学版)㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第３８卷∂∂T r １(X ,T )－２αk ∂２∂X２r １(X ,T )＝０,∂∂T r ２(X ,T )－２αk ∂２∂X ２r ２(X ,T )＝０．ìîíïïïï(７)－α∂２∂X ２r １(X ,T )＋β(r １(X ,T ))３＋㊀㊀(αk ２－ω)r １(X ,T )＋μr ２(X ,T )＝０,－α∂２∂X２r ２(X ,T )＋β(r ２(X ,T ))３＋㊀㊀(αk ２－ω)r ２(X ,T )＋μr １(X ,T )＝０．ìîíïïïïïïïï(８)求解(７)可得r １(X ,T )＝F １(ξ),r ２(X ,T )＝F ２(ξ)．{(９)其中ξ＝２T αk ＋X２αk,F i (ξ)(i ＝１,２)为任意函数,其具体形式根据F i (ξ)(i ＝１,２)满足的条件确定．将(９)代入(８)得－１４αk ２∂２∂ξ２F １(ξ)＋β(F １(ξ))３＋㊀㊀(αk ２－ω)F １(ξ)＋μF ２(ξ)＝０,－１４αk ２∂２∂ξ２F ２(ξ)＋β(F ２(ξ))３＋㊀㊀(αk ２－ω)F ２(ξ)＋μF １(ξ)＝０．ìîíïïïïïïïï(１０)在方程组(１０)中,假设F i (ξ)(i ＝１,２)有如下形式:F i (ξ)＝E i s i n (h (ξ))＋G i c o s (h (ξ))＋H i (i ＝１,２),(１１)其中E i ,G i 和H i (i ＝１,２)是待定常数,同时h (ξ)满足常微分方程:d h (ξ)d ξ＝A s i n (h (ξ))＋B c o s (h (ξ))＋E ,(１２)其中A ,B 和E 是待定常数．再将(１１),(１２)代入(１０)中,整理得到关于s i n (h (ξ)),c o s (h (ξ))的多项式,令其系数为零,得到关于E １,E ２,G １,G ２,H １,H ２,A ,B ,E ,k 和ω的代数方程组．将得到的解带回(１２)中,再利用文献[１０]中介绍的S i n e ＧG o r d o n 方程(１２)的解,可以得到方程组(４)的解．2㊀方程组的求解本节使用S i n e Ｇc o s i n e 方法和特殊变换求方程组(２)的一组精确解．定义下列函数:T (t )＝－１t ,b (x ,t )＝－１２ln (２t ),a (x ,t )＝－(t －x )２４t,X (x ,t )＝x ２t ．ìîíïïïïïïïïïï(１３)方程(２)可经过变换:㊀u (x ,t )＝U (X (x ,t ),T (t ))e i a (x ,t )＋b (t ),v (x ,t )＝V (X (x ,t ),T (t ))e i a (x ,t )＋b (t ){(１４)转化为方程(４)．故先求解方程(４)得到方程的解U (X ,T ),V (X ,T ),然后再通过变换(１４)就可以得到原方程组(２)的解．由第一节求解方程组(４)可以得到E １,E ２,G １,G ２,H １,H ２,A ,B ,E ,k ,ω的代数方程组,令D １＝４H １α２k ４－４H １αk ２ω＋４H ２αk ２μ＋２A E E １－B E G １,D ２＝４H ２α２k ４＋４H １αk ２μ－４H ２αk ２ω＋２A E E ２－B E G ２,D ３＝４E ２α２k ４＋４E １αk ２μ－４E ２αk ２ω＋A ２E ２－A B G ２＋E ２E ２,D ４＝４G １αk ２μ－４G ２αk ２ω＋２A ２G ２＋３A B E ２－B ２G ２＋E ２G ２,则代数方程组有如下表示,－２４Ε１G １H １αβk ２＋３A E G １＋３B E E １＝０,(１５)１２E １２H １αβk ２－１２G １２H １αβk ２－３A E E １＋３B E G １＝０,(１６)１２E １２G １αβk ２－４G １３αβk ２－２A ２G １－４A B E １＋２B ２G １＝０,(１７)４E １３αβk ２－１２E １G １２αβk ２－２A ２E １＋４A B G １＋２B ２E １＝０,(１８)㊀－１２E １２H １αβk ２－４H １３αβk ２＋D １＝０,(１９)－４G １αk ２ω＋４G ２αk ２μ＋２A ２G １＋３AB E １－B ２G １＋E ２G １＋４＝０,(２０)－２４E ２G ２H ２αβk ２＋３A E G ２＋３B E E ２＝０,(２１)１２E ２２H ２αβk ２－１２G ２２H ２αβk ２－３A E E ２＋３B E G ２＝０,(２２)１２E ２２G ２αβk ２－４G ２２αβk ２－２A ２G ２－４A B E ２＋２B ２G ２＝０,(２３)４E ２３αβk ２－１２E ２G ２２αβk ２－１４第１期仁世杰等:一类耦合非线性薛定谔方程组的求解２A ２E ２＋４A B G ２＋２B ２E ２＝０,(２４)－１２E ２２H ２αβk ２－４H ２３αβk ２＋D ２＝０,(２５)－４E ２３αβk ２－１２E ２H ２２αβk ２＋D ３＝０,(２６)－１２E ２２G ２αβk ２－１２G ２H ２２αβk ２＋４G ２α２k ４＋D ４＝０．(２７)求解方程组(１５)－(２７),选取其中一组非平凡解:A ＝３３B ,B ＝B ,E ＝０,E １＝E ２,E ２＝E ２,H １＝０,H ２＝０,G １＝－３３E ２,G ２＝－３３E ２,k ＝－B ２E ２２αβ,ω＝－８E ４２β２－６E ２２βμ＋３B ２６E ２２β．ìîíïïïïïïïï(２８)将(２８)代入方程(１２),得d h (ξ)d ξ＝３３B s i n (h (ξ))＋B c o s (h (ξ))．(２９)求解微分方程(２９),得h (ξ)＝２a r c t a n ３(１＋e ２３３B ξ)－３＋e ２３３B ξéëêêùûúú．(３０)取特定例子如下:取定常数μ＝１０,β＝－１,α＝１,B ＝－１,E ２＝３,将(３０)代入方程组(１１),得F １(ξ)＝F ２(ξ)＝３s i n２a r c t a n ３(１＋e ２３３B ξ)－３＋e ２３３B ξéëêêùûúú{}－３c o s２a r c t a n ３(１＋e ２３３B ξ)－３＋e ２３３B ξéëêêùûúú{}．(３１)相应F ２i (ξ)(i ＝１,２)的图像如图１所示,特别地,当待定系数αβ＜０时,发现F ２i (ξ)(i ＝１,２)的能量凹陷,即为暗孤立子解．根据(５)和(２８)可知U (X ,T )＝V (X ,T )．当常数确定后,则k ＝－２６,ω＝３９７１８,ξ＝T ＋２６X ．(３２)由此U (X ,T ),V (X ,T )表示为U (X ,T )＝V (X ,T )＝{３s i n２a r c t a n ３１＋e －２３３(T ＋２６X )()－３＋e－２３３(T ＋２６X )éëêêùûúú{}－３c o s２a r c t a n ３１＋e －２３３(T ＋２６X )()－３＋e－２３３(T ＋２６X )éëêêùûúú{}}e I (３９７１８T －２６X )．(３３)图１㊀F ２i (ξ)的图像㊀㊀限制自变量的范围,得到U (X ,T )２图像,如图２所示．图２㊀U (X ,T )２的图像从图２发现U (X ,T )２的能量凹陷,即为暗孤立子解．将(１３)代入(３３)中,令D (x ,t )＝e －I (９x ２＋９t ２＋３２x －１８t x ＋７９４)＋１８t l n (２t )３６t,u (x ,t ),v (x ,t )表示为u (x ,t )＝v (x ,t )＝{３s i n２a r c t a n ３(１＋e －３２x －４３６t )－３＋e －３２x －４３６t éëêêùûúú{}－２４㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀兰州文理学院学报(自然科学版)㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第３８卷３c o s２a r c t a n ３１＋e －３２x －４３６t ()－３＋e－３２x －４３６t éëêêùûúú{}}D (x ,t)．(３４)限制自变量的范围,得到u (x ,t )２图像如图３所示．图３㊀u (x ,t )２的图像㊀㊀从图３可以发现u (x ,t )２的部分能量突起,即为亮孤立子解．3㊀结语本文主要研究的是一类薛定谔方程组在可积条件下,通过特殊变换法和S i n e Ｇc o s i n e 求解其精确解,然后给定待定的常数,确定方程组精确解的图像．本文的目标方程可进行适当地调整,若将部分常系数改为变量系数,那么可积条件将会发生变化,同时可使用上述方法求方程的精确解．参考文献:[１]G O V I N D A R A J A N A ,A R UMU G AM M ,U T HA Y A ＧK UMA R A．I n t e r a c t i o nd y n a m i c so fb r i gh ts o l i t i o n s i n L i n e a r l y c o u p l e d a s y mm e t r i c s y s t e m s [J ]．O p t Q u a n tE l e c t r o n ,２０１６,４８(１２):５６３．[２]G A R D N E R C S ,G R E E N EJ M ,K R U S K A L M D ,e ta l ．M e t h o d f o r s o l v i n g t h eK o r t e w e g Ｇd eV r i e s e q u a t i o n [J ]．P h y sR e v ,１９６７,１９:１０９５Ｇ１０９７．[３]郭玉翠．非线性偏微分方程引论[M ]．北京:清华大学出版社,２００８．[４]F A N E G ,Z HA N G H Q．N e we x c e pt s o l u t i o n s t oa s y s t e mo fc o u p l e de q u a t i o n s [J ]．P h y Le t t A ,１９９８,２４５:３８９Ｇ３９２．[５]WA N G M L ．E x a c ts o l u t i o n sf o rac o m po u n d K d v ＧB u r g e r s e q u a t i o n [J ]．P h ys L e t t A ,１９９６,２１３:２７９Ｇ２８７．[６]M I U R A M R．B a c k l u n dt r a n s f o r m a t i o n [M ]．B e r l i n :S p r i n g e r ＧV e r l a g,１９７８．[７]C A O X F ．B äc k l u n dt r a n s f o r m a t i o nf o raf a m i l y of c o u p l e dK d ve q u a t i o n s [J ]．P h y sS c r ,２０２３,９８:１１５Ｇ２０９．[８]李新月,祁娟娟,赵敦,等．自旋Ｇ轨道耕合二分量玻色Ｇ爱因斯坦凝聚系统的孤子解[J ]．物理学报,２０２３,７２(１０):２８５Ｇ２９５．[９]X I AJ ,Y A N GD ,Z HO U H ,e t a l ．E v o l v i n g ke r n e l e x Ｇt r e m e l e a r n i n g m a df o r m e d i c a ld i ag n o s i sv i aad i s Ｇp e r s e f o r a g i n g s i n ec o n s i n ea l g o r i th m [J ]．C o m pu t e r s i nB i o l o g y an d M e d i c i n e ,２０２２,１４１:１０５１３７．[１０]Y A N C T．S o m e t h i n g hi d d e ni nt h eF o u r i e rs e r i e s a n d i t s p a r t i a l s u m :S o l i t a r y w a v e s o l u t i o n t o p o l y n o Ｇm i a l n o n l i n e a r d i f f e r e n t i a l e qu a t i o nw a v em o t i o n [J ]．P h y Le t tA ,１９９７,２６:２１９Ｇ２３７．[责任编辑:赵慧霞]３４第１期仁世杰等:一类耦合非线性薛定谔方程组的求解。
创维总线进入方法
创维总线1、数码3008系列，4S02，4S10工厂模式进入：先按遥控器“清除”键，再遥控器音量“减”键，最后按“AFT”键（遥控器最下面三个键中间的键）；退出：按遥控器“PIC”键。
2、数码8000S系列，5S01工厂模式进入：同时按键控板上的TV/AV键和菜单键（MENU），再开机。
进入后，按PIC进行项目菜单的选择，按节目+/-键进行子项目的选择，按音量+/-进行项目参数的调整。
退出：按遥控器上的图像模式键。
注：该机芯换CPU后，如无中文菜单，请进入工厂模式，将OPTION项改为0261，如有超重低音，改为1261。
3、数码5000系列，3N10、4N01、5N01工厂模式进入：同时按键控板上的音量+/-键，再开机。
设置内容及设置参数退出：关机即可。
3N10存储器重写方法：1、同时按键控板频道+/-键，再开机，按OPTION调整菜单；2、同时按一下S.M和P.M键,画面轻微变化一下(跳动或闪烁一下),表示存储器初始化完成；3、写入第二行数据（仅供参考）创维总线3N10功能参数表：功能参数一：彩色制式SECANL、SECAM、NTSC选择功能参数二：环绕声、超重低音、锐度频率提升选择功能参数三：声音制式BG、I、M选择功能参数四：S端子、第三路AV、两路AV选择功能参数五：R/B增益比例、GAMMA校正开关、智慧拼图游戏选择功能参数六:图像中频、无信号自动关机、X射线保护选择功能参数七:声音中频、ISUD5、ISUD3（后两项为5198K/5199K软件内部位，请不要改动，缺省值为1）功能参数八：开机画面类型、开机画面显示开关、菜单风格选择功能参数九：QSS开关、ISUD4（5195/5199软件内部位，请不要改动，缺省值为1）、菜单提示开关选择功能参数十：彩色制式PAL-M/N选择位、束流控制开关（RGB limit）、自动亮度控制（ABL）选择创维总线3N10的系统调试进入：同进按下键控板上的音量+/-然后打开电视机的电源即可。
诊断卡代码的明细
2 诊断卡代码.明细18 测试视频存储器，如果安装选用的视频BIOS通过，则可绕过。
第0通道计时器测试结束；即将开始更新存储器。
第一个64K RAM第8位故障。
19 测试第1通道的中断控制器（8259）屏蔽位。
已开始更新存储器，接着将完成存储器的更新。
第一个64K RAM第9位故障。
1A 测试第2通道的中断控制器（8259）屏蔽位。
正在触发存储器更新线路，即将检查15微秒通/断时间。
第一个64K RAM第10位故障。
1B 测方式CMOS电池电平。
完成存储器更新时间30微秒测试；即将开始基本的64K存储器测试。
第一个64K RAM 第11位故障。
1C 测试COMS检查总和。
无意义。
第一个64K RAM第12位故障。
1D 调定COMS的配置。
无意义。
第一个64K RAM第13位故障。
1E 测定系统存储器的大小，并且把客观存在和COMS值比较。
无意义。
第一个64K RAM第14位故障。
f=1F 测试64K存储器至最高640K。
无意义。
第一个64K RAM第15位故障。
20 测量固定的8259中断位。
开始基本的64K存储器测试；即将测试地址线。
从属DMA寄存器测试正在进行或失灵。
21 维持不可屏蔽中断（NMI）位（奇偶性或输入/输出通道的检查）。
通过地址线测试；即将触发奇偶性。
主DMA寄存器测试正在进行或失灵。
)fH22 测试8259的中断功能。
结束触发奇偶性；将开始串行数据读/写测试。
主中断屏蔽寄存器正在进行或失灵。
23 测试保护方式8086虚似方式和8186页面方式。
基本的64K串行数据读/写测试正常；即将开始中断矢量初始化之前的任何调节。
从属中断屏蔽寄存器测试正在进行或失灵。
24 测定1Mb以上的扩展存储器。
矢量初始化之前的任何调节完成，即将开始中断矢量的初始准备。
设置ES段地址寄存器注册表到内存高端。
25 测试除头一个64K之后的所有存储器。
完成中断矢量初始准备；将为旋转武断续开始读出8042的输入/输出端口。
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需求的收入弹性 =
记住，所有弹性都是用一个变量的百分比变 化除以另一个变量的百分比变化来衡量的。
© 2007 Thomson South-Western
其他需求弹性
• 收入弹性
– 物品类型
• 正常物品 • 劣等品
– 更高的收入增加对正常物品的需求量，而减少 对劣等品的需求量。
© 2007 Thomson South-Western
• 只取变动数量，不考虑方向
• 与导数含义的不同 • 弹性是一个变量对另一个变量敏感性的一种度量，即一个 变量发生1％的变化将会引起另一个变量变动的百分比。
© 2007 Thomson South-Western
需求的弹性
• 需求的价格弹性是一种物品的需求量对其
价格变动的反应程度的衡量。 • 当我们讨论弹性时，反应总是用百分比来 衡量。 • 特别地，需求的价格弹性是需求量的变化 百分比除以价格的变化百分比。
© 2007 Thomson South-Western
需求的价格弹性与其决定因素
• 相近替代品的可获得性
• 必需品与奢侈品
• 市场的定义
• 时间的长短
© 2007 Thomson South-Western
需求的价格弹性及其决定因素
• 需求倾向于更富有弹性：
– 相近替代品的数量更多
– 如果物品是奢侈品
§5 弹性理论：弹性及其应用
© 2007 Thomson South-Western
弹性（Elasticity）理论
• 思考： 火车票为什么提价而飞机票却要打折； 保护农民的积极性为什么要采用支持价格政 策？
© 2007 Thomson South-Western
弹性 . . .
• …使我们可以更精确地分析供给与需求。 • … …是衡量买者和卖者对市场条件变动的反应程度的指 标。
需求价格弹性 = (Q2 Q1 ) /[(Q2 Q1 ) / 2] ( P2 P ) /[( P2 P ) / 2] 1 1
© 2007 Thomson South-Western
中点法:一种计算百分比变化和弹性的更 好方法
• 例子:如果冰激凌蛋卷的价格从2美元上升
到2.2美元，你的购买量从10个下降到8个，
TR=0
TR上升 TR达到最大
TR下降
TR=0 Q
其他需求弹性
• 需求的收入弹性
– 需求的收入弹性 衡量消费者收入变动时需求量 如何变动。 – 它是用需求量变动的百分比除以收入变动的百 分比来计算的。
© 2007 Thomson South-Western
其他需求弹性
• 计算收入弹性
需求量变动的百分比 收入变动的百分比
Margarine
Natural Gas Fuel Oil All other lively arts All other lively arts
0.67
0.20 0.44 0.12 0.53
数据来源：Principles of Economics,Richard,w.Tresch,1994 ,P 122
弹性程度 缺乏弹性 缺乏弹性 缺乏弹性 单位弹性 富有弹性 富有弹性 富有弹性
图4. 一条线形需求曲线的弹性
价格
$7
需求富有弹性；需求 对价格变化反应强烈。
当价格从4美元上升到5美元 时，总收益从24美元下降到 20美元。
在此区间弹性 > 1
6 5 4
在此区间弹性 < 1
3 2 1
需求缺乏弹性；需求对
供给
1.价格上 $5 升… 4
100 2. …供給量不变。
数量
图5. 供给的价格弹性
• 富有弹性的需求
– 需求量随着价格变化而强烈变化。
– 需求价格弹性大于1。
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多种需求曲线
单位弹性（unitary elastic）：如果弹性正 好是1，从而需求量与价格同比例变动时 需求是单位弹性的。 完全无弹性（perfect inelastic）：弹性为 0 完全富有弹性（perfect elastic）：弹性为 无穷大
总收益与需求价格弹性
• 总收益是一种物品买者的支付量和卖者得到的量。
• 用该物品的价格乘以销售量来计算。
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图2. 总收益
价格
当价格是4美元时，消费者的需求量 是100个单位，所以花费400美元购买 此物品。
$4
P
P × Q = $400 (收益)
– 市场定义的范围更窄
– 时期更长
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弹性计算公式: (1) 弧弹性计算
ed = ΔP
ΔQ P Q
（实际计算中不使用）
（2）弹性的中点计算公式
ed =
Q1 Q2 Q ΔQ P1 P2 2 ΔP Q 1 Q 2 P1 P2 P 2
价格变化反应不强烈。 当价格从2美元上升到3美元 时，总收益从20美元增加到 24美元。
0 2 4 6 8 10 12
14
数量
沿着一条线性需求曲线的弹性和总收益
需求函数：Q=14-2P P 计算以下各点 需求价格弹性： A:P=7,Q=0 B: P=5,Q=4 C: P=3.5,Q=7 D: P=2,Q=10 E: P=0,Q=14
奢侈品
书籍 新车 教育
耐用消费品（家用电器等）
2.90
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部分产品的交叉价格弹性
PRODUCT BEEF SUBSTITUTE PRODUCT Pork CROSS-PRICE ELASTICITY 0.28
BUTTER
ELECTRICITY NATURAL GAS THEATER SYMPHONY
需求
0 Q
100
数量
沿着线性需求曲线的弹性与总收益
• 如果需求是缺乏弹性的，价格上升导致需
求量减少的比例小于价格上升的比例，所
以总收益是增加的。
© 2007 Thomson South-Western
图3.总收益如何随着价格变化而变化： 缺乏弹性的需求
价格 价格
价格从1美元上升到3 美元...
…导致总收益从100美 元增加到240美元
价格
$5 4 1. 价格上升 22%... 需求
0 2. . . . 使需求量减少11％。
90
100
数量
图1. 需求的价格弹性
(c) 单位弹性: 弹性等于 1 价格
$5
4
1. 价格上升 22%...
需求
0
80
100
数量
2. . . . 使需求量减少22％。
图1. 需求的价格弹性
(d) 富有弹性的需求: 弹性大于 1 价格
（实际使用的公式）
（3）点弹性
ed = lim
Q P
p 0
P Q
=
dQ dP
P Q
© 2007 Thomson South-Western
计算需求价格弹性
例子: 如果冰激凌蛋卷的价格从2美元上升到2.2美 元，你的购买量从10个下降到8个，你的需求价格 弹性计算如下：
需求价格弹性 = 需求量变动的百分比 价格变动的百分比
© 2007 Thomson South-Western
多种需求曲线
• 由于需求的价格弹性衡量需求量对价格变
化的反应程度，所以它与需求曲线的斜率
密切相关。
• 但是，价格弹性和斜率不是一回事！
© 2007 Thomson South-Western
计算需求的价格弹性
(100-50) ED (4.00-5.00)
其他需求弹性
• 收入弹性
– 消费者认为的必需品往往收入弹性小
• 例如：食物、燃油、衣服和医疗服务。
– 消费者认为的奢侈品往往收入弹性大
• 例如：运动跑车、皮衣和昂贵物品。
© 2007 Thomson South-Western
其他需求弹性
• 需求的交叉价格弹性
• 定义：一种物品需求量对另一种物品价格变动的 反应程度的衡量。用这种物品需求量变动的百分 比除以另一物品价格变动的百分比来计算。
利用中点法你的需求价格弹性计算如下:
(10 8) 22% (10 8) / 2 2.32 (2.20 2.00) 9.5% (2.00 2.20) / 2
© 2007 Thomson South-Western
多种需求曲线
• 缺乏弹性的需求
– 需求量不随着价格变化而强烈变化。 – 需求价格弹性小于1。
(10 8) 100 20 ％ 10 2 (2.20 2.00) 10 ％ 100 2.00
© 2007 Thomson South-Western
中点法:一种计算百分比变化和弹性的更 好方法
• 中点法 是计算需求价格弹性的更好方法， 因为无论变动的方向如何，中点法给出了 同一个答案。
$3 收益=240美元 $1 收益 = 100美元
需求
100
需求
0 80
0
数量
数量
沿着线性需求曲线的弹性与总收益
• 如果需求富有弹性，价格上升导致的需求
量减少的比例大于价格上升的比例，因此
总收益是减少的。
© 2007 Thomson South-Western
图3. 总收益如何随着价格变化而变化： 富有弹性的需求
价格 价格
价格从4美元上升到5 美元…
…导致总收益从200美 元减少到100美元