RF射頻電路設計英文課件Lecture10_Manufacturability of a product desig

1、Lecture 10精選ppt11. Introduction2. Implication of 6 Design o 6 and Yield Rate o 6 Design for a Circuit Block3. Approaching 6 Design o By Changing Parts Value o By Replacing a Single Part with Multiple Parts 4. Monte Carlo Analysis o A BPF (Band Pass Filter) o Simulation with Monte Carlo Analysis o Se

2、nsitivity of Parts on the Parameter of PerformanceAppendixes o Fundamentals of Random Process o Table of the Normal Distribution Lecture 10 : Manufacturability of a Product DesignRichard Chi-Hsi Li 李緝熙李緝熙Email : Lecture 10精選ppt2 1. IntroductionThe unique criterion to measure success or failure of pr

3、oduct development is The manufacturability of a product. What is the manufacturability of a product? 1) High yield rate, including * Satisfication of specifications; * Good repetition or identity of product; * High reliability. 2) Low cost, including the cost of * Material and parts, * Manpower, * M

4、anufactory maintenance and equipment. Lecture 10精選ppt3SpecificationsSimulationsFabrication of samples by handTestingALTTOPPilot productionMassive productionTolerance analysisFigure 1 Typical design procedures of a new product with acceptable manufacturability3rd stage : Production2nd stage : Pre-Pro

5、duction 1st stage : R & DLecture 10精選ppt4o 6 and Yield Rate(z)Figure 2 Definition of design tolerance Toldesign and process capability 6USLLSLDesign tolerance = ToldesignProcess capability = 6Defects = 6.68%Defects = 6.68% -4 -3 -2 -1.5 -1 0 +1 +1.5 +2 +3 +4 z =(C-m)/mCzLSLUSLToldesign)()(1LSLzfUSLz

6、fDefects)()(2210222zzeerfdxzfxImplications of 6 Design Lecture 10精選ppt5Figure 3 Relationship between yield rate f(z) and Design tolerance Toldesign . 0 1 2 3 4 5 6 7 100%90%80%70%60%50%40%30%20%10% 0%Yield rate f(z), %Design tolerance Toldesign , 99.74%95.44%68.26%38.30%86.64%98.76%0%99.98% Table 1

7、Relationship between the yield rate f(z) and the design tolerance Toldesign Design tolerance Yield rate Toldesign f(z) 0 0% 1 38.30% 2 68.26% 3 38.30% 4 86.64% 5 98.76% 6 99.74% 7 99.98%Lecture 10精選ppt6o 6 Design for a Circuit BlockA 6 circuit design is a design such that the yield rate of this circ

8、uit block in mass-production reaches 99.74% when 6 tolerance of all the parts applied in the circuit block is allowed. Actually, the expected yield rate is 100%, although 99.74% is close to 100%.Lecture 10精選ppt73. Approaching 6 Design o By Changing Parts 6 Value(z)USLLSLDesign tolerance Process capa

9、bility = 6Defects = 6.68%Defects = 6.68%USLLSLDefects = 0.13%Defects = 0.13%Process capability = 6 -4 -3 -2-1 0 +1 +2 +3 +4 -4 -3 -2 -1 0 +1 +2 +3 +4 Design tolerance = Toldesignz =(C-m)/z =(C-m)/Design tolerance = ToldesignUSLLSLFigure 4 Convert 3 design to 6 design by 50%reduction of standard devi

10、ation from to , that is, = /2 = original = /2Lecture 10精選ppt8o By Replacing a Single Part with Multiple Parts 2 k6 k(a) One resistor of 2 k is replaced by three 6 k resistors in parallelm = 2k = 200 m = 6 k/3 = 120 4 pF16pF(b) One capacitor of 5 pF is replaced by four 16 pF capacitors in seriesm = 4

11、 pF = 0.5 pF m = 16 pF/4 = 0.2 pF 7 nH(c) One inductor of 7 nH is replaced by two 14 nH inductors in parallel.m = 7 nH = 0.2 nH m = 14 nH/2 = 0.15 nH Figure 5 One part is replaced by multi-parts.14 nH14 nH6 k6 k16pF16pF16pFLecture 10精選ppt9Table 1 Replacement of original 1 resistor, 1 capacitor, and

12、1 inductor by 3 resistors, 4 capacitors, and 2 inductors.Original partMulti-partsm m .Resistor 2 k200 6 k/3120 (1 resistor)(3 resistors in parallel)Capacitor4 pF0.5 pF16 pF/40.2 pF(1 capacitor)(4 capacitors in series)Inductor7 nH0.2 nH14 nH/20.15 nH(1 inductor)(2 inductors in parallel)Lecture 10精選pp

13、t104. Monte Carlo AnalysisCVR1R1C2L3L2L1L1InL1L1OutL2C3C4VR1(C1)VR1(C1)VR1(C1)VR1(C1)L1 : Inductor 4.5 nH / 27 k / 0.2 pFL2 : Inductor 8.8 nH / 27 k / 0.2 pFL3 : Inductor 40.5 nH / 27 k / 0.2 pFC1 : Capacitance of varactor 13.75 pF when CV=5vC2 : Capacitor 2.4 pF C3 : Capacitor 100 pFC4 : Capacitor

14、10000 pFR1 : Resistor 20 k CV : 5 vFigure 6 Schematic of a UHF tunable filter o BPTF (Band Pass Tunable Filter)Lecture 10精選ppt11 Tunable FLTLNAMixerFLTFigure 7 A tunable filter is added in the front end of the receiver for better selectivityLecture 10精選ppt12frequencyFigure 8 Frequency response of a

15、tunable filter moved from low end to high end as the control voltage is increased(a) Popular cases : Bandwidth is changed as the frequency response is movedfrequency(b) Ideal cases : Bandwidth is kept unchanged as the frequency response is movedLecture 10精選ppt13* Main coupling : Inductive coupling -

16、 An improper coupling unable a tunable filter tuned over a wide frequency tuning range . where Q = Quality factor of filter ;o = Tuned central frequency ;BW = Bandwidth o ;L = Inductance of coupling inductor ;R = Equivalent resonant resistance of tank circuit o .ooRCBW40oBWooRCBWQ21RLBWQoo222oRCBWLR

17、BW2- In the case of inductor coupling,- In the case of capacitor coupling,Lecture 10精選ppt14From the above expressions , it is found that1) In the case of capacitor-coupling, the bandwidth of the filter is dependent of the tuning frequency. It is increased as the tuning frequency is increased. 2) In

18、the case of inductor-coupling, the bandwidth of the filter is an independent of the tuning frequency. The bandwidth could be kept in an almost constant for a wide tuning frequency range. It is therefore concluded that The correct coupling element between the 2 tank circuits must be an inductor, but

19、not a capacitor nor others. Lecture 10精選ppt15* Second coupling : Capacitive coupling - The capacitor, C2, is the second coupling component between the two tank circuits; - It forms a “zero” at the imaginary frequency; - This “zero” traces the central frequency, o , over a wide frequency tuning range

20、. Lecture 10精選ppt16* Monte Carlo AnalysisFigure 7.15 Simulation page for Monte-Carlo analysis (Strictly speaking, it is not a Gaussian but a normal distribution here.)FLTPort 1Port 250 Terminator50 TerminatorC1 = CaC2 = CbL1 = LaL2 = LbL3 = LcEquation Ca = Randvar Gaussian, 13.75 pF 5%Equation Cb =

21、Randvar Gaussian, 2.4 pF 5%Equation La = Randvar Gaussian, 4.5 nH 7%Equation Lb = Randvar Gaussian, 8.8 nH 7%Equation Lc = Randvar Gaussian, 40.5 nH 7%Figure 9 Simulation page for Monte-Carlo analysis (Strictly speaking, it is not a Gaussian but a normal distribution here.) Lecture 10精選ppt17* Freque

22、ncy response without tolerance200 300 400 fo 500 600 700 -10S21, dB0-20-40-60 10-50-70-80-90-30f , MHzIL=1.76 dBImag. Rej. =83.1 dBf o =435.43 MHzFigure 10 Typical frequency response of tunable filter without tolerance Lecture 10精選ppt18* Case #1 : Bandwidth is too wide 200 300 400 fo 500 600 700 -10

23、S21, dB0-20-40 10-50-90-30 f , MHzIL=1.76 dBImag. Rej. =80.1 dBf o =435.43 MHzFigure 11 Frequency response of tunable filter with tolerance - Bandwidth is too wide-70-80-60Lecture 10精選ppt19* Case #3 : Bandwidth is too narrowS21, dB 200 300 400 fo 500 600 700 -100-20-40-60 10-50-70-80-90-30f , MHzIL=

24、1.76 dBImag. Rej. =80.1 dBf o =435.43 MHzFigure 12 Frequency response of tunable filter with tolerance - Bandwidth is too narrowIL=5.10 dBLecture 10精選ppt20* Case #2 : Bandwidth is appropriate 200 300 400 fo 500 600 700 -10S21, dB0-20-40 10-50-70-80-90-30f , MHzIL=1.76 dBImag. Rej. =80.1 dBf o =435.4

25、3 MHz-60Figure 13 Frequency response of tunable filter with tolerance -Bandwidth is appropriateLecture 10精選ppt21* Yield rate & its histogram of IL less than 2.5 dB ( For case #2 )Yield rate, % 100.00-2.16 -1.71IL, dB350%Figure 14 Display of insertion loss histogram and yield rate for IL60 dB Lecture

26、 10精選ppt24* Image Rejection performance of parts with tolerance ( For case #2 )-64-8413.2 142Imag.Rej., dBC1 , pF-64-842.3 2.5C2 , pFImag.Rej., dB-64-848.3 9.3L2 , nHImag.Rej., dBL1 , nH-64-844.2 4.8Imag.Rej., dB-64-8438.1 42.6L3 , nHImag.Rej., dBNote : Capacitors are more sensitive to the image rej

27、ection than inductors !Figure 17 The effect of individual parts value on the image rejection Lecture 10精選ppt25o A BPF (Band Pass Filter)C1 L C3 L C4 L C3 L C1Port 1InC2 C2 C2 C2 C5 C2 C2 C2Figure 18 BPF (Band Pass Filter), 403 470 MHz. L = 20 nH C1 = 3.9 pF C2 = 4.3 pF C3 = 7.5 pF C4 = 9.1 pF C5 = 3

28、.9 pFPort 2OutLecture 10精選ppt26Figure 19 Frequency response of band pass filter f = 403 470 MHz 200 300 400 fo 500 600 700 -10S21, dB-20-400 0-50-30f , MHzIL= -1.05 dBf o =435.21 MHz-70-80-60-90-100Lecture 10精選ppt27VNSWOEUFigure 20 S11 of band pass filter f = 403 470 MHz 200MHz403MHz470MHz700MHzLect

29、ure 10精選ppt28* Simulation with Monte Carlo Analysis BPF(Band Pass Filter)403 = 470 MHzPort 1Port 250 Terminator50 TerminatorL = LaC1 = CaC2 = CbC3 = CcC4 = CdC5 = CeEquation La = Randvar Gaussian, 20 nH 7%Equation Ca = Randvar Gaussian, 3.9 pF 5%Equation Cb = Randvar Gaussian, 4.3 pF 5%Equation Cc =

30、 Randvar Gaussian, 7.5 pF5%Equation Cd = Randvar Gaussian, 9.1 pF 5%Equation Ce = Randvar Gaussian, 3.9 pF 5%Figure 21 Simulation page for Monte-Carlo analysis. Number of iteration = 50.Lecture 10精選ppt29Figure 22 Frequency response of band pass filter, 403 470 MHz, Number of iteration = 50 200 300 4

31、00 fo 500 600 700 -10S21, dB-20-400 0-50-30IL= -2.30 dB-70-80-60-90-100f , MHzf o =435.21 MHzLecture 10精選ppt30SWOEVNU200MHz403MHz470MHz700MHzFigure 23 S11 of band pass filter, 403 470 MHz Number of iteration = 50Lecture 10精選ppt31Yield rate, % 100.00-2.3 -0.8IL, dB0Figure 24 Display of insertion loss

32、 histogram and yield rate for |IL| 2.5 dB (Iteration number = 50) Number in iteration2010 0 Table 2 Distribution of iteration number vs. insertion loss Insertion loss, dB -2.30 to -2.05 -2.05 to -1.80 -1.80 to -1.55 -1.55 to -1.30 -1.30 to -1.05 -1.05 to -0.8Number in iteration 4 12 1 20 12 1Lecture

33、 10精選ppt32-0.8-2.318.86 20 20.14IL, dBL=La , nH(IL vs. L) Tolerance of L : 7%-0.8-2.34.085 4.3 4.515IL, dBC2=Cb , pF(IL vs. C2) Tolerance of C2 : 5%-0.8-2.33.705 3.9 4.095 IL, dBC1=Ca , pF(IL vs. C1) Tolerance of C1 : 5%Figure 25 Sensitivity of individual parts value on the insertion loss-0.8-2.3IL,

34、 dBC5=Ce , pF3.705 3.9 4.095(IL vs. C5) Tolerance of C5 : 5%-0.8-2.38.645 9.1 9.555IL, dBC4=Cd , pF(IL vs. C4) Tolerance of C4 : 5%-0.8-2.37.125 7.5 7.875 IL, dBC3=Cc , pF(IL vs. C3 ) Tolerance of C3 : 5%Lecture 10精選ppt33-0.8-2.38.645 9.1 9.555IL, dBC4=Cd , pFFigure 26 Sensitivity of C4 on the inser

35、tion loss after its tolerance of 5% is replaced by 7%(IL vs. C4) Tolerance of C4 : 7%Lecture 10精選ppt34A.1 Fundamentals of Random ProcessAppendixesRelative number of resistorsFigure A.1 Histogram of relative number of resistors versus the value of resistor 0.800k 0.850k 0.900k 0.950k 1.000k 1.050k 1.

36、100k 1.105k 1.120k R, ohmLecture 10精選ppt35 ohms , 1000m%52RemmRToliilativeiiR2 ohms .mRz2222)(xexdxdxxzfzezx020222)()(* Gaussian probability function , * Average value :* Relative tolerance :* Variance or standard deviation Ri , * Sample value :where* Gaussion distribution :Lecture 10精選ppt36 -4 -3 -

37、2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4 R, ohm(z)Figure A.2 Distribution of the random variable, R, is a Normal probability function or a Gaussian distributionLecture 10精選ppt37* Tolerance and normal distribution (z)Figure A.3 Integral of (z) from 0 to z or from m to m+z . -4 -3

38、 -2 -1 0 +1 z +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+z m+2 m+3 m+4 R, ohmLecture 10精選ppt38* Six sigma and 100% yield rateGaussian distribution :dxzfzemx022222)(where m = average of the variable x ; = square root of the variable x.Normal probability function is a Gaussian distribution function whe

39、n :m = 0 , and = 1 .)()(2210222zzeerfdxzfxdyexerfxy022)(Lecture 10精選ppt39Figure A.4 At each interval, z, the appearing percentage of a random variable with a Normal distribution when the interval is-1 z +1 ,then the area isf(z) = 68.26%,when the interval is-2 z +2 ,then the area isf(z) = 95.44%,when

40、 the interval is-3 z +3 ,then the area isf(z) = 99.74%,when the interval isz +3,then the area isf(z) = 0.26%, (z)0.13%0.13%34.13%34.13%13.59%13.59%2.15%2.15% -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4 R, ohmLecture 10精選ppt40* 6, Cp, and CpkFigure A.5 The various terminologi

41、es of a process with normal distribution mUSLLSLDesign tolerance Process capability = 6 DefectsDefects -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4 R, ohmUSL = Upper specification limit, , LSL = Lower specification limit, .Lecture 10精選ppt41LSLUSLTolerance)()(1LSLzfUSLzfDefect

42、s6_Pr_LSLUSLCapabilityocessToleranceDesignCpCapability Index, Cp , is defined as)1(KCCppk2/LSLUSLmmKwhere m = Nominal process mean, , m = Actual process mean, .Adjusted Capability Index, Cpk, is defined aswhere USL = Upper specification limit, , LSL = Lower specification limit, .Lecture 10精選ppt42Exa

43、mple #102/LSLUSLmmK%56. 5%72.47*21)2(21zfDefects6667. 0646LSLUSLCp6667. 0)01 (6667. 01KCCppkFigure A.6 A normal distribution with m=10, =0.01, USL-LSL=4, m=m .Specification mean, m Process mean, m USLLSL2.28%2.28% -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4 R, ohmLecture 10精

44、選ppt43Example #202/LSLUSLmmK%26. 0%87.49*21)3(21zfDefects0000.1666LSLUSLCp0000. 1)01 (0000. 11KCCppkFigure A.7 A normal distribution with m=10, =0.01, USL-LSL=6, m=m .USLLSL0.13%0.13%Specification mean, m Process mean, m -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4 R, ohmLect

45、ure 10精選ppt44Example #3 5000. 02/412/LSLUSLmmK%16%87.49%13.341)()3(1zfzfDefects6667.0646LSLUSLCp3334. 0)5 . 01 (6667. 01KCCppkFigure A.8 A normal distribution with m=10, =0.01, USL-LSL=4, m=9.99 .Specification mean, m Process mean, m USLLSL0.13%15.87% -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2 m

46、-1 m m+1 m+2 m+3 m+4 R, ohmLecture 10精選ppt45Example #412/422/LSLUSLmmK%50%50%01)4()0(1zfzfDefects6667.0646LSLUSLCp0) 11 (0000. 11KCCppkFigure A.9 A normal distribution with m=10, =0.01, USL-LSL=4, m=10.02 .USLLSL50%Specification mean, m Process mean, m -4 -3 -2 -1 0 +1 +2 +3 +4 z =(R-m)/m-4 m-3 m-2

47、m-1 m m+1 m+2 m+3 m+4 R, ohmLecture 10精選ppt46* Yield rate and DPU pdNNDPUwhere Nd = Number of defects found at all acceptance points,Np = Number of units processed.Lecture 10精選ppt47 !xexPx* Poisson distributionPoisson distribution, the occurrence of random defects in manufactured product can be stat

48、istically predicted. Poisson distribution is a mathematic model to describe the probability distribution of the arrived entities. For instance, in one hour lunch time, say, statistically from 12.00 to 13.00 oclock, the number of customers getting into a restaurant for lunch. Assuming that the averag

49、e number of customers is , and the random number of arrivals at the same time interval is x, then the probability of the random arrival number, Px, isLecture 10精選ppt48 DPUDPUeeDPUP!000DPUeFTY !xeDPUxPDPUx And, in generalthis is the relationship between the defect-free probability and the average DPU

50、. The first time yield, FTY, can be approximated by the formula:Lecture 10精選ppt49CountPartsDPUpartPPMrateDefectpartPPM_/_/ NFTYDFTYCFTYBFTYAFTYFTYrolled*.*Regardless of process flow or order, the rolled yield can be calculated from the summation of the DPU values in all the steps.If a process with N

51、 steps, 1,2,3,4.N, and the value of DPU in each step is a, b, c, d, n respectively. Then, in terms of the formula, the first time yield, FTY, is e-a, e-b, e-c, e-de-n correspondingly. The fist time rolled yield for the process isndcbarolledeFTY.Lecture 10精選ppt50Example : Rolled yield for a printed c

52、ircuit board. Assuming that there are totally 3 steps : Parts placed, parts soldered, and parts assembly. a) Part placement = 300 PPM, it means 300 parts failed in 1million parts.b) Part assembly defect rate = 800 PPM, it means 800 assembly-components failed in 1 million parts.c) Solder defect rate

53、= 200 PPM, it means 200 connected points failed in 1million parts.*) On average, there are 2.3 connections for each part. Table A.1 Calculated FTY for a printed circuit board assembly by 3 process stepsParts Parts Parts # of parts placementassemblysoldered TotalRolled FTYabc a+b+ce-(a+b+c) 1000.0300

54、.0800.046 0.15685.6%5000.1500.4000.230 0.78045.8%10000.3000.8000.460 1.56021.0% Lecture 10精選ppt51A.2 Table of the normal distriution Z 01 234 5 6 7 8 90.0.0000.0040.0080.0120.0160.0199.0239.0279.0319.03590.1.0398.0438.0478.0517.0557.0596.0636.0675.0714.07540.2.0793.0832.0871.0910.0948.0987.1026.1064.1103.11410.3.1179.1217.1255.1293.1331.1368.1406.1443.1480.15170.4.1554.1591.1628.1664.1700.1736.1772.1808.1844.18790.5.1915.1950.1985.2019.2054.2088.2123.2157.2190.22240.6.2258.2291.2324.2357.2389.2422.2454.2486.2518.25490.7.2580.2