This simulation is about PTC protection of power semiconductor (BJT, mosfet of IGBT). In a circuit like the one of figure 1, a lot of heat is generated by both fixed resistors and bipolar transistor. This heat is transferred to an heat sink on which all elements are fixed, and the final heat sink temperature is then measured by a Vishay PTCSL03 leaded through hole components in order to strongly reduce the current passing through the transistor by decreasing strongly the base voltage.
The heat generation is modeled via the supplementary pins created for a simple fixed resistor and a npn transistor. Both netlists will be found in the appendixes of
this project.
figure 1
figure 2
The figure 2 represents the PTC resistance variation in time showing the strong resistance increase at a defined temperature (here between 115 and 120°C) (figure 3)
figure 3
Above this temperature, the current through the load (U2) will be strongly reduced.
LTspice netlist for Vishay PTC sensing thermistors
Plain textuse it as a nelist for an LTspice library
********************************
* Copyright: *
* Vishay Intertechnology, Inc. *
********************************
* LTpice Model Editor
*$
* Library of Vishay PTC sensing Thermistors
*
*
* $Revision: 1.0 $
* $Author: Alain Stas $
* $Date: dec 2020 $
* $Revision History :
*---------------------------------------------------------------
*
* Vishay PTC Thermistors included in this file : PTCSL03
* DESCRIPTION: through hole PTC disc thermistors for temperature sensing
* For power rating and temperature range limitations, see
* PTCSL03 : http://www.vishay.com/thermistors/list/product-29160/
* or use the search engine of Vishay for visualizing particular data sheet at http://www.vishay.com/
* the model is applicable for transient and steady states conditions under bias including self heating.
* The tolerance on resistance characteristics is implemented via the tolerance on R27
*
*----------------------------------------------------------------
.SUBCKT PTCSL03_base Rn Rp Ti InvK LnLn PARAMS: tsw=1 cth=1 k=0.001 gth=1 tol=0 tmin=0 rsw=1
+ tmax=1
R_R1 0 OUT 1T TC=0,0
E_E2 INVK 0 VALUE { +1/(273.15+ V(Ti)+limit(V(HH),0,Tmax- V(Ti))) }
V_V5 N RN 0.Vdc
G_G8 H 0 VALUE { -abs((V(P)-V(N))*I(V_V5)) }
C_C1 0 H {Cth} IC=0 TC=0,0
E_E3 OUT 0 VALUE { +abs(limit(exp(exp(V(LNLN,
+ 0))),1m,1T))*IF( v(Ti)<25,1,exp(0.003 * (V(TOL)-1)* (V(Ti)-25)))* V(TOL) }
G_G10 H 0 VALUE { V(H)*(Gth ) }
R_R3 0 H 1T TC=0,0
G_G5 N P VALUE { V(N, RP)/(V(out)) }
E_E20 HH 0 VALUE { limit(V(H),0,Tmax-V(Ti)) }
R_R26 0 HH 1T TC=0,0
R_R27 0 TOL {mc(1,0.1)}
*.model R_R27 RES R=1 DEV=10% TC1=0 TC2=0
I_I1 0 TOL DC 1
R_R23 RP P {K} TC=0,0
.ENDS
*$
$
.SUBCKT PTCSL03T081 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=80 cth=0.026 k=0.001 gth=5m tol=-25 tmin=-40
+ tmax=130
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00251161622504081,2.70052302818763)
+ (0.00254355843825512,2.6687835168695)
+ (0.00257632358624243,2.62617839776182)
+ (0.00260994388620645,2.57183301321147)
+ (0.00264445325928864,2.5050116479391)
+ (0.00267988744472732,2.42477312458303)
+ (0.0027162841233193,2.33118588800281)
+ (0.00275368305108082,2.21585991083099)
+ (0.00279212620410443,2.0792344527942)
+ (0.00283165793572136,1.9277590247498)
+ (0.00287232514720666,1.77658791238635)
+ (0.00291417747340813,1.6827069521257)
+ (0.002957267484844,1.60394230271382)
+ (0.0030016509079994,1.54655996187321)
+ (0.00304738686576261,1.49789221607182)
+ (0.00309453814018258,1.46480305417665)
+ (0.00314317146000314,1.43631574393993)
+ (0.00319335781574325,1.41292527987464)
+ (0.00324517280545189,1.39923326397539)
+ (0.0032986970146792,1.38782614154972)
+ (0.00335401643468053,1.37905963203229)
+ (0.00341122292341805,1.37781128558586)
+ (0.00347041471455839,1.37752386116459)
+ (0.00353169698039908,1.37830240381305)
+ (0.00359518245550962,1.38026347452183)
+ (0.00366099212886692,1.3835365735581)
+ (0.00372925601342532,1.39040978996121)
+ (0.0038001140034201,1.39795094723295)
+ (0.00387371683129963,1.40622294890989)
+ (0.00395022713806044,1.4152956091917)
+ (0.00402982067298005,1.42524654864632)
+ (0.00411268764137364,1.43616222554687)
+ (0.00419903422212891,1.44813912654248)
+ (0.00428908428050611,1.4612851450927) )
.ENDS
*$
$
.SUBCKT PTCSL03T091 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs:tsw=90 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40
+ tmax=155
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00236322816967978,2.71465130528791)
+ (0.00239148630874088,2.69033401984185)
+ (0.0024204284158296,2.66270263942767)
+ (0.0024500796275879,2.63153397418642)
+ (0.0024804663276696,2.59658866954238)
+ (0.00251161622504081,2.55760986744344)
+ (0.00254355843825512,2.51432174042502)
+ (0.00257632358624243,2.46640548389709)
+ (0.00260994388620645,2.39634687647177)
+ (0.00264445325928864,2.30832992648217)
+ (0.00267988744472732,2.20018819293831)
+ (0.0027162841233193,2.07949703378151)
+ (0.00275368305108082,1.94091326140111)
+ (0.00279212620410443,1.78937664575774)
+ (0.00283165793572136,1.64106797814195)
+ (0.00287232514720666,1.53797991492544)
+ (0.00291417747340813,1.4669087126627)
+ (0.002957267484844,1.40885500016206)
+ (0.0030016509079994,1.36948301348907)
+ (0.00304738686576261,1.33702078842248)
+ (0.00309453814018258,1.31715080751383)
+ (0.00314317146000314,1.3006546038527)
+ (0.00319335781574325,1.28788836181428)
+ (0.00324517280545189,1.28244311103302)
+ (0.0032986970146792,1.27843052273105)
+ (0.00335401643468053,1.27604207200429)
+ (0.00341122292341805,1.27727185177644)
+ (0.00347041471455839,1.27958251627666)
+ (0.00353169698039908,1.28308729652109)
+ (0.00359518245550962,1.28791166208748)
+ (0.00366099212886692,1.29419482307316)
+ (0.00372925601342532,1.30442947607836)
+ (0.0038001140034201,1.31541518760419)
+ (0.00387371683129963,1.32721704786004)
+ (0.00395022713806044,1.33990701754706)
+ (0.00402982067298005,1.3535647976324)
+ (0.00411268764137364,1.36827882880027)
+ (0.00419903422212891,1.38414744299342)
+ (0.00428908428050611,1.40128019389221) )
.ENDS
*$
$
.SUBCKT PTCSL03T101 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=100 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40 tmax=160
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00233563003620227,2.79939002210763)
+ (0.00236322816967978,2.78472801990074)
+ (0.00239148630874088,2.762643246796)
+ (0.0024204284158296,2.73262807717219)
+ (0.0024500796275879,2.69618637328019)
+ (0.0024804663276696,2.64854712156284)
+ (0.00251161622504081,2.58889578831611)
+ (0.00254355843825512,2.52430056314211)
+ (0.00257632358624243,2.42996436863942)
+ (0.00260994388620645,2.30348764321867)
+ (0.00264445325928864,2.1300300967841)
+ (0.00267988744472732,1.95487670951724)
+ (0.0027162841233193,1.7327154807204)
+ (0.00275368305108082,1.5903111115181)
+ (0.00279212620410443,1.53024948864313)
+ (0.00283165793572136,1.48313047774067)
+ (0.00287232514720666,1.45406901518506)
+ (0.00291417747340813,1.43261833006777)
+ (0.002957267484844,1.42712453027595)
+ (0.0030016509079994,1.42334738488295)
+ (0.00304738686576261,1.42145268160874)
+ (0.00309453814018258,1.42364558056336)
+ (0.00314317146000314,1.42614190008744)
+ (0.00319335781574325,1.42896758583059)
+ (0.00324517280545189,1.43198483027867)
+ (0.0032986970146792,1.43555156869388)
+ (0.00335401643468053,1.43971846370168)
+ (0.00341122292341805,1.44603280309521)
+ (0.00347041471455839,1.45239689789219)
+ (0.00353169698039908,1.45880425256435)
+ (0.00359518245550962,1.46524723615177)
+ (0.00366099212886692,1.47171691604961)
+ (0.00372925601342532,1.47757665644959)
+ (0.0038001140034201,1.48371759600105)
+ (0.00387371683129963,1.49015954033921)
+ (0.00395022713806044,1.49692413910059)
+ (0.00402982067298005,1.50403510039959)
+ (0.00411268764137364,1.51151843538133)
+ (0.00419903422212891,1.51940273781338)
+ (0.00428908428050611,1.5277195046251) )
.ENDS
*$
$
.SUBCKT PTCSL03T111 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=110 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40 tmax=160
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00233563003620227,2.7258368032572)
+ (0.00236322816967978,2.68042546682781)
+ (0.00239148630874088,2.62669555771769)
+ (0.0024204284158296,2.56407929174366)
+ (0.0024500796275879,2.49196787987299)
+ (0.0024804663276696,2.40970815783624)
+ (0.00251161622504081,2.3165988986443)
+ (0.00254355843825512,2.20004976565463)
+ (0.00257632358624243,2.06436951182091)
+ (0.00260994388620645,1.90540502695643)
+ (0.00264445325928864,1.72953758862235)
+ (0.00267988744472732,1.59624606804081)
+ (0.0027162841233193,1.51827571994653)
+ (0.00275368305108082,1.4626737779449)
+ (0.00279212620410443,1.41893007743887)
+ (0.00283165793572136,1.388125978991)
+ (0.00287232514720666,1.36136905977448)
+ (0.00291417747340813,1.34251001349697)
+ (0.002957267484844,1.32803019391637)
+ (0.0030016509079994,1.31981520477296)
+ (0.00304738686576261,1.31846232050533)
+ (0.00309453814018258,1.31675901606707)
+ (0.00314317146000314,1.31873174347186)
+ (0.00319335781574325,1.32473808618053)
+ (0.00324517280545189,1.32922599809378)
+ (0.0032986970146792,1.33510543486864)
+ (0.00335401643468053,1.34251001349676)
+ (0.00341122292341805,1.34904410538156)
+ (0.00347041471455839,1.35591881171469)
+ (0.00353169698039908,1.36315831469504)
+ (0.00359518245550962,1.37078898458746)
+ (0.00366099212886692,1.37883962185788)
+ (0.00372925601342532,1.38720179039332)
+ (0.0038001140034201,1.39599077731029)
+ (0.00387371683129963,1.40523784216141)
+ (0.00395022713806044,1.41497723451105)
+ (0.00402982067298005,1.42524654864637)
+ (0.00411268764137364,1.436239938512)
+ (0.00419903422212891,1.44791621832888)
+ (0.00428908428050611,1.46033386390705) )
.ENDS
*$
$
.SUBCKT PTCSL03T121 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=120 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40
+ tmax=180
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00223139573803414,2.75282506605773)
+ (0.00225657226672684,2.73637998049406)
+ (0.00228232340522652,2.70821758273856)
+ (0.00230866905229135,2.662841895596)
+ (0.00233563003620227,2.60876901449367)
+ (0.00236322816967978,2.54541670532426)
+ (0.00239148630874088,2.4722046261613)
+ (0.0024204284158296,2.39363083677151)
+ (0.0024500796275879,2.29597465641039)
+ (0.0024804663276696,2.17760783123656)
+ (0.00251161622504081,2.05555619387432)
+ (0.00254355843825512,1.91216261084418)
+ (0.00257632358624243,1.76566807336251)
+ (0.00260994388620645,1.68876717954182)
+ (0.00264445325928864,1.6390886028936)
+ (0.00267988744472732,1.59641385497438)
+ (0.0027162841233193,1.57554285740533)
+ (0.00275368305108082,1.55653278877564)
+ (0.00279212620410443,1.53948607048441)
+ (0.00283165793572136,1.52459353355855)
+ (0.00287232514720666,1.51208269011123)
+ (0.00291417747340813,1.5068519074824)
+ (0.002957267484844,1.50231431721091)
+ (0.0030016509079994,1.49853987869146)
+ (0.00304738686576261,1.4956052128075)
+ (0.00309453814018258,1.49359430564535)
+ (0.00314317146000314,1.49354499165717)
+ (0.00319335781574325,1.49418838439563)
+ (0.00324517280545189,1.49558723220293)
+ (0.0032986970146792,1.497815861979)
+ (0.00335401643468053,1.50095854281418)
+ (0.00341122292341805,1.50601660826479)
+ (0.00347041471455839,1.51176589280315)
+ (0.00353169698039908,1.51827081503315)
+ (0.00359518245550962,1.52560246041539)
+ (0.00366099212886692,1.53383938110518)
+ (0.00372925601342532,1.54486945743145)
+ (0.0038001140034201,1.55619124326952)
+ (0.00387371683129963,1.56781413984545)
+ (0.00395022713806044,1.57974768295806)
+ (0.00402982067298005,1.59200149403189)
+ (0.00411268764137364,1.60458521726067)
+ (0.00419903422212891,1.61750843961594)
+ (0.00428908428050611,1.63078058973547) )
.ENDS
*$
$
.SUBCKT PTCSL03T131 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=130 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40
+ tmax=180
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00223139573803414,2.54294487117689)
+ (0.00225657226672684,2.5250982336674)
+ (0.00228232340522652,2.49751331393143)
+ (0.00230866905229135,2.45952601326152)
+ (0.00233563003620227,2.41312551767832)
+ (0.00236322816967978,2.35220914452781)
+ (0.00239148630874088,2.27576128039496)
+ (0.0024204284158296,2.18272302377601)
+ (0.0024500796275879,2.07533859568736)
+ (0.0024804663276696,1.94958436755238)
+ (0.00251161622504081,1.79046038517609)
+ (0.00254355843825512,1.59768116956263)
+ (0.00257632358624243,1.48568130056366)
+ (0.00260994388620645,1.42848861633408)
+ (0.00264445325928864,1.39236907872666)
+ (0.00267988744472732,1.36189100198071)
+ (0.0027162841233193,1.34898569086366)
+ (0.00275368305108082,1.33756359994242)
+ (0.00279212620410443,1.32770125288182)
+ (0.00283165793572136,1.31954582533968)
+ (0.00287232514720666,1.31327247473086)
+ (0.00291417747340813,1.31261187016847)
+ (0.002957267484844,1.31255219072645)
+ (0.0030016509079994,1.31314884829678)
+ (0.00304738686576261,1.31446238652957)
+ (0.00309453814018258,1.31655901568018)
+ (0.00314317146000314,1.32027391787363)
+ (0.00319335781574325,1.32458154294324)
+ (0.00324517280545189,1.32952990857193)
+ (0.0032986970146792,1.33517591499043)
+ (0.00335401643468053,1.34158405472425)
+ (0.00341122292341805,1.3495921480303)
+ (0.00347041471455839,1.35815811082881)
+ (0.00353169698039908,1.36732658916564)
+ (0.00359518245550962,1.37714654402505)
+ (0.00366099212886692,1.38767174921412)
+ (0.00372925601342532,1.40012828227313)
+ (0.0038001140034201,1.41289807690861)
+ (0.00387371683129963,1.42598985245615)
+ (0.00395022713806044,1.43941225312393)
+ (0.00402982067298005,1.45317376190383)
+ (0.00411268764137364,1.46728259397412)
+ (0.00419903422212891,1.48174656509563)
+ (0.00428908428050611,1.49657292947234) )
.ENDS
*$
$
.SUBCKT PTCSL03T141 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs: tsw=140 cth=0.026 k=0.001 gth=5m tol=0 tmin=-40
+ tmax=180
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00228232340522652,2.41505506202227)
+ (0.00230866905229135,2.35647249832247)
+ (0.00233563003620227,2.28048137441315)
+ (0.00236322816967978,2.18588495095522)
+ (0.00239148630874088,2.08028324978133)
+ (0.0024204284158296,1.94697919033013)
+ (0.0024500796275879,1.75318496597384)
+ (0.0024804663276696,1.54197487161491)
+ (0.00251161622504081,1.42044523838723)
+ (0.00254355843825512,1.35658527918093)
+ (0.00257632358624243,1.31321203451327)
+ (0.00260994388620645,1.28160417324049)
+ (0.00264445325928864,1.25905133689693)
+ (0.00267988744472732,1.23971890355651)
+ (0.0027162841233193,1.22979885312085)
+ (0.00275368305108082,1.22101297950519)
+ (0.00279212620410443,1.21343566109444)
+ (0.00283165793572136,1.20718085827535)
+ (0.00287232514720666,1.20238199867044)
+ (0.00291417747340813,1.20140024176081)
+ (0.002957267484844,1.20112671329085)
+ (0.0030016509079994,1.20162699430817)
+ (0.00304738686576261,1.20297274769237)
+ (0.00309453814018258,1.20524235245071)
+ (0.00314317146000314,1.20913655957636)
+ (0.00319335781574325,1.21385850048111)
+ (0.00324517280545189,1.21947980524279)
+ (0.0032986970146792,1.2260825025024)
+ (0.00335401643468053,1.23375955013858)
+ (0.00341122292341805,1.24368224740767)
+ (0.00347041471455839,1.25440191080687)
+ (0.00353169698039908,1.26598516046023)
+ (0.00359518245550962,1.27850519274386)
+ (0.00366099212886692,1.29204254863369)
+ (0.00372925601342532,1.30750625459238)
+ (0.0038001140034201,1.3238110815361)
+ (0.00387371683129963,1.3410209175015)
+ (0.00395022713806044,1.3592059075785)
+ (0.00402982067298005,1.37844320859824)
+ (0.00411268764137364,1.39881785258893)
+ (0.00419903422212891,1.4204237373334)
+ (0.00428908428050611,1.4433647659197) )
.ENDS
*$
$
.SUBCKT PTCSL03T151 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs:tsw=150 cth=0.026 k=0.001 gth=5m tol=+25 tmin=-40
+ tmax=180
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00228232340522652,2.29281533430176)
+ (0.00230866905229135,2.18212022781948)
+ (0.00233563003620227,2.05066712995176)
+ (0.00236322816967978,1.89706534217947)
+ (0.00239148630874088,1.72621746522634)
+ (0.0024204284158296,1.5917288671472)
+ (0.0024500796275879,1.50360944906821)
+ (0.0024804663276696,1.44171802028994)
+ (0.00251161622504081,1.39868976694667)
+ (0.00254355843825512,1.36818568785172)
+ (0.00257632358624243,1.34452185808579)
+ (0.00260994388620645,1.32666950880871)
+ (0.00264445325928864,1.31377024314024)
+ (0.00267988744472732,1.30326929992626)
+ (0.0027162841233193,1.2995287095056)
+ (0.00275368305108082,1.29673528771365)
+ (0.00279212620410443,1.29495017330882)
+ (0.00283165793572136,1.29426298787538)
+ (0.00287232514720666,1.29477817294214)
+ (0.00291417747340813,1.29826913922831)
+ (0.002957267484844,1.30241216266634)
+ (0.0030016509079994,1.30726168332475)
+ (0.00304738686576261,1.31287701121453)
+ (0.00309453814018258,1.31932282496612)
+ (0.00314317146000314,1.32863400948472)
+ (0.00319335781574325,1.33804199438048)
+ (0.00324517280545189,1.34753053128555)
+ (0.0032986970146792,1.3570923016292)
+ (0.00335401643468053,1.36671510147029)
+ (0.00341122292341805,1.37503384708098)
+ (0.00347041471455839,1.3840055257485)
+ (0.00353169698039908,1.39368436330905)
+ (0.00359518245550962,1.40412992194463)
+ (0.00366099212886692,1.41540772254858)
+ (0.00372925601342532,1.42902148924758)
+ (0.0038001140034201,1.44298594979921)
+ (0.00387371683129963,1.45731161096554)
+ (0.00395022713806044,1.47200901436861)
+ (0.00402982067298005,1.48708865827305)
+ (0.00411268764137364,1.50256089942705)
+ (0.00419903422212891,1.51843583048676)
+ (0.00428908428050611,1.53472312751071) )
.ends
*$
.SUBCKT PTCSL03T161 Rn Rp Ti
X Rn Rp Ti invK LnLn PTCSL03_BASE PARAMs:tsw=160 cth=0.026 k=0.001 gth=5m tol=25 tmin=-40 tmax=205
E_E4 LNLN 0 TABLE { V(INVK, 0) }
+ ( (0.00211349466342597,2.45732238898154)
+ (0.00213606749973299,2.42057262740608)
+ (0.00215912771240419,2.37825802028387)
+ (0.00218269125832151,2.33003845120239)
+ (0.0022067747986318,2.27731897287527)
+ (0.00223139573803414,2.21441204327621)
+ (0.00225657226672684,2.15325641587532)
+ (0.00228232340522652,2.05537863284823)
+ (0.00230866905229135,1.91826952900567)
+ (0.00233563003620227,1.7850814893256)
+ (0.00236322816967978,1.66331780079548)
+ (0.00239148630874088,1.56743353939949)
+ (0.0024204284158296,1.49227872978797)
+ (0.0024500796275879,1.45959310258448)
+ (0.0024804663276696,1.43138077598952)
+ (0.00251161622504081,1.40801185102621)
+ (0.00254355843825512,1.39981457844242)
+ (0.00257632358624243,1.3927128097822)
+ (0.00260994388620645,1.38680125657133)
+ (0.00264445325928864,1.38218241667561)
+ (0.00267988744472732,1.37896728451687)
+ (0.0027162841233193,1.37997572084742)
+ (0.00275368305108082,1.38140104178295)
+ (0.00279212620410443,1.38327723164709)
+ (0.00283165793572136,1.38564114848217)
+ (0.00287232514720666,1.38853279953598)
+ (0.00291417747340813,1.39266663141268)
+ (0.002957267484844,1.39711340845524)
+ (0.0030016509079994,1.40189593588165)
+ (0.00304738686576261,1.40703894808508)
+ (0.00309453814018258,1.41256930024525)
+ (0.00314317146000314,1.41825604219946)
+ (0.00319335781574325,1.42450858649406)
+ (0.00324517280545189,1.43137348062409)
+ (0.0032986970146792,1.43890161756145)
+ (0.00335401643468053,1.44714870878894)
+ (0.00341122292341805,1.45734280026222)
+ (0.00347041471455839,1.46786170809545)
+ (0.00353169698039908,1.47872107827477)
+ (0.00359518245550962,1.48993756750794)
+ (0.00366099212886692,1.50152892507946)
+ (0.00372925601342532,1.51385284058565)
+ (0.0038001140034201,1.52644088302295)
+ (0.00387371683129963,1.53929630492117)
+ (0.00395022713806044,1.55242164136037)
+ (0.00402982067298005,1.5658185375452)
+ (0.00411268764137364,1.579487542495)
+ (0.00419903422212891,1.59342786197786)
+ (0.00428908428050611,1.60763706230589) )
.ENDS
*$
Comments
Please log in or sign up to comment.