From 6d26a6bd8b30ad893da0315655d2f68aee787515 Mon Sep 17 00:00:00 2001 From: Permondes Date: Tue, 10 Sep 2024 16:53:45 +0200 Subject: [PATCH 1/1] Potential of charged sphere Application: Potential of charged sphere LACE: major rework of the syntax --- Analog Engine Example Applications.odt | Bin 1350930 -> 1407487 bytes Language for Analog Computing Engines.odt | Bin 0 -> 62323 bytes ...on Language for Analog Circuit Engines.odt | Bin 41265 -> 0 bytes scripts/CompoundFunctions.LACE | 30 ++++++++++++ scripts/TP1 03.08 Charge in em field.LACE | 31 ++++++++++++ scripts/TP1 09.27 Bead on Cycloid.LACE | 24 +++++----- scripts/TP1 10.30 Linear Molecule.LACE | 44 +++++++++++------- ...2 10.28 Potential of a charged sphere.LACE | 44 ++++++++++++++++++ scripts/Template.AESL | 26 +++++++++++ 9 files changed, 170 insertions(+), 29 deletions(-) create mode 100644 Language for Analog Computing Engines.odt delete mode 100644 description Language for Analog Circuit Engines.odt create mode 100644 scripts/CompoundFunctions.LACE create mode 100644 scripts/TP1 03.08 Charge in em field.LACE create mode 100644 scripts/TP2 10.28 Potential of a charged sphere.LACE create mode 100644 scripts/Template.AESL diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index f0413c627995b48681621a8dd9c62a3b70a8f76f..c59148e8d3b551f3d4f84c4cd6c2b212085e7968 100644 GIT binary patch delta 142699 zcmZs@1z1#T)HW;!L8L>FMq0W%r9(iFPAO@Sh9S11NDrM7(jX5S@&2QG_fYQL`{c?PiJ^c9{uMvughTib zKX?3_K`fH^YD7GW=nSSGR#UbHTG3Y|zq}($T(`WqjNJN_cKnyF2o_KTq8L#{m&8|U za2B1PbD@SHEtOTIP`rDpH2;GEeD(=dm@IT{8rz5 z!h0$#s>Mt08}>+{IlBgDNz&u!ZRY2|Hw_-R4^-d4f?WM&FtY{KN`=(>*!+RK(6Q8S zU&N1PV2qvZFGN}^RSZuO^1mpm3CeS$NhU8o6(ux53fn#OKBo+`wG38Kfv@8)H!q7l z?7n8z#xd=Tqx)2p+J;WE%!c_3QZ4SyJdq{76s7d$iHm)BLOlK_w>%=M46~474xIB) zewmm5m^?wo#o116#C!b;66%56Nkhr~nY^$)osqI-h5u=uhB-;`YKDkYr!IcHff+6t z4rv5qe{FrXf%GTAY=TE8Td46QBUnUoq%#jyo^?jpj6RG|_<^;lqUp|4k*C@ws;1%^ zOEBjxKS!A=;XPX{-S*i}V^m`v+xouck{??$Bk7!SFfX?1(L8S1!ynAE`SCI^+$Yi8 z)HDQK9_x96nVKnPQmILV5n`Od4Xz2pf$^VVxP%;Q>HsEDwNtSd ziVsk}oyXM#Al|$8k@()d--<^;LAh0Yym12-A;8bgX6j(?Vs7uk>S1T=AJwe<4+r+g zJ<+zThYx8K;%Vt#RjsVbv*u|j>D1XS+1Fd4g>aBJoXLm=lq`$ClSYC)=bM9H1A_4A zp)bs@7>ZuXa1C$C+|N?(d%ht+ed<2(7?E?)LY~1JbMgxrb?xaGezvQD`X=OZ2--1W4m=04QQ&F(7E(``5=^us9N#`MRl8SRK?nvNv zhO!Xl7xs<@zdh7E=a!v&{zw^jUIyt<@|k1(7*7*I6%u#&FGXi&lHhAAhh(wcg@;ZU zKEv$gRBhi`a(?bO%n)HAKfLjaT6L_k4-5zJTCb6s{e1O4>Zy}J$^w>?ccj85h|9%0yTkQ86f_OyHshqgcZ}AB3Uf|#Y zpV`mO{NHzJ9{kq?$~oD55dMATHVniEU*KWI`wU`X-UWj43?@fJ+`rp4-FhS~d_&Ft|cw{7Hc=$M@o5!EV554^75n#O~FZE2_V|phABj(Xq z;%QnU87{UqX2)Z(r^g=1?r)#|l>P@9FA#z1;Zs{Es;_+@jz5iAG$D7w2aN+`D#!AN zpWZer$&E^>^7$I0Kl4klydSxg@h*YCM3&*r%5iVcKM2&u^B3w`$LbU6?pp3z;LpwV z>8QH-3griE36%8vqvPY}?l1!KSbMA3IK!U$daf!3 z8=Hbdo!q!M0*m4vD7i?|)o$A9bhZ6Wb*8{pLqi>wL7Ir6O-O~ygZ^d%f>~g4-*0Vk zU}^t@-ICGnLc5R{TX;O1N8dqez1NlB1mpJQ@x?-2csH zzwkw)0D_J`(dn_F!q$b?H1$--eK+Rn;&hFW;@YlW$;W%ubFHUPr+oQKL9r9#aq9kI z=FCkdpw)Km09@#~QCxRlwuh0J_l#Sl97bo(33y(1d=hZZL8lNE?)m(&?enwu%a=rJ zUCUk3UORfH?mgA<=BHd4rZvpE6`fPp;U87QSGu@_FDF=fC-;lv%h7Kh-5p2a6GBGp zNz+ArQ%_a*-bLC?ei9-1?geR0-Spv+tQcLd7?sID7hXLS>L^{Br=~|288ZI0 z2Jdt5rCz8#Hd=X4arp{5A?sOvu6rpG-l50_qZz2XKoQa$JVQy9o#c_Z)Ac@JxxL*> zLZ>%jTh#4~wj-pFYP~a&MsL(8aWUlT-(Nd6Z^d&)&-tp= znz6nTVg7ydmvNeiR~4wgob6-y!8&Ktr#w zlG!D+@GvX`-@b-|m9iez9?i|eHuDce_vcHm@ZB7yiVfdCx4NKfBOj7oUeyRT2|!>nE`Nv`mTqE?Pp^EXeW^>v?5U_pid=l$BtgC4IPt~2Xsv3V+^ zN== zgUTaO2bi+-K>j~Mt$SC$R(;tzdni4x;D(qwT1DM%kCrlYOUV3F0&cvD7{{|og^cDU zyy2o9R+eLj$I>X2qsfe`j!!i``>PEmecvx+E;Cp(0b{)5i<}+}hxUhBZmz{eSBMWV zT@3jS;%uJF$;!&IWlAuu5F_~YFO`Kua%6qUmS#z6o)m-#dr!dGcKqHx3I92K+NQ+SZ(T#|Vrsx_9M0v8j&w!3 zJzxDuG6UD&llNm=MU!>s9+Fi|umwyrE~L#)3fAv$B7j;H(i8FROdM3j`WJI-NG1AL zz`K;%zrQj;!c@G%qzGYVlV@%W47g|cog0!Uhg%Uk%lbG^a!8a;)S;5eJ@tg|WS}YNs zKjX3$cU+XPrry^mit&04ZE2rZHwaLzW-c1_Dmx3NuEm|js^LZ;lYL1Fe+KrR|Qn$^o#g4F2)Sx;*ilMciO^JW?)+){oba8h=ax3z zD%Kc9a)?<{%S=CfkgLZZe+&QWe2^9bF^rLXzxRG^2P;DM4ptmnJRNmfXggTuVrQIk zVCaqArnl_ zYl4T3^u#Ujqi~5f+;cO?b)>hU@RdsSSbR8jxlPc4rY5%;sfs9tL2yOdOA)FiFhtCV zcMyycqIrC?7p$PGxp{E>e2U3c!O# z3EcWQc?=%nqDIVs&|bsfx5KZcEPgCEx?SU_O-)V|Rj}1VWIpDKg&!7dHxERAAyVWs1F3yOz-i?w@$0gpN6_#Or zb$-n0x;eVqpj#diVD9ebrr_n}weM5pnOKhnK2jnNb8Pf@js`vAHPQs(qdokuooboJ zZs>zluPYz3YV>f-!VQun$Pa5icN z_in|`9jx&+vk?=&uuwLCmhT^xm|RjLi; z4-N5lq;~xENXSU|$?yAq3*nn8k|~YCfSM}PT3GiIAB0`p(&|nLzc19t()%xB^gLD2 zuz-?RL&Nv}-93UV2Gd!r`ZbeA=|lu=re)4B`cglK)i${*lulw6L?)C** zi1zw_Zh3+pF&Y?$3~DG-m2mhVJmmrvG$!%9d<<+|;@i&=zPj7l|Ig=+g5r?l0gHdg z?$h{WWXFqG|3d=E&e=?UHJ%z!mANTCBJ}m_Kr22?lPz@}6SP48^T0pmmFH(1A>}Vx zqjKZe0^PVZ2G-aA_m+42KZ#H)PZ+tQe!cx4>-&Zv3+6?fhll#hpW;oAb6d`Gu(9hWjf1T}ZW*6g;yeGrri}d*l zg*n;$i)H}ve~c7V0Iho67Q@F(O=K0?UJvpAXd&-8Tf-Blb|R%E1csAy)i*x4Yd^%o zCANZz)Qw@U{E5gK{G=5T|9IQ&$sdwXt`xHItk(~o*NjUG5+nU6*64HiZ;Vok0?Q@|}YJ`a2j1j4?>HDOfNrP9NJL$SG7@ z{wrLiHXKtQ>=nj*amXJ*x%NlIp`!j4JClF)76}we z;0swm@x#(!x>Uq?iBWj=TLeFU%>P)u6S1%d`?$mi$rFDQwkT_>7X|eZ4`?3N`q
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Division +define idivide (numerator, denominator) -> -quotient + openamp (numerator, product) -> -quotient + multiply (-quotient, denominator) -> product + +# Integration extension +define iintegrate (weight*: variable-1, …, ic: variable-IC, limit: gt0) -> variable-n + iintegrate (weight*: variable-1, …) -> variable-n + diode (cat:variable-n) -> DA + connect (DA) -> sj +# diode and connect used to limit the result to values >0 + +# Building an additional integrator with the help of an openamp +define iintegrate.additional (variable) -> integral + openamp variable -> integral + connect SJ -> cp + capacitor.100nF (integral) -> cp +# NB: The 100 nF capacitor is available on a THAT. This capacitance corresponds to those of the SLOW settings. In order to use the standard time constant an external 1 nF capacitor has to be used. + +# Summing extension +define isum (weight*: variable-1, …, /divisor) -> -result + isum (weight*: variable-1, …) -> -result + connect (-result, …) -> IN diff --git a/scripts/TP1 03.08 Charge in em field.LACE b/scripts/TP1 03.08 Charge in em field.LACE new file mode 100644 index 0000000..955f475 --- /dev/null +++ b/scripts/TP1 03.08 Charge in em field.LACE @@ -0,0 +1,31 @@ +#PROGRAM-ID ChargeInEMfield +#VERSION 20240116 +# A mass m with charge q>0 is located in a static electro-magnetic field [0,0,E], [0,-B,0]. +# Find the trajetory +# Differential equation (Lorentz force): +# x'' = omega*z' +# z'' = a*omega^2 - omega*x' +# good start settings are omega=0,92, a*omega^2=0,05 + +# coefficient definition +alias coefficient.1 -> omega_x # -omega for x' +coefficient.2 (+1) -> a*omega^2 +alias coefficient(3) -> omega_z # omega for z' + +# solving the DE +iintegrate (x'') -> -x' +iintegrate (-x') -> x + +coefficient.omega_x (-x') -> -omega*x' +#cmultiply (-x', omega_x) -> omega*x' + +iintegrate (a*omega^2, -omega*x') -> -z' # input is z'' +iintegrate (-z') -> z +invert (-z') -> z' + +coefficient.omega_z (z') -> omega*z' +#cmultiply (z', omega_z) -> omega*z' +assign omega*z' -> x'' + +output(x) -> out.x +output(z) -> out.z diff --git a/scripts/TP1 09.27 Bead on Cycloid.LACE b/scripts/TP1 09.27 Bead on Cycloid.LACE index 3f28dd3..8931f63 100644 --- a/scripts/TP1 09.27 Bead on Cycloid.LACE +++ b/scripts/TP1 09.27 Bead on Cycloid.LACE @@ -4,32 +4,32 @@ # equation of motion: # mu'' = - g/4a * mu, with mu = sin(phi/2) and phi a parameter of the cycloid -coefficient(1): g/4a -coefficient(2): 1 -> mu0' -coefficient(3): -1 -> -mu0 -coefficient(4): 4ax -coefficient(5): 4ay # same as 4ax +alias coefficient.1 g/4a +coefficient.2 (+1) -> mu0' +coefficient.3 (-1) -> -mu0 +alias coefficient.4 4ax +alias coefficient.5 4ay # same as 4ax iintegrate mu'' -> -mu' IC: mu0' iintegrate -mu' -> mu IC: -mu0 invert mu -> -mu --mu * g/4a -> -g/4a*mu -mu'' = -g/4a*mu +coefficient.g/4a (-mu) -> -g/4a*mu +assign -g/4a*mu -> mu'' # the following is for displaying the cycloid in x-y space # calculating x (NB: this includes some unacceptable approximations) -mu * 4ax -> 4a*mu -output(x): 4a*mu +coefficient.4ax (mu) -> 4a*mu +output(4a*mu) -> out.x # calculating y multiply mu, mu -> mu^2 -mu^2 * 4ay -> 4ay*mu^2 +coefficient.4ay (mu^2) -> 4ay*mu^2 isum 4a*mu^2 -> -2a*mu^2 # just serves to devide by 2 because we need 2a instead of 4a /2 invert -2a*mu^2 -> 2a*mu^2 -output(y): 2a*mu^2 +output(2a*mu^2) -> out.y # display mu, so the sinus -output(z): mu +output(mu) -> out.z diff --git a/scripts/TP1 10.30 Linear Molecule.LACE b/scripts/TP1 10.30 Linear Molecule.LACE index fd9806e..810dcc8 100644 --- a/scripts/TP1 10.30 Linear Molecule.LACE +++ b/scripts/TP1 10.30 Linear Molecule.LACE @@ -7,35 +7,45 @@ # NB: all integrators have to run with 100 nF capacitance, i.e. SLOW mode -coefficient(1): omega0^2_1 # omega0^2 for s1 -coefficient(2): omega0^2_2 # omega0^2 for s2 # same as omega0^2_1 -coefficient(3): omega0^2_3 # omega0^2 for s3 # same as omega0^2_1 -coefficient(4): my -coefficient(5): -1 -> -s1_0 # initial position of s1 -coefficient(6): -1 -> -s3_0 # initial position of s3 +# the following integrator has to be built up manually as THAT only has 5 integrators and we need 6 +# iintegrate -s2' -> s2 +define openamp (variable) -> result + isum (variable) -> result + connect (FB) -> GND + +define iintegrate6 (variable) -> integral + openamp variable -> integral + connect SJ -> cp + capacitor.100nF (integral) -> cp +# this capacitance requires SLOW settings on all other capacitors. Better use an external 1 nF capacitor. + +alias coefficient.1 -> coefficient.omega0^2_1 # omega0^2 for s1 +alias coefficient.2 -> coefficient.omega0^2_2 # omega0^2 for s2 # same as omega0^2_1 +alias coefficient.3 -> coefficient.omega0^2_3 # omega0^2 for s3 # same as omega0^2_1 +alias coefficient.4 -> coefficient.my +coefficient.5 (-1) -> -s1_0 # initial position of s1 +coefficient.6 (-1) -> -s3_0 # initial position of s3 # initial positon of s2, the central mass, is set to 0 iintegrate -omega0^2_1*s1, omega0^2_2*s2 -> -s1' # input is s1'' iintegrate -s1' -> s1 IC: -s1_0 invert s1 -> -s1 --s1 * omega0^2_1 -> -omega0^2_1*s1 +coefficient.omega0^2_1 (-s1) -> -omega0^2_1*s1 iintegrate -my*bracket -> -s2' # input is s2'' -# the following integrator has to be built up manually as THAT only has 5 integrators and we need 6 -# iintegrate -s2' -> s2 -openamp -s2' -> s2 - loopback: capacitor(100nF) -s2 * omega0^2_2 -> omega0^2_2*s2 +iintegrate6 -s2' -> s2 +coefficient.omega0^2_2 (s2) -> omega0^2_2*s2 isum -omega0^2_1*s1, omega0^2_2*s2, omega0^2_2*s2, -omega0^2_3*s3 -> -bracket --bracket * my -> -my*bracket +coefficient.my (-bracket) -> -my*bracket iintegrate omega0^2_2*s2, -omega0^2_3*s3 -> -s3' # input is s3'' iintegrate -s3' -> s3 IC: -s3_0 invert s3 -> -s3 --s3 * omega0^2_3 -> -omega0^2_3*s3 +coefficient.omega0^2_3 (-s3) -> -omega0^2_3*s3 + +output s1 -> out.x +output s2 -> out.y +output s3 -> out.z - output(x): s1 - output(y): s2 - output(z): s3 diff --git a/scripts/TP2 10.28 Potential of a charged sphere.LACE b/scripts/TP2 10.28 Potential of a charged sphere.LACE new file mode 100644 index 0000000..1284191 --- /dev/null +++ b/scripts/TP2 10.28 Potential of a charged sphere.LACE @@ -0,0 +1,44 @@ +# Determine the potential (inside and outside) of a charged sphere (radius R) with a constant internal charge density rho0. +# +# phi(r)'' = -rho0/epsilon0 - 2/r * phi(r)' +# with rho0 = 0 outside of sphere +# using t as variable for r +# +# compound functions used: +# Open Amplifier +define openamp (weight*: variable-1, weight*: variable-2) -> output + isum (weight*: variable-1, weight*: variable-2) -> output + connect (FB:) -> GND + +# Division +define idivide (numerator, denominator) -> -quotient + openamp (numerator, product) -> -quotient + multiply (-quotient, denominator) -> product + +# coefficients +coefficient.1 -> factor0,2 # shall be set to 0.2 +coefficient.2 (-1) -> -rho0/epsilon0 +coefficient.3 (-1) -> -phi0 +coefficinet.4 (-1) -> -R # -radius of sphere + +# generate a ramp of t +iintegrate (-1) -> t + +# distinguish in sphere or outside +compare (t, -R) -> -rho/epsilon0_l + LT0: -rho/epsilon0 # in sphere, + GT0: GND # outside sphere + +# calculate phi +iintegrate (1*: -rho0/epsilon0_l, 10*: -0.2/r*phi') -> -phi' # need 2/r*phi' thus 10* input +iintegrate (-phi') -> phi + IC: -phi0 +invert(-phi') -> phi' + +# doing this division by t first because phi' is low when also t is, thus there is the chance of less overload +idivide (phi', t) -> -phi'/t +cmultiply (-phi'/t, factor0.2) -> -0.2/r*phi' + +output(t) -> out.x +output(phi') -> out.y +output(phi) -> out.z diff --git a/scripts/Template.AESL b/scripts/Template.AESL new file mode 100644 index 0000000..48143fb --- /dev/null +++ b/scripts/Template.AESL @@ -0,0 +1,26 @@ +IDENTIFICATION DIVISION +PROGRAM-ID ... +VERSION ... +COMMENT ... + +ENVIRONMENT DIVISION +ENGINE Anabrid-THAT +TIMEBASE 1ms +REQUIRES ... + +DATA DIVISION +INPUT ... +OUTPUT OUTPUT.X ... +OUTPUT OUTPUT.Y ... +OUTPUT OUTPUT.Z ... +OUTPUT OUTPUT.U ... +COEFFICIENT.n ... + +PROGRAM DIVISION +# INTEGRATOR is inverting! +# SUMMER is inverting! +... + +OPERATION DIVISION +MODE REPEAT +OP-TIME ... -- 2.39.5