# 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