def test_RC_ivp(self):
"""Lcapy: check RC IVP"""
a = Circuit("""
C 1 0 C v0
R 1 0""")
self.assertEqual(a.is_ivp, True, "Initial value problem incorrect")
self.assertEqual(a.R.I, -a.C.I, "R + C current different")
self.assertEqual(a.R.V, a.C.V, "R + C voltage different")
self.assertEqual(a.C.I(s), sympify('-v0 / (s * R + 1 / C)'),
"C current wrong")
def test_RL_ivp(self):
"""Lcapy: check RL IVP"""
a = Circuit("""
L 1 0 L i0
R 1 0""")
self.assertEqual(a.is_ivp, True, "Initial value problem incorrect")
# Note, a positive current through an inductor is from the
# positive node to the negative node.
self.assertEqual(a.R.I, -a.L.I, "R + L current different")
self.assertEqual(a.R.V, a.L.V, "R + L voltage different")
self.assertEqual(a.L.I(s), sympify('i0 / (s + R / L)'),
"L current wrong")
from lcapy import s, sympify, j, sqrt
zeta = sympify('zeta_', real=True)
omega0 = sympify('omega0', real=True)
p1a = -omega0
p1b = -omega0
H = p1a * p1b / ((s - p1a) * (s - p1b))
G = H / s
#g = G.partfrac().inverse_laplace(causal=True).simplify()
#h = H.partfrac().inverse_laplace(causal=True).simplify()
g = G.inverse_laplace(causal=True)
h = H.inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace('^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
a = sympify('alpha')
tau = sympify('tau')
H = (s + 1 / tau) / (s + 1 / (a * tau)) / a
G = H / s
g = G.inverse_laplace(causal=True)
h = H.inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
a1 = sympify('alpha_1')
b1 = sympify('beta_1')
o1 = sympify('omega_1')
H = (a1**2 + o1**2) * (s + b1) / ((s + a1 + j * o1) * (s + a1 - j * o1)) / b1
G = H / s
g = G.partfrac().inverse_laplace(causal=True).simplify()
h = H.partfrac().inverse_laplace(causal=True).simplify()
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
a = sympify('alpha')
b = sympify('beta_')
H = (s + b) / (s + a)
G = H / s
g = G.inverse_laplace(causal=True)
h = H.inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace('^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
a1 = sympify('alpha_1')
o1 = sympify('omega_1')
H = 2 * a1 * s / ((s + a1 + j * o1) * (s + a1 - j * o1))
G = H / s
g = G.partfrac().inverse_laplace(causal=True).simplify()
h = H.partfrac().inverse_laplace(causal=True).simplify()
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
a = sympify('alpha')
H = a / (s + a)
G = H / s
g = G.inverse_laplace(causal=True)
h = H.inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j, sqrt
a1 = sympify('alpha_1', real=True)
a2 = sympify('alpha_2', real=True)
H = (s**2 + a1 * a2) / ((s + a1) * (s + a2))
G = H / s
g = G.partfrac().inverse_laplace(causal=True)
h = H.partfrac().inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace('^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j, sqrt
zeta = sympify('zeta_', real=True)
omega0 = sympify('omega0', real=True)
p1a = -zeta * omega0 + j * omega0 * sqrt(1 - zeta**2)
p1b = -zeta * omega0 - j * omega0 * sqrt(1 - zeta**2)
alpha1 = sympify('alpha_1', real=True)
omega1 = sympify('omega_1', real=True)
p1a = -alpha1 + j * omega1
p1b = -alpha1 - j * omega1
H = p1a * p1b / ((s - p1a) * (s - p1b))
G = H / s
g = G.partfrac().inverse_laplace(causal=True)
h = H.partfrac().inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)').replace('/', ' / ')
return s
print(topy(g))
from lcapy import s, sympify, j
a1 = sympify('alpha')
b1 = sympify('beta_')
H = a1 * (s + b1) / (b1 * (s + a1))
G = H / s
g = G.partfrac().inverse_laplace(causal=True)
h = H.partfrac().inverse_laplace(causal=True)
def topy(expr):
s = str(expr)
s = s.replace('**', '^').replace('_', '').replace('*', ' * ').replace(
'^', '**').replace('Heaviside(t)', '(t >= 0)')
return s
print(topy(g))
print(topy(h))
from lcapy import s, sympify, j
alpha1 = sympify('alpha_1')
omega1 = sympify('omega_1')
alpha2 = sympify('alpha_2')
s1a = alpha1 + j * omega1
s1b = alpha1 - j * omega1
s2 = alpha2
H = 1 / ((s - s1a) * (s - s1b) * (s - s2))
h = H.inverse_laplace()
