def test_potential_2layer():
ri = 8e-3
er1, t1 = 6.0, 2e-3
er2, t2 = 3.0, 20e-3
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
R = np.array([8e-3, 10e-3, 30e-3])
V = cc.potential(R, Va=12500)
assert V == approx(np.array([12500, 11347, 0]), abs=1)
def test_efield_2layer():
ri = 8e-3
er1, t1 = 6.0, 2e-3
er2, t2 = 3.0, 20e-3
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
R = np.array([8e-3, 10e-3, 10.001e-3, 30e-3])
E = cc.efield(R, Va=12500)
assert E == approx(np.array([0.6456e6, 0.5165e6, 1.033e6, 0.3443e6]),
abs=1e3)
def test_potential_2layer_2():
# Cheng Ex. 3-16
ri = 4e-3
er1, t1 = 3.2, (6.16e-3 - ri)
er2, t2 = 2.6, (8.32e-3 - 6.16e-3)
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
R = np.array([ri, ri + t1, ri + t1 + t2])
V = cc.potential(R, Va=20e3)
assert V == approx(np.array([20e3, 9.3e3, 0]), rel=0.01)
def test_2layer():
ri = 20e-3
er1, t1 = 2.0, 2.5e-3
er2, t2 = 5.0, 2.5e-3
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
X, er = cc.get_arrays(N=5)
assert cc.ro == approx(ri + t1 + t2)
assert X == approx([20e-3, 21.25e-3, 22.5e-3, 23.75e-3, 25e-3])
assert er == approx([er1, er1, er2, er2])
def test_efield_2layer_2():
# Cheng Ex. 3-16
ri = 4e-3
er1, t1 = 3.2, (6.16e-3 - ri)
er2, t2 = 2.6, (8.32e-3 - 6.16e-3)
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
R = np.array([ri, 0.999 * (ri + t1), 1.001 * (ri + t1), ri + t1 + t2])
E = cc.efield(R, Va=20e3)
assert E == approx(np.array([6.25e6, 4.06e6, 5.00e6, 3.71e6]), rel=0.01)
def test_potential_inner():
ri = 0.5e-3
ro = 4.0e-3
N = 5
cc = CoaxCapacitor(ri, 5.2, ro - ri)
X = np.linspace(0, ri, N)
Va = 10.0
potential = cc.potential(X, Va=Va)
assert potential == approx(Va)
def test_efield():
ri = 0.5e-3
ro = 4.0e-3
N = 5
cc = CoaxCapacitor(ri, 5.2, ro - ri)
X = np.linspace(ri, ro, N)
Va = 10.0
expected = -Va / X / np.log(ri / ro)
efield = cc.efield(X, Va=Va)
assert efield == approx(expected)
def test_potential():
ri = 0.5e-3
ro = 4.0e-3
N = 5
cc = CoaxCapacitor(ri, 5.2, ro - ri)
X = np.linspace(ri, ro, N)
Va = 10.0
expected = Va / np.log(ri / ro) * np.log(X / ro)
potential = cc.potential(X, Va=Va)
assert potential == approx(expected)
def test_potential_outer():
ri = 0.5e-3
ro = 4.0e-3
Vref = 5.0
N = 5
cc = CoaxCapacitor(ri, 5.2, ro - ri)
X = np.linspace(ro, 10 * ro, N)
Va = 10.0
potential = cc.potential(X, Va=Va, Vref=Vref)
assert potential == approx(Vref)
def test_potential_diagonal():
ri = 0.5e-3
ro = 4.0e-3
N = 5
cc = CoaxCapacitor(ri, 5.2, ro - ri)
R = np.linspace(ri, ro, N)
theta = np.pi / 4
X = R * np.cos(theta)
Y = R * np.sin(theta)
Va = 10.0
expected = Va / np.log(ri / ro) * np.log(R / ro)
potential = cc.potential(X, Y, Va=Va)
assert potential == approx(expected)
def test_gauss_1d_coax():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
X, er = cc.get_arrays(101)
v1 = 10.0
V = cc.potential(X, Va=v1)
# 1D gauss returns a charge density over circumference
# Result is negative due to direction of X
Q = np.array([
-2 * np.pi * X[i] * fdm.gauss_1d(X, V, er, i)
for i in range(1,
len(X) - 1)
])
Qa = cc.charge(v1)
assert Q == approx(Qa, rel=0.01)
def test_poisson_2d_coax():
ri = 2.0e-3
ro = 4.0e-3
w = 1.1 * ro
N = 101
Va = 10.0
x = np.linspace(-w, w, N)
y = np.linspace(-w, w, N)
X, Y = np.meshgrid(x, y, indexing='ij')
R = np.sqrt(X**2 + Y**2)
bc_bool = np.logical_or(R < ri, R > ro)
bc_val = np.select([R < ri, R > ro], [Va, 0])
bc = (bc_bool, bc_val)
cc = CoaxCapacitor(ri, 1.0, ro - ri)
expected = cc.potential(X, Y, Va=Va)
potential = fdm.poisson_2d(X, Y, bc=bc, conv=1e-5)
assert potential == approx(expected, abs=0.4)
def test_poisson_2d_coax_xysym():
ri = 2.0e-3
ro = 4.0e-3
w = 1.1 * ro
dx = ri / 40
Va = 10.0
x = np.arange(0, w, dx)
y = np.arange(0, w, dx)
X, Y = np.meshgrid(x, y, indexing='ij')
R = np.sqrt(X**2 + Y**2)
bc_bool = np.logical_or(R < ri, R > ro)
bc_val = np.select([R < ri, R > ro], [Va, 0])
bc = (bc_bool, bc_val)
cc = CoaxCapacitor(ri, 1.0, ro - ri)
expected = cc.potential(X, Y, Va=Va)
potential = fdm.poisson_2d(X, Y, bc=bc, conv=1e-6, xsym=True, ysym=True)
assert potential == approx(expected, abs=0.4)
def test_poisson_2d_coax_2layer():
ri = 2.0e-3
re = 2.8e-3
ro = 4.0e-3
er1, er2 = 4.0, 1.0
w = 1.1 * ro
N = 101
Va = 10.0
x = np.linspace(-w, w, N)
y = np.linspace(-w, w, N)
X, Y = np.meshgrid(x, y, indexing='ij')
R = np.sqrt(X**2 + Y**2)
er = np.select([R <= re, R > re], [er1, er2])[:-1, :-1]
bc_bool = np.logical_or(R < ri, R > ro)
bc_val = np.select([R < ri, R > ro], [Va, 0])
bc = (bc_bool, bc_val)
cc = CoaxCapacitor(ri, (er1, er2), (re - ri, ro - re))
expected = cc.potential(X, Y, Va=Va)
np.savetxt('e2d.csv', expected, delimiter=',', fmt='%.3f')
potential = fdm.poisson_2d(X, Y, dielectric=er, bc=bc, conv=1e-5)
assert potential == approx(expected, abs=0.6)
def test_gauss_2d_coax_xysym():
ri = 1.0e-3
ro = 4.0e-3
rm = 0.5 * (ri + ro)
assert rm * 1.414 < ro
w = 1.1 * ro
dx = ri / 40
Va = 10.0
x = np.arange(0, w, dx)
y = np.arange(0, w, dx)
X, Y = np.meshgrid(x, y, indexing='ij')
cc = CoaxCapacitor(ri, 1.0, ro - ri)
V = cc.potential(X, Y, Va=Va)
expected = cc.charge(Va)
er = np.ones_like(V)[:-1, :-1]
xi1 = 0
xi2 = np.searchsorted(x, rm)
yi1 = 0
yi2 = np.searchsorted(y, rm)
gauss = fdm.gauss_2d(X, Y, V, er, xi1, xi2, yi1, yi2)
assert gauss == approx(expected, rel=0.01, abs=1e-14)
def test_capacitance_2layer():
ri = 20e-3
er1, t1 = 2.0, 2.5e-3
er2, t2 = 5.0, 2.5e-3
cc = CoaxCapacitor(ri, (er1, er2), (t1, t2))
assert cc.capacitance() == approx(695.7e-12)
def test_capacitance():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
assert cc.capacitance() == approx(139.1e-12, abs=0.1e-12)
def test_charge():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
Va = 10.0
expected = cc.capacitance() * Va
assert cc.charge(Va) == approx(expected)
def test_energy():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
Va = 10.0
expected = 0.5 * cc.capacitance() * Va**2
assert cc.energy(Va) == approx(expected)
def test_get_arrays():
N = 11
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3)
X, er = cc.get_arrays(N=N)
assert X == approx(np.linspace(0.5e-3, 4e-3, N))
assert er == approx(5.2 * np.ones(N - 1))
def test_2layer_mixed_type():
er1, t1 = 5.0, 1e-3
er2 = 1.0
with pytest.raises(Exception):
CoaxCapacitor(20e-3, (er1, er2), t1)
def test_capacitance_length():
cc = CoaxCapacitor(0.5e-3, 5.2, 3.5e-3, length=10.0)
assert cc.capacitance() == approx(1.391e-9)
def test_2layer_mixed_length():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
with pytest.raises(Exception):
CoaxCapacitor(20e-3, (er1, er2), (t1, t2, t2))