def test_potential_2layer():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
pp = ParallelPlates((er1, er2), (t1, t2))
X = np.linspace(0, 4e-3, 5)
V = pp.potential(X, 200)
assert V == approx([0, 12.5, 75, 137.5, 200])
def test_poisson_1d_dielectric2():
pp = ParallelPlates((1.0, 5.0, 1.0), (2e-3, 1e-3, 1e-3))
v0 = 0
v1 = 200
X, er = pp.get_arrays(101)
V = fdm.poisson_1d(X, dielectric=er, v_left=v0, v_right=v1, conv=1e-7)
Va = pp.potential(X, v1 - v0, v0)
assert V == approx(Va, abs=0.01)
def test_gauss_1d_dielectric():
pp = ParallelPlates((2.0, 4.0), (3e-3, 2e-3))
X, er = pp.get_arrays(101)
v1 = 10.0
V = pp.potential(X, v1)
Q = np.array([fdm.gauss_1d(X, V, er, i) for i in range(1, len(X) - 1)])
Qa = pp.charge(v1)
assert Q == approx(Qa)
def test_2layer():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
pp = ParallelPlates((er1, er2), (t1, t2))
X, er = pp.get_arrays(N=5)
assert pp.thickness == approx(t1 + t2)
assert X == approx([0.0, 1e-3, 2e-3, 3e-3, 4e-3])
assert er == approx([er1, er2, er2, er2])
def test_poisson_1d():
pp = ParallelPlates(1.0, 5e-3)
X, _ = pp.get_arrays(101)
v0 = -2
v1 = 5
V = fdm.poisson_1d(X, v_left=v0, v_right=v1, conv=1e-5)
Va = pp.potential(X, v1 - v0, v0)
assert V == approx(Va, abs=0.01)
def test_potential():
t = 1e-3
N = 5
pp = ParallelPlates(3.5, t)
X = np.linspace(0, t, N)
Va = 10.0
expected = Va / t * X
potential = pp.potential(X, Va)
assert potential == approx(expected)
def test_efield_2layer():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
pp = ParallelPlates((er1, er2), (t1, t2))
X = np.linspace(0, 4e-3, 5)
E = pp.efield(X, 200)
E1 = -12.5 / t1
E2 = -187.5 / t2
assert E == approx([E1, E1, E2, E2, E2])
def test_efield():
t = 1e-3
N = 5
pp = ParallelPlates(3.5, t)
X = np.linspace(0, t, N)
Va = 10.0
expected = -Va / t * np.ones(N)
efield = pp.efield(X, Va)
assert efield == approx(expected)
def test_potential_ref():
t = 1e-3
N = 5
pp = ParallelPlates(3.5, t)
X = np.linspace(0, t, N)
Va = 10.0
Vref = 5.0
expected = Va / t * X + Vref
potential = pp.potential(X, Va, Vref=Vref)
assert potential == approx(expected)
def test_2layer_area():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
A = 3.0
pp1 = ParallelPlates((er1, er2), (t1, t2))
pp2 = ParallelPlates((er1, er2), (t1, t2), area=A)
Va = 25.0
X = np.linspace(0, t1 + t2, 11)
assert pp1.capacitance() == approx(pp2.capacitance() / A)
assert pp1.efield(X, Va) == approx(pp2.efield(X, Va))
assert pp1.potential(X, Va) == approx(pp2.potential(X, Va))
def test_efield_pplate():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
Va = 200
pp = ParallelPlates((er1, er2), (t1, t2))
X, dx = np.linspace(0, 4e-3, 21, retstep=True)
V = pp.potential(X, Va)
E = pp.efield(X, Va)
Ec = em.efield_1d(V, dx)
assert Ec[:5] == approx(E[:5])
# discontinuity at boundary [5]
assert Ec[6:] == approx(E[6:])
def test_efield_pplate_fdm():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
Va = 200
pp = ParallelPlates((er1, er2), (t1, t2))
X, dx = np.linspace(0, 4e-3, 21, retstep=True)
V = pp.potential(X, Va)
E = em.efield_1d(V, dx)
er = np.where(X[:-1] < t1, er1, er2)
Vfdm = fdm.poisson_1d(X, dielectric=er, v_right=Va)
Efdm = em.efield_1d(Vfdm, dx)
assert Efdm == approx(E, rel=0.001)
def test_get_arrays():
N = 11
pp = ParallelPlates(3.5, 1e-3)
X, er = pp.get_arrays(N=N)
assert X == approx(np.linspace(0, 1e-3, N))
assert er == approx(3.5 * np.ones(N - 1))
def test_capacitance_2layer():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
pp = ParallelPlates((er1, er2), (t1, t2))
assert pp.capacitance() == approx(2.767e-9)
def test_capacitance():
pp = ParallelPlates(3.5, 1e-3)
assert pp.capacitance() == approx(30.989e-9)
def test_2layer_mixed_length():
er1, t1 = 5.0, 1e-3
er2, t2 = 1.0, 3e-3
with pytest.raises(Exception):
ParallelPlates((er1, er2), (t1, t2, t2))
def test_2layer_mixed_type():
er1, t1 = 5.0, 1e-3
er2 = 1.0
with pytest.raises(Exception):
ParallelPlates((er1, er2), t1)
def test_charge():
pp = ParallelPlates(3.5, 1e-3)
Va = 10.0
expected = pp.capacitance() * Va
assert pp.charge(Va) == approx(expected)
def test_energy():
pp = ParallelPlates(3.5, 1e-3)
Va = 10.0
expected = 0.5 * pp.capacitance() * Va**2
assert pp.energy(Va) == approx(expected)
def test_capacitance_area():
pp = ParallelPlates(3.5, 1e-3, area=10.0)
assert pp.capacitance() == approx(309.89e-9, rel=0.001)