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matching.py
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import unittest
import numpy as np
class NegativeQ(ValueError):
pass
class SqrtValueError(ValueError):
pass
def L_matching(Rs, Rl, f0, tp):
'''
Rs: Source resistor
Rl: Load resistor
f0: Central frequency(MHz)
tp: Circuit type
return: Q, L, C
'''
w0 = (f0 * (10 ** 6)) * (2 * np.pi)
if Rl > Rs:
Q = np.sqrt((Rl / Rs) - 1)
X1 = Rl / Q
X2 = Rs * Q
if tp == "low-pass":
return (Q, (X2 / w0), (1 / (X1 * w0))), "shunt-"+tp
elif tp == "high-pass":
return (Q, (X1 / w0), (1 / (X2 * w0))), "shunt-"+tp
elif Rl < Rs:
Q = np.sqrt((Rs / Rl) - 1)
X1 = Q * Rl
X2 = Rs / Q
if tp == "low-pass":
return (Q, (X1 / w0), (1 / (X2 * w0))), "serial-"+tp
elif tp == "high-pass":
return (Q, (X2 / w0), (1 / (X1 * w0))), "serial-"+tp
else:
return (0, 0, 0), ""
def pi_matching(Rs, Rl, f0, dsrQ, tp):
'''
Rs: Source resistor
Rl: Load resistor
f0: Central frequency(MHz)
dsrQ: Desired Q
tp: Circuit type
return Q, L1, L2, C1, C2
'''
if dsrQ < 0:
raise NegativeQ()
w0 = (f0 * (10 ** 6)) * (2 * np.pi)
if Rs < Rl:
Q1 = dsrQ
Rint = Rl / (1+Q1**2) # Rint: intermediate resistor
if (Rs / Rint) <= 1:
raise SqrtValueError()
Q2 = np.sqrt(Rs/Rint - 1)
X2 = Rint * (Q1 + Q2)
B1 = Q1/Rl
B3 = Q2/Rs
# print("Q1={0:f}, Q2={1:f}, Rint={2:f}".format(Q1, Q2, Rint))
if tp == "low-pass":
return [dsrQ, (X2 / w0), 0, (B3 / w0), (B1 / w0)]
elif tp == "high-pass":
return [dsrQ, ((1 / B3) / w0), ((1 / B1) / w0), ((1 / X2) / w0), 0]
elif Rs > Rl:
Q2 = dsrQ
Rint = Rs / (1+Q2**2)
if (Rl / Rint) <= 1:
raise SqrtValueError()
Q1 = np.sqrt(Rl/Rint - 1)
X2 = Rint * (Q1 + Q2)
B1 = Q1 / Rl
B3 = Q2 / Rs
# print("Q1={0:f}, Q2={1:f}, Rint={2:f}".format(Q1, Q2, Rint))
if tp == "low-pass":
return [dsrQ, (X2 / w0), 0, (B3 / w0), (B1 / w0)]
elif tp == "high-pass":
return [dsrQ, ((1 / B3) / w0), ((1 / B1) / w0), ((1 / X2) / w0), 0]
else:
return [0, 0, 0, 0, 0]
def T_matching(Rs, Rl, f0, dsrQ, tp):
'''
Rs: Source resistor
Rl: Load resistor
f0: Central frequency(MHz)
dsrQ: Desired Q
tp: Circuit type
return Q, L1, L2, C1, C2
'''
if dsrQ < 0:
raise NegativeQ()
w0 = (f0 * (10 ** 6)) * (2 * np.pi)
if Rs > Rl:
Q1 = dsrQ
Rint = Rl * (1 + Q1**2)
if (Rint / Rs) <= 1:
raise SqrtValueError()
Q2 = np.sqrt(Rint/Rs - 1)
X1 = Q1 * Rl
B2 = (Q1 + Q2) / Rint
X3 = Q2 * Rs
if tp == "low-pass":
return [dsrQ, (X3 / w0), (X1 / w0), (B2 / w0), 0]
elif tp == "high-pass":
return [dsrQ, ((1 / B2) / w0), 0, ((1 / X3) / w0), ((1 / X1) / w0)]
elif Rs < Rl:
Q2 = dsrQ
Rint = Rs * (1 + Q2**2)
if (Rint / Rl) <= 1:
raise SqrtValueError()
Q1 = np.sqrt(Rint/Rl - 1)
X1 = Q1 * Rl
B2 = (Q1 + Q2) / Rint
X3 = Q2 * Rs
if tp == "low-pass":
return [dsrQ, (X3 / w0), (X1 / w0), (B2 / w0), 0]
elif tp == "high-pass":
return [dsrQ, ((1 / B2) / w0), 0, ((1 / X3) / w0), ((1 / X1) / w0)]
else:
return [0, 0, 0, 0]
def tapped_cap_matching(Rs, Rl, f0, dsrQ):
'''
Rs: Source resistor
Rl: Load resistor
f0: Central frequency(MHz)
dsrQ: desired Q
return Q1, L, C1, C2
'''
if dsrQ < 0:
raise NegativeQ()
w0 = (f0 * (10 ** 6)) * (2 * np.pi)
L = Rs / (w0 * dsrQ)
if ((Rl / Rs) * (1 + dsrQ ** 2)) <= 1:
raise SqrtValueError()
Qp = np.sqrt((Rl / Rs) * (1 + dsrQ ** 2) - 1)
C2 = Qp / (w0 * Rl)
Ceq = (C2 * (1 + Qp ** 2)) / (Qp ** 2)
C1 = (Ceq * C2) / (Ceq - C2)
return [dsrQ, L, C1, C2]
class UTTMatching(unittest.TestCase):
'''
Unit test for all the matching algorithms
'''
def test_L(self):
(Q, L, C), tp = L_matching(50, 250, 900, "low-pass")
self.assertTrue(np.abs(Q - 2) < 1e-1)
self.assertTrue(np.abs(L - 17.684e-9) < 1e-11)
self.assertTrue(np.abs(C - 1.415e-12) < 1e-14)
(Q, L, C), tp = L_matching(50, 250, 900, "high-pass")
self.assertTrue(np.abs(Q - 2) < 1e-1)
self.assertTrue(np.abs(L - 22.105e-9) < 1e-11)
self.assertTrue(np.abs(C - 1.768e-12) < 1e-14)
(Q, L, C), tp = L_matching(250, 100, 500, "low-pass")
self.assertTrue(np.abs(Q - 1.22) < 1e-1)
self.assertTrue(np.abs(L - 38.985e-9) < 1e-11)
self.assertTrue(np.abs(C - 1.559e-12) < 1e-14)
(Q, L, C), tp = L_matching(250, 100, 500, "high-pass")
self.assertTrue(np.abs(Q - 1.22) < 1e-1)
self.assertTrue(np.abs(L - 64.975e-9) < 1e-11)
self.assertTrue(np.abs(C - 2.599e-12) < 1e-14)
def test_Pi(self):
Q, L1, L2, C1, C2 = pi_matching(50, 250, 100, 3, "high-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 7.957e-8, delta=1e-10)
self.assertAlmostEqual(L2, 1.326e-7, delta=1e-9)
self.assertAlmostEqual(C1, 1.591e-11, delta=1e-13)
Q, L1, L2, C1, C2 = pi_matching(50, 250, 100, 3, "low-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 1.591e-7, delta=1e-9)
self.assertAlmostEqual(C1, 3.183e-11, delta=1e-13)
self.assertAlmostEqual(C2, 1.909e-11, delta=1e-13)
Q, L1, L2, C1, C2 = pi_matching(250, 50, 100, 3, "high-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 1.326e-7, delta=1e-9)
self.assertAlmostEqual(L2, 7.957e-8, delta=1e-10)
self.assertAlmostEqual(C1, 1.591e-11, delta=1e-13)
Q, L1, L2, C1, C2 = pi_matching(250, 50, 100, 3, "low-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 1.591e-7, delta=1e-9)
self.assertAlmostEqual(C1, 1.909e-11, delta=1e-13)
self.assertAlmostEqual(C2, 3.183e-11, delta=1e-13)
def test_T(self):
Q, L1, L2, C1, C2 = T_matching(50, 250, 100, 3, "high-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 1.989e-7, delta=1e-9)
self.assertAlmostEqual(C1, 1.061e-11, delta=1e-13)
self.assertAlmostEqual(C2, 6.366e-12, delta=1e-14)
Q, L1, L2, C1, C2 = T_matching(50, 250, 100, 3, "low-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 2.387e-7, delta=1e-9)
self.assertAlmostEqual(L2, 3.978e-7, delta=1e-9)
self.assertAlmostEqual(C1, 1.273e-11, delta=1e-13)
Q, L1, L2, C1, C2 = T_matching(250, 50, 100, 3, "high-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 1.989e-7, delta=1e-9)
self.assertAlmostEqual(C1, 6.366e-12, delta=1e-14)
self.assertAlmostEqual(C2, 1.061e-11, delta=1e-13)
Q, L1, L2, C1, C2 = T_matching(250, 50, 100, 3, "low-pass")
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L1, 3.978e-7, delta=1e-9)
self.assertAlmostEqual(L2, 2.387e-7, delta=1e-9)
self.assertAlmostEqual(C1, 1.273e-11, delta=1e-13)
def test_tapped_cap(self):
# cannot ensure the correctness
Q, L, C1, C2 = tapped_cap_matching(50, 10, 100, 3)
self.assertAlmostEqual(Q, 3, delta=1e-2)
self.assertAlmostEqual(L, 2.652e-8, delta=1e-10)
self.assertAlmostEqual(C1, 3.183e-10, delta=1e-12)
self.assertAlmostEqual(C2, 1.591e-10, delta=1e-12)
if __name__ == "__main__":
unittest.main()