388 lines
11 KiB
Python
388 lines
11 KiB
Python
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# Based on scripts from Andy H. va rfcafe
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# IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. VOL 42, NO 2. FEBRUARY 1994
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# Conversions Between S, Z, Y, h, ABCD, and T Parameters which are Valid for Complex Source and Load Impedances
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# Dean A. Frickey, Member, EEE
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# Tables I and II
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import numpy
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def s_to_z(s, z0):
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"""
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Scattering (S) to Impedance (Z)
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Args:
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s: The scattering matrix.
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z0: The port impedances (Ohms).
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Returns:
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The impedance matrix.
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"""
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z0c = numpy.conj(z0)
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z = numpy.empty([2, 2], dtype=complex)
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z[0, 0] = (z0c[0] + s[0, 0] * z0[0]) * (1 - s[1, 1]) + s[0, 1] * s[1, 0] * z0[0]
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z[0, 1] = 2 * s[0, 1] * numpy.sqrt(z0[0].real * z0[1].real)
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z[1, 0] = 2 * s[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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z[1, 1] = (1 - s[0, 0]) * (z0c[1] + s[1, 1] * z0[1]) + s[0, 1] * s[1, 0] * z0[1]
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z /= (1 - s[0, 0]) * (1 - s[1, 1]) - s[0, 1] * s[1, 0]
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return z
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def z_to_s(z, z0):
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"""
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Impedance (Z) to Scattering (S)
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Args:
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z: The impedance matrix.
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z0: The port impedances (Ohms).
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Returns:
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The scattering matrix.
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"""
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z0c = numpy.conj(z0)
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s = numpy.empty([2, 2], dtype=complex)
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s[0, 0] = (z[0, 0] - z0c[0]) * (z[1, 1] + z0[1]) - z[0, 1] * z[1, 0]
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s[0, 1] = 2 * z[0, 1] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 0] = 2 * z[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 1] = (z[0, 0] + z0[0]) * (z[1, 1] - z0c[1]) - z[0, 1] * z[1, 0]
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s /= (z[0, 0] + z0[0]) * (z[1, 1] + z0[1]) - z[0, 1] * z[1, 0]
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return s
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def s_to_y(s, z0):
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"""
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Scattering (S) to Admittance (Y)
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Args:
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s: The scattering matrix.
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z0: The port impedances (Ohms).
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Returns:
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The admittance matrix.
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"""
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z0c = numpy.conj(z0)
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y = numpy.empty([2, 2], dtype=complex)
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y[0, 0] = (1 - s[0, 0]) * (z0c[1] + s[1, 1] * z0[1]) + s[0,1] * s[1, 0] * z0[1]
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y[0, 1] = -2 * s[0,1] * numpy.sqrt(z0[0].real * z0[1].real)
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y[1, 0] = -2 * s[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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y[1, 1] = (z0c[0] + s[0, 0] * z0[0]) * (1 - s[1,1]) + s[0,1] * s[1, 0] * z0[0]
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y /= (z0c[0] + s[0, 0] * z0[0]) * (z0c[1] + s[1, 1] * z0[1]) - s[0,1] * s[1, 0] * z0[0] * z0[1]
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return y
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def y_to_s(y, z0):
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"""
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Admittance (Y) to Scattering (S)
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Args:
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y: The admittance matrix.
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z0: The port impedances (Ohms).
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Returns:
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The scattering matrix.
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"""
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z0c = numpy.conj(z0)
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s = numpy.empty([2, 2], dtype=complex)
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s[0, 0] = (1 - y[0, 0] * z0c[0]) * (1 + y[1, 1] * z0[1]) + y[0,1] * y[1, 0] * z0c[0] * z0[1]
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s[0, 1] = -2 * y[0,1] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 0] = -2 * y[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 1] = (1 + y[0, 0] * z0[0]) * (1 - y[1,1] * z0c[1]) + y[0,1] * y[1, 0] * z0[0] * z0c[1]
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s /= (1 + y[0, 0] * z0[0]) * (1 + y[1, 1] * z0[1]) - y[0,1] * y[1, 0] * z0[0] * z0[1]
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return s
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def s_to_h(s, z0):
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"""
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Scattering (S) to Hybrid (H)
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Args:
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s: The scattering matrix.
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z0: The port impedances (Ohms).
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Returns:
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The hybrid matrix.
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"""
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z0c = numpy.conj(z0)
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h = numpy.empty([2, 2], dtype=complex)
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h[0, 0] = (z0c[0] + s[0, 0] * z0[0]) * (z0c[1] + s[1, 1] * z0[1]) - s[0,1] * s[1, 0] * z0[0] * z0[1]
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h[0, 1] = 2 * s[0,1] * numpy.sqrt(z0[0].real * z0[1].real)
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h[1, 0] = -2 * s[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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h[1, 1] = (1 - s[0, 0]) * (1 - s[1,1]) - s[0,1] * s[1, 0]
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h /= (1 - s[0, 0]) * (z0c[1] + s[1, 1] * z0[1]) + s[0,1] * s[1, 0] * z0[1]
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return h
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def h_to_s(h, z0):
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"""
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Hybrid (H) to Scattering (S)
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Args:
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h: The hybrid matrix.
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z0: The port impedances (Ohms).
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Returns:
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The scattering matrix.
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"""
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z0c = numpy.conj(z0)
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s = numpy.empty([2, 2], dtype=complex)
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s[0, 0] = (h[0, 0] - z0c[0]) * (1 + h[1, 1] * z0[1]) - h[0,1] * h[1, 0] * z0[1]
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s[0, 1] = 2 * h[0,1] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 0] = -2 * h[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 1] = (z0[0] + h[0, 0]) * (1 - h[1,1] * z0c[1]) + h[0,1] * h[1, 0] * z0c[1]
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s /= (z0[0] + h[0, 0]) * (1 + h[1, 1] * z0[1]) - h[0,1] * h[1, 0] * z0[1]
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return s
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def s_to_abcd(s, z0):
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"""
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Scattering to Chain (ABCD)
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Args:
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s: The scattering matrix.
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z0: The port impedances (Ohms).
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Returns:
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The chain matrix.
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"""
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z0c = numpy.conj(z0)
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ans = numpy.empty([2, 2], dtype=complex)
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ans[0, 0] = (z0c[0] + s[0, 0] * z0[0]) * (1 - s[1, 1]) + s[0,1] * s[1, 0] * z0[0]
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ans[0, 1] = (z0c[0] + s[0, 0] * z0[0]) * (z0c[1] + s[1,1] * z0[1]) - s[0,1] * s[1, 0] * z0[0] * z0[1]
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ans[1, 0] = (1 - s[0, 0]) * (1 - s[1, 1]) - s[0,1] * s[1, 0]
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ans[1, 1] = (1 - s[0, 0]) * (z0c[1] + s[1,1] * z0[1]) + s[0,1] * s[1, 0] * z0[1]
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ans /= 2 * s[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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return ans
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def abcd_to_s(abcd, z0):
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"""
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Chain (ABCD) to Scattering (S)
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Args:
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abcd: The chain matrix.
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z0: The port impedances (Ohms).
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Return:
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The scattering matrix.
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"""
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A = abcd[0, 0]
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B = abcd[0, 1]
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C = abcd[1, 0]
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D = abcd[1, 1]
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z0c = numpy.conj(z0)
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s = numpy.empty([2, 2], dtype=complex)
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s[0, 0] = A * z0[1] + B - C * z0c[0] * z0[1] - D * z0c[0]
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s[0, 1] = 2 * (A * D - B * C) * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 0] = 2 * numpy.sqrt(z0[0].real * z0[1].real)
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s[1, 1] = -A * z0c[1] + B - C * z0[0] * z0c[1] + D * z0[0]
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s /= A * z0[1] + B + C * z0[0] * z0[1] + D * z0[0]
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return s
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def t_to_z(t, z0):
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"""
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Chain Transfer (T) to Impedance (Z)
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Args:
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t: The chain transfer matrix.
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z0: The port impedances (Ohms).
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Returns:
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The impedance matrix.
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"""
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z0c = numpy.conj(z0)
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z = numpy.empty([2, 2], dtype=complex)
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z[0, 0] = z0c[0] * (t[0, 0] + t[0, 1]) + z0[0] * (t[1, 0] + t[1,1])
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z[0, 1] = 2 * numpy.sqrt(z0[0].real * z0[1].real) * (t[0, 0] * t[1,1] - t[0,1] * t[1, 0])
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z[1, 0] = 2 * numpy.sqrt(z0[0].real * z0[1].real)
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z[1, 1] = z0c[1] * (t[0, 0] - t[1, 0]) - z0[1] * (t[0,1] - t[1,1])
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z /= t[0, 0] + t[0, 1] - t[1, 0] - t[1,1]
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return z
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def z_to_t(z, z0):
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"""
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Impedance (Z) to Chain Transfer (T)
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Args:
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z: The impedance matrix.
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z0: The port impedances (Ohms).
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Returns:
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The chain transfer matrix.
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"""
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z0c = numpy.conj(z0)
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t = numpy.empty([2, 2], dtype=complex)
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t[0, 0] = (z[0, 0] + z0[0]) * (z[1, 1] + z0[1]) - z[0,1] * z[1, 0]
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t[0, 1] = (z[0, 0] + z0[0]) * (z0c[1] - z[1,1]) + z[0,1] * z[1, 0]
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t[1, 0] = (z[0, 0] - z0c[0]) * (z[1, 1] + z0[1]) - z[0,1] * z[1, 0]
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t[1, 1] = (z0c[0] - z[0, 0]) * (z[1,1] - z0c[1]) + z[0,1] * z[1, 0]
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t /= 2 * z[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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return t
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def t_to_y(t, z0):
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"""
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Chain Transfer (T) to Admittance (Y)
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Args:
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t: The chain transfer matrix.
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z0: The port impedances (Ohms).
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Returns:
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The admittance matrix.
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"""
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z0c = numpy.conj(z0)
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y = numpy.empty([2, 2], dtype=complex)
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y[0, 0] = z0c[1] * (t[0, 0] - t[1, 0]) - z0[1] * (t[0, 1] - t[1,1])
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y[0, 1] = -2 * numpy.sqrt(z0[0].real * z0[1].real) * (t[0, 0] * t[1,1] - t[0,1] * t[1, 0])
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y[1, 0] = -2 * numpy.sqrt(z0[0].real * z0[1].real)
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y[1, 1] = z0c[0] * (t[0, 0] + t[0,1]) + z0[0] * (t[1, 0] + t[1,1])
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y /= t[0, 0] * z0c[0] * z0c[1] - t[0, 1] * z0c[0] * z0[1] + t[1, 0] * z0[0] * z0c[1] - t[1,1] * z0[0] * z0[1]
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return y
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def y_to_t(y, z0):
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"""
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Admittance (Y) to Chain Transfer (T)
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Args:
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y: The admittance matrix.
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z0: The port impedances (Ohms).
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Returns:
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The chain transfer matrix.
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"""
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z0c = numpy.conj(z0)
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t = numpy.empty([2, 2], dtype=complex)
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t[0, 0] = (-1 - y[0, 0] * z0[0]) * (1 + y[1, 1] * z0[1]) + y[0,1] * y[1, 0] * z0[0] * z0[1]
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t[0, 1] = (1 + y[0, 0] * z0[0]) * (1 - y[1,1] * z0c[1]) + y[0,1] * y[1, 0] * z0[0] * z0c[1]
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t[1, 0] = (y[0, 0] * z0c[0] - 1) * (1 + y[1, 1] * z0[1]) - y[0,1] * y[1, 0] * z0c[0] * z0[1]
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t[1, 1] = (1 - y[0, 0] * z0c[0]) * (1 - y[1,1] * z0c[1]) - y[0,1] * y[1, 0] * z0c[0] * z0c[1]
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t /= 2 * y[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
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return t
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def t_to_h(t, z0):
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"""
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Chain Transfer (T) to Hybrid (H)
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Args:
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t: The chain transfer matrix.
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z0: The port impedances (Ohms).
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Returns:
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The hybrid matrix.
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"""
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z0c = numpy.conj(z0)
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h = numpy.empty([2, 2], dtype=complex)
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h[0, 0] = z0c[1]*(t[0, 0] * z0c[0] + t[1, 0] * z0[0]) - z0[1] * (t[0, 1] * z0c[0] + t[1,1] * z0[0])
|
||
|
|
h[0, 1] = 2 * numpy.sqrt(z0[0].real * z0[1].real) * (t[0, 0] * t[1,1] - t[0,1] * t[1, 0])
|
||
|
|
h[1, 0] = -2 * numpy.sqrt(z0[0].real * z0[1].real)
|
||
|
|
h[1, 1] = t[0, 0] + t[0,1] - t[1, 0] - t[1,1]
|
||
|
|
|
||
|
|
h /= z0c[1] * (t[0, 0] - t[1, 0]) - z0[1] * (t[0, 1] - t[1,1])
|
||
|
|
return h
|
||
|
|
|
||
|
|
|
||
|
|
def h_to_t(h, z0):
|
||
|
|
"""
|
||
|
|
Hybrid (H) to Chain Transfer (T)
|
||
|
|
|
||
|
|
Args:
|
||
|
|
t: The hybrid matrix.
|
||
|
|
z0: The port impedances (Ohms).
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
The chain transfer matrix.
|
||
|
|
"""
|
||
|
|
z0c = numpy.conj(z0)
|
||
|
|
|
||
|
|
t = numpy.empty([2, 2], dtype=complex)
|
||
|
|
t[0, 0] = (-h[0, 0] - z0[0]) * (1 + h[1, 1] * z0[1]) + h[0,1] * h[1, 0] * z0[1]
|
||
|
|
t[0, 1] = (h[0, 0] + z0[0]) * (1 - h[1,1] * z0c[1]) + h[0,1] * h[1, 0] * z0c[1]
|
||
|
|
t[1, 0] = (z0c[0] - h[0, 0]) * (1 + h[1, 1] * z0[1]) + h[0,1] * h[1, 0] * z0[1]
|
||
|
|
t[1, 1] = (h[0, 0] - z0c[0]) * (1 - h[1,1] * z0c[1]) + h[0,1] * h[1, 0] * z0c[1]
|
||
|
|
|
||
|
|
t /= 2 * h[1, 0] * numpy.sqrt(z0[0].real * z0[1].real)
|
||
|
|
return t
|
||
|
|
|
||
|
|
|
||
|
|
def t_to_abcd(t, z0):
|
||
|
|
"""
|
||
|
|
Chain Transfer (T) to Chain (ABCD)
|
||
|
|
|
||
|
|
Args:
|
||
|
|
t: The chain transfer matrix.
|
||
|
|
z0: The port impedances (Ohms).
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
The chain matrix.
|
||
|
|
"""
|
||
|
|
z0c = numpy.conj(z0)
|
||
|
|
ans = numpy.empty([2, 2], dtype=complex)
|
||
|
|
ans[0, 0] = z0c[0] * (t[0, 0] + t[0, 1]) + z0[0] * (t[1, 0] + t[1, 1])
|
||
|
|
ans[0, 1] = z0c[1] * (t[0, 0] * z0c[0] + t[1, 0] * z0[0]) - z0[1] * (t[0, 1] * z0c[0] + t[1, 1] * z0[0])
|
||
|
|
ans[1, 0] = t[0, 0] + t[0, 1] - t[1, 0] - t[1, 1]
|
||
|
|
ans[1, 1] = z0c[1] * (t[0, 0] - t[1, 0]) - z0[1] * (t[0, 1] - t[1, 1])
|
||
|
|
|
||
|
|
ans /= 2 * numpy.sqrt(z0[0].real * z0[1].real)
|
||
|
|
return ans
|
||
|
|
|
||
|
|
|
||
|
|
def abcd_to_t(abcd, z0):
|
||
|
|
"""
|
||
|
|
Chain (ABCD) to Chain Transfer (T)
|
||
|
|
|
||
|
|
Args:
|
||
|
|
abcd: The chain matrix.
|
||
|
|
z0: The port impedances (Ohms).
|
||
|
|
|
||
|
|
Returns:
|
||
|
|
The chain transfer matrix.
|
||
|
|
"""
|
||
|
|
# Break out the components
|
||
|
|
A = abcd[0, 0]
|
||
|
|
B = abcd[0, 1]
|
||
|
|
C = abcd[1, 0]
|
||
|
|
D = abcd[1, 1]
|
||
|
|
|
||
|
|
z0c = numpy.conj(z0)
|
||
|
|
|
||
|
|
t = numpy.empty([2, 2], dtype=complex)
|
||
|
|
t[0, 0] = A * z0[1] + B + C * z0[0] * z0[1] + D * z0[0]
|
||
|
|
t[0, 1] = A * z0c[1] - B + C * z0[0] * z0c[1] - D * z0[0]
|
||
|
|
t[1, 0] = A * z0[1] + B - C * z0c[0] * z0[1] - D * z0c[0]
|
||
|
|
t[1, 1] = A * z0c[1] - B - C * z0c[0] * z0c[1] + D * z0c[0]
|
||
|
|
|
||
|
|
t /= 2 * numpy.sqrt(z0[0].real * z0[1].real)
|
||
|
|
return t
|