def test_D():
s = symbols('s')
C = Rational(3, 2)
L = Rational(1, 3)
r = Rational(1, 2)
# series L, shunt C
C0 = Cascade.Series(L * s)
C1 = Cascade.Series(1 / (C * s))
C2 = Cascade.Shunt(1 / r)
print("test_D")
print(C0)
print(C1)
print(C2)
print(C1.hit(C0))
print(C2.hit(C1.hit(C0)))
Y = ratsimp(1 / C2.hit(C1.hit(C0)).terminate(0))
print(Y)
Z = ratsimp(1 / (Y - 2))
print(Z)
Y = ratsimp(Z - s / 3)
print(Y)
def test_B():
s, L, C, r = symbols('s L C r')
# series L, shunt C
C0 = Cascade.Series(L * s)
C1 = Cascade.Shunt(C * s)
print(simplify(C0.hit(C1).terminate(r)))
def test_E():
"Chop Chop example"
s = symbols('s')
print("test_E")
Z = (2 * s**2 + 2 * s + 1) / (s * (s**2 + s + 1))
print(f"Z: {Z}")
Z = ratsimp(Z)
print(f"Z: {Z}")
Z = ratsimp(Z - 1 / s)
print(f"Z-1/s: {Z}")
C = Cascade.Series(1 / s)
Y = ratsimp(1 / Z - s)
print(f"Y: {Y}")
C = C.hit(Cascade.Shunt(s))
Z = ratsimp(1 / Y)
print(f"Z: {Z-1-s}")
C = C.hit(Cascade.Series(1 + s)).terminate(0)
print(ratsimp(C))
def test_F():
"Hazony example 5.2.2"
s = symbols('s')
print("test_F")
Z = (s**2 + s + 1) / (s**2 + 2 * s + 2)
print(f"Z: {Z}")
min_r = (3 - sympy.sqrt(2)) / 4
Z1 = ratsimp(Z - min_r)
print(f"Z1: {Z1}")
#plot_real_part( sympy.lambdify(s, Z1, "numpy"))
Y1 = ratsimp(1 / Z - 1)
print(f"Y1: {Y1}")
C = Cascade.Shunt(1)
Z2 = ratsimp(1 / Y1 - s)
print(f"Z2: {Z2}")
C = C.hit(Cascade.Series(s))
Y3 = ratsimp(1 / Z2 - s - 1)
print(f"Y3: {Y3}")
Ytotal = C.hit(Cascade.Shunt(1).hit(
Cascade.Shunt(s))).terminate_with_admittance(0)
assert sympy.Eq(0, ratsimp(1 / Ytotal - Z))
assert sympy.Eq(1, ratsimp(Ytotal * Z))
Ytotal = C.hit(Cascade.Shunt(s)).terminate_with_admittance(1)
assert sympy.Eq(0, ratsimp(1 / Ytotal - Z))
assert sympy.Eq(1, ratsimp(Ytotal * Z))
Ytotal = C.terminate_with_admittance(1 + s)
assert sympy.Eq(0, ratsimp(1 / Ytotal - Z))
assert sympy.Eq(1, ratsimp(Ytotal * Z))
def test_J():
"Second problem in Guillemin"
s, k = symbols('s k')
w = symbols('w', real=True)
pprint("test_I")
Z = (s**2 + s + 8) / (s**2 + 2 * s + 2)
pprint(f"Z: {Z}")
Y = 1 / Z
#plot_real_part( sympy.lambdify(s, Y, "numpy"))
real_part = cancel(sympy.re(Y.subs({s: sympy.I * w})))
print(f"real_part: {real_part}")
roots = sympy.solveset(real_part, w)
print(f"roots for w: {roots}")
#plot( sympy.lambdify(w, real_part, "numpy"))
w0 = 2
target0 = radsimp(Y.subs({s: sympy.I * w0}) / (sympy.I * w0))
print(f"target: {target0.evalf()}")
target0 = Rational(1, 2)
target1 = radsimp(Y.subs({s: sympy.I * w0}) * (sympy.I * w0))
print(f"target: {target1.evalf()}")
target1 = Rational(2, 1)
assert target0 > 0
eq = sympy.Eq(Y.subs({s: k}) / k, target0)
#assert target1 > 0
#eq = sympy.Eq( Z.subs({s:k})*k, target1)
roots = sympy.solveset(eq, k)
print(f"roots for k: {roots}")
k0 = Rational(1, 1)
Y_k0 = Y.subs({s: k0})
print(k0, Y_k0)
print(k0.evalf(), Y_k0.evalf())
den = cancel((k0 * Y_k0 - s * Y))
print(f"den factored: {sympy.factor(den)}")
num = cancel((k0 * Y - s * Y_k0))
print(f"num factored: {sympy.factor(num)}")
eta = cancel(num / den)
print(k0, Y_k0, eta)
print("normal")
Y0 = eta * Y_k0
print(f"Y0: {Y0}")
Z1 = ratsimp(1 / Y0 - 4)
print(f"Z1: {Z1}")
C = Cascade.Series(4)
Y2 = ratsimp(1 / Z1)
print(f"Y2: {Y2}")
C = C.hit(Cascade.Shunt(s / 10))
C = C.hit(Cascade.Shunt(2 / (5 * s)))
eta_Y_k0 = cancel(C.terminate_with_admittance(0))
print(f"eta_Y_k0: {eta_Y_k0}")
assert sympy.Eq(cancel(eta_Y_k0 - Y0), 0)
print("recip")
Y0 = ratsimp(Y_k0 / eta)
print(f"Y0: {Y0}")
Y1 = ratsimp(Y0 - 1)
print(f"Y1: {Y1}")
C = Cascade.Shunt(1)
Z2 = ratsimp(1 / Y1 - 2 * s / 5 - 8 / (5 * s))
print(f"Z2: {Z2}")
C = C.hit(Cascade.Series(2 * s / 5))
C = C.hit(Cascade.Series(8 / (5 * s)))
eta_over_Y_k0 = cancel(1 / C.terminate(0))
print(f"eta_over_Y_k0: {eta_over_Y_k0}")
assert sympy.Eq(cancel(eta_over_Y_k0 - Y0), 0)
def p(a, b):
return a * b / (a + b)
constructed_Y = cancel(
p(eta_Y_k0, (k0 * Y_k0) / s) + p(eta_over_Y_k0, (Y_k0 * s) / k0))
print(f"constructed_Y: {constructed_Y}")
assert sympy.Eq(cancel(constructed_Y - Y), 0)
def test_I():
"Hazony problem 5.3.a"
s, k = symbols('s k')
w = symbols('w', real=True)
pprint("test_I")
Z = (s**3 + 3 * s**2 + s + 1) / (s**3 + s**2 + 3 * s + 1)
pprint(f"Z: {Z}")
#plot_real_part( sympy.lambdify(s, Z, "numpy"))
real_part = cancel(sympy.re(Z.subs({s: sympy.I * w})))
print(f"real_part: {real_part}")
roots = sympy.solveset(real_part, w)
print(f"roots for w: {roots}")
#plot( sympy.lambdify(w, real_part, "numpy"))
w0 = 1
target0 = radsimp(Z.subs({s: sympy.I * w0}) / (sympy.I * w0))
print(f"target: {target0}")
target1 = radsimp(Z.subs({s: sympy.I * w0}) * (sympy.I * w0))
print(f"target: {target1}")
assert target0 > 0
eq = sympy.Eq(Z.subs({s: k}) / k, target0)
#assert target1 > 0
#eq = sympy.Eq( Z.subs({s:k})*k, target1)
roots = sympy.solveset(eq, k)
print(f"roots for k: {roots}")
k0 = Rational(1, 1)
Z_k0 = Z.subs({s: k0})
print(k0, Z_k0)
print(k0.evalf(), Z_k0.evalf())
den = cancel((k0 * Z_k0 - s * Z))
print(f"den factored: {sympy.factor(den)}")
num = cancel((k0 * Z - s * Z_k0))
print(f"num factored: {sympy.factor(num)}")
eta = cancel(num / den)
print(k0, Z_k0, eta)
print("normal")
Z0 = eta * Z_k0
print(f"Z0: {Z0}")
Y1 = ratsimp(1 / Z0 - 1)
print(f"Y1: {Y1}")
C = Cascade.Shunt(1)
Z2 = ratsimp(1 / Y1 - s / 2 - 1 / (2 * s))
print(f"Z2: {Z2}")
C = C.hit(Cascade.Series(s / 2))
C = C.hit(Cascade.Series(1 / (2 * s)))
eta_Z_k0 = cancel(C.terminate(0))
print(f"eta_Z_k0: {eta_Z_k0}")
assert sympy.Eq(cancel(eta_Z_k0 - Z0), 0)
print("recip")
Z0 = cancel(Z_k0 / eta)
print(f"Z0: {Z0}")
Z1 = ratsimp(Z0 - 1)
print(f"Z1: {Z1}")
C = Cascade.Series(1)
Y2 = ratsimp(1 / Z1 - s / 2 - 1 / (2 * s))
print(f"Y2: {Y2}")
C = C.hit(Cascade.Shunt(s / 2))
C = C.hit(Cascade.Shunt(1 / (2 * s)))
eta_over_Z_k0 = cancel(1 / C.terminate_with_admittance(0))
print(f"eta_over_Z_k0: {eta_over_Z_k0}")
assert sympy.Eq(cancel(eta_over_Z_k0 - Z0), 0)
def p(a, b):
return a * b / (a + b)
constructed_Z = cancel(
p(eta_Z_k0, (k0 * Z_k0) / s) + p(eta_over_Z_k0, (Z_k0 * s) / k0))
print(f"constructed_Z: {constructed_Z}")
assert sympy.Eq(cancel(constructed_Z - Z), 0)
def test_H():
"Hazony problem 5.3.a"
s, k = symbols('s k')
w = symbols('w', real=True)
pprint("test_H")
Z = (s**3 + 4 * s**2 + 5 * s + 8) / (2 * s**3 + 2 * s**2 + 20 * s + 9)
pprint(f"Z: {Z}")
#plot_real_part( sympy.lambdify(s, Z, "numpy"))
real_part = cancel(sympy.re(Z.subs({s: sympy.I * w})))
print(f"real_part: {real_part}")
roots = sympy.solveset(real_part, w)
print(f"roots for w: {roots}")
#plot( sympy.lambdify(w, real_part, "numpy"))
w0 = sympy.sqrt(6)
target0 = radsimp(Z.subs({s: sympy.I * w0}) / (sympy.I * w0))
print(f"target: {target0}")
target1 = radsimp(Z.subs({s: sympy.I * w0}) * (sympy.I * w0))
print(f"target: {target1}")
assert target0 > 0
eq = sympy.Eq(Z.subs({s: k}) / k, target0)
#eq = sympy.Eq( Z.subs({s:k})*k, target1)
print(f"eq: {eq}")
roots = sympy.solveset(eq, k)
print(f"roots for k: {roots}")
k0 = Rational(1, 4) + sympy.sqrt(33) / 4
Z_k0 = Z.subs({s: k0})
print(k0, Z_k0)
print(k0.evalf(), Z_k0.evalf())
return
f = s**2 + 6
den = cancel((k0 * Z_k0 - s * Z) / f)
print(f"den factored: {sympy.factor(den)}")
num = cancel((k0 * Z - s * Z_k0) / f)
print(f"num factored: {sympy.factor(num).evalf()}")
print(sympy.factor(cancel(den / num)))
return
eta = cancel(((k0 * Z - s * Z_k0) / (k0 * Z_k0 - s * Z)).evalf())
print(k0, Z_k0, eta)
print(k0, Z_k0, eta.evalf())
print("normal")
Z0 = eta * Z_k0
print(f"Z0: {Z0}")
Y1 = cancel(1 / Z0 - 4)
print(f"Y1: {Y1}")
C = Cascade.Shunt(4)
Z2 = cancel(1 / Y1 - s / 6 - 1 / (3 * s))
print(f"Z2: {Z2}")
C = C.hit(Cascade.Series(s / 6))
C = C.hit(Cascade.Series(1 / (3 * s)))
eta_Z_k0 = cancel(C.terminate(0))
print(f"eta_Z_k0: {eta_Z_k0}")
assert sympy.Eq(cancel(eta_Z_k0 - Z0), 0)
print("recip")
Z0 = cancel(Z_k0 / eta)
print(f"Z0: {Z0}")
Z1 = cancel(Z0 - 1)
print(f"Z1: {Z1}")
C = Cascade.Series(1)
Y2 = cancel(1 / Z1 - 2 * s / 3 - 4 / (3 * s))
print(f"Y2: {Y2}")
C = C.hit(Cascade.Shunt(2 * s / 3))
C = C.hit(Cascade.Shunt(4 / (3 * s)))
eta_over_Z_k0 = cancel(1 / C.terminate_with_admittance(0))
print(f"eta_over_Z_k0: {eta_over_Z_k0}")
assert sympy.Eq(cancel(eta_over_Z_k0 - Z0), 0)
def p(a, b):
return 1 / (1 / a + 1 / b)
constructed_Z = cancel(
p(eta_Z_k0, (k0 * Z_k0) / s) + p(eta_over_Z_k0, (Z_k0 * s) / k0))
print(f"constructed_Z: {constructed_Z}")
assert sympy.Eq(cancel(constructed_Z - Z), 0)
def test_G():
"Hazony example 5.2.2"
s, k = symbols('s k')
pprint("test_G")
Z = (s**2 + s + 1) / (s**2 + s + 4)
pprint(f"Z: {Z}")
#plot_real_part( sympy.lambdify(s, Z, "numpy"))
w0 = sympy.sqrt(2)
target = radsimp(Z.subs({s: sympy.I * w0}) / (sympy.I * w0))
print(f"target: {target}")
eq = sympy.Eq(Z.subs({s: k}) / k, target)
roots = sympy.solveset(eq, k)
if True:
for k0 in roots:
Z_k0 = Z.subs({s: k0})
eta = cancel((k0 * Z - s * Z_k0) / (k0 * Z_k0 - s * Z))
print(k0, Z_k0, eta)
#plot_real_part( sympy.lambdify(s, eta, "numpy"))
k0 = 1
Z_k0 = Z.subs({s: k0})
eta = cancel((k0 * Z - s * Z_k0) / (k0 * Z_k0 - s * Z))
print(k0, Z_k0, eta)
print("normal")
Z0 = eta * Z_k0
print(f"Z0: {Z0}")
Y1 = cancel(1 / Z0 - 4)
print(f"Y1: {Y1}")
C = Cascade.Shunt(4)
Z2 = cancel(1 / Y1 - s / 6 - 1 / (3 * s))
print(f"Z2: {Z2}")
C = C.hit(Cascade.Series(s / 6))
C = C.hit(Cascade.Series(1 / (3 * s)))
eta_Z_k0 = cancel(C.terminate(0))
print(f"eta_Z_k0: {eta_Z_k0}")
assert sympy.Eq(cancel(eta_Z_k0 - Z0), 0)
print("recip")
Z0 = cancel(Z_k0 / eta)
print(f"Z0: {Z0}")
Z1 = cancel(Z0 - 1)
print(f"Z1: {Z1}")
C = Cascade.Series(1)
Y2 = cancel(1 / Z1 - 2 * s / 3 - 4 / (3 * s))
print(f"Y2: {Y2}")
C = C.hit(Cascade.Shunt(2 * s / 3))
C = C.hit(Cascade.Shunt(4 / (3 * s)))
eta_over_Z_k0 = cancel(1 / C.terminate_with_admittance(0))
print(f"eta_over_Z_k0: {eta_over_Z_k0}")
assert sympy.Eq(cancel(eta_over_Z_k0 - Z0), 0)
def p(a, b):
return 1 / (1 / a + 1 / b)
constructed_Z = cancel(
p(eta_Z_k0, (k0 * Z_k0) / s) + p(eta_over_Z_k0, (Z_k0 * s) / k0))
print(f"constructed_Z: {constructed_Z}")
assert sympy.Eq(cancel(constructed_Z - Z), 0)
def test_A():
r0, r1, r = 100, 200, 1
R0 = Cascade.Series(r0)
R1 = Cascade.Series(r1)
assert 301 == R0.hit(R1).terminate(r)