def find_f_res():
# Secant method root finding algorithm
# Loosely based upon http://www.see.ed.ac.uk/~jwp/JavaScript/programming/chop2.html
x_1 = c_0 / l_w_eff / 40
x_2 = x_1 * 100
max_tries = 40
for tries in range(-1, max_tries + 1): # <= max
if tries == -1:
x = x_1
if tries == 0:
x = x_2
if tries > 0:
x = (x_1 + x_2) / 2
# First, solve the sheath helix dispersion function for tau at frequency x.
omega = 2 * pi * x
k_0 = omega / c_0
F = lambda tau: K1(tau * a) * I1(tau * a) / K0(tau * a) / I0(
tau * a) - (tau / k_0 * tan(psi))**2
tau_1 = k_0 * cot(psi)**2 - k_0**2 # an estimate
tau_2 = k_0 # another estimate
zero = fzero(F, tau_1, tau_2)
if zero['error_code'] == 2:
alert(
'An error occurred when solving for the resonant frequency.\n'
+ 'However, all shown results are useable.\n\n' +
zero['error_msg'])
document['f_res'].value = ''
tau = zero['zero']
# Then, check for resonance.
# β² = k_0² + τ²
# βℓ → π/2
fx = sqrt(k_0**2 + tau**2) * l - pi / 2
if tries == -1:
fx_1 = fx
if tries == 0:
fx_2 = fx
if tries <= 0:
continue
if fx * fx_1 > 0:
fx_1 = fx
x_1 = x
else:
fx_2 = fx
x_2 = x
return x
def myCalculate(D, N, l, d, f, plating_nr='hard-drawn copper'):
try:
rho = plating[plating_nr].rho * 1E-9
mu_r_w = plating[plating_nr].mu_r
print('rho = {:.2f}'.format(rho * 1E9))
print('mu_r_w = {:.2f}'.format(mu_r_w))
l = float(l) * 1E-3
p = l / N
D = float(D) * 1E-3
d = float(d) * 1E-3
Phi = lookup_Phi(l, D, p, d)
D_eff = D - d * (1 - 1 / sqrt(Phi))
# Correction factors
if l <= D_eff: # The short coil expression gives a value that agrees better with the AGM result.
k_L = 1 + 0.383901 * (l / D_eff)**2 + 0.017108 * (l / D_eff)**4
k_L /= 1 + 0.258952 * (l / D_eff)**2
k_L *= log(4 * D_eff / l) - 0.5
k_L += 0.093842 * (l / D_eff)**2 + 0.002029 * (
l / D_eff)**4 - 0.000801 * (l / D_eff)**6
k_L *= 2 / pi * l / D_eff
else:
k_L = 1 + 0.383901 * (D_eff / l)**2 + 0.017108 * (D_eff / l)**4
k_L /= 1 + 0.258952 * (D_eff / l)**2
k_L -= 4 / 3 / pi * D_eff / l
k_s = 5 / 4 - log(2 * p / d)
c_9 = -log(2 * pi) + 3 / 2 + 0.33084236 + 1 / 120 - 1 / 504 + 0.0011925
k_m = log(2 * pi) - 3 / 2 - log(N) / 6 / N - 0.33084236 / N - 1 / (
120 * N**3) + 1 / (504 * N**5) - 0.0011925 / N**7 + c_9 / N**9
# Effective series AC resistance
l_w_phys = sqrt((N * pi * D)**2 + l**2)
l_w_eff = sqrt((N * pi * D_eff)**2 + l**2)
f = float(f) * 1E6
delta_i = sqrt(rho / pi / f / mu_0 / mu_r_w)
R_eff_s = rho * l_w_eff
R_eff_s /= pi * (d * delta_i - delta_i**2)
R_eff_s *= Phi
if (N > 1):
R_eff_s *= (N - 1) / N
# Corrected current-sheet geometrical formula
mu_r_core = 1
L_s = pi * (D_eff * N)**2 / 4 / l * k_L
L_s -= D_eff * N * (k_s + k_m) / 2
L_s *= mu_r_core * mu_0
psi = atan(p / pi / D_eff)
# Copy & paste text field
offset = 28
print('{:{offset}} D = {:3.1f} mm'.format('mean diameter of the coil',
D / 1e-3,
offset=offset))
print('{:{offset}} N = {:4.1f}'.format('number of turns',
N,
offset=offset))
print('{:{offset}} ℓ = {:3.1f} mm'.format('length of the coil',
l / 1e-3,
offset=offset))
print('{:{offset}} d = {:3.1f} mm'.format('wire or tubing diameter',
d / 1e-3,
offset=offset))
print('{:{offset}} f = {:3.1f} MHz'.format('design frequency',
f / 1e6,
offset=offset))
print(' The (plating) material is {}.\n'.format(
plating[plating_nr].description))
print('\nINTERMEDIATE RESULTS')
print(' {:{offset}} p = {:3.1f} mm'.format('winding pitch',
p / 1e-3,
offset=offset))
print(' {:{offset}} ℓ_w_phys = {:3.1f} mm'.format(
'physical conductor length', l_w_phys / 1e-3, offset=offset))
print(' {:{offset}} ψ = {:3.1f}°'.format('effective pitch angle',
psi,
offset=offset))
# Characteristic impedance of the sheath helix waveguide mode
offset = 55
try:
omega = 2 * pi * f
k_0 = omega / c_0
a = D_eff / 2
# Sheath helix dispersion function
F = lambda tau: K1(tau * a) * I1(tau * a) / (K0(tau * a) * I0(
tau * a)) - (tau / k_0 * tan(psi))**2
tau_1 = k_0 # smallest tau estimate
tau_2 = k_0 * cot(psi)**2 # largest tau estimate
zero = fzero(F, tau_1, tau_2)
tau = zero['zero']
beta = sqrt(k_0**2 + tau**2)
Z_c = 60 * beta / k_0 * I0(tau * a) * K0(tau * a)
# Effective equivalent circuit
# Corrected sheath helix waveguide formula
L_eff_s = Z_c / omega * tan(beta * l) * k_L
L_eff_s -= mu_0 * D_eff * N * (k_s + k_m) / 2
X_eff_s = omega * L_eff_s
Q_eff = X_eff_s / R_eff_s
# Effective circuit results in copy & paste text field
print('\nEffective equivalent circuit ')
print('{:{offset}} L_eff_s = {:1.3e} H'.format(
'effective series inductance @ design frequency',
L_eff_s,
offset=offset))
print('{:{offset}} X_eff_s = {:1.3e} Ω'.format(
'effective series reactance @ design frequency',
X_eff_s,
offset=offset))
print('{:{offset}} R_eff_s = {:3.3e} Ω'.format(
'effective series AC resistance @ design frequency',
R_eff_s,
offset=offset))
print('{:{offset}} Q_eff = {:3.1f}'.format(
'effective unloaded quality factor @ design frequency',
Q_eff,
offset=offset))
except:
print('\nLumped circuit equivalent')
print(' {:{offset}} L_s = {:1.3e} Hy'.format(
'f-independent series inductance; geometrical formula',
L_s / 1e-6,
offset=offset))
print(
' An error occurred when solving the dispersion function!')
print(' However, all shown results are useable.')
try:
# Lumped equivalent circuit
R_p = (Q_eff**2 + 1) * R_eff_s
X_L_s = omega * L_s
# https://en.wikipedia.org/wiki/Quadratic_equation#Reduced_quadratic_equation
P = R_p / (2 * X_L_s)
Q_L = P + sqrt(P**2 - 1)
R_s = X_L_s / Q_L
X_eff_p = (Q_eff**2 + 1) / Q_eff**2 * X_eff_s
X_L_p = (Q_L**2 + 1) / Q_L**2 * X_L_s
L_p = X_L_p / omega
X_C_p = X_eff_p * X_L_p / (X_L_p - X_eff_p)
C_p = -1 / omega / X_C_p
# Lumped circuit results in copy & paste text field
print('\nLumped circuit equivalent (serie)')
print(' {:{offset}} L_s = {:1.3e} Hy'.format(
'f-independent series inductance; geometrical formula',
L_s,
offset=offset))
print(' {:{offset}} R_s = {:1.3e} Ω'.format(
'series AC resistance @ design frequency', R_s, offset=offset))
print(' {:{offset}} C_p = {:1.3e} F'.format(
'parallel stray capacitance @ design frequency',
C_p,
offset=offset))
print('\nLumped circuit equivalent (paralelo)')
print(' {:{offset}} L_p = {:1.3e} Hy'.format(
'f-independent series inductance; geometrical formula',
L_s,
offset=offset))
print(' {:{offset}} R_p = {:1.3e} Ω'.format(
'series AC resistance @ design frequency', R_p, offset=offset))
print(' {:{offset}} C_p = {:1.3e} F'.format(
'parallel stray capacitance @ design frequency',
C_p,
offset=offset))
except:
print('\nLumped circuit equivalent')
print(' {:{offset}} L_s = {:1.3e} Hy\n'.format(
'f-independent series inductance; geometrical formula',
L_s,
offset=offset))
print(' No lumped circuit equivalent is available!\n')
print(' However, all shown results are useable.\n')
offset = 40
try:
# Self‑resonant frequency
f_res = find_f_res(l_w_eff, a, l, psi)
# Resonant frequency in copy & paste text field
print('{:{offset}} f_res = {:1.3e} Hz\n'.format(
'Self-resonant frequency', f_res, offset=offset))
except:
print(
' An error occurred when solving for the self-resonant frequency!\n'
)
print(' However, all shown results are useable.\n')
except:
#document['txt'].clear() # COMMENT THIS LINE FOR TESTING PROGRESS
outputs = [
'p', 'Phi', 'D_eff', 'k_L', 'k_s', 'k_m', 'l_w_phys', 'l_w_eff',
'delta_i', 'R_eff_s', 'L_s', 'psi'
]
outputs += [
'beta', 'Z_c', 'L_eff_s', 'X_eff_s', 'Q_eff', 'R_s', 'C_p', 'f_res'
]
def calculate(event):
document['txt'].clear()
try:
plating_nr = int(document['plating'].value)
rho = plating[plating_nr].rho * 1E-9
mu_r_w = plating[plating_nr].mu_r
document['rho'].value = '%.2f' % (rho * 1E9)
document['mu_r_w'].value = '%.8f' % mu_r_w
N = float(document['N'].value)
global l
l = float(document['l'].value) * 1E-3
p = l / N
document['p'].value = '%.2f' % round(p * 1E3, 2)
D = float(document['D'].value) * 1E-3
d = float(document['d'].value) * 1E-3
Phi = lookup_Phi(l, D, p, d)
document['Phi'].value = '%.2f' % round(Phi, 2)
D_eff = D - d * (1 - 1 / sqrt(Phi))
document['D_eff'].value = '%.2f' % round(D_eff * 1E3, 2)
# Correction factors
if l <= D_eff: # The short coil expression gives a value that agrees better with the AGM result.
k_L = 1 + 0.383901 * (l / D_eff)**2 + 0.017108 * (l / D_eff)**4
k_L /= 1 + 0.258952 * (l / D_eff)**2
k_L *= log(4 * D_eff / l) - 0.5
k_L += 0.093842 * (l / D_eff)**2 + 0.002029 * (
l / D_eff)**4 - 0.000801 * (l / D_eff)**6
k_L *= 2 / pi * l / D_eff
else:
k_L = 1 + 0.383901 * (D_eff / l)**2 + 0.017108 * (D_eff / l)**4
k_L /= 1 + 0.258952 * (D_eff / l)**2
k_L -= 4 / 3 / pi * D_eff / l
document['k_L'].value = '%.6f' % round(k_L, 6)
k_s = 5 / 4 - log(2 * p / d)
document['k_s'].value = '%.6f' % round(k_s, 6)
c_9 = -log(2 * pi) + 3 / 2 + 0.33084236 + 1 / 120 - 1 / 504 + 0.0011925
k_m = log(2 * pi) - 3 / 2 - log(N) / 6 / N - 0.33084236 / N - 1 / (
120 * N**3) + 1 / (504 * N**5) - 0.0011925 / N**7 + c_9 / N**9
document['k_m'].value = '%.8f' % round(k_m, 8)
# Effective series AC resistance
l_w_phys = sqrt((N * pi * D)**2 + l**2)
document['l_w_phys'].value = '%.1f' % round(l_w_phys * 1E3, 1)
global l_w_eff
l_w_eff = sqrt((N * pi * D_eff)**2 + l**2)
document['l_w_eff'].value = '%.1f' % round(l_w_eff * 1E3, 1)
f = float(document['f'].value) * 1E6
delta_i = sqrt(rho / pi / f / mu_0 / mu_r_w)
document['delta_i'].value = '%.2f' % round(delta_i * 1E6, 2)
R_eff_s = rho * l_w_eff
R_eff_s /= pi * (d * delta_i - delta_i**2)
R_eff_s *= Phi
if (N > 1):
R_eff_s *= (N - 1) / N
document['R_eff_s'].value = '%.3f' % round(R_eff_s, 3)
# Corrected current-sheet geometrical formula
mu_r_core = 1
L_s = pi * (D_eff * N)**2 / 4 / l * k_L
L_s -= D_eff * N * (k_s + k_m) / 2
L_s *= mu_r_core * mu_0
document['L_s'].value = '%.3f' % round(L_s * 1E6, 3)
global psi
psi = atan(p / pi / D_eff)
document['psi'].value = '%.2f' % round(psi / pi * 180, 2)
# Copy & paste text field
t = time.time()
document['txt'] <= 'QOIL™ — https://hamwaves.com/qoil/ — v{}\n'.format(
VERSION)
document['txt'] <= time.strftime(' Coil design %Y-%m-%d %H:%M\n',
time.localtime(t))
offset = 28
document['txt'] <= '\nINPUT\n'
document['txt'] <= ' {:{offset}} D = {} mm\n'.format(
'mean diameter of the coil', document['D'].value, offset=offset)
document['txt'] <= ' {:{offset}} N = {}\n'.format(
'number of turns', document['N'].value, offset=offset)
document['txt'] <= ' {:{offset}} ℓ = {} mm\n'.format(
'length of the coil', document['l'].value, offset=offset)
document['txt'] <= ' {:{offset}} d = {} mm\n'.format(
'wire or tubing diameter', document['d'].value, offset=offset)
document['txt'] <= ' {:{offset}} f = {} MHz\n'.format(
'design frequency', document['f'].value, offset=offset)
document['txt'] <= ' The (plating) material is {}.\n'.format(
plating[plating_nr].description)
document['txt'] <= '\nINTERMEDIATE RESULTS\n'
document['txt'] <= ' {:{offset}} p = {} mm\n'.format(
'winding pitch', document['p'].value, offset=offset)
document['txt'] <= ' {:{offset}} ℓ_w_phys = {} mm\n'.format(
'physical conductor length',
document['l_w_phys'].value,
offset=offset)
document['txt'] <= ' {:{offset}} ψ = {}°\n'.format(
'effective pitch angle', document['psi'].value, offset=offset)
# Characteristic impedance of the sheath helix waveguide mode
offset = 55
try:
omega = 2 * pi * f
k_0 = omega / c_0
global a
a = D_eff / 2
# Sheath helix dispersion function
F = lambda tau: K1(tau * a) * I1(tau * a) / (K0(tau * a) * I0(
tau * a)) - (tau / k_0 * tan(psi))**2
tau_1 = k_0 # smallest tau estimate
tau_2 = k_0 * cot(psi)**2 # largest tau estimate
zero = fzero(F, tau_1, tau_2)
tau = zero['zero']
beta = sqrt(k_0**2 + tau**2)
document['beta'].value = '%.4f' % round(beta, 4)
Z_c = 60 * beta / k_0 * I0(tau * a) * K0(tau * a)
document['Z_c'].value = '%.1f' % round(Z_c, 1)
# Effective equivalent circuit
# Corrected sheath helix waveguide formula
L_eff_s = Z_c / omega * tan(beta * l) * k_L
L_eff_s -= mu_0 * D_eff * N * (k_s + k_m) / 2
document['L_eff_s'].value = '%.3f' % round(L_eff_s * 1E6, 3)
X_eff_s = omega * L_eff_s
document['X_eff_s'].value = '%.1f' % round(X_eff_s, 1)
Q_eff = X_eff_s / R_eff_s
document['Q_eff'].value = '%d' % int(Q_eff)
# Effective circuit results in copy & paste text field
document['txt'] <= '\nRESULTS\n'
document['txt'] <= ' Effective equivalent circuit\n'
document['txt'] <= ' {:{offset}} L_eff_s = {} μH\n'.format(
'effective series inductance @ design frequency',
document['L_eff_s'].value,
offset=offset)
document['txt'] <= ' {:{offset}} X_eff_s = {} Ω\n'.format(
'effective series reactance @ design frequency',
document['X_eff_s'].value,
offset=offset)
document['txt'] <= ' {:{offset}} R_eff_s = {} Ω\n'.format(
'effective series AC resistance @ design frequency',
document['R_eff_s'].value,
offset=offset)
document['txt'] <= ' {:{offset}} Q_eff = {}\n'.format(
'effective unloaded quality factor @ design frequency',
document['Q_eff'].value,
offset=offset)
except:
document['txt'] <= ' Lumped circuit equivalent\n'
document['txt'] <= ' {:{offset}} L_s = {} μH\n'.format(
'f-independent series inductance; geometrical formula',
document['L_s'].value,
offset=offset)
document[
'txt'] <= ' An error occurred when solving the dispersion function!\n'
document['txt'] <= ' However, all shown results are useable.\n'
outputs = [
'beta', 'Z_c', 'L_eff_s', 'X_eff_s', 'Q_eff', 'R_s', 'C_p',
'f_res'
]
for i in range(len(outputs)):
document[outputs[i]].value = ''
try:
# Lumped equivalent circuit
R_p = (Q_eff**2 + 1) * R_eff_s
X_L_s = omega * L_s
# https://en.wikipedia.org/wiki/Quadratic_equation#Reduced_quadratic_equation
P = R_p / (2 * X_L_s)
Q_L = P + sqrt(P**2 - 1)
R_s = X_L_s / Q_L
document['R_s'].value = '%.3f' % round(R_s, 3)
X_eff_p = (Q_eff**2 + 1) / Q_eff**2 * X_eff_s
X_L_p = (Q_L**2 + 1) / Q_L**2 * X_L_s
X_C_p = X_eff_p * X_L_p / (X_L_p - X_eff_p)
C_p = -1 / omega / X_C_p
document['C_p'].value = '%.1f' % round(C_p * 1E12, 1)
# Lumped circuit results in copy & paste text field
document['txt'] <= ' Lumped circuit equivalent\n'
document['txt'] <= ' {:{offset}} L_s = {} μH\n'.format(
'f-independent series inductance; geometrical formula',
document['L_s'].value,
offset=offset)
document['txt'] <= ' {:{offset}} R_s = {} Ω\n'.format(
'series AC resistance @ design frequency',
document['R_s'].value,
offset=offset)
document['txt'] <= ' {:{offset}} C_p = {} pF\n'.format(
'parallel stray capacitance @ design frequency',
document['C_p'].value,
offset=offset)
except:
document['txt'] <= ' Lumped circuit equivalent\n'
document['txt'] <= ' {:{offset}} L_s = {} μH\n'.format(
'f-independent series inductance; geometrical formula',
document['L_s'].value,
offset=offset)
document[
'txt'] <= ' No lumped circuit equivalent is available!\n'
document['txt'] <= ' However, all shown results are useable.\n'
outputs = ['R_s', 'C_p', 'f_res']
for i in range(len(outputs)):
document[outputs[i]].value = ''
offset = 57
try:
# Self‑resonant frequency
f_res = find_f_res()
document['f_res'].value = '%.3f' % round(f_res * 1E-6, 3)
# Resonant frequency in copy & paste text field
document['txt'] <= ' {:{offset}} f_res = {} MHz\n'.format(
'Self-resonant frequency',
document['f_res'].value,
offset=offset)
except:
document[
'txt'] <= ' An error occurred when solving for the self-resonant frequency!\n'
document['txt'] <= ' However, all shown results are useable.\n'
document['f_res'].value = ''
document['txt'] <= '\nDONATE\n'
document['txt'] <= ' If this calculator proved any useful to you,\n'
document['txt'] <= ' please, consider making a one-off donation\n'
document[
'txt'] <= ' towards keeping me and the server up and running.\n'
document['txt'] <= ' Thank you!'
except:
document['txt'].clear() # COMMENT THIS LINE FOR TESTING PROGRESS
outputs = [
'p', 'Phi', 'D_eff', 'k_L', 'k_s', 'k_m', 'l_w_phys', 'l_w_eff',
'delta_i', 'R_eff_s', 'L_s', 'psi'
]
outputs += [
'beta', 'Z_c', 'L_eff_s', 'X_eff_s', 'Q_eff', 'R_s', 'C_p', 'f_res'
]
for i in range(len(outputs)):
document[outputs[i]].value = ''