Boost Converter: CCM

The steady-state diode current $i_D(t)$ for a boost converter is given below. The inductor current is continuous, and the capacitance is large enough to make the output voltage constant.
  1. Find the rms value of the inductor current.
  2. If $V_s=8\,$V, what is $R$?
  3. Find $L$ required for the above conditions.
  4. Verify your design using simulation.
In [1]:
from IPython.display import Image
Image(filename =r'boost_ccm_11_fig_1.png', width=700)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat boost_ccm_11_orig.in

We now replace the strings \$Vin, \$L, \$C, \$R, \$D, \$f_hz with the values of our choice by running the python script given below. It takes an existing circuit file boost_ccm_11_orig.in and produces a new circuit file boost_ccm_11.in, after replacing \$L, \$C, \$R, \$D, \$f_hz with the values of our choice.

In [3]:
import gseim_calc as calc

s_Vin = '8'
s_D = '0.75'
s_f_hz = '10e3'
s_R = '15' # to be changed by user
s_L = '80e-6' # to be changed by user
s_C = '0.5e-3'

l = [
  ('$Vin', s_Vin),
  ('$L', s_L),
  ('$C', s_C),
  ('$R', s_R),
  ('$D', s_D),
  ('$f_hz', s_f_hz)
]
calc.replace_strings_1("boost_ccm_11_orig.in", "boost_ccm_11.in", l)
print('boost_ccm_11.in is ready for execution')

boost_ccm_11.in is ready for execution
Execute the following cell to run GSEIM on boost_ccm_10.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("boost_ccm_11.in")
os.system('run_gseim boost_ccm_11.in')

get_lib_elements: filename gseim_aux/xbe.aux
get_lib_elements: filename gseim_aux/ebe.aux
Circuit: filename = boost_ccm_11.in
main: i_solve = 0
main: calling solve_trns
mat_ssw_1_ex: n_statevar: 3
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=0, rhs_ssw_norm=1.1347e+01
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=1, rhs_ssw_norm=2.2011e+01
Transient simulation starts...
i=0
i=1000
solve_ssw_ex: ssw_iter_newton=2, rhs_ssw_norm=2.2506e-12
solve_ssw_ex: calling solve_ssw_1_ex for one more trns step
Transient simulation starts...
i=0
i=1000
solve_ssw_1_ex over (after trns step for output)
solve_ssw_ex ends, slv.ssw_iter_newton=2
GSEIM: Program completed.
Out[4]:
0

The circuit file (boost_ccm_11.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on boost_ccm_11.in) creates a data file boost_ccm_11.dat in the same directory. We can now use the python code below to view the inductor current as a function of time.

In [5]:
import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

slv = calc.slv("boost_ccm_11.in")

i_slv = 0
i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u = np.loadtxt(filename)
t = u[:, 0]

col_IL = slv.get_index(i_slv,i_out,"IL")
col_IS = slv.get_index(i_slv,i_out,"IS")
col_ID = slv.get_index(i_slv,i_out,"ID")
col_IC = slv.get_index(i_slv,i_out,"IC")
col_IR = slv.get_index(i_slv,i_out,"IR")
col_v_out = slv.get_index(i_slv,i_out,"v_out")
col_clock = slv.get_index(i_slv,i_out,"clock")

# since we have stored two cycles, we need to divide the last time point
# by 2 to get the period:

T = t[-1]/2

l_IL = calc.avg_rms_2(t, u[:,col_IL], 0.0, 2.0*T, 1.0e-3*T)
l_IS = calc.avg_rms_2(t, u[:,col_IS], 0.0, 2.0*T, 1.0e-3*T)
l_ID = calc.avg_rms_2(t, u[:,col_ID], 0.0, 2.0*T, 1.0e-3*T)
l_IC = calc.avg_rms_2(t, u[:,col_IC], 0.0, 2.0*T, 1.0e-3*T)
l_IR = calc.avg_rms_2(t, u[:,col_IR], 0.0, 2.0*T, 1.0e-3*T)
l_v_out = calc.avg_rms_2(t, u[:,col_v_out], 0.0, 2.0*T, 1.0e-3*T)

t_IL = np.array(l_IL[0])
t_IS = np.array(l_IS[0])
t_ID = np.array(l_ID[0])
t_IC = np.array(l_IC[0])
t_IR = np.array(l_IR[0])
t_v_out = np.array(l_v_out[0])

print('average output voltage:'  , "%11.4E"%l_v_out[1][0])
print('average switch current:'  , "%11.4E"%l_IS[1][0])
print('average diode current:'   , "%11.4E"%l_ID[1][0])
print('average load current:'    , "%11.4E"%l_IR[1][0])
print('average inductor current:', "%11.4E"%l_IL[1][0])
print('rms inductor current:'    , "%11.4E"%l_IL[2][0])
print('rms capacitor current:'   , "%11.4E"%l_IC[2][0])

l1 = calc.min_max_1(t, u[:,col_IL], 0.0, 2.0*T)
IL_ptop = l1[1] - l1[0]
print('IL_ptop:', "%11.4E"%IL_ptop)

print('IL(p-to-p)/IL(avg):', "%11.4E"%(IL_ptop/l_IL[1][0]))

fig, ax = plt.subplots(7, sharex=False)
plt.subplots_adjust(wspace=0, hspace=0.0)

set_size(6.5, 10, ax[0])

for i in range(7):
    ax[i].set_xlim(left=0.0, right=2.0*T*1e6)
    ax[i].grid(color='#CCCCCC', linestyle='solid', linewidth=0.5)

for i in range(6):
    ax[i].tick_params(labelbottom=False)

ax[0].set_ylabel(r'clock', fontsize=12)
ax[1].set_ylabel(r'$i_L$', fontsize=12)
ax[2].set_ylabel(r'$i_C$', fontsize=12)
ax[3].set_ylabel(r'$i_D$', fontsize=12)
ax[4].set_ylabel(r'$i_S$', fontsize=12)
ax[5].set_ylabel(r'$i_R$', fontsize=12)
ax[6].set_ylabel(r'$v_o$', fontsize=12)

ax[0].set_ylim(bottom=-0.2, top=1.2)
ax[0].set_yticks([0.0, 1.0])

color1 = "blue"
color2 = "tomato"
color3 = "dodgerblue"
color4 = "olive"
color5 = "green"
color6 = "red"
color7 = "darkcyan"

ax[0].plot(t*1e6, u[:,col_clock], color=color1, linewidth=1.0, label="clock")

ax[1].plot(t*1e6, u[:,col_IL], color=color2, linewidth=1.0, label="$i_L$")
ax[1].plot(t_IL*1e6, l_IL[1] , color=color2, linewidth=1.0, label="$i_L^{avg}$", linestyle='--', dashes=(5,3))

ax[2].plot(t*1e6, u[:,col_IC], color=color3, linewidth=1.0, label="$i_C$")
ax[2].plot(t_IC*1e6, l_IC[1] , color=color3, linewidth=1.0, label="$i_C^{avg}$", linestyle='--', dashes=(5,3))

ax[3].plot(t*1e6, u[:,col_ID], color=color4, linewidth=1.0, label="$i_D$")
ax[3].plot(t_ID*1e6, l_ID[1] , color=color4, linewidth=1.0, label="$i_D^{avg}$", linestyle='--', dashes=(5,3))

ax[4].plot(t*1e6, u[:,col_IS], color=color5, linewidth=1.0, label="$i_S$")
ax[4].plot(t_IS*1e6, l_IS[1] , color=color5, linewidth=1.0, label="$i_S^{avg}$", linestyle='--', dashes=(5,3))

ax[5].plot(t*1e6, u[:,col_IR], color=color6, linewidth=1.0, label="$i_R$")
ax[5].plot(t_IR*1e6, l_IR[1] , color=color6, linewidth=1.0, label="$i_R^{avg}$", linestyle='--', dashes=(5,3))

ax[6].plot(t*1e6, u[:,col_v_out]  , color=color7, linewidth=1.0, label="$v_o$")
ax[6].plot(t_v_out*1e6, l_v_out[1], color=color7, linewidth=1.0, label="$v_o^{avg}$", linestyle='--', dashes=(5,3))

ax[6].set_xlabel('time ($\mu$sec)', fontsize=12)

for i in range(1,7):
    ax[i].legend(loc = 'lower right',frameon = True, fontsize = 10, title = None,
      markerfirst = True, markerscale = 1.0, labelspacing = 0.5, columnspacing = 2.0,
      prop = {'size' : 12})

#plt.tight_layout()
plt.show()

filename: boost_ccm_11.dat
average output voltage:  3.1970E+01
average switch current:  6.4101E+00
average diode current:  2.1384E+00
average load current:  2.1313E+00
average inductor current:  8.5486E+00
rms inductor current:  8.8184E+00
rms capacitor current:  3.8588E+00
IL_ptop:  7.4995E+00
IL(p-to-p)/IL(avg):  8.7728E-01
No description has been provided for this image

This notebook was contributed by Prof. Nakul Narayanan K, Govt. Engineering College, Thrissur. He may be contacted at nakul@gectcr.ac.in.

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