#!/usr/bin/python #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> # # author: Luciano Augusto Kruk # website: www.kruk.eng.br # # description: Calculates the values for the resistors # given R2. The circuit is available at # Lipo-protection-LT1389_0699_Mag.pdf # # +-----------------------------------------------------------------------------------------------------------------+ # | | # | PMOS | # | ........................................................................................ ........o | # | c c o | ^ | o | # | c c MMM ccccocccc o | # | c c R1 MMM c o o | # | c MMM MMM c c. o .o | # | Vi o R3 MMM o o cc. o o | # | ------------- MMM Vb oocc...ccco + cc. c o | # | ------ MMM c o .cc Va MMMMMM c o | # | ------------- c c o .OcccccoMoccMMMMMMccccc. cMc | # | ------ cOc.ccccccccccc.....oc.. .....o - .cc. O MMMMMM .MO. | # | o o o o .c. o R6 oWMc Rc | # | c o vvv o .c. o oOO. | # | c MMM Vd M cc o o | # | o R4 MMM MMM c o o | # | o MMM o MMMMMM cO c | # | o MMM o...........MMMMMMo........c c | # | o c R2 MMM MMMMMM cc | # | .o c MMM R5 .c | # | .o o o .o | # | ..............................................l....................................................... | # | | # | | # +-----------------------------------------------------------------------------------------------------------------+ # #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> from scipy.optimize import fsolve import sys import numpy as np import matplotlib; import matplotlib.pyplot as plt; import math #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> def fn_paral(a,b): return (1./((1./a) + (1./b))) #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> # Voltage at Vb when Va=LOW(vt) def fn_vb1(R1,R2,R5,vi,vd,vt): k = (R1/R2) * (1. + (R2/R5)) vb1 = (vi+(k*vd)+(R1*vt/R5))/(1.+k) return vb1 # Voltage at Vb when Va=HIGH(vT) def fn_vb2(R1,R2,R5,vi,vd,vT): alfa = (1.+(R1/R2))/R1 beta = (R2+(R2*R5/R1))/(1.+(alfa*R5)) vb2 = (vd*(1.+(beta*(alfa-(1./R2)))-(R2/R1))) + (beta*vi/R2) + (vT*((R2/R1)-alfa)) return vb2 def equations(var, PARAM): # when the discharge reaches vi_low, va-->HIGH [OFF] # when the charge reaches vi_high, va-->LOW [ON] # vt = residual level from rail-to-rail at GND # vT = residual level from rail-to-rail at V_bat [R1,R5,k] = var [R2,imin,vi_low,vi_high,vd,vt,vT] = PARAM eq = ( fn_vb1(R1,R2,R5,vi_low,vd,vt) - (vi_low*k), fn_vb2(R1,R2,R5,vi_high,vd,vT) - (vi_high*k), R1 + fn_paral(R2,R5) - ((vi_low-vd)/imin) ) return eq #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> def fn_save_log(data, x_rec): nb = len(x_rec) x_rec = np.asarray(x_rec) x_rec = x_rec.reshape((1,nb)) if (len(data) == 0): data = x_rec.copy(); else: data = np.vstack((data, x_rec)) return data #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> def fn_main(): R2_log10 = np.log10(np.linspace(1,300e3,1000)) data = []; vd = 1.25 # [V] vi_low = 6.6 # [V] vi_high = 6.9 # [V] vt = 0.1 # [V] LOW to rail vT = 0.1 # [V] rail to HIGH imin = 30e-6; # [A] #%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%# # put here the adopted solution: if True: R2 = 15e3 PARAM = [R2,imin,vi_low,vi_high,vd,vt,vT] (res,infodict,ier,msg) = fsolve(equations, (1e5,1e5,1), args=PARAM, full_output=True, maxfev=int(1e6), xtol=1e-13) [R1,R5,k] = res print ier print msg print res print "############################################################" if True: # replacement for commercial values: R1 = 163.5e3 R2 = 15e3 R5 = 2.2e6 res = (R1,R5) PARAM[0] = R2 if (ier == 1): print "for R2 = %1.3f [kOhm]," % (R2/1e3) print "R1 = %1.3f [kOhm]; R5 = %1.3f [MOhm]" % (R1/1000., R5/1e6) print "vb1 = %1.2f [V]" % (fn_vb1(R1,R2,R5,vi_low,vd,vt)) print "vb2 = %1.2f [V]" % (fn_vb2(R1,R2,R5,vi_high,vd,vT)) # relation between R3 and R4: aux = fn_vb1(R1,R2,R5,vi_low,vd,vt); aux = (vi_low - aux) / aux print "R3 = %1.2e * R4" % aux print "R4 = %1.2e * R3" % (1./aux) else: print "msg = %s" % msg print "############################################################" #sys.exit(0); #%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%#%# # calculations: for r2_log10 in R2_log10: R2 = 10.**r2_log10 PARAM = [R2,imin,vi_low,vi_high,vd,vt,vT] (res,infodict,ier,msg) = fsolve(equations, (1e5,1e5,1), args=PARAM, full_output=True, maxfev=int(1e6), xtol=1e-13) [R1,R5,k] = res if (ier == 1) and (R1>0) and (R5>0): print "R1 = %1.3f [kOhm]; R2 = %1.3f [kOhm]; R5 = %1.3f [MOhm]" % (R1/1000., R2/1e3, R5/1e6) x_rec = (R1, R2, R5, fn_vb1(R1,R2,R5,vi_low,vd,vt), fn_vb2(R1,R2,R5,vi_high,vd,vT), 0,0) data = fn_save_log(data, x_rec) # pictures: fig = 0; #---- new figure: fig = fig + 1; pfig = plt.figure(fig); plt.clf(); pfig.canvas.set_window_title("vb x R") for i in range(3): plt.subplot(1,3,i+1) resistor = "R%d" % ([1,2,5][i]) plt.plot(data[:,i]/1e3, data[:,3], data[:,i]/1e3, data[:,4], hold=False); plt.legend(('vb1', 'vb2')) plt.xlabel("%s [kOhm]" % resistor) plt.grid(); #-- new figure: fig = fig + 1; pfig = plt.figure(fig); plt.clf(); pfig.canvas.set_window_title("(R1,R5) x R2") plt.subplot(2,1,1) plt.plot(data[:,1]/1e3, data[:,0]/1e3, linestyle='None', marker='x', markersize=5, hold=False); plt.ylabel('R1 [kOhm]'); plt.xlabel("R2 [kOhm]") plt.grid(); plt.subplot(2,1,2) plt.plot(data[:,1]/1e3, data[:,2]/1e6, linestyle='None', marker='x', markersize=5, hold=False) plt.ylabel('R5 [MOhm]'); plt.xlabel("R2 [kOhm]") plt.grid(); return data #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>> if (__name__ == "__main__"): data = fn_main() plt.show(block=False); #>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>--<<..>>