用S参数设计LNA的笔记

clear all;

clc;



syms rf rb re rbe ro rc gm I1 I2 

R0=50

M=[1,0;0,1]

VA=50

VT=26e-3

IC=10e-3

beta0=150

gm=IC/VT

ro=VA/IC

rbe=beta0/gm

rc=330



Y11=1/rb+1/rbe+1/rf

Y12=-1/rf

Y13=-1/rbe



Y21=-1/rf+gm

Y22=1/rf+1/ro+1/rc

Y23=-1/ro-gm



Y31=-1/rbe-gm

Y32=-1/ro

Y33=1/rbe+1/re+1/ro+gm

Y=[Y11,Y12,Y13;Y21,Y22,Y23;Y31,Y32,Y33]

I=[I1;I2;0]

U=inv(Y)*I

Z=[diff(U(1),I1),diff(U(1),I2);diff(U(2),I1),diff(U(2),I2)]

S=inv(Z+R0*M)*(Z-R0*M);

import math

import itertools



def generate_E_set(a='E6',minmax=[0,1]):

    E24_T=[1.0,1.1,1.2,1.3,1.5,1.6,1.8,2,2.2,2.4,2.7,3,3.3,3.6,3.9,4.3,4.7,5.1,5.6,6.2,6.8,7.5,8.2,9.1]

    E6_T=[1.0,1.5,2.2,3.3,4.7,6.8]

    E12_T=[1.0,1.5,2.2,3.3,4.7,6.8]

    _E_ALL=[]

    if(a=='E6'):

        _E_T=E6_T

    elif(a=='E12'):

        _E_T=E12_T

    elif(a=='E24'):

        _E_T=E24_T

    else:

        return []

    for i in range(minmax[0],minmax[1]):

        for v in _E_T:

            _E_ALL.append(v*math.pow(10,i))

    return _E_ALL



def get_s11(rf,re,rb):

    return -(1888475000.0*re + 103350000.0*rf + rb*(1888475.0*re - 1802000.0*rf - 793157.0*re*rf + 1893350000.0) + 39660475.0*re*rf + 4875000000.0)/(1888475000.0*re + 103350000.0*rf + 39660475.0*re*rf + rb*(77427475.0*re + 2332000.0*rf + 793262.0*re*rf + 2088350000.0) + 4875000000.0)





def get_s22(rf,re,rb):

    return -(1888475000.0*re - 91650000.0*rf + rb*(1888475.0*re - 2068000.0*rf - 717618.0*re*rf + 1893350000.0) - 35878525.0*re*rf + 4875000000.0)/(1888475000.0*re + 103350000.0*rf + 39660475.0*re*rf + rb*(77427475.0*re + 2332000.0*rf + 793262.0*re*rf + 2088350000.0) + 4875000000.0)



def get_s21(rf,re,rb):

    return (100.0*rb*(755390.0*re - 750000.0*rf + re*rf + 1950000.0))/(2088350000.0*rb + 1888475000.0*re + 103350000.0*rf + 77427475.0*rb*re + 2332000.0*rb*rf + 39660475.0*re*rf + 793262.0*rb*re*rf + 4875000000.0)



def show(comb):

    rf=combination[0]

    re=combination[1]

    rb=combination[2]

    print("rf=%.0f,re=%.1f,rb=%.0f,s11=%.3f,s22=%.3f,s21=%.3f" % (rf,re,rf,get_s11(rf,re,rb),get_s22(rf,re,rb),get_s21(rf,re,rb)))



# 子收敛函数

def good_enough_approach(x,ref):

    return ((abs(x-ref)/ref)<ERROR_MAX)



def good_enough_less(x,ref):

    return abs(x)<ref



def good_enough_great(x,ref):

    return abs(x)>ref



# 总收敛函数

def set_is_good_enough(comb):

    rf=combination[0]

    re=combination[1]

    rb=combination[2]

    s11=get_s11(rf,re,rb)

    s21=get_s21(rf,re,rb)

    s22=get_s22(rf,re,rb)

    return good_enough_less(s11,0.05) and good_enough_less(s22,0.05) and good_enough_great(s21,4.0)



E_RF=generate_E_set('E6',[2,3])

E_RE=generate_E_set('E6',[0,1])

E_RB=generate_E_set('E6',[2,4])

# 穷举

for combination in itertools.product(E_RF,E_RE,E_RB):

    if(set_is_good_enough(combination)):

        show(combination)

rf=330,re=4.7,rb=330,s11=-0.041,s22=-0.008,s21=-5.305

rf=330,re=4.7,rb=330,s11=-0.033,s22=-0.013,s21=-5.348

rf=330,re=4.7,rb=330,s11=-0.028,s22=-0.016,s21=-5.375

rf=330,re=4.7,rb=330,s11=-0.025,s22=-0.019,s21=-5.395

rf=330,re=4.7,rb=330,s11=-0.022,s22=-0.020,s21=-5.407

rf=330,re=4.7,rb=330,s11=-0.021,s22=-0.022,s21=-5.416

rf=470,re=3.3,rb=470,s11=0.026,s22=0.048,s21=-7.366

rf=470,re=3.3,rb=470,s11=0.030,s22=0.045,s21=-7.394

rf=470,re=3.3,rb=470,s11=0.032,s22=0.043,s21=-7.412

rf=470,re=3.3,rb=470,s11=0.034,s22=0.042,s21=-7.424

rf=680,re=1.0,rb=680,s11=-0.046,s22=0.012,s21=-11.634

rf=680,re=1.0,rb=680,s11=-0.041,s22=0.008,s21=-11.694

rf=680,re=1.0,rb=680,s11=-0.037,s22=0.005,s21=-11.736

rf=680,re=1.0,rb=680,s11=-0.035,s22=0.004,s21=-11.762

rf=680,re=1.0,rb=680,s11=-0.034,s22=0.002,s21=-11.780