U2 D2 , . 1.6.
U2
q1 = U1/U,
U1 ; U .
Kc = q1/q2,
q2 .
, . . D2. . , :
u(t) ;
ω = 2π/T.
, :
A sin ωt + B cos ωt = M sin (ωt + ψ);
;
ψ = arctg (A/B).
u(t) :
u(t) = B0 + M1 sin(ωt + ψ) + + Mn sin(nωt + ψn) +
M1, M2,... Mn . ψn n- t =0. , .
f(t) = f(-t).
. An = 0, ψn = π/2. :
u1(t) = B0 + B1 cos ωt + B2 cos 2ωt +...+ + Bn cos nωt,
ω = 2πf, f .
f(-t) = -f(t).
:
u2(t) = A1 sin ωt + A2 sin 2ωt +... An sin nωt.
D2 :
- .
- k .
- An
An - n- ;
m , 1, 2, 3,..., k;
am m- ;
θm m- 2πm/k [].
- Bn
, . 2.20. , .
. 2.20.
. 2.3.
2.3
m | am | θm | cos θm | am cos θm | sin θm | am sin θm |
-1 -1 -1 -1 -1 | 0,809 0,309 -0,309 -0,809 -1,0 -0809 -0,309 0,309 0,809 1,0 | 0,809 0,309 0,309 0,809 1,0 0,809 0,309 0,309 0,809 1,0 ∑=6,472 | 0,588 0,951 0,951 0,588 -0,588 -0,951 -0,951 -0,588 | 0,588 0,951 -0,951 -0,588 0,588 0,951 -0,951 -0,588 ∑=0 |
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B1 = 6,472∙2/10 = 1,294.
. 2.4.
2.4
m | am | θm | 2∙θm | cos 2θm | am cos 2θm | sin 2θm | am sin θm |
-1 -1 -1 | 0,309 -0,809 -0,809 0,309 1,0 | 0,309 -0,809 0,809 0,309 -1,0 | 0,951 0,588 -0,588 -0,951 | 0,951 0,588 0,588 0,951 |
. 2.4
m | am | θm | 2∙θm | cos 2θm | am cos 2θm | sin 2θm | sin 2θm |
-1 -1 | 0,309 -0,809 -0,809 0,309 1,0 | -0,309 0,809 -0,809 0,309 1,0 ∑ = 0 | 0,951 0,588 -0,588 -0,951 | -0,951 -0,588 -0,588 -0,951 ∑ = 0 |
B2 = 0.
, . 2.21.
. 2.21.
U = (A21∙τ + 2∙A22∙τ) / T.
, . 1.6, q1 = 1,57, q2 = 0,01. f1 = 5000 . K = 2.
.
R0 = 24 ;
R = R0 / K = 12 ;
K = 20∙lg 2 = 6 ;
Kc = q1 / q2 = 1,57 / 0,01 = 157;
K 20∙lg 157 = 43,9;
(. 2.22)
K = 6 K1 = K - K = 6 43 = -37,9 .
, (K1, f1), 20 / K = 6 . f = 30 . . 2.23.
. 2.22.
. 2.23.
f R
C = 1 / 2∙π∙f∙R0 = 1,3∙10-9
(. 1.2):
u21=16; u22=8; u23=2; f1=110; f2=11;
n=2*f1/f2;
d=360/n;
gm=d:d:360;
for m=1:n
am(m)=-u23;
u23=-u23;
end
am1=am;
am1(1)=u22; am1(2)=u21;
am2=am1;
rm=gm.*pi/180;
cm=cos(rm);
sm=sin(rm);
acm=am2.*cm;
asm=am2.*sm;
cms=sum(acm.');
sms=sum(asm.');
b1=2*cms/n;
a1=2*sms/n;
ab2=b1^2+a1^2;
um1=sqrt(ab2)% 1-
ss=sum(am2.');
sss=ss/n %
Kp=um1/sss %
F1=f2 % 1-
Kc=Kp/0.01 %
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Kcdb=20*log10(Kc)
K=0.9/sss %
Kdb=20*log10(K) %
Kdb1=Kdb-Kcdb
% .2
x=logspace(-1,3);%
a=abs(x)-abs(x);
aa=a+20;%
bb=a-60;%
semilogx(x,aa,x,bb,x,Kdb,'.r',x,Kdb1,'.r')
grid
xlabel('Frequency, Hz')
ylabel('Db')
fk=F1/1000;%
Kdb2=Kdb1+60;
hold on
line([fk F1],[Kdb2 Kdb1],'color','red')% -20 dB/dec
line([1 100],[0 -40],'color','blue')% .
hold off
figure
stem(am2,'k'),grid
um1 = 2.3713 sss = 1.2000 Kp = 1.9761
F1 = 11
Kc = 197.6065 Kcdb = 45.9160 K = 0.7500
Kdb = 2.4988 Kdb1 = 48.4148
. 2.24 , . 2.25 - () ( 1).
. 2.24.
. 2.25. ( 1)
R, C , . 2.26.
. 2.26.
(. 2.27) , 16.51 42.36 . f2 Kdb1 = 42.3927 . Kdb .
. 2.27.
U4 D2 . U4 .
. 2.32.
U4 (. 2.33) , 55,604 . q2 = 55,604/1190 = 0,0467 (4,67%).
. 2.33. U2i D2
U4
.
. 1.7. . 1.8, 1.9 U5 =10 , . 1.10 U5 = 2 . R3, R4, R5 R6 :
Ek , Gk .
R6 Ua:
%
% R3=0 - 200
E1=12; E2=-12;
Ua=0.02;%
R5=1e3; R4=0.9e3;
R3=0;
% R6
R34=R4+R3;
g34=1/R34;
g5=1/R5;
g6=((E1*g34+E2*g5)/Ua)-g34-g5;
R6=1/g6
% -Ua
R3=200;
R34=R4+R3;
g34=1/R34;
Ua=(E1*g34+E2*g5)/(g34+g5+g6)
: R6 = 15.4905, Ua = 0.0164.
Ua , R6 20 .
Ua = f(R6):
R6=15.49;%
E1=12; E2=-12;
R5=1e3; R4=0.9e3;
R3=1:200;% R3
%
R34=R4+R3;
g34=1./R34;
g5=1/R5; g6=1/R6;
Ua=(E1.*g34+E2.*g5)./(g34+g5+g6);
R6=20;%
g6=1/R6;
Ua1=(E1.*g34+E2.*g5)./(g34+g5+g6);
plot(R3,Ua,':K',R3,Ua1,'K')
grid
xlabel('R6=15.49 ; R6=20 - ')
ylabel('Ua')
: R6 = 15.4905, Ua = 0.0164.
. 2.34 Ua = f(R6) R6.
. 2.34. Ua = f(R6)
Ua. , . 2.35 R3 = 0 ( ). Ua , U5 = 3Ua.
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. 2.35. R3 = 0
. 2.36 , R3 = 200 .
. 2.36. R3 = 200
Ua .