Прикладные математические методы в статистической радиотехнике. Федосов В.П. - 23 стр.

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u
1
(t)=-U
m
(t)sin[Z
0
t-M(t)]+Q(t). (6.3)
ɂɡ ɮɨɪɦɭɥɵ (6.3) ɜɢɞɧɨ, ɱɬɨ ɟɫɥɢ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɮɭɧɤɰɢɟɣ Q(t), ɬɨ ɫɨ-
ɩɪɹɠɟɧɧɵɣ ɩɨ Ƚɢɥɶɛɟɪɬɭ ɍɋɉ ɢɦɟɟɬ ɬɚɤɭɸ ɠɟ ɨɝɢɛɚɸɳɭɸ, ɱɬɨ ɢ ɢɫɯɨɞɧɵɣ
ɍɋɉ.
ɂɡ ɬɚɛɥɢɰ ɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ ɢɡɜɟɫɬɧɨ:

¯
®
f
f
³
1;+2k=nɪȹ•sin
2k;=nɪȹ•cos
!2
cos
1
0
1
0
1
0
0
tj
tj
n
xdxtx
n
n
n
n
Z
Z
Z
Z
S

¯
®
f
f
³
1,+2k=nɪȹ•cos
2k;=nɪȹ•sin
!2
sin
1
0
1
0
1
0
0
tj
tj
n
xdxtx
n
n
n
n
Z
Z
Z
Z
S
k=0,1,2,...
ɋ ɭɱɟɬɨɦ ɷɬɢɯ ɜɵɪɚɠɟɧɢɣ ɮɨɪɦɭɥɭ ɞɥɹ Q(t) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
0,5Q(t)=1/Z
0
(U
c
'(t)cosZ
0
t -U
s
'(t)sinZ
0
t)-
-1/Z
0
2
(U
c
''(t)sinZ
0
t -U
s
''(t)cosZ
0
t)+...
ɋɱɢɬɚɟɦ, ɱɬɨ ɩɨɥɨɫɚ ɨɝɢɛɚɸɳɟɣ ɪɚɜɧɚ 'Z, ɩɨɷɬɨɦɭ ɜɬɨɪɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɩɨ
ɫɜɨɢɦ ɡɧɚɱɟɧɢɹɦ ɧɟ ɩɪɟɜɨɫɯɨɞɹɬ 'ZU
m
(t). ɉɨɷɬɨɦɭ ɦɨɠɧɨ ɩɨɥɚɝɚɬɶ, ɱɬɨ Q(t) = '
ZU
m
(t)/ Z
0
.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ:
u
1
(t)= -U
m
(t)sin[Z
0
t-M(t)]+'ZU
m
(t)/Z
0
.
Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɍɋɉ ɮɭɧɤɰɢɢ u(t) ɢ u
1
(t) ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɭɸ ɨɝɢ-
ɛɚɸɳɭɸ ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ, ɡɚɜɢɫɹɳɟɣ ɨɬ ɨɬɧɨɲɟɧɢɹ ɲɢɪɢɧɵ ɫɩɟɤɬɪɚ ɤ ɟɝɨ ɫɪɟɞ-
ɧɟɣ ɱɚɫɬɨɬɟ. Ⱦɥɹ ɭɡɤɨɩɨɥɨɫɧɵɯ ɫɥɭɱɚɣɧɵɯ ɩɪɨɰɟɫɫɨɜ ɨɛɹɡɚɬɟɥɶɧɵɦ ɹɜɥɹɟɬɫɹ
ɜɵɪɚɠɟɧɢɟ 'Z/Z
0
<<1, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɝɢɛɚɸɳɚɹ ɭɞɨɜɥɟɬɜɨɪɹɟɬ ɬɪɟɛɨɜɚɧɢɹɦ,
ɤɨɬɨɪɵɟ ɤ ɧɟɣ ɩɪɟɞɴɹɜɥɹɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɩɪɟɞɟɥɟɧɢɟɦ ɍɋɉ, ɬ.ɟ. ɹɜɥɹɟɬɫɹ
ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɬɨɱɤɚɯ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɦɚɤɫɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦ ɍɋɉ ɢ ɢɦɟɟɬ
ɨɛɳɢɟ ɡɧɚɱɟɧɢɹ ɫ ɧɢɦ ɜ ɬɨɱɤɚɯ ɤɚɫɚɧɢɹ.
Ɏɚɡɚ M(t) ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡɜɟɫɬɧɵɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ ɞɥɹ ɩɪɟɞ-
ɫɬɚɜɥɟɧɢɹ ɤɨɦɩɥɟɤɫɧɨɝɨ ɱɢɫɥɚ ɜ ɩɨɤɚɡɚɬɟɥɶɧɨɣ ɮɨɪɦɟ.
Ƚɪɚɮɢɱɟɫɤɢ ɍɋɉ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɜɟɤɬɨɪɚ, ɜɪɚɳɚɸɳɟɝɨɫɹ ɫ ɭɝ-
ɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z
0
, ɞɥɢɧɚ ɜɟɤɬɨɪɚ ɦɟɞɥɟɧɧɨ ɦɟɧɹɟɬɫɹ ɜɨ ɜɪɟɦɟɧɢ ɬɚɤ ɠɟ, ɤɚɤ ɢ
ɮɚɡɨɜɵɣ ɭɝɨɥ M(t). ɂɫɯɨɞɧɵɣ ɍɋɉ ɹɜɥɹɟɬɫɹ ɩɪɨɟɤɰɢɟɣ ɜɟɤɬɨɪɚ ɧɚ ɝɨɪɢɡɨɧɬɚɥɶ-
ɧɭɸ ɨɫɶ. ȿɫɥɢ ɜɫɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɡɚɫɬɚɜɢɬɶ ɜɪɚɳɚɬɶɫɹ ɫ ɬɨɣ ɠɟ ɭɝɥɨɜɨɣ
ɫɤɨɪɨɫɬɶɸ, ɧɨ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɬɨ ɬɚ ɠɟ ɩɪɨɟɤɰɢɹ ɛɭɞɟɬ ɨɝɢ-
ɛɚɸɳɟɣ U
c
(t).
ȿɫɥɢ ɢɫɯɨɞɧɵɣ ɍɋɉ ɹɜɥɹɟɬɫɹ ɧɨɪɦɚɥɶɧɵɦ, ɬɨ U
c
(t) ɢ U
s
(t) ɬɚɤɠɟ ɹɜɥɹɸɬɫɹ
ɧɨɪɦɚɥɶɧɵɦɢ ɫɥɭɱɚɣɧɵɦɢ ɩɪɨɰɟɫɫɚɦɢ. ȿɫɥɢ ɍɋɉ u(t) ɧɨɪɦɚɥɟɧ, ɫɬɚɰɢɨɧɚɪɟɧ,
ɢɦɟɟɬ ɧɭɥɟɜɨɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɢ ɮɭɧɤɰɢɸ ɤɨɪɪɟɥɹɰɢɢ K(W)=V
2
U(W) cosZ
0
W ɬɨ
U
c
(t) ɢ U
s
(t) ɬɚɤɠɟ ɢɦɟɸɬ ɧɭɥɟɜɵɟ ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ɢ ɤɨɪɪɟɥɹɰɢɨɧɧɭɸ ɮɭɧɤ-
ɰɢɸ K(W). ȼɬɨɠɟɜɪɟɦɹU
c
(t) ɢ U
s
(t) ɜɡɚɢɦɧɨ ɧɟɤɨɪɪɟɥɢɪɨɜɚɧɵ, ɚɬɚɤɤɚɤɨɧɢ
ɧɨɪɦɚɥɶɧɵ, ɬɨ ɢ ɜɡɚɢɦɧɨ ɧɟɡɚɜɢɫɢɦɵ. ɋɨɦɧɨɠɢɬɟɥɶ U(W) ɹɜɥɹɟɬɫɹ ɨɝɢɛɚɸɳɟɣ
ɤɨɪɪɟɥɹɰɢɨɧɧɨɣ ɮɭɧɤɰɢɢ R(W).

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