Воробьев М.С. Устройства генерирования радиосигналов

Подождите немного. Документ загружается.

( )

[ ]

rSI

EuSi

ɉɉ

′

≥

−−

′

−= coscos

ττ

ɂɫɩɨɥɶɡɭɹ ɫɨɨɬɧɨɲɟɧɢɹ

= h

21ɗ

;

(2.5)

= h

21ɗ

ɝɪ

(2.6)

ɝɞɟ

21ɗ

— ɫɬɚɬɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɬɨɤɭ ɜ ɫɯɟɦɟ ɫ Ɉɗ;

ɝɪ

— ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ, ɬ.ɟ. ɱɚɫɬɨɬɚ, ɧɚ ɤɨɬɨɪɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ

ɬɨɤɭ ɜ ɫɯɟɦɟ ɫ Ɉɗ ɪɚɜɟɧ ɟɞɢɧɢɰɟ, ɩɨɥɭɱɢɦ

i I

ɤ ɛ

− −

1 ( )

[cos( ) cos ].

τ τ Θ

Ʉɚɤ ɩɪɚɜɢɥɨ, ɩɪɢ ɪɚɫɱɟɬɟ ɌɍɆ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɜɟɥɢɱɢɧɵ 1-ɣ ɝɚɪɦɨɧɢɤɢ

ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ ɢ ɟɝɨ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ. Ɂɚɩɢɲɟɦ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ

ɧɢɯ.

ɤ ɛ

1 1

−

( )

( ) ;

ɤ ɛ

0 1

+ ( )

( ).

γ Θ

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, 1-ɹ ɝɚɪɦɨɧɢɤɚ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ ɨɬɫɬɚɺɬ ɩɨ ɮɚɡɟ ɨɬ ɜɯɨɞɧɨɝɨ

ɬɨɤɚ ɧɚ ɜɟɥɢɱɢɧɭ

. ȼɟɥɢɱɢɧɵ ɬɨɤɨɜ

ɤ1

ɤ0

ɩɨɥɧɨɫɬɶɸ ɨɩɪɟɞɟɥɹɸɬɫɹ

ɚɦɩɥɢɬɭɞɨɣ ɛɚɡɨɜɨɝɨ ɬɨɤɚ

ɛ1

ɢ ɭɝɥɨɦ ɨɬɫɟɱɤɢ

2. ȼɵɫɨɤɨɱɚɫɬɨɬɧɵɣ ɞɢɚɩɚɡɨɧ, ɜ ɤɨɬɨɪɨɦ

ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɟɞɢɧɢɰɟɣ ɜ ɤɜɚɞɪɚɬɧɨɦ ɤɨɪɧɟ ɜ (2.8), (2.9) ɢ

ɭɱɢɬɵɜɚɹ, ɱɬɨ

≅ π

⁄ 2,

ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ

( )

;

ɝɪ

eĬj

−

−= II

(2.10)

( )

ĬII

ɝɪ

ɛɤ

(2.11)

(2.7)

(2.8)

(2.9)

ȼɵɪɚɠɟɧɢɹ (2.10), (2.11) ɹɜɥɹɸɬɫɹ ɬɨɱɧɵɦɢ ɪɟɲɟɧɢɹɦɢ ɫɢɫɬɟɦɵ (2.3) ɞɥɹ

ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɣ ɨɛɥɚɫɬɢ ɩɪɢ

→ ∞.

ɍɜɟɥɢɱɟɧɢɟ

ɨɛɴɹɫɧɹɟɬɫɹ

ɭɦɟɧɶɲɟɧɢɟɦ ɪɟɤɨɦɛɢɧɚɰɢɣ ɧɟɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ ɜ ɛɚɡɟ ɡɚ ɫɱɟɬ

ɭɦɟɧɶɲɟɧɢɹ ɜɪɟɦɟɧɢ ɨɬɤɪɵɬɨɝɨ ɫɨɫɬɨɹɧɢɹ ɷɦɢɬɬɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ. ȼɪɟɦɹ ɩɪɨ-

ɥɟɬɚ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɩɨ ɮɨɪɦɭɥɟ

≈

0,4/

ɝɪ

2.3. Ɂɚɞɚɧɢɟ ɭɝɥɚ ɨɬɫɟɱɤɢ

ɍɝɨɥ ɨɬɫɟɱɤɢ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɪɚɛɨɬɵ

ɤɚɫɤɚɞɚ. Ʉɚɤɢɦ ɨɛɪɚɡɨɦ ɟɝɨ ɦɨɠɧɨ ɡɚɞɚɜɚɬɶ? Ɍɚɤ ɤɚɤ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ ɜ ɪɟ-

ɠɢɦɟ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɡɚɩɢɪɚɧɢɹ ɷɦɢɬɬɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɧɚɛɥɸɞɚɟɬɫɹ ɭɜɟ-

ɥɢɱɟɧɢɟ

, ɬɨ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɛɚɡɨɜɨɝɨ

ɬɨɤɚ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɤ ɦɚɥɨɦɭ ɩɚɞɟɧɢɸ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɧɚɩ-

ɪɹɠɟɧɢɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɢ

. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɟɫɩɟɱɢɜɚɬɶ ɡɚɞɚɧɧɵɣ ɭɝɨɥ

ɨɬɫɟɱɤɢ

ɭɞɨɛɧɨ ɫ ɩɨɦɨɳɶɸ ɢɫɬɨɱɧɢɤɚ ɧɚɩɪɹɠɟɧɢɹ ɫɦɟɳɟɧɢɹ. ɇɚ ɪɢɫ. 2.4

ɩɨɤɚɡɚɧɚ ɜɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɷɦɢɬɬɟɪɧɨɦ ɩɟɪɟɯɨɞɟ

ɬɪɚɧɡɢɫɬɨɪɚ. ɗɬɚ ɞɢɚɝɪɚɦɦɚ ɨɬɥɢ-

ɱɚɟɬɫɹ ɨɬ ɚɧɚɥɨɝɢɱɧɨɣ ɞɢɚɝɪɚɦɦɵ ɧɚ

ɪɢɫ. 2.3 ɬɟɦ, ɱɬɨ ɡɞɟɫɶ ɬɨɱɧɟɟ

ɜɵɞɟɪɠɚɧɵ ɦɚɫɲɬɚɛɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ

ɦɟɠɞɭ ɧɚɩɪɹɠɟɧɢɹɦɢ ɜ ɨɬɤɪɵɬɨɦ ɢ

ɡɚɤɪɵɬɨɦ ɫɨɫɬɨɹɧɢɹɯ ɩɟɪɟɯɨɞɚ. Ɍɨ

ɟɫɬɶ, ɜ ɨɬɤɪɵɬɨɦ ɫɨɫɬɨɹɧɢɢ ɧɚɩɪɹ-

ɠɟɧɢɟ ɧɚ ɩɟɪɟɯɨɞɟ ɩɪɟɧɟɛɪɟɠɢɦɨ

ɦɚɥɨ ɢ ɩɪɢɦɟɪɧɨ ɪɚɜɧɨ ɧɚɩɪɹɠɟɧɢɸ

ɨɬɫɟɱɤɢ

′

. ɉɨɷɬɨɦɭ ɧɚɩɪɹɠɟɧɢɟ ɧɚ

ɩɟɪɟɯɨɞɟ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ

ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɵɯ

ɢɦɩɭɥɶɫɨɜ ɫ ɭɝɥɨɦ ɨɬɫɟɱɤɢ

π−Θ

. ɋɪɟɞɧɟɟ ɧɚɩɪɹɠɟɧɢɟ ɷɬɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ

U E E

ɫ ɫɦ

( ) ( ).=

′

− = −

γ π Θ

ɂɫɩɨɥɶɡɭɹ (2.10) ɢ ɭɱɢɬɵɜɚɹ, ɱɬɨ

(

π−Θ

) =

(

) + cos

ɩɨɥɭɱɢɦ

E E

ɫɦ

ɝ ɷ

′

− ⋅

1 0

( ) cos

( )

ɑɚɫɬɨ ɧɚ ɩɪɚɤɬɢɤɟ ɢɫɩɨɥɶɡɭɸɬ ɧɭɥɟɜɨɟ ɫɦɟɳɟɧɢɟ

ɫɦ

= 0

, ɱɬɨ ɭɞɨɛɧɟɟ ɫ

ɤɨɧɫɬɪɭɤɬɢɜɧɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ, ɟɫɥɢ ɭɝɨɥ ɨɬɫɟɱɤɢ, ɩɪɢ ɷɬɨɦ, ɧɚɯɨɞɢɬɫɹ ɜ

ɩɪɟɞɟɥɚɯ 90

... 120

π−Θ)

′

ɫɦ

ɫɪ

Ɋɢɫ. 2.4. ȼɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɧɚɩɪɹ-

ɠɟɧɢɹ ɧɚ ɷɦɢɬɬɟɪɧɨɦ ɩɟɪɟɯɨɞɟ

(2.12)

2.4. ɍɱɟɬ ɺɦɤɨɫɬɢ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɩɪɢ

ɝɚɪɦɨɧɢɱɟɫɤɨɦ ɚɧɚɥɢɡɟ ɌɍɆ

ɋɨɨɬɧɨɲɟɧɢɹ (2.8)–(2.11) ɩɨɥɭɱɟɧɵ ɛɟɡ ɭɱɟɬɚ ɜɥɢɹɧɢɹ ɺɦɤɨɫɬɢ ɤɨɥ-

ɥɟɤɬɨɪɧɨɝɨ ɩɟɪɟɯɨɞɚ, ɱɬɨ ɨɩɪɚɜɞɚɧɨ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɢɡɤɢɯ ɱɚɫɬɨɬ. ɉɪɢ

ɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ ɷɬɭ ɟɦɤɨɫɬɶ ɨɛɹɡɚɬɟɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ. Ⱦɥɹ ɷɬɨɝɨ

ɺɦɤɨɫɬɢ

ɤɚ

ɤɩ

ɡɚɦɟɧɢɦ ɨɛɳɟɣ ɟɦɤɨɫɬɶɸ

ɤɚ

ɤɩ

, ɬ.ɟ. ɩɪɟɧɟɛɪɟɠɟɦ

ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ

. ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ, ɤɨɬɨɪɭɸ ɦɵ ɛɭɞɟɦ ɚɧɚɥɢɡɢɪɨɜɚɬɶ,

ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 2.5. Ȼɚɡɨɜɵɣ ɬɨɤ

ɞɟɥɢɬɫɹ ɧɚ ɭɩɪɚɜɥɹɸɳɢɣ

ɭɩɪ

ɬɨɤ

ɫɤ

ɱɟɪɟɡ ɺɦɤɨɫɬɶ

ɭɩɪ

ɫɤ

Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɧɚ

ɧɚɝɪɭɡɤɟ ɧɚɦɧɨɝɨ ɩɪɟɜɵɲɚɟɬ

ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɛɚɡɟ

>> U.

Ɍɚɤ

ɤɚɤ,

ɢɦɟɟɬ ɝɚɪɦɨɧɢɱɟɫɤɭɸ ɮɨɪ-

ɦɭ, ɬɨ ɢ ɬɨɤ

ɫɤ

ɹɜɥɹɟɬɫɹ ɝɚɪ-

ɦɨɧɢɱɟɫɤɢɦ ɫ ɚɦɩɥɢɬɭɞɨɣ

ɫɤ

(2.13)

Ɉɬɫɸɞɚ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɫɜɹɡɶ

ɦɟɠɞɭ ɚɦɩɥɢɬɭɞɚɦɢ:

ɛ1

= I

ɭɩɪ

ɫɤ

(2.14)

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɧɚɝɪɭɡɤɟ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɚɦɩɥɢɬɭɞɭ 1-ɣ ɝɚɪɦɨɧɢɤɢ

ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ

U I Z I Z

ɧ ɤ ɧ ɭɩ

j= = − ⋅ ⋅

1 1ɪ

( ) .

γ Θ

ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ (2.13) ɩɨɥɭɱɢɦ

I I Z

ɫɤ ɭɩ ɝ ɤ ɧ

ɪ ɪ

( ).

Ɍɨɝɞɚ ɦɨɠɧɨ ɪɚɫɤɪɵɬɶ (2.14):

I I Z I

ɛ ɭɩ ɝ ɤ ɧ ɭɩ

1 1

ɪ ɪ ɪ

[ ( )] ,

(2.15)

ɝɞɟ

1ɝ ɤ ɧ

( )Z

(2.16)

ɧɟɤɨɬɨɪɵɣ ɛɟɡɪɚɡɦɟɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɜɥɢɹɧɢɟ

. ɗɬɨ ɜɥɢɹɧɢɟ

ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɬɜɟɬɜɥɟɧɢɢ ɱɚɫɬɢ ɜɯɨɞɧɨɝɨ ɬɨɤɚ ɜ ɺɦɤɨɫɬɶ

. ɉɨɷɬɨɦɭ

ɧɟɨɛɯɨɞɢɦɨ ɭɬɨɱɧɢɬɶ (2.11):

( )

.exp)(

Tjj

ɝɪ

ωγ

−Θ−= II

(2.17)

ɫɤ

ɭɩɪ

Ɋɢɫ 2.5. ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ

ɛɢɩɨɥɹɪɧɨɝɨ ɬɪɚɧɡɢɫɬɨɪɚ

2.5. ȼɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɌɍɆ ɜ ɫɯɟɦɟ ɫ Ɉɗ

ȼɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɌɍɆ, ɪɚɛɨɬɚɸɳɟɝɨ ɜ ɪɟɠɢɦɟ ɫ ɨɬɫɟɱɤɨɣ ɬɨɤɚ,

ɧɟɥɢɧɟɣɧɨ, ɩɨɷɬɨɦɭ ɟɝɨ ɩɪɢɧɹɬɨ ɨɩɪɟɞɟɥɹɬɶ ɩɨ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɟ ɜɯɨɞɧɨɝɨ

ɧɚɩɪɹɠɟɧɢɹ:

11 ɛɛ

ɜɯ

Ɉɗ

IUZ =

Ɉɩɪɟɞɟɥɟɧɢɟ ɜɯɨɞɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɥɹ ɨɛɳɟɝɨ ɫɥɭɱɚɹ ɱɪɟɡɜɵɱɚɣɧɨ ɫɥɨɠɧɚɹ

ɡɚɞɚɱɚ, ɩɪɢɜɨɞɹɳɚɹ ɤ ɝɪɨɦɨɡɞɤɢɦ ɮɨɪɦɭɥɚɦ. ɉɨɷɬɨɦɭ ɦɵ ɨɝɪɚɧɢɱɢɦɫɹ

ɧɚɢɛɨɥɟɟ ɢɧɬɟɪɟɫɧɵɦ ɞɥɹ ɩɪɚɤɬɢɤɢ ɫɥɭɱɚɟɦ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ. ɉɪɢ ɷɬɨɦ ɫɞɟɥɚɟɦ

ɫɥɟɞɭɸɳɢɟ ɭɩɪɨɳɟɧɢɹ ɜ ɚɧɚɥɢɡɟ:

•

ɺɦɤɨɫɬɢ

ɤɚ

ɤɩ

ɡɚɦɟɧɢɦ ɨɛɳɟɣ ɟɦɤɨɫɬɶɸ

ɤɚ

ɤɩ

;

• ɛɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɺɦɤɨɫɬɢ

ɧɚ ɪɚɛɨɱɢɯ ɱɚɫɬɨɬɚɯ

ɜɟɥɢɤɨ ɜ ɫɪɚɜɧɟɧɢɢ ɫ

;

• ɩɪɢɦɟɦ

= 0, r

= 0

ɉɨ ɯɨɞɭ ɚɧɚɥɢɡɚ ɛɭɞɭɬ ɜɜɟɞɟɧɵ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɩɪɨɳɟɧɢɹ, ɧɟ ɨɤɚɡɵɜɚɸɳɢɟ

ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɤɨɥɢɱɟɫɬɜɟɧɧɭɸ ɨɰɟɧɤɭ ɜɯɨɞɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ.

ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ ɬɪɚɧɡɢɫɬɨɪɚ ɩɪɢ ɩɪɢɧɹɬɵɯ ɭɩɪɨɳɟɧɢɹɯ ɢɦɟɟɬ ɜɢɞ,

ɩɨɤɚɡɚɧɧɵɣ ɧɚ ɪɢɫ. 2.6.

ɛ1

ɫɤ

Ȼ L

ɭɩɪ

ɤ1

ɉ1

ɛ1

Lɷ

Ɋɢɫ. 2.6. ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ ɛɢɩɨɥɹɪɧɨɝɨ ɬɪɚɧɡɢɫɬɨɪɚ

ɂɡ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ ɫɥɟɞɭɟɬ

ɛɛ

ɨɷ

ɜɯ

Lɗɉ

rLj

++=

(2.18)

ɝɞɟ

ɉ1

— ɚɦɩɥɢɬɭɞɚ 1-ɣ ɝɚɪɦɨɧɢɤɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɩɟɪɟɯɨɞɟ ɛɚɡɚ-ɷɦɢɬɬɟɪ;

Lɗ

— ɚɦɩɥɢɬɭɞɚ 1-ɣ ɝɚɪɦɨɧɢɤɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɢɧɞɭɤɬɢɜɧɨɫɬɢ

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɩɟɪɟɯɨɞɟ

ɉ1

ɫɨɡɞɚɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɡɚ ɫɱɟɬ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɚ

ɭɩɪ

ɩɨ ɺɦɤɨɫɬɢ

(ɪɢɫ. 2.6):

(

)

ɭɩɪ

πγ

−

−= IU

(2.19)

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɢɧɞɭɤɬɢɜɧɨɫɬɢ

ɫɨɡɞɚɟɬɫɹ ɡɚ ɫɱɟɬ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɨɜ

ɭɩɪ

ɤ1

Lɷ

ɭɩɪ

ɤ1

. (2.20)

ɍɱɢɬɵɜɚɹ (2.10) ɢ ɩɪɟɧɟɛɪɟɝɚɹ

, ɩɨɥɭɱɢɦ

Lɷ

= I

ɭɩɪ

ɝɪ

(

)].

(2.21)

ɉɨɞɫɬɚɜɥɹɹ (2.15), (2.19) ɢ (2.21) ɜ (2.18), ɩɨɥɭɱɢɦ

ɜɯ

ɨɷ

ɛ ɛ

ɝ ɷ

j L r j

= ⋅ + −

−

+ +

γ π

ω χ

( )

ɉɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɪɹɞ ɜɵɜɨɞɨɜ, ɤɨɬɨɪɵɟ ɦɵ

ɪɚɫɫɦɨɬɪɢɦ ɧɢɠɟ.

2.6. ɋɜɨɣɫɬɜɚ ɌɍɆ ɜ ɫɯɟɦɟ ɫ Ɉɗ

Ɂɚ ɫɱɟɬ ɷɥɟɦɟɧɬɨɜ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ

ɜɨɡɧɢɤɚɸɬ ɨɛɪɚɬɧɵɟ

ɫɜɹɡɢ, ɤɨɬɨɪɵɟ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɸɬ ɧɚ ɪɟɠɢɦ ɪɚɛɨɬɵ ɌɍɆ.

ɋɜɹɡɶ ɱɟɪɟɡ

ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɜɯɨɞɧɨɝɨ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɹ. ɉɪɢɫɭɬɫɬɜɢɟ ɠɟ ɫɚɦɨɣ ɚɤɬɢɜɧɨɣ ɱɚɫɬɢ ɨɡɧɚɱɚɟɬ ɩɨɬɪɟɛɥɟɧɢɟ ɷɧɟɪɝɢɢ.

ɗɬɚ ɷɧɟɪɝɢɹ ɪɚɫɫɟɢɜɚɟɬɫɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ

(ɜ (2.22)

ɧɟ ɭɱɢɬɵɜɚɟɬɫɹ),

ɱɚɫɬɢɱɧɨ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɷɧɟɪɝɢɸ ɩɨɫɬɨɹɧɧɨɝɨ ɛɚɡɨɜɨɝɨ ɬɨɤɚ, ɚ ɱɚɫɬɢɱɧɨ

ɩɪɨɫɚɱɢɜɚɟɬɫɹ ɜ ɜɵɯɨɞɧɭɸ ɰɟɩɶ ɱɟɪɟɡ ɢɧɞɭɤɬɢɜɧɨɫɬɶ L

. ɉɨɫɬɨɹɧɧɵɣ ɬɨɤ ɛɚɡɵ

ɛ0

ɜ ɫɯɟɦɟ ɫ Ɉɗ ɜ ɧɟɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ ɨɱɟɧɶ ɦɚɥ, ɢ

ɷɧɟɪɝɢɸ, ɤɨɬɨɪɚɹ ɬɪɚɬɢɬɫɹ ɧɚ ɩɨɥɭɱɟɧɢɟ ɟɝɨ, ɢ ɤɨɬɨɪɚɹ ɪɚɫɫɟɢɜɚɟɬɫɹ ɜ

ɢɫɬɨɱɧɢɤɟ ɫɦɟɳɟɧɢɹ, ɦɨɠɧɨ ɧɟ ɭɱɢɬɵɜɚɬɶ. Ɇɨɠɧɨ ɬɚɤɠɟ ɞɥɹ

ɨɪɢɟɧɬɢɪɨɜɨɱɧɨɝɨ ɚɧɚɥɢɡɚ ɩɪɟɧɟɛɪɟɱɶ ɢ ɷɧɟɪɝɢɟɣ, ɪɚɫɫɟɢɜɚɟɦɨɣ ɜ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɹɯ

. ɉɨɷɬɨɦɭ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɌɍɆ ɩɨ ɦɨɳɧɨɫɬɢ

P P

ɜɯ

ɜɯ ɜɯ

≈

= +

1 1

ɝɞɟ

— ɦɨɳɧɨɫɬɶ, ɪɚɡɜɢɜɚɟɦɚɹ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɝɟɧɟɪɚɬɨɪɨɦ ɬɨɤɚ:

P I R

ɤ ɧ1 1

05= ⋅ ⋅.

ȼɯɨɞɧɭɸ ɦɨɳɧɨɫɬɶ ɨɩɪɟɞɟɥɢɦ ɚɧɚɥɨɝɢɱɧɨ

P I

ɜɯ ɛ

ɝ ɷ

≈ ⋅ ⋅

( )

ɉɨɞɫɬɚɜɥɹɹ (2.24), (2.25) ɢ (2.10) ɜ (2.23) ɩɨɥɭɱɢɦ

ɝ ɧ

= +

ω χ

( )

ɂɡ ɩɨɥɭɱɟɧɧɨɝɨ ɜɵɪɚɠɟɧɢɹ ɜɢɞɧɨ, ɱɬɨ ɢɡ-ɡɚ ɜɥɢɹɧɢɹ

ɫ ɪɨɫɬɨɦ ɱɚɫɬɨɬɵ

ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ

ɞɨɜɨɥɶɧɨ ɛɵɫɬɪɨ ɩɚɞɚɟɬ. ɉɪɢ ɩɪɢɛɥɢɠɟɧɢɢ ɤ

(2.22)

(2.23)

(2.24)

(2.25)

(2.26)

ɝɪɚɧɢɱɧɨɣ ɱɚɫɬɨɬɟ

ɝɪ

ɭɫɢɥɢɬɟɥɶ, ɩɨɫɬɪɨɟɧɧɵɣ ɩɨ ɫɯɟɦɟ ɫ Ɉɗ, ɫɬɚɧɨɜɢɬɫɹ

ɧɟɷɮɮɟɤɬɢɜɧɵɦ.

ɋɜɹɡɶ ɱɟɪɟɡ

ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɜɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɡɚɜɢɫɢɬ ɨɬ

ɧɚɫɬɪɨɣɤɢ ɜɵɯɨɞɧɨɣ ɰɟɩɢ. Ɍɨ ɟɫɬɶ, ɟɫɥɢ ɤɨɥɥɟɤɬɨɪɧɚɹ ɧɚɝɪɭɡɤɚ ɧɟ ɱɢɫɬɨ ɚɤ-

ɬɢɜɧɚɹ (

= R

+ jX

), ɬɨ ɤɨɷɮɮɢɰɢɟɧɬ

ɹɜɥɹɟɬɫɹ ɤɨɦɩɥɟɤɫɧɨɣ ɜɟɥɢɱɢɧɨɣ ɢ

ɜɥɢɹɟɬ ɧɚ ɯɚɪɚɤɬɟɪ ɜɯɨɞɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ. ɉɪɢ ɢɧɞɭɤɬɢɜɧɨɦ ɯɚɪɚɤɬɟɪɟ ɧɚɝ-

ɪɭɡɤɢ (

) ɜɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɨɠɟɬ ɢɦɟɬɶ ɨɬɪɢɰɚɬɟɥɶɧɭɸ ɜɟɳɟɫɬ-

ɜɟɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɝɟɧɟɪɚɬɨɪ ɦɨɠɟɬ ɜɨɡɛɭɞɢɬɶɫɹ ɢɡ-ɡɚ

ɧɚɥɢɱɢɹ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ ɱɟɪɟɡ

2.7. ɋɜɨɣɫɬɜɚ ɌɍɆ ɜ ɫɯɟɦɟ ɫ ɈȻ

Ⱦɥɹ ɨɰɟɧɤɢ ɨɛɳɢɯ ɫɜɨɣɫɬɜ ɌɍɆ, ɩɨɫɬɪɨɟɧɧɨɝɨ ɩɨ ɫɯɟɦɟ ɫ ɈȻ,

ɪɚɫɫɦɨɬɪɢɦ ɭɩɪɨɳɟɧɧɭɸ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɫɯɟɦɭ ɬɪɚɧɡɢɫɬɨɪɚ, ɩɨɤɚɡɚɧɧɭɸ ɧɚ

ɪɢɫ. 2.7. Ʉɨɦɩɥɟɤɫɧɚɹ ɚɦɩɥɢɬɭɞɚ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ

ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɛɚɡɟ

U U I

ɛ ɩ ɛ ɛ

j L

1 1 1

ȼɯɨɞɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ

I I

ɜɯ ɜɯ ɜɯ

ɛ ɤ

G j B= + ⋅ = =

1 1

ɉɨɞɫɬɚɜɥɹɹ ɜ (2.27) ɜɵɪɚɠɟɧɢɹ (2.27) ɢ (2.10)

ɩɨɥɭɱɚɟɦ ɛɟɡ ɭɱɟɬɚ ɩɚɪɚɦɟɬɪɚ

L C

ɜɯ

ɝ ɷ

ɛ ɷ

− −

γ π ω

( )

;

L C

ɜɯ

ɛ ɷ

− −

γ π ω

( )

ȼ ɫɯɟɦɟ ɫ ɈȻ ɧɚ ɱɚɫɬɨɬɚɯ, ɝɞɟ

(

π−Θ

)

(

)

, ɞɟɣɫɬɜɢɬɟɥɶɧɚɹ ɱɚɫɬɶ

ɜɯɨɞɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɫɬɚɧɨɜɢɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ. ɗɬɨ ɭɤɚɡɵɜɚɟɬ ɧɚ ɜɨɡ-

ɦɨɠɧɨɫɬɶ ɜɨɡɛɭɠɞɟɧɢɹ ɩɚɪɚɡɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɜɨ ɜɯɨɞɧɨɣ ɰɟɩɢ ɌɍɆ.

ȼ ɫɯɟɦɟ ɈȻ ɩɪɚɤɬɢɱɟɫɤɢ ɜɫɹ ɜɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ

ɜɯ

ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ

ɦɨɳɧɨɫɬɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɢ ɩɨɷɬɨɦɭ

≅

/ P

ɜɯ

, ɝɞɟ

P I R

ɜɯ

ɜɵɯ ɤ ɧ

= ⋅ ≅ ⋅ = ⋅

; ,

ɢɥɢ ɫ ɭɱɺɬɨɦ (2.29)

(

)

( )

ɇɗ

ɇP

CLĬ

RCĬ

GRK

ɝɪ

ɜɯ

ωπγ

ωγ

−−

=≅

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɯɟɦɟ ɈȻ ɨɛɳɚɹ ɢɧɞɭɤɬɢɜɧɨɫɬɶ

ɭɜɟɥɢɱɢɜɚɟɬ

ɩɪɢ

ɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ, ɱɬɨ ɨɛɴɹɫɧɹɟɬɫɹ ɨɛɪɚɬɧɵɦ ɩɪɨɯɨɠɞɟɧɢɟɦ ɜɵɯɨɞɧɨɣ

ɦɨɳɧɨɫɬɢ ɧɚ ɜɯɨɞ ɬɪɚɧɡɢɫɬɨɪɚ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɫɧɢɠɟɧɢɟɦ

ɜɯ

. Ɉɞɧɚɤɨ ɷɬɨ

ɫɩɪɚɜɟɞɥɢɜɨ ɬɨɥɶɤɨ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ, ɝɞɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ

ɫɨɢɡɦɟɪɢɦɨ ɫɨ

ɤ1

ɛ1

Ɋɢɫ. 2.7. ɗɤɜɢɜɚɥɟɧɬɧɚɹ

ɫɯɟɦɚ ɬɪɚɧɡɢɫɬɨɪɚ ɫ ɈȻ

(2.27)

(2.28)

(2.29)

ɫɪɟɞɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ

. ɇɚ ɛɨɥɟɟ ɧɢɡɤɢɯ ɱɚɫɬɨɬɚɯ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ

ɌɍɆ ɜ ɫɯɟɦɟ ɫ ɈȻ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɫɯɟɦɟ ɫ Ɉɗ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɧɚ

ɱɚɫɬɨɬɚɯ

≤ 0,5

ɝɪ

ɩɪɢɦɟɧɹɬɶ ɫɯɟɦɭ ɫ Ɉɗ, ɚ ɧɚ ɱɚɫɬɨɬɚɯ

ɝɪ

— ɫɯɟɦɭ ɫ

ɈȻ. ɉɨɫɤɨɥɶɤɭ, ɧɚ ɭɦɟɪɟɧɧɵɯ ɱɚɫɬɨɬɚɯ ɜɫɟɝɞɚ ɦɨɠɧɨ ɧɚɣɬɢ ɩɨɞɯɨɞɹɳɢɣ ɬɢɩ

ɬɪɚɧɡɢɫɬɨɪɚ ɫ ɧɟɨɛɯɨɞɢɦɵɦ

ɝɪ

, ɬɨ ɫɯɟɦɚ ɫ ɈȻ ɧɚɲɥɚ ɩɪɚɤɬɢɱɟɫɤɨɟ ɩɪɢɦɟ-

ɧɟɧɢɟ ɬɨɥɶɤɨ ɜ ɋȼɑ ɞɢɚɩɚɡɨɧɟ (

≥

1 ȽȽɰ). ɇɨ ɧɚ ɬɚɤɢɯ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ

ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɜɥɢɹɧɢɟ ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ

ɬɪɚɧɡɢɫɬɨɪɚ (ɪɢɫ. 2.1). Ⱦɥɹ ɪɚɫɱɟɬɚ ɌɍɆ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɪɟɤɨɦɟɧɞɨɜɚɬɶ

ɦɟɬɨɞɢɤɭ ɪɚɫɱɟɬɚ, ɩɪɢɜɟɞɟɧɧɭɸ ɜ [3].

2.8. Ɉɫɨɛɟɧɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɥɟɜɵɯ

ɬɪɚɧɡɢɫɬɨɪɨɜ ɜ ɭɫɢɥɢɬɟɥɹɯ ɦɨɳɧɨɫɬɢ

ȼ ɞɢɚɩɚɡɨɧɟ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ ɜ ɤɚɱɟɫɬɜɟ ɚɤɬɢɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɭɫɢɥɢɬɟɥɟɣ

ɦɨɳɧɨɫɬɢ ɦɨɝɭɬ ɛɵɬɶ ɩɪɢɦɟɧɟɧɵ ɦɨɳɧɵɟ ɩɨɥɟɜɵɟ ɬɪɚɧɡɢɫɬɨɪɵ (ɉɌ) ɫɨ

ɫɬɪɭɤɬɭɪɨɣ ɆȾɉ. ȼ ɞɢɚɩɚɡɨɧɟ ɋȼɑ ɱɚɳɟ ɩɪɢɦɟɧɹɸɬ ɉɌ ɫ ɡɚɬɜɨɪɨɦ ɒɨɬɤɢ

(ɉɌɒ). ɉɨɥɟɜɵɟ ɬɪɚɧɡɢɫɬɨɪɵ ɨɛɥɚɞɚɸɬ ɪɹɞɨɦ ɩɪɟɢɦɭɳɟɫɬɜ ɩɟɪɟɞ

ɛɢɩɨɥɹɪɧɵɦɢ [5].

• Ɍɨɤ ɜ ɤɚɧɚɥɟ ɦɟɠɞɭ ɢɫɬɨɤɨɦ ɢ ɫɬɨɤɨɦ ɨɛɪɚɡɭɟɬɫɹ ɡɚ ɫɱɟɬ ɷɥɟɤɬɪɨɧɨɜ,

ɹɜɥɹɸɳɢɯɫɹ ɨɫɧɨɜɧɵɦɢ ɧɨɫɢɬɟɥɹɦɢ ɡɚɪɹɞɚ. ɉɨɷɬɨɦɭ ɨɬɫɭɬɫɬɜɭɸɬ ɹɜɥɟɧɢɹ

ɧɚɤɨɩɥɟɧɢɹ ɡɚɪɹɞɚ ɢ ɢɯ ɦɟɞɥɟɧɧɨɟ ɪɚɫɫɚɫɵɜɚɧɢɟ, ɱɬɨ ɭɜɟɥɢɱɢɜɚɟɬ ɛɵɫɬ-

ɪɨɞɟɣɫɬɜɢɟ ɩɪɢɛɨɪɚ.

• ɋɚɦɨɨɝɪɚɧɢɱɟɧɢɟ ɬɨɤɚ ɫɬɨɤɚ ɩɪɟɩɹɬɫɬɜɭɟɬ ɬɨɤɨɜɵɦ ɩɟɪɟɝɪɭɡɤɚɦ. ɉɌ

ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɭɩɪɚɜɥɹɟɦɵɣ ɩɨɥɟɦ ɪɟɡɢɫɬɨɪ. ɂ ɤɚɤ ɜɨ ɜɫɹɤɨɦ

ɪɟɡɢɫɬɨɪɟ, ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɩɨ ɧɟɦɭ ɬɨɤɚ ɪɟɡɢɫɬɨɪ ɧɚɝɪɟɜɚɟɬɫɹ, ɟɝɨ

ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɫɧɢɠɚɟɬɫɹ ɤɪɭɬɢɡɧɚ ɩɪɨɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

ɬɨɤɚ ɫɬɨɤɚ, ɩɪɨɢɫɯɨɞɢɬ ɫɚɦɨɪɟɝɭɥɢɪɨɜɚɧɢɟ. ɉɨ ɷɬɨɣ ɩɪɢɱɢɧɟ ɉɌ ɦɨɠɧɨ ɜɤɥɸ-

ɱɚɬɶ ɩɚɪɚɥɥɟɥɶɧɨ, ɩɪɢɱɟɦ ɛɥɚɝɨɞɚɪɹ ɫɚɦɨɪɟɝɭɥɢɪɨɜɚɧɢɸ ɨɞɢɧɚɤɨɜɵɟ ɩɪɢɛɨɪɵ

ɫ ɧɚɱɚɥɶɧɵɦ ɪɚɡɛɪɨɫɨɦ ɩɚɪɚɦɟɬɪɨɜ ɜɵɪɚɜɧɢɜɚɸɬ ɫɜɨɢ ɩɚɪɚɦɟɬɪɵ.

• ɉɨɜɵɲɟɧɧɚɹ ɬɟɩɥɨɭɫɬɨɣɱɢɜɨɫɬɶ, ɬ.ɟ. ɨɬɫɭɬɫɬɜɢɟ ɬɟɩɥɨɜɨɝɨ ɩɪɨɛɨɹ,

ɱɬɨ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɫɚɦɨɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ.

• ɉɨɜɵɲɟɧɧɚɹ ɥɢɧɟɣɧɨɫɬɶ ɜ ɭɫɢɥɢɬɟɥɶɧɵɯ ɪɟɠɢɦɚɯ, ɫɧɢɠɚɸɳɚɹ

ɭɪɨɜɟɧɶ ɢɧɬɟɪɦɨɞɭɥɹɰɢɨɧɧɵɯ ɢɫɤɚɠɟɧɢɣ.

Ɉɞɧɚɤɨ ɉɌ ɨɛɥɚɞɚɸɬ ɬɚɤɠɟ ɢ ɧɟɞɨɫɬɚɬɤɚɦɢ:

• ɜɵɯɨɞ ɢɡ ɫɬɪɨɹ ɩɪɢ ɩɟɪɟɝɪɭɡɤɚɯ ɩɨ ɧɚɩɪɹɠɟɧɢɸ;

• ɩɨɜɵɲɟɧɧɵɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ȻɌ ɨɫɬɚɬɨɱɧɵɟ ɧɚɩɪɹɠɟɧɢɹ;

• ɯɭɞɲɚɹ ɪɚɞɢɚɰɢɨɧɧɚɹ ɫɬɨɣɤɨɫɬɶ;

• ɛɨɥɟɟ ɜɵɫɨɤɚɹ ɫɬɨɢɦɨɫɬɶ.

Ɋɚɫɱɟɬ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɉɌ, ɪɚɛɨɬɚɸɳɢɯ ɧɚ ɱɚɫɬɨɬɚɯ ɞɨ 50-60 ɆȽɰ

ɩɪɨɜɨɞɹɬ, ɫɱɢɬɚɹ ɝɚɪɦɨɧɢɱɟɫɤɢɦ ɜɨɡɛɭɠɞɚɸɳɟɟ ɧɚɩɪɹɠɟɧɢɟ. Ɋɚɫɱɟɬ ɚɧɚɥɨ-

ɝɢɱɟɧ ɪɚɫɱɟɬɭ ɥɚɦɩɨɜɵɯ ɍɆ. ɇɚ ɛɨɥɟɟ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ ɢɫɩɨɥɶɡɭɸɬ ɦɟɬɨɞɢɤɭ,

ɨɫɧɨɜɚɧɧɭɸ ɧɚ ɞɨɩɭɳɟɧɢɢ ɨ ɝɚɪɦɨɧɢɱɟɫɤɨɣ ɮɨɪɦɟ ɜɯɨɞɧɨɝɨ ɬɨɤɚ.

Ƚɥɚɜɚ 3. ɐȿɉɂ ɋɈȽɅȺɋɈȼȺɇɂə ȺɄɌɂȼɇɈȽɈ ɗɅȿɆȿɇɌȺ

ɋ ɇȺȽɊɍɁɄɈɃ

3.1. Ɍɪɟɛɨɜɚɧɢɹ ɤ ɰɟɩɹɦ ɫɨɝɥɚɫɨɜɚɧɢɹ

Ⱦɥɹ ɪɚɛɨɬɵ Ⱥɗ Ƚȼȼ ɜ ɨɩɬɢɦɚɥɶɧɨɦ (ɤɪɢɬɢɱɟɫɤɨɦ) ɪɟɠɢɦɟ ɟɝɨ ɧɟɨɛɯɨ-

ɞɢɦɨ ɧɚɝɪɭɠɚɬɶ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɧɚɝɪɭɡɤɢ

ɧ ɤɪ

. ɉɨɷɬɨɦɭ ɨɫɧɨɜɧɚɹ ɡɚɞɚɱɚ

ɜɵɯɨɞɧɨɣ ɐɋ ɷɬɨ ɬɪɚɧɫɮɨɪɦɚɰɢɹ ɪɟɚɥɶɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨɬɪɟɛɢɬɟɥɹ

. ɜ

ɧ ɤɪ

. ɇɨ, ɤɪɨɦɟ ɷɬɨɝɨ, ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɹɞɚ ɬɪɟɛɨɜɚɧɢɣ, ɩɪɟɞɴɹɜɥɹɟɦɵɯ ɤ

ɩɟɪɟɞɚɬɱɢɤɭ, ɐɋ ɞɨɥɠɧɚ ɜɵɩɨɥɧɹɬɶ ɟɳɺ ɢ ɫɥɟɞɭɸɳɢɟ ɮɭɧɤɰɢɢ:

• ɮɢɥɶɬɪɨɜɚɬɶ ɜɵɫɲɢɟ ɝɚɪɦɨɧɢɤɢ ɜ ɧɚɝɪɭɡɤɟ (ɧɚ ɜɯɨɞɟ ɫɥɟɞɭɸɳɟɝɨ

ɤɚɫɤɚɞɚ ɢɥɢ ɜ ɚɧɬɟɧɧɟ) ɬɚɤ, ɱɬɨɛɵ ɢɯ ɦɨɳɧɨɫɬɶ ɧɟ ɩɪɟɜɨɫɯɨɞɢɥɚ

ɞɨɩɭɫɬɢɦɵɟ ɡɧɚɱɟɧɢɹ;

• ɜɧɨɫɢɬɶ ɧɟɡɧɚɱɢɬɟɥɶɧɵɟ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ;

• ɩɟɪɟɫɬɪɚɢɜɚɬɶɫɹ ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɱɚɫɬɨɬ ɢ ɢɦɟɬɶ ɪɟɝɭɥɢɪɭɟɦɭɸ

ɫɜɹɡɶ ɫ ɩɨɬɪɟɛɢɬɟɥɟɦ;

• ɨɛɟɫɩɟɱɢɜɚɬɶ ɡɚɞɚɧɧɵɟ ɚɦɩɥɢɬɭɞɧɨ-ɮɚɡɨɜɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ

ɧɟɤɨɬɨɪɨɣ ɩɨɥɨɫɟ ɱɚɫɬɨɬ.

ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɨɫɥɟɞɧɟɝɨ ɬɪɟɛɨɜɚɧɢɹ ɩɪɟɞɵɞɭɳɢɟ ɮɭɧɤɰɢɢ ɪɟɚɥɢɡɭɸɬɫɹ ɩɨ

ɪɚɡɧɨɦɭ. Ⱦɢɚɩɚɡɨɧ ɱɚɫɬɨɬ, ɜ ɤɨɬɨɪɨɦ ɪɚɛɨɬɚɟɬ ɐɋ, ɛɭɞɟɦ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɤɨɷɮ-

ɮɢɰɢɟɧɬɨɦ ɩɟɪɟɤɪɵɬɢɹ

= f

/ f

, ɝɞɟ

— ɜɟɪɯɧɹɹ ɪɚɛɨɱɚɹ ɱɚɫɬɨɬɚ,

—

ɧɢɠɧɹɹ ɪɚɛɨɱɚɹ ɱɚɫɬɨɬɚ. ɉɪɢ

< 1,1 ... 1,2 ɐɋ ɛɭɞɟɦ ɫɱɢɬɚɬɶ

ɭɡɤɨɞɢɚɩɚɡɨɧɧɨɣ. ɂɦɟɧɧɨ ɬɚɤɢɦ ɰɟɩɹɦ ɫɨɝɥɚɫɨɜɚɧɢɹ ɩɨɫɜɹɳɟɧɚ ɞɚɧɧɚɹ ɝɥɚɜɚ.

Ɂɚɞɚɱɚ ɮɢɥɶɬɪɨɜɚɧɢɹ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɩɨɞɪɚɡɭɦɟɜɚɟɬ ɧɚɥɢɱɢɟ ɜ

ɫɨɫɬɚɜɟ ɐɋ ɪɟɡɨɧɚɧɫɧɵɯ ɰɟɩɟɣ, ɧɚɩɪɢɦɟɪ, ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɤɨɥɟɛɚɬɟɥɶɧɨɝɨ

ɤɨɧɬɭɪɚ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɨɛɫɬɜɟɧɧɨɣ ɞɨɛɪɨɬɧɨɫɬɶɸ

. ɉɨɞɤɥɸɱɟɧɢɟ

ɩɨɬɪɟɛɢɬɟɥɹ ɤ ɤɨɧɬɭɪɭ ɫɧɢɠɚɟɬ ɫɭɦɦɚɪɧɭɸ ɞɨɛɪɨɬɧɨɫɬɶ, ɤɨɬɨɪɚɹ ɧɚɡɵɜɚɟɬɫɹ

ɧɚɝɪɭɠɟɧɧɨɣ

. ɋɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ

. ɨɩɪɟɞɟɥɹɟɬ ɤɚɤɚɹ ɱɚɫɬɶ ɦɨɳ-

ɧɨɫɬɢ, ɪɚɡɜɢɜɚɟɦɨɣ ɝɟɧɟɪɚɬɨɪɨɦ, ɬɪɚɬɢɬɫɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɩɨɬɪɟɛɢɬɟɥɹ

(ɩɨɥɟɡɧɚɹ ɱɚɫɬɶ), ɚ ɤɚɤɚɹ — ɜ ɚɤɬɢɜɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɷɥɟɦɟɧɬɨɜ ɤɨɧɬɭɪɚ

(ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ). Ɉɛɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɄɉȾ ɤɨɧɬɭɪɚ, ɤɨɬɨɪɨɟ ɛɭɞɟɬ

ɨɛɨɫɧɨɜɚɧɨ ɧɢɠɟ, ɢɦɟɟɬ ɜɢɞ:

./1 QQ

ɧɤ

−

(3.1)

ɍɜɟɥɢɱɟɧɢɟ ɧɚɝɪɭɠɟɧɧɨɣ ɞɨɛɪɨɬɧɨɫɬɢ

ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɬɨɤɨɜ ɜ

ɤɨɧɬɭɪɟ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɧɢɠɚɟɬ ɄɉȾ. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ ɫɧɢɠɟɧɢɟ

ɭɯɭɞɲɚɟɬ ɮɢɥɶɬɪɚɰɢɸ. Ɉɩɬɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ ɫɱɢɬɚɟɬɫɹ

= 10 ... 15.

ɇɚɩɪɢɦɟɪ, ɩɪɢ

= 200 ɢ

= 10

= 0,95. Ɉɬɧɨɫɢɬɟɥɶɧɨ ɧɟɜɵɫɨɤɨɟ ɡɧɚɱɟɧɢɟ

ɩɨɡɜɨɥɹɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜ ɤɚɱɟɫɬɜɟ ɰɟɩɟɣ ɫɨɝɥɚɫɨɜɚɧɢɹ ɩɪɨɫɬɵɟ Ƚ-

ɨɛɪɚɡɧɵɟ ɢ ɉ-ɨɛɪɚɡɧɵɟ ɰɟɩɨɱɤɢ, ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɧɢɠɟ.

ȼ ɋȼɑ ɞɢɚɩɚɡɨɧɟ, ɝɞɟ ɡɚɬɪɭɞɧɢɬɟɥɶɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɟ

ɷɥɟɦɟɧɬɵ, ɩɪɢɦɟɧɹɸɬ ɰɟɩɢ ɫ ɪɚɫɩɪɟɞɟɥɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɜ ɜɢɞɟ ɨɬɪɟɡɤɨɜ

ɥɢɧɢɣ ɩɟɪɟɞɚɱɢ ɫ ɩɨɞɤɥɸɱɟɧɧɵɦɢ ɤ ɧɢɦ ɲɥɟɣɮɚɦɢ. ɉɨ ɩɪɢɱɢɧɚɦ, ɢɡɥɨɠɟɧɧɵɦ

ɜɵɲɟ, ɡɞɟɫɶ ɬɚɤɠɟ ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɞɨɜɨɥɶɧɨ ɩɪɨɫɬɵɟ ɫɯɟɦɧɵɟ ɪɟɲɟɧɢɹ.

3.2.

ɐɟɩɶ ɫɨɝɥɚɫɨɜɚɧɢɹ ɧɚ ɨɫɧɨɜɟ Ƚ-ɨɛɪɚɡɧɨɣ ɰɟɩɨɱɤɢ

Ɋɚɫɫɦɨɬɪɢɦ ɬɪɚɧɫɮɨɪɦɢɪɭɸɳɢɟ ɫɜɨɣɫɬɜɚ Ƚ-ɨɛɪɚɡɧɨɣ ɰɟɩɨɱɤɢ, ɫɯɟɦɚ

ɤɨɬɨɪɨɣ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 3.1. Ɏɭɧɤɰɢɢ ɪɟɚɤɬɢɜɧɵɯ

ɷɥɟɦɟɧɬɨɜ ɡɞɟɫɶ ɱɟɬɤɨ ɪɚɡɞɟɥɟɧɵ: ɷɥɟɦɟɧɬ

ɨɫɭ-

ɳɟɫɬɜɥɹɟɬ ɬɪɚɧɫɮɨɪɦɚɰɢɸ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ɜ ɬɪɟ-

ɛɭɟɦɭɸ ɜɟɥɢɱɢɧɭ

; ɷɥɟɦɟɧɬ

ɤɨɦɩɟɧɫɢɪɭɟɬ ɜɨɡ-

ɧɢɤɚɸɳɭɸ ɩɪɢ ɷɬɨɦ ɪɟɚɤɬɢɜɧɨɫɬɶɸ. Ɋɚɫɫɦɨɬɪɢɦ,

ɤɚɤ ɷɬɨ ɩɪɨɢɫɯɨɞɢɬ.

Ɋɚɫɫɱɢɬɚɟɦ ɩɪɨɜɨɞɢɦɨɫɬɶ, ɫɨɡɞɚɜɚɟɦɭɸ

ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɫɨɟɞɢɧɟɧɢɟɦ

2 2

−

+R j x

R j x

R x

Ⱦɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɪɟɚɤɬɢɜɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɢɬɶ ɭɫɥɨɜɢɟ

R x

= −

, .

ɢɥɢ

ɍɞɨɛɧɟɟ (3.2) ɡɚɩɢɫɚɬɶ ɜ ɮɨɪɦɟ

x x

1 2

= − + = −( ), .ɝɞɟ ɞɨɛɪɨɬɧɨɫɬɶ ɰɟɩɢ

ȼɟɳɟɫɬɜɟɧɧɚɹ ɱɚɫɬɶ ɰɟɩɨɱɤɢ

ɞɨɥɠɧɚ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɭɪɚɜɧɟɧɢɸ

1 2

R x

R R Q=

= +

ɢɥɢ

( ).

ɂɡ ɩɪɢɜɟɞɟɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ:

• ɞɨɛɪɨɬɧɨɫɬɶ Ƚ-ɨɛɪɚɡɧɨɣ ɰɟɩɨɱɤɢ ɨɞɧɨɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬ-

ɧɨɲɟɧɢɟɦ

= −

1 ;

• ɬɚɤ ɤɚɤ

ɜɟɥɢɱɢɧɚ ɜɟɳɟɫɬɜɟɧɧɚɹ, ɬɨ ɞɥɹ ɮɢɡɢɱɟɫɤɨɣ ɪɟɚɥɢɡɭɟɦɨɫɬɢ

ɫɯɟɦɵ ɧɟɨɛɯɨɞɢɦɨ ɱɬɨɛɵ

, ɬ.ɟ. Ƚ-ɨɛɪɚɡɧɚɹ ɰɟɩɨɱɤɚ ɭɜɟɥɢɱɢɜɚɟɬ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɟ ɩɨɬɪɟɛɢɬɟɥɹ;

• ɡɧɚɤɢ

ɩɪɨɬɢɜɨɩɨɥɨɠɧɵ.

Ɋɢɫ. 3.1. Ƚ-ɨɛɪɚɡɧɚɹ

ɰɟɩɨɱɤɚ

(3.2)

(3.3)

(3.4)

(3.5)

ɑɚɳɟ ɜɫɟɝɨ ɢɫɩɨɥɶɡɭɸɬ ɫɯɟɦɭ ɜ ɜɢɞɟ Ɏɇɑ, ɬɚɤ ɤɚɤ

ɜ ɷɬɨɣ ɫɯɟɦɟ ɥɭɱɲɟ ɮɢɥɶɬɪɭɸɬɫɹ ɜɵɫɲɢɟ

ɝɚɪɦɨɧɢɤɢ (ɪɢɫ.3.2) .

Ɉɱɟɜɢɞɟɧ ɝɥɚɜɧɵɣ ɧɟɞɨɫɬɚɬɨɤ Ƚ-ɨɛɪɚɡɧɨɣ

ɐɋ, ɤɨɬɨɪɵɣ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɞɨɛɪɨɬɧɨɫɬɶ

ɰɟɩɢ ɨɞɧɨɡɧɚɱɧɨ ɡɚɞɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɚɧɫ-

ɮɨɪɦɚɰɢɢ

ɬɪ

ɢ ɩɪɢ ɦɚɥɨɦ ɟɝɨ ɡɧɚɱɟɧɢɢ

ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɟɞɨɫɬɚɬɨɱɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬ

ɮɢɥɶɬɪɚɰɢɢ. Ɍɟɦ ɧɟ ɦɟɧɟɟ, Ƚ-ɨɛɪɚɡɧɵɟ ɰɟɩɢ

ɩɪɢɦɟɧɹɸɬɫɹ ɧɚ ɩɪɚɤɬɢɤɟ ɜ ɤɚɱɟɫɬɜɟ ɦɟɠɤɚɫɤɚɞɧɵɯ ɰɟɩɟɣ ɫɨɝɥɚɫɨɜɚɧɢɹ, ɤɨɝɞɚ

ɛɨɥɟɟ ɜɵɫɨɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɪɟɞɵɞɭɳɟɝɨ ɤɚɫɤɚɞɚ ɧɟɨɛɯɨɞɢɦɨ ɫɨɝɥɚɫɨɜɚɬɶ ɫ

ɛɨɥɟɟ ɧɢɡɤɢɦ ɜɯɨɞɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɩɨɫɥɟɞɭɸɳɟɝɨ. Ʉɨɷɮɮɢɰɢɟɧɬ

ɮɢɥɶɬɪɚɰɢɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɵɱɧɨ ɧɟɜɵɫɨɤ.

Ɋɚɫɫɱɢɬɚɟɦ ɄɉȾ Ƚ-ɨɛɪɚɡɧɨɣ ɰɟɩɨɱɤɢ

ɰɫ

ɝɞɟ

— ɦɨɳɧɨɫɬɶ ɧɚ ɜɯɨɞɟ ɐɋ,

— ɦɨɳɧɨɫɬɶ, ɪɚɫɫɟɢɜɚɟɦɚɹ ɜ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɢ ɩɨɬɪɟɛɢɬɟɥɹ

ȼɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ

ɪɚɫɩɪɟɞɟɥɹɟɬɫɹ ɦɟɠɞɭ ɦɨɳɧɨɫɬɶɸ ɩɨɬɟɪɶ

ɜ ɐɋ

P P P I R r

R r R1 2 2

0 5= + = ⋅ +, ( ),

ɝɞɟ

— ɬɨɤ ɱɟɪɟɡ

— ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɚɬɭɲɤɢ

ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɜ (3.6) ɩɨɥɭɱɚɟɦ

ɰɫ

R r

R r r

R r

+ −

= −

( )

ȼɜɟɞɟɦ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ:

= − ɫɨɛɫɬɜɟɧɧɚɹ ɞɨɛɪɨɬɧɨɫɬɶ ɤɚɬɭɲɤɢ ;

R r

jx R=

− +

2 2

ɧɚɝɪɭɠɟɧɧɚɹ ɞɨɛɪɨɬɧɨɫɬɶ ɰɟɩɢ

Ɉɬɫɸɞɚ

ɰɫ

= −1

ɗɬɨ ɜɵɪɚɠɟɧɢɟ ɫɨɜɩɚɞɚɟɬ ɫ ɜɵɪɚɠɟɧɢɟɦ (3.1) ɞɥɹ ɄɉȾ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɤɨɧɬɭɪɚ

ɢ ɦɨɠɟɬ ɩɪɢɦɟɧɹɬɶɫɹ ɞɥɹ ɪɚɫɱɟɬɚ ɄɉȾ ɩɪɨɢɡɜɨɥɶɧɨɣ ɐɋ, ɷɤɜɢɜɚɥɟɧɬɧɨɣ

ɨɞɢɧɨɱɧɨɦɭ ɤɨɥɟɛɚɬɟɥɶɧɨɦɭ ɤɨɧɬɭɪɭ ɩɪɢ

≥ 3.

C R

Ɋɢɫ.3.2. Ƚ-ɨɛɪɚɡɧɚɹ

ɰɟɩɨɱɤɚ ɜ ɜɢɞɟ Ɏɇɑ

(3.6)

(3.7)