Воробьев М.С. Устройства генерирования радиосигналов

51

Ʉɨɦɩɥɟɤɫɧɨɟ ɭɪɚɜɧɟɧɢɟ (5.2) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ:

S

1

(

U

ɜɯ

)

k

ɨɫ

Z

ɧ

= 1,

(5.3)

ϕ

s

+

ϕ

k

+

ϕ

ɧ

= 2

π

n, n

= 0, ±1, ±2, ... (5.4)

ɍɪɚɜɧɟɧɢɟ (5.3) ɧɚɡɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɛɚɥɚɧɫɚ ɚɦɩɥɢɬɭɞ, ɩɨɫɤɨɥɶɤɭ

ɨɩɪɟɞɟɥɹɟɬ ɚɦɩɥɢɬɭɞɭ ɤɨɥɟɛɚɧɢɣ ȺȽ. ɍɪɚɜɧɟɧɢɟ (5.4) ɧɚɡɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ

ɛɚɥɚɧɫɚ ɮɚɡ ɢ ɨɩɪɟɞɟɥɹɟɬ ɱɚɫɬɨɬɭ ɤɨɥɟɛɚɧɢɣ ȺȽ.

5.2. ɋɯɟɦɵ ɚɜɬɨɝɟɧɟɪɚɬɨɪɨɜ

Ɍɪɚɧɡɢɫɬɨɪ ɹɜɥɹɟɬɫɹ ɬɪɟɯɩɨɥɸɫɧɢɤɨɦ, ɧɨ ɟɝɨ ɦɨɠɧɨ ɢɫɤɭɫɫɬɜɟɧɧɨ

ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɤ ɱɟɬɵɪɟɯɩɨɥɸɫɧɢɤɭ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 5.2. ɉɪɢ ɷɬɨɦ ɩɨɥɸɫɵ

1′ ɢ 2′ ɚɤɬɢɜɧɨɝɨ ɱɟɬɵɪɟɯɩɨɥɸɫɧɢɤɚ ɨɛɴɟɞɢ-

ɧɟɧɵ ɨɛɳɟɣ ɲɢɧɨɣ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɨɥɠɧɵ

ɛɵɬɶ ɨɛɴɟɞɢɧɟɧɵ ɩɨɥɸɫɵ 3′ ɢ 4′ ɩɚɫɫɢɜɧɨɝɨ

ɱɟɬɵɪɟɯɩɨɥɸɫɧɢɤɚ, ɤɨɬɨɪɵɣ ɜ ɷɬɨɦ ɫɥɭɱɚɟ

ɞɨɥɠɟɧ ɛɵɬɶ ɩɨɫɬɪɨɟɧ ɩɨ ɉ-ɨɛɪɚɡɧɨɣ ɫɯɟɦɟ ɢɡ

ɬɪɟɯ ɷɥɟɦɟɧɬɨɜ:

Z

1

= R

1

+ j

⋅

X

1

,

Z

2

= R

2

+ j

⋅

X

2

,

Z

3

= R

3

+ j

⋅

X

3

. Ɍɚɤɚɹ ɫɯɟɦɚ ɧɚɡɵɜɚɟɬɫɹ ɬɪɟɯɬɨ-

ɱɟɱɧɨɣ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɨɣ ɫɬɚɛɢɥɶɧɨɫɬɢ

ɱɚɫɬɨɬɵ ɷɥɟɦɟɧɬɵ Ʉɋ ɫɬɚɪɚɸɬɫɹ ɞɟɥɚɬɶ ɫ

ɦɚɥɵɦɢ ɩɨɬɟɪɹɦɢ, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɩɪɟɞɩɨ-

ɥɨɠɢɬɶ, ɱɬɨ

R

X

R

X

R

X

1

2

3

1 1 1<< << <<; ; .

ɇɚɣɞɟɦ ɡɧɚɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɧɚɝɪɭɡɤɢ

Z

ɧ

ɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɛɪɚɬɧɨɣ

ɫɜɹɡɢ

k

ɨɫ

:

Z

Z Z Z

k

Z

Z Z

ɧ ɨɫ

=

+

+ +

=

−

+

2 1 3

1 2 3

1

1 3

( )

; .

ɇɚɣɞɟɦ ɩɪɨɢɡɜɟɞɟɧɢɟ

Z

ɧ

k

ɨɫ

ɢ ɭɱɬɟɦ (5.5):

Z k

Z Z

Z Z Z

ɧ ɨɫ

X X

r j x

⋅ =

−

⋅

+ +

≅

⋅

+ ⋅

1 2

1 2 3

1 2

,

ɝɞɟ

r = R

1

+ R

2

+ R

3

; x = X

1

+ X

2

+ X

3

.

ȿɫɥɢ

S

1

=

S

1

(ɱɢɫɬɨ ɚɤɬɢɜɧɚɹ ɜɟɥɢɱɢɧɚ), ɬɨ ɩɪɨɢɡɜɟɞɟɧɢɟ (5.6) ɬɚɤɠɟ

ɞɨɥɠɧɨ ɛɵɬɶ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɜɟɳɟɫɬɜɟɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɱɬɨ ɜɨɡɦɨɠɧɨ ɩɪɢ

X

1

+ X

2

+ X

3

= 0, X

1

X

2

> 0.

ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ

X

1

ɢ

X

2

ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɞɢɧɚɤɨɜɵɟ ɡɧɚɤɢ, ɚ

X

3

,

ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ ɡɧɚɤ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨɡɦɨɠɧɵ ɞɜɚ ɜɚɪɢɚɧɬɚ

ɩɨɫɬɪɨɟɧɢɹ ɬɪɟɯɬɨɱɟɱɧɵɯ ɫɯɟɦ ɚɜɬɨɝɟɧɟɪɚɬɨɪɨɜ: ɺɦɤɨɫɬɧɚɹ ɢ ɢɧɞɭɤɬɢɜɧɚɹ (ɪɢɫ.

5.3).

2

1

1′ 2′

3

Z

3

4

Z

1

Z

2

3′ 4′

Ɋɢɫ. 5.2. Ɉɛɨɛɳɟɧɧɚɹ ɫɯɟɦɚ

ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ɝɟɧɟɪɚɬɨɪɚ

(5.5)

(5.6)

52

L3 C3

ɚ) C2 ɛ) L2

L1

C1

Ɋɢɫ. 5.3. Ɍɪɟɯɬɨɱɟɱɧɵɟ ɫɯɟɦɵ ȺȽ: ɚ) ɺɦɤɨɫɬɧɚɹ, ɛ) ɢɧɞɭɤɬɢɜɧɚɹ

ɉɚɪɚɦɟɬɪɵ ɷɥɟɦɟɧɬɨɜ ɧɚ ɪɢɫ. 5.3 ɫɜɹɡɚɧɵ ɫ ɩɚɪɚɦɟɬɪɚɦɢ ɷɥɟɦɟɧɬɨɜ ɧɚ ɪɢɫ 5.2 ɫ

ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɢɯ ɫɨɨɬɧɨɲɟɧɢɣ:

Z Z Z

1 2 3

1

2

3= = =

j C j C

j L

ɝ ɝ

ɝ

ω ω

ω

, ,

ɞɥɹ ɟɦɤɨɫɬɧɨɣ ɬɪɟɯɬɨɱɤɢ;

Z Z Z

1 2 3

1 2

1

3

= = =j L j L

j C

ɝ ɝ

ɝ

ω ω

ω

, ,

ɞɥɹ ɢɧɞɭɤɬɢɜɧɨɣ ɬɪɟɯɬɨɱɤɢ,

ɝɞɟ

ω

ɝ

— ɱɚɫɬɨɬɚ ɝɟɧɟɪɚɰɢɢ ȺȽ. ɍɫɥɨɜɢɟ

x = 0

ɨɡɧɚɱɚɟɬ, ɱɬɨ ɱɚɫɬɨɬɚ ɝɟɧɟɪɚɰɢɢ

ɫɨɜɩɚɞɚɟɬ ɫ ɫɨɛɫɬɜɟɧɧɨɣ ɱɚɫɬɨɬɨɣ ɤɨɧɬɭɪɚ

ω

ɝ

LC= 1 ,

ɝɞɟ

L= L3, 1/C = 1/C1+1/C2

— ɞɥɹ ɺɦɤɨɫɬɧɨɣ ɬɪɟɯɬɨɱɤɢ;

L= L1 + L2, C = C3

— ɞɥɹ ɢɧɞɭɤɬɢɜɧɨɣ ɬɪɟɯɬɨɱɤɢ.

Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɨɤɚ ɧɢɤɚɤɢɯ ɨɝɪɚɧɢɱɟɧɢɣ ɧɚ ɫɬɪɭɤɬɭɪɭ

Z

1

,

Z

2

ɢ

Z

3

ɧɟ

ɜɜɨɞɢɥɨɫɶ. ȿɫɥɢ ɤɚɠɞɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɨɫɬɨɢɬ ɬɨɥɶɤɨ ɢɡ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ

ɜɤɥɸɱɟɧɧɵɯ ɤɚɬɭɲɟɤ ɢɧɞɭɤɬɢɜɧɨɫɬɢ ɢ ɤɨɧɞɟɧɫɚɬɨɪɨɜ, ɬɨ ɤɨɥɟɛɚɬɟɥɶɧɚɹ

ɫɢɫɬɟɦɚ ɹɜɥɹɟɬɫɹ ɨɞɢɧɨɱɧɵɦ ɤɨɧɬɭɪɨɦ, ɢɦɟɸɳɢɦ ɟɞɢɧɫɬɜɟɧɧɭɸ ɫɨɛɫɬɜɟɧɧɭɸ

ɱɚɫɬɨɬɭ. ɇɨ ɟɫɥɢ ɢɦɟɸɬɫɹ ɪɚɡɜɟɬɜɥɟɧɢɟ ɰɟɩɢ — ɩɚɪɚɥɥɟɥɶɧɵɟ ɤɨɧɬɭɪɵ, ɬɨ Ʉɋ

ɫɬɚɧɨɜɢɬɫɹ ɦɧɨɝɨɤɨɧɬɭɪɧɨɣ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɫɨɛɫɬɜɟɧɧɵɦɢ ɱɚɫɬɨɬɚɦɢ. Ɋɟɚɥɶɧɵɟ

ɫɯɟɦɵ ɜɫɟɝɞɚ ɦɧɨɝɨɤɨɧɬɭɪɧɵɟ, ɬɚɤ ɤɚɤ ɤɚɠɞɨɟ ɢɡ

Z

1

,

Z

2

ɢ

Z

3

ɨɛɪɚɡɭɟɬɫɹ

ɩɚɪɚɥɥɟɥɶɧɵɦ ɫɨɟɞɢɧɟɧɢɟɦ ɷɥɟɦɟɧɬɨɜ Ʉɋ, ɪɟɚɤɬɢɜɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ

ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ ɬɪɚɧɡɢɫɬɨɪɚ ɢ ɪɚɡɞɟɥɢɬɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɰɟɩɟɣ ɩɢɬɚɧɢɹ.

ɉɨɷɬɨɦɭ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ȺȽ ɧɟɨɛɯɨɞɢɦɨ ɩɨ ɜɨɡɦɨɠɧɨɫɬɢ ɞɚɥɶɲɟ

ɪɚɡɧɨɫɢɬɶ ɩɚɪɚɡɢɬɧɵɟ ɫɨɛɫɬɜɟɧɧɵɟ ɱɚɫɬɨɬɵ Ʉɋ ɢ ɨɫɧɨɜɧɭɸ ɱɚɫɬɨɬɭ.

ɇɚ ɩɪɚɤɬɢɤɟ ɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɚ ɟɦɤɨɫɬɧɚɹ ɬɪɟɯɬɨɱɤɚ ɩɨ

ɫɥɟɞɭɸɳɢɦ ɩɪɢɱɢɧɚɦ:

• ɩɚɫɫɢɜɧɵɣ ɱɟɬɵɪɟɯɩɨɥɸɫɧɢɤ ɟɦɤɨɫɬɧɨɣ ɬɪɟɯɬɨɱɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ

Ɏɇɑ, ɚ ɢɧɞɭɤɬɢɜɧɨɣ — Ɏȼɑ. ɉɨɷɬɨɦɭ ɮɢɥɶɬɪɚɰɢɹ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɜ ɟɦɤɨɫɬ-

ɧɨɣ ɬɪɟɯɬɨɱɤɟ ɥɭɱɲɟ, ɚ ɷɬɨ ɨɬɪɚɠɚɟɬɫɹ ɧɚ ɫɬɚɛɢɥɶɧɨɫɬɢ ɱɚɫɬɨɬɵ;

• ɟɦɤɨɫɬɧɚɹ ɬɪɟɯɬɨɱɤɚ ɫɨɞɟɪɠɢɬ ɜɫɟɝɨ ɨɞɧɭ ɢɧɞɭɤɬɢɜɧɨɫɬɶ, ɱɬɨ ɭɞɨɛɧɟɟ ɫ

ɤɨɧɫɬɪɭɤɬɢɜɧɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ;

53

• ɜ ɟɦɤɨɫɬɧɨɣ ɬɪɟɯɬɨɱɤɟ ɥɟɝɱɟ ɪɟɚɥɢɡɭɟɬɫɹ ɤɜɚɪɰɟɜɚɹ ɫɬɚɛɢɥɢɡɚɰɢɹ

ɱɚɫɬɨɬɵ.

Ɉɞɧɚɤɨ ɟɦɤɨɫɬɧɚɹ ɬɪɟɯɬɨɱɤɚ ɜ ɜɢɞɟ, ɩɨɤɚɡɚɧɧɨɦ ɧɚ ɪɢɫ. 5.3, ɚ ɬɚɤɠɟ ɪɟɞɤɨ

ɢɫɩɨɥɶɡɭɟɬɫɹ. ɗɬɨ ɫɜɹɡɚɧɨ ɫɨ ɫɥɟɞɭɸɳɢɦɢ ɧɟɞɨɫɬɚɬɤɚɦɢ ɷɬɨɣ ɫɯɟɦɵ:

• Ʉɨɷɮɮɢɰɢɟɧɬ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ

k

X

X X

X

ɨɫ

=

−

+

= −

1

3 1

1

2

,

ɨɬ ɤɨɬɨɪɨɝɨ ɡɚɜɢɫɢɬ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ȺȽ, ɢ ɤɨɷɮɮɢɰɢɟɧɬ

ɜɤɥɸɱɟɧɢɹ ɬɪɚɧɡɢɫɬɨɪɚ ɜ ɤɨɧɬɭɪ

p

X

X X

=

+

2

1 2

,

ɨɬ ɤɨɬɨɪɨɝɨ ɡɚɜɢɫɢɬ ɫɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬɵ, ɠɟɫɬɤɨ ɫɜɹɡɚɧɵ ɦɟɠɞɭ ɫɨɛɨɣ.

ɗɬɨ ɢɫɤɥɸɱɚɟɬ ɨɩɬɢɦɚɥɶɧɵɣ ɜɵɛɨɪ ɪɟɠɢɦɚ ȺȽ.

• ɉɪɢ ɜɚɪɢɚɰɢɢ ɱɚɫɬɨɬɵ ɫɥɟɞɭɟɬ ɢɡɦɟɧɹɬɶ ɜɟɥɢɱɢɧɭ

Z

3

, ɬɚɤ ɤɚɤ ɢɡɦɟɧɟɧɢɟ

ɩɚɪɚɦɟɬɪɨɜ

Z

1

ɢɥɢ

Z

2

ɩɪɢɜɟɞɟɬ ɤ ɢɡɦɟɧɟɧɢɸ ɪɟɠɢɦɚ ȺȽ. Ⱦɥɹ ɟɦɤɨɫɬɧɨɣ

ɬɪɟɯɬɨɱɤɢ ɷɬɨ ɨɡɧɚɱɚɟɬ ɜɚɪɢɚɰɢɸ ɢɧɞɭɤɬɢɜɧɨɫɬɢ, ɱɬɨ ɦɟɧɟɟ ɭɞɨɛɧɨ, ɱɟɦ

ɜɚɪɢɚɰɢɹ ɟɦɤɨɫɬɢ.

ɗɬɢ ɧɟɞɨɫɬɚɬɤɢ ɟɦɤɨɫɬɧɨɣ ɬɪɟɯɬɨɱɤɢ ɭɫɬɪɚɧɟɧɵ ɜ ɫɯɟɦɟ Ʉɥɚɩɩɚ, ɤɨɬɨɪɚɹ

ɨɛɪɚɡɭɟɬɫɹ ɜɜɟɞɟɧɢɟɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ

ɢɧɞɭɤɬɢɜɧɨɫɬɶɸ L ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɟɦɤɨɫɬɢ C3

(ɪɢɫ. 5.4). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɧɟɡɚɜɢɫɢɦɨ

ɜɵɛɢɪɚɬɶ ɨɩɬɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɞɥɹ

p

ɢ

k

oc

:

k

C

p

C

ɨɫ

= =

2

1 2

, ,

Σ

ɝɞɟ

1/C

Σ

= 1/C1+1/C2+1/C3

— ɫɭɦɦɚɪɧɚɹ ɺɦ-

ɤɨɫɬɶ Ʉɋ. ɑɚɫɬɨɬɭ ɤɨɥɟɛɚɧɢɣ ɦɨɠɧɨ ɜɚɪɶɢɪɨɜɚɬɶ ɫ

ɩɨɦɨɳɶɸ ɤɨɧɞɟɧɫɚɬɨɪɚ ɩɟɪɟɦɟɧɧɨɣ ɺɦɤɨɫɬɢ

C3

.

Ʉɪɨɦɟ ɷɬɨɝɨ, ɞɥɹ ɫɯɟɦɵ Ʉɥɚɩɩɚ ɯɚɪɚɤɬɟɪɟɧ

ɦɟɧɶɲɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɜɤɥɸɱɟɧɢɹ

p

ɢ ɛɨ′ɥɶɲɚɹ

L

, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ

ɞɨɛɪɨɬɧɨɫɬɢ Ʉɋ.

5.3. ɋɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ ȺȽ. ɍɫɥɨɜɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ

ɋɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ ȺȽ ɷɬɨ ɪɟɠɢɦ ɭɫɬɨɣɱɢɜɵɯ ɤɨɥɟɛɚɧɢɣ ɫ ɩɨɫɬɨɹɧɧɨɣ

ɚɦɩɥɢɬɭɞɨɣ, ɤɨɬɨɪɵɣ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɨɫɥɟ ɨɤɨɧɱɚɧɢɹ ɜɫɟɯ ɩɟɪɟɯɨɞɧɵɯ ɩɪɨ-

ɰɟɫɫɨɜ ɩɪɢ ɜɤɥɸɱɟɧɢɢ ȺȽ. ɋɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ (5.3),

ɤɨɬɨɪɨɟ ɭɞɨɛɧɟɟ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ

( )

ɧoc

ɜɯ1

Rk

US

1

=

. (5.7)

L

C3 C2

C1

Ɋɢɫ. 5.4. ɋɯɟɦɚ Ʉɥɚɩɩɚ

54

ɍɫɥɨɜɢɟ (5.7) ɨɩɪɟɞɟɥɹɟɬ ɚɦɩɥɢɬɭɞɭ ɤɨɥɟɛɚɧɢɣ ȺȽ, ɢ ɞɥɹ ɟɝɨ ɜɵɩɨɥɧɟɧɢɹ

ɬɪɟɛɭɟɬɫɹ, ɱɬɨɛɵ ɬɪɚɧɡɢɫɬɨɪ ɧɚɯɨɞɢɥɫɹ ɜ ɧɟɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ

ɫɪɟɞɧɹɹ ɤɪɭɬɢɡɧɚ ɩɪɨɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɪɚɧɡɢɫɬɨɪɚ

S

1

ɪɚɜɧɚ

(

)

ĬSS

11

γ

0

=

, (5,8)

ɝɞɟ

S

0

— ɤɪɭɬɢɡɧɚ ɩɪɨɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ. Ɍɨ ɟɫɬɶ

ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɜɥɢɹɟɬ ɧɚ

S

1

ɩɨɫɪɟɞɫɬɜɨɦ ɢɡɦɟɧɟɧɢɹ ɭɝɥɚ ɨɬɫɟɱɤɢ

Θ

, ɱɬɨ

ɛɵɥɨ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɟɧɨ ɜ ɩɚɪɚɝɪɚɮɟ 1.5.

ɇɚ ɪɢɫ. 5.5 ɩɪɟɞɫɬɚɜɥɟɧɵ ɬɪɢ

ɜɨɡɦɨɠɧɵɯ ɜɚɪɢɚɧɬɚ ɡɚɜɢɫɢɦɨɫɬɢ

S

1

(U

ɜɯ

)

: 1) ɩɪɢ

E

ɫɦ

> E

′

, 2) ɩɪɢ

E

ɫɦ

= E

′

, 3) ɩɪɢ

E

ɫɦ

< E

′

. ȼ ɩɟɪɜɨɦ

ɫɥɭɱɚɟ ɢɦɟɟɬɫɹ ɭɱɚɫɬɨɤ ɥɢɧɟɣɧɨɝɨ

ɪɟɠɢɦɚ, ɜ ɤɨɬɨɪɨɦ

S

1

=

S

0

. ɉɪɢ ɩɨɹɜ-

ɥɟɧɢɢ ɨɬɫɟɱɤɢ ɭɝɨɥ

Θ

ɢɡɦɟɧɹɟɬɫɹ ɨɬ

π

ɞɨ

π/

2

ɩɪɢ

U

ɜɯ

→ ∞,

S

1

ɫɬɪɟɦɢɬɫɹ

ɤ

0,5S

0

, ɧɨ ɩɪɢ ɩɟɪɟɯɨɞɟ ɜ ɉɊ ɪɟɡɤɨ

ɩɚɞɚɟɬ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɭɝɨɥ

ɨɬɫɟɱɤɢ

Θ

=

π

/ 2

, ɚ

S

1

=

0,5S

0

ɞɨ ɜɨɡ-

ɧɢɤɧɨɜɟɧɢɹ ɉɊ. ȼ ɬɪɟɬɶɟɦ ɫɥɭɱɚɟ

ɫɭɳɟɫɬɜɭɟɬ ɭɱɚɫɬɨɤ, ɝɞɟ

U

ɜɯ

<

|E

′

– E

ɫɦ

|

ɢ

S

1

=

0.

ɉɪɢ ɜɨɡɪɚɫɬɚɧɢɢ

U

ɜɯ

ɭɝɨɥ

Θ

ɢɡɦɟɧɹɟɬɫɹ ɨɬ 0 ɞɨ

π

/ 2

,

S

1

ɜɨɡɪɚɫɬɚɟɬ ɨɬ

0

ɞɨ

0,5S

0

, ɧɨ ɧɟ ɞɨɫɬɢɝɚɟɬ ɷɬɨɝɨ

ɡɧɚɱɟɧɢɹ, ɬɚɤ ɤɚɤ ɬɪɚɧɡɢɫɬɨɪ ɩɟɪɟɯɨɞɢɬ ɜ ɉɊ.

Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (5.7) ɧɚɯɨɞɢɬɫɹ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɤɪɢɜɨɣ

S

1

(

U

ɜɯ

) ɫ

ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɪɹɦɨɣ ɧɚ ɭɪɨɜɧɟ

1/R

ɭ

, ɝɞɟ ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɩɪɢɧɹɬɨ ɨɛɨɡɧɚɱɟɧɢɟ

R

ɭ

=

k

ɨɫ

R

ɧ

. ɉɪɢ ɦɚɥɨɦ ɭɪɨɜɧɟ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ, ɤɨɝɞɚ

1/R

ɭ

>

S

0

, ɝɟɧɟɪɚɰɢɹ

ɧɟɜɨɡɦɨɠɧɚ. Ʉɨɝɞɚ

0,5S

0

<

1/R

ɭ

<

S

0

ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɨɞɧɭ ɫɬɚɰɢɨɧɚɪɧɭɸ

ɬɨɱɤɭ a. Ⱥ ɞɥɹ ɤɪɢɜɨɣ 3) ɧɚ ɪɢɫ. 5.5 ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɞɜɟ ɫɬɚɰɢɨɧɚɪɧɵɯ ɬɨɱɤɢ (b

ɢ c), ɟɫɥɢ

0

<

1/R

ɭ

<

0,5S

0

. Ʉ ɫɬɚɰɢɨɧɚɪɧɵɦ ɬɚɤɠɟ ɫɥɟɞɭɟɬ ɨɬɧɟɫɬɢ ɢ ɬɨɱɤɭ

ɩɨɤɨɹ

U

ɜɯ

=

0

.

ɇɟ ɜɫɟ ɩɨɥɭɱɟɧɧɵɟ ɫɬɚɰɢɨɧɚɪɧɵɟ ɬɨɱɤɢ ɹɜɥɹɸɬɫɹ ɭɫɬɨɣɱɢɜɵɦɢ. Ⱦɥɹ

ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɬɨɱɤɭ b. ȿɫɥɢ ɩɨ ɤɚɤɢɦ-ɥɢɛɨ ɩɪɢɱɢɧɚɦ ɜɯɨɞɧɨɟ ɧɚɩɪɹ-

ɠɟɧɢɟ

U

ɜɯ

ɭɦɟɧɶɲɢɥɨɫɶ, ɬɨ ɭɦɟɧɶɲɚɟɬɫɹ

S

1

, ɚ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ

U

ɜɵɯ

. ɇɚɩɪɹɠɟɧɢɟ

U

ɜɵɯ

ɫɜɹɡɚɧɨ ɫ

U

ɜɯ

ɱɟɪɟɡ ɤɨɷɮɮɢɰɢɟɧɬ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ

U

ɜɯ

=

U

ɜɵɯ

k

ɨɫ

. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɩɨɞɞɟɪɠɢɜɚɟɬ ɩɪɨɰɟɫɫ

ɭɦɟɧɶɲɟɧɢɹ ɚɦɩɥɢɬɭɞɵ

U

ɜɯ

ɢ ɤɨɥɟɛɚɧɢɹ ɩɪɟɤɪɚɬɹɬɫɹ. ȿɫɥɢ, ɧɚɩɪɨɬɢɜ, ɚɦɩɥɢ-

ɬɭɞɚ

U

ɜɯ

ɜ ɬɨɱɤɟ b ɧɚɱɧɟɬ ɫɩɨɧɬɚɧɧɨ ɜɨɡɪɚɫɬɚɬɶ, ɬɨ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ ɛɭɞɟɬ

ɩɨɞɞɟɪɠɢɜɚɬɶ ɩɪɨɰɟɫɫ ɭɜɟɥɢɱɟɧɢɹ

U

ɜɯ

.

Ɋɚɫɫɭɠɞɚɹ ɚɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ, ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ

ɫɬɪɟɦɢɬɫɹ ɭɞɟɪɠɚɬɶ ɤɨɥɟɛɚɧɢɹ ɨɤɨɥɨ ɬɨɱɤɢ c. ɗɬɚ ɬɨɱɤɚ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɬɨɱɤɢ b,

ɹɜɥɹɟɬɫɹ ɭɫɬɨɣɱɢɜɨɣ. Ɉɛɳɟɟ ɭɫɥɨɜɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɢɦɟɟɬ ɜɢɞ

S

1

S

0

ɇɊ

1/ R

ɭ1

a 1

2

S

0

/

2

b ɉɊ

3 c

|E

′

– E

ɫɦ

|

U

ɜɯ

Ɋɢɫ. 5.5. Ɂɚɜɢɫɢɦɨɫɬɶ ɫɪɟɞɧɟɣ ɤɪɭ-

ɬɢɡɧɵ

S

1

ɨɬ ɚɦɩɥɢɬɭɞɵ ɜɨɡɛɭɠɞɟɧɢɹ

1/ R

ɭ2

55

∂

S U

U

ɜɯ

1

0

( )

.<

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɱɤɚ a ɧɚ ɤɪɢɜɨɣ 1) ɹɜɥɹɟɬɫɹ ɬɚɤɠɟ ɭɫɬɨɣɱɢɜɨɣ.

ɋ ɩɨɧɹɬɢɟɦ ɭɫɬɨɣɱɢɜɨɫɬɢ ɬɟɫɧɨ ɫɜɹɡɚɧɵ ɩɨɧɹɬɢɹ ɦɹɝɤɨɝɨ ɢ ɠɟɫɬɤɨɝɨ

ɪɟɠɢɦɨɜ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ. ȼ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɬɨɱɤɚɯ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ

(5.3). ɉɪɢ ɷɬɨɦ, ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ

S

1

(U

ɜɯ

) k

ɨɫ

Zɧ > 1,

ɬɨ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɧɚɪɚɫɬɚɟɬ, ɚ ɟɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ

S

1

(U

ɜɯ

) k

ɨɫ

Zɧ < 1,

ɬɨ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɭɛɵɜɚɟɬ.

Ɍɨɱɤɚ ɩɨɤɨɹ, ɤɚɤ ɥɸɛɚɹ ɫɬɚɰɢɨɧɚɪɧɚɹ ɬɨɱɤɚ, ɦɨɠɟɬ ɛɵɬɶ ɭɫɬɨɣɱɢɜɨɣ ɢɥɢ

ɧɟɭɫɬɨɣɱɢɜɨɣ. ɇɚɩɪɢɦɟɪ, ɩɪɢ

E

′

< E

ɫɦ

(ɤɪɢɜɚɹ 1 ɧɚ ɪɢɫ. 5.5) ɬɨɱɤɚ ɩɨɤɨɹ

ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ. ɉɨɷɬɨɦɭ ɥɸɛɨɟ ɫɥɭɱɚɣɧɨɟ ɤɨɥɟɛɚɧɢɟ ɜ ɦɨɦɟɧɬ

ɜɤɥɸɱɟɧɢɹ ȺȽ ɩɪɢɜɨɞɢɬ ɤ ɛɵɫɬɪɨɦɭ ɧɚɪɚɫɬɚɧɢɸ ɚɦɩɥɢɬɭɞɵ ɢ ɩɟɪɟɯɨɞɭ ɜ

ɭɫɬɨɣɱɢɜɭɸ ɫɬɚɰɢɨɧɚɪɧɭɸ ɬɨɱɤɭ

a

. ɗɬɨ ɪɟɠɢɦ ɦɹɝɤɨɝɨ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ. ȿɫɥɢ

ɞɥɹ ɫɦɟɳɟɧɢɹ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ

E

′

> E

ɫɦ

, ɬɨ ɬɨɱɤɚ ɩɨɤɨɹ ɹɜɥɹɟɬɫɹ

ɭɫɬɨɣɱɢɜɨɣ. Ⱦɥɹ ɜɨɡɛɭɠɞɟɧɢɹ ȺȽ ɧɟɨɛɯɨɞɢɦ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ

ɩɟɪɜɨɧɚɱɚɥɶɧɵɣ ɬɨɥɱɨɤ, ɬɚɤ ɱɬɨɛɵ

U

ɜɯ

>

E

′

– E

ɫɦ

. ɗɬɨ ɪɟɠɢɦ ɠɟɫɬɤɨɝɨ

ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ.

5.4. Ⱦɢɚɝɪɚɦɦɚ ɫɪɵɜɚ ȺȽ. Ⱥɜɬɨɦɚɬɢɱɟɫɤɨɟ ɫɦɟɳɟɧɢɟ

Ɋɚɫɫɦɨɬɪɢɦ ɤɚɤ ɦɟɧɹɟɬɫɹ ɚɦɩɥɢɬɭɞɚ

U

ɜɯ

ɨɬ ɢɡɦɟɧɟɧɢɹ

E

ɫɦ

. ɗɬɭ ɡɚɜɢ-

ɫɢɦɨɫɬɶ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɪɢɫ. 5.5, ɨɞɧɚɤɨ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɧɚɣɬɢ ɩɪɹɦɭɸ ɫɜɹɡɶ

U

ɜɯ

ɢ

E

ɫɦ

, ɧɟ ɜɵɱɢɫɥɹɹ ɩɪɨɦɟɠɭɬɨɱɧɭɸ ɜɟɥɢɱɢɧɭ

S

1

.

Ɂɚɜɢɫɢɦɨɫɬɶ

U

ɜɯ

(

E

ɫɦ

) ɩɪɢ ɡɚɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɚɯ

k

ɨɫ

,

S

0

ɢ

R

ɧ

ɧɚɡɵɜɚɟɬɫɹ

ɞɢɚɝɪɚɦɦɨɣ ɫɪɵɜɚ. ɂɡ (5.7) ɢ (5.8) ɫɥɟɞɭɟɬ, ɱɬɨ ɟɫɥɢ ɩɚɪɚɦɟɬɪɵ

k

ɨɫ

,

S

0

ɢ

R

ɧ

ɩɨɫɬɨɹɧɧɵ, ɬɨ ɭɝɨɥ ɨɬɫɟɱɤɢ

Θ

ɬɚɤɠɟ ɩɨɫɬɨɹɧɟɧ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɢɚɝɪɚɦɦɚ ɫɪɵɜɚ

ɨɩɢɫɵɜɚɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

U E E

ɜɯ ɫɦ

= − −

′

1

cos

( ).

Θ

ȼ ɉɊ ɪɚɫɱɟɬ ɞɢɚɝɪɚɦɦɵ ɫɪɵɜɚ ɫɥɨɠɟɧ. ɉɪɢɛɥɢɠɟɧɧɨ ɟɺ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ,

ɨɪɢɟɧɬɢɪɭɹɫɶ ɧɚ ɩɨɥɨɠɟɧɢɟ ɥɢɧɢɢ ɤɪɢɬɢɱɟɫɤɨɝɨ ɪɟɠɢɦɚ. ȼɵɜɟɞɟɦ ɮɨɪɦɭɥɭ

ɞɥɹ ɧɟɺ, ɞɥɹ ɱɟɝɨ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɨɱɟɜɢɞɧɵɦ ɫɨɨɬɧɨɲɟɧɢɟɦ

[U

ɜɯ

– (E

′

– E

ɫɦ

)] S

0

= (E

ɉ

– U

ɜɵɯ

) S

ɤɪ

.

ȿɫɥɢ ɜɜɟɫɬɢ ɨɛɨɡɧɚɱɟɧɢɟ

χ =

S

0

/

S

ɤɪ

, ɢ ɭɱɟɫɬɶ, ɱɬɨ

U

ɜɵɯ

=

U

ɜɯ

/

k

ɨɫ

, ɬɨ ɦɨɠɧɨ

ɩɨɥɭɱɢɬɶ

( )

[ ]

ɫɦ

oc

ɜɯ

EEE

k

U

ɉ

−

′

+

=

χ

1

. (5.11)

Ⱦɢɚɝɪɚɦɦɵ ɫɪɵɜɚ ɞɥɹ ɪɚɡɧɵɯ ɭɝɥɨɜ ɨɬɫɟɱɤɢ

Θ

ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 5.6.

(5.9)

(5.10)

56

U

ɜɯ

c

Θ

< 90

o

Θ

= 90

o

Θ

> 90

o

ɉɊ

ɥɢɧɢɹ ɄɊ

Θ

=

0

b a

Θ

=180

o

ɇɊ

E

′

ɫɦ

E

′′

ɫɦ

E

ɫɦ

Ɋɢɫ. 5.6. Ⱦɢɚɝɪɚɦɦɵ ɫɪɵɜɚ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚ

Ɍɨɱɤɢ a, b, ɢ c ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɚɧɚɥɨɝɢɱɧɵɦ ɬɨɱɤɚɦ ɧɚ ɪɢɫ. 5.5. ɉɨɫɤɨɥɶɤɭ ɬɨɱɤɚ

b ɹɜɥɹɟɬɫɹ ɧɟɭɫɬɨɣɱɢɜɨɣ, ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ. ȼ ɪɟɠɢɦɟ ɦɹɝɤɨɝɨ

ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɚɜɬɨɝɟɧɟɪɚɬɨɪ ɦɨɠɟɬ ɪɚɛɨɬɚɬɶ ɬɨɥɶɤɨ ɫ ɭɝɥɚɦɢ ɨɬɫɟɱɤɢ

Θ

> 90

o

, ɩɪɢ ɤɨɬɨɪɵɯ ɧɚɛɥɸɞɚɟɬɫɹ ɛɨɥɟɟ ɜɵɫɨɤɨɟ ɡɧɚɱɟɧɢɟ ɩɨɫɬɨɹɧɧɨɣ

ɫɨɫɬɚɜɥɹɸɳɟɣ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ, ɱɬɨ ɭɜɟɥɢɱɢɜɚɟɬ ɮɥɭɤɬɭɚɰɢɢ ɱɚɫɬɨɬɵ, ɬ.ɟ.

ɫɧɢɠɚɟɬɫɹ ɫɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬɵ ȺȽ. Ɉɩɬɢɦɚɥɶɧɵɦɢ ɭɝɥɚɦɢ ɨɬɫɟɱɤɢ ɞɥɹ

ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ȺȽ ɹɜɥɹɸɬɫɹ

Θ

= 60

ɨ

...75

ɨ

, ɧɨ ɷɬɢ ɡɧɚɱɟɧɢɹ ɜɨɡɦɨɠɧɵ ɬɨɥɶɤɨ

ɩɪɢ ɠɟɫɬɤɨɦ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɢ. ɉɪɢ ɷɬɨɦ ɬɪɚɧɡɢɫɬɨɪ ɪɚɛɨɬɚɟɬ ɜ ɉɊ, ɱɬɨ ɫɨɜɟɪ-

ɲɟɧɧɨ ɧɟɞɨɩɭɫɬɢɦɨ, ɬɚɤ ɤɚɤ ɜɨɡɪɚɫɬɚɸɬ ɝɚɪɦɨɧɢɤɢ ɜ ɜɵɯɨɞɧɨɦ ɬɨɤɟ ɢ,

ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɟɡɤɨ ɫɧɢɠɚɟɬɫɹ ɫɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬɵ. ɉɟɪɟɱɢɫɥɟɧɧɵɟ ɜɵɲɟ

ɩɪɨɛɥɟɦɵ ɫɜɹɡɚɧɵ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɫɦɟɳɟɧɢɹ, ɢ ɢɯ ɦɨɠɧɨ

ɨɛɨɣɬɢ, ɩɪɢɦɟɧɢɜ ɚɜɬɨɦɚɬɢɱɟɫɤɨɟ ɫɦɟɳɟɧɢɟ.

Ɋɚɫɫɦɨɬɪɢɦ ɫɯɟɦɭ ȺȽ ɧɚ ɛɢɩɨɥɹɪɧɨɦ ɬɪɚɧɡɢɫɬɨɪɟ ɫ ɤɨɦɛɢɧɢɪɨɜɚɧɧɵɦ

ɚɜɬɨɫɦɟɳɟɧɢɟɦ (ɪɢɫ. 5.7) ɢ ɜɵɹɫɧɢɦ, ɤɚɤ ɫɜɹɡɚɧɵ ɧɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ ɧɚ

ɛɚɡɟ

E

ɫɦ

ɢ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ

U

ɜɯ

.

ɇɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ

ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɫɦɟɳɟɧɢɹ

U

ɛ0

ɢ ɩɚɞɟɧɢɣ

ɧɚɩɪɹɠɟɧɢɣ ɧɚ ɪɟɡɢɫɬɨɪɚɯ

R

ɛ

ɢ

R

ɷ

ɡɚ ɫɱɟɬ

ɩɪɨɬɟɤɚɧɢɹ ɩɨɫɬɨɹɧɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ

ɬɨɤɨɜ ɛɚɡɵ

I

ɛ0

ɢ ɷɦɢɬɬɟɪɚ

I

ɷ0

:

E U I R I R

ɫɦ ɛ ɛ ɛ ɷ ɷ

=

−

⋅

−

⋅

=

0 0 0

= U

ɛ0

– U

ɜɯ

γ

0

(

Θ

)(S

ɛ

R

ɛ

+ S

0

R

ɷ

),

ɝɞɟ

S

ɛ

— ɤɪɭɬɢɡɧɚ ɛɚɡɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫ-

ɬɢɤɢ, ɢ ɫɱɢɬɚɟɬɫɹ, ɱɬɨ

I

ɷ0

≈

I

ɤ0

. Ɉɬɫɸɞɚ

ɧɚɯɨɞɢɦ

( ) ( )

Θ+

−

=

0ɷ0ɛɛ

ɫɦ0ɛ

ɜɯ

RSRS

EU

U

γ

. (5.12)

ɍɝɨɥ ɨɬɫɟɱɤɢ ɜ (5.12), ɤɚɤ ɢ ɩɪɟɠɞɟ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ (5.10). Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ

ɫɬɚɰɢɨɧɚɪɧɨɣ ɬɨɱɤɢ ȺȽ ɫ ɚɜɬɨɦɚɬɢɱɟɫɤɢɦ ɫɦɟɳɟɧɢɟɦ, ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ

ɫɨɜɦɟɫɬɧɨɟ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɣ (5.12) ɢ (5.10). ɋɞɟɥɚɟɦ ɷɬɨ ɝɪɚɮɢɱɟɫɤɢɦ ɫɩɨ-

ɫɨɛɨɦ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 5.8.

I

ɛ0

R

ɛ

C

ɛ

I

ɷ0

U

ɛ0

R

ɷ

ɋ

ɷ

Ɋɢɫ. 5.7. ɐɟɩɶ ɤɨɦɛɢɧɢɪɨɜɚɧɧɨɝɨ

ɚɜɬɨɫɦɟɳɟɧɢɹ

57

U

ɜɯ

50

ɨ

70

ɨ

ɥɢɧɢɹ ɄɊ

Θ

= 0 90

ɨ

140

ɨ

Θ

= 180

ɨ

90

ɨ

Θ

= 0

50

ɨ

140

ɨ

70

ɨ

Θ

=180

ɨ

E

′

U

ɛ0

E

ɫɦ

Ɋɢɫ. 5.8. Ⱦɢɚɝɪɚɦɦɵ ɫɦɟɳɟɧɢɹ ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚ

ɍɪɚɜɧɟɧɢɟ (5.10) ɞɚɟɬ ɫɟɦɟɣɫɬɜɨ ɩɪɹɦɵɯ, ɢɫɯɨɞɹɳɢɯ ɢɡ ɬɨɱɤɢ

E

′

, ɚ

ɭɪɚɜɧɟɧɢɟ (5.12) — ɬɚɤɨɟ ɠɟ ɫɟɦɟɣɫɬɜɨ, ɢɫɯɨɞɹɳɟɟ ɢɡ ɬɨɱɤɢ

U

ɛ0

. Ɋɟɲɟɧɢɟ

ɧɚɯɨɞɢɬɫɹ ɤɚɤ ɩɟɪɟɫɟɱɟɧɢɟ ɩɪɹɦɵɯ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɨɞɢɧɚɤɨɜɵɦ ɭɝɥɚɦ

ɨɬɫɟɱɤɢ. Ɋɟɲɟɧɢɟ ɩɨɥɭɱɚɟɬɫɹ ɟɞɢɧɫɬɜɟɧɧɵɦ, ɚ ɫɬɚɰɢɨɧɚɪɧɚɹ ɬɨɱɤɚ ɹɜɥɹɟɬɫɹ

ɭɫɬɨɣɱɢɜɨɣ ɩɪɢ ɥɸɛɨɦ

Θ

.

Ⱦɥɹ ɢɫɤɥɸɱɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ ɩɨ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɟ ɱɟɪɟɡ

ɪɟɡɢɫɬɨɪɵ

R

ɛ

ɢ

R

ɷ

, ɨɧɢ ɲɭɧɬɢɪɭɸɬɫɹ ɟɦɤɨɫɬɹɦɢ

C

ɛ

ɢ

C

ɷ

. ɗɬɨ ɩɪɢɞɚɟɬ ɚɜɬɨɦɚ-

ɬɢɱɟɫɤɨɦɭ ɫɦɟɳɟɧɢɸ ɨɩɪɟɞɟɥɟɧɧɭɸ ɢɧɟɪɰɢɨɧɧɨɫɬɶ. Ʉɨɥɟɛɚɬɟɥɶɧɚɹ ɫɢɫɬɟɦɚ ȺȽ

ɬɚɤɠɟ ɹɜɥɹɟɬɫɹ ɢɧɟɪɰɢɨɧɧɨɣ. ȼɨɡɦɨɠɧɚ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɚɜɬɨɫɦɟɳɟɧɢɟ ɧɟ ɛɭɞɟɬ

ɭɫɩɟɜɚɬɶ ɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɫɥɭɱɚɣɧɵɟ ɢɡɦɟɧɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ȺȽ. ȼ

ɷɬɨɦ ɫɥɭɱɚɟ ɜɨɡɧɢɤɚɟɬ ɩɪɟɪɵɜɢɫɬɚɹ ɝɟɧɟɪɚɰɢɹ — ɩɟɪɢɨɞɢɱɟɫɤɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɢ

ɫɪɵɜ ɝɟɧɟɪɚɰɢɢ. ɉɟɪɟɱɢɫɥɢɦ ɭɫɥɨɜɢɹ, ɩɪɢ ɤɨɬɨɪɵɯ ɜɨɡɧɢɤɚɟɬ ɷɬɨ ɹɜɥɟɧɢɟ:

• ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɰɟɩɢ ɚɜɬɨɫɦɟɳɟɧɢɹ ɛɨɥɶɲɟ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ

ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ:

τ

ω

ɫɦ ɷ ɷ

ɝ

R C

Q

≈ ⋅ >

2

,

ɝɞɟ

Q

— ɞɨɛɪɨɬɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ;

• ɭɝɨɥ ɨɬɫɟɱɤɢ

Θ

< 90

o

;

• ɞɢɚɝɪɚɦɦɵ ɫɪɵɜɚ ɢ ɫɦɟɳɟɧɢɹ ɩɟɪɟɫɟɤɚɸɬɫɹ ɧɢɠɟ ɥɢɧɢɢ ɄɊ.

5.5. Ɋɚɫɱɟɬ ɜɧɟɲɧɢɯ ɰɟɩɟɣ ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚ.

ɇɚ ɪɢɫ. 5.9 ɩɪɟɞɫɬɚɜɥɟɧɚ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ȺȽ. Ɋɚɫ-

ɫɦɨɬɪɢɦ ɩɪɢɧɰɢɩɵ ɪɚɫɱɟɬɚ ɟɝɨ ɜɧɟɲɧɢɯ ɰɟɩɟɣ.

Ɋɚɫɱɟɬ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ. Ɉɧɚ ɫɨɫɬɨɢɬ ɢɡ ɤɨɧɬɭɪɚ L C1 C2 C3.

ɑɚɫɬɨɬɚ ɚɜɬɨɤɨɥɟɛɚɧɢɣ ɪɚɜɧɚ ɪɟɡɨɧɚɧɫɧɨɣ ɱɚɫɬɨɬɟ ɤɨɧɬɭɪɚ

ω

ɝ

LC= 1

Σ

,

ɝɞɟ

C

Σ

— ɫɭɦɦɚɪɧɚɹ ɟɦɤɨɫɬɶ ɤɨɧɬɭɪɚ;

58

1 1 1 1 2 1 3C C C C

Σ

=

+

′

+

,

C C C

ɫɜ

′

=

+

′

2 2 ,

C

′

ɫɜ

— ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɟɦɤɨɫɬɶ

ɫɜɹɡɢ ɫ ɧɚɝɪɭɡɤɨɣ, ɩɟɪɟɫɱɢ-

ɬɚɧɧɚɹ ɜ ɩɚɪɚɥɥɟɥɶɧɭɸ ɫɯɟɦɭ.

Ʉɨɧɬɭɪ ɩɨɞɤɥɸɱɟɧ ɤ ɬɪɚɧ-

ɡɢɫɬɨɪɭ ɧɟ ɩɨɥɧɨɫɬɶɸ. Ʉɨɷɮ-

ɮɢɰɢɟɧɬ ɜɤɥɸɱɟɧɢɹ

p U U

ɤ ɤɨɧɬ

=

1

,

ɝɞɟ

U

ɤ1

— ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚ-

ɧɢɣ ɧɚ ɤɨɥɥɟɤɬɨɪɟ ɬɪɚɧɡɢɫ-

ɬɨɪɚ, ɚ

U

ɤɨɧɬ

— ɚɦɩɥɢɬɭɞɚ

ɤɨɥɟɛɚɧɢɣ ɧɚ ɜɫɟɦ ɤɨɧɬɭɪɟ (ɧɚ

ɢɧɞɭɤɬɢɜɧɨɫɬɢ L), ɨɛɟɫɩɟɱɢ-

ɜɚɟɬ ɧɟɨɛɯɨɞɢɦɭɸ ɧɚɝɪɭɡɤɭ ɞɥɹ ɤɨɥɥɟɤɬɨɪɧɨɣ ɰɟɩɢ. ɇɚɝɪɭɡɤɚ ɜ ɰɟɩɢ

ɤɨɥɥɟɤɬɨɪɚ

R

ɤ

= p

2

R

ɪ

, ɝɞɟ

R

ɪ

— ɪɟɡɨɧɚɧɫɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ.

Ɋɚɫɱɟɬ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɛɵɱɧɨ ɧɚɱɢɧɚɟɬɫɹ ɫ ɜɵɛɨɪɚ ɩɨ ɤɨɧɫɬ-

ɪɭɤɬɢɜɧɵɦ ɫɨɨɛɪɚɠɟɧɢɹɦ ɢɧɞɭɤɬɢɜɧɨɫɬɢ L. ɋɜɹɡɶ ɫ ɧɚɝɪɭɡɤɨɣ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ

ɫɬɚɛɢɥɶɧɨɫɬɢ ɱɚɫɬɨɬɵ ɞɟɥɚɸɬ ɨɫɥɚɛɥɟɧɧɨɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɝɪɭɠɟɧɧɚɹ ɞɨɛ-

ɪɨɬɧɨɫɬɶ ɤɨɧɬɭɪɚ

Q

ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɞɨɛɪɨɬɧɨɫɬɢ ɤɚɬɭɲɤɢ ɢɧɞɭɤɬɢɜɧɨɫɬɢ, ɢ

ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ

R

ɪ

=

ρ

Q

, ɝɞɟ

ρ = ω

ɝ

L

— ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɟ ɫɨ-

ɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ. Ⱦɚɥɟɟ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɭɦɦɚɪɧɚɹ ɟɦɤɨɫɬɶ

C

Σ

ɢ ɤɨɷɮ-

ɮɢɰɢɟɧɬ ɜɤɥɸɱɟɧɢɹ

p.

ȿɦɤɨɫɬɢ ɤɨɧɞɟɧɫɚɬɨɪɨɜ ɤɨɧɬɭɪɚ ɪɚɫɫɱɢɬɵɜɚɸɬ ɢɡ

ɜɵɪɚɠɟɧɢɣ

p = C

Σ

/C2

ɢ

k

ɨɫ

=

C2

/

C1

.

Ɋɚɫɱɟɬ ɰɟɩɢ ɫɦɟɳɟɧɢɹ. ɇɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ ɦɟɠɞɭ ɛɚɡɨɣ ɢ ɷɦɢɬɬɟɪɨɦ

E

R

R1 R

E I R I

R1 R

ɫɦ ɉ ɷ ɗ ɛ

=

+

− ⋅ − ⋅

⋅

+

2

0 0

.

ɍɱɢɬɵɜɚɹ, ɱɬɨ

I

ɷ0

≈

I

ɤ0

ɢ

I

ɛ0

=

I

ɤ0

/

h

21ɷ

, ɡɚɩɢɲɟɦ

Σ

−=

¸

¹

·

¨

©

§

+−≅ RIU

h

R

RIUE

ɤ

ɛ

ɢɫɬ

ɤ

ɛ

ɫɦ

ɗ

0

21

,

ɝɞɟ

U E

R

R1 R

ɛ ɉ0

2

=

+

,

R R

R

h

ɷ

ɢɫɬ

ɷ

Σ

= +

21

,

R

R1 R

ɢɫɬ

=

⋅

+

2

.

ɍɪɚɜɧɟɧɢɟ (5.13) ɨɩɢɫɵɜɚɟɬ ɫɬɚɰɢɨɧɚɪɧɵɣ ɪɟɠɢɦ ɤɨɥɟɛɚɧɢɣ, ɜ ɤɨɬɨɪɨɦ

E E U

ɫɦ ɜɯ

=

′

−

cos .

Θ

ȼ ɦɨɦɟɧɬ ɜɨɡɛɭɠɞɟɧɢɹ, ɤɨɝɞɚ

U

ɜɯ

= 0, ɧɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ ɢɦɟɟɬ ɞɪɭɝɨɟ

ɡɧɚɱɟɧɢɟ:

(

)

(

)

Σ

−= RIUE

0ɤ

0ɛɫɦ

0

R

Ɏ

C

ɋȼ

E

ɉ

C

ɛɥ

L

R1 C2 R

ɇ

C3

R2 C1 R

ɗ

ɋ

ȻɅ

Ɋɢɫ. 5.9. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ

ɫɯɟɦɚ ɬɪɚɧɡɢɫɬɨɪɧɨɝɨ ȺȽ

(5.13)

(5.14)

59

ɝɞɟ ɜɟɪɯɧɢɟ ɢɧɞɟɤɫɵ (0) ɭɤɚɡɵɜɚɸɬ ɧɚ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɜ ɦɨɦɟɧɬ

ɜɨɡɛɭɠɞɟɧɢɹ ȺȽ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ (5.13) ɢ (5.15) ɜɜɟɞɟɦ ɟɳɟ

ɬɪɢ ɭɫɥɨɜɢɹ.

• Ⱥɜɬɨɫɦɟɳɟɧɢɟ ɛɭɞɟɦ ɫɨɡɞɚɜɚɬɶ ɜ ɨɫɧɨɜɧɨɦ ɡɚ ɫɱɟɬ ɬɨɤɚ ɷɦɢɬɬɟɪɚ

I

ɷ

0

, ɚ

ɷɬɨ ɡɧɚɱɢɬ, ɱɬɨ

R

ɷ

>> R

ɢɫɬ

/h

21

ɷ

.

• ȼ ɦɨɦɟɧɬ ɜɨɡɛɭɠɞɟɧɢɹ, ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɹɝɤɨɝɨ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ, ɬɪɚɧ-

ɡɢɫɬɨɪ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɜ ɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ:

(

)

(

)

(

)

(

)

(

)

ȿRIUSȿESI

0ɤ

0ɛ0ɫɦ0

0ɤ

′

−−=

′

−=

Σ

0

Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ

( )

0

0ɛ

ɤ

S

R

ȿU

I

1

0

+

′

−

=

Σ

•ɉɨɬɪɟɛɭɟɦ, ɱɬɨɛɵ ɩɨɫɬɨɹɧɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ ɫɥɚɛɨ

ɡɚɜɢɫɟɥɚ ɨɬ ɢɡɦɟɧɟɧɢɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɢ ɨɩɪɟɞɟɥɹɥɚɫɶ

ɜɧɟɲɧɢɦɢ ɷɥɟɦɟɧɬɚɦɢ ɰɟɩɢ, ɱɬɨ ɭɜɟɥɢɱɢɜɚɟɬ ɫɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬɵ.

Ⱦɥɹ ɷɬɨɝɨ ɧɚɣɞɟɦ ɬɨɤ

I

ɤ

0

.

I U S

E E

S

E U I R

S

ɤ ɜɯ

ɫɦ ɛ ɤ

0 0 0 0 0

0 0

= =

′

−

=

′

−

+

γ γ γ

cos cos

.

Θ Θ

Σ

Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ

I

U E

R

S

ɤ

ɛ

0

0 0

=

−

′

−

Σ

Θ

cos

.

γ

ɂɡ ɫɪɚɜɧɟɧɢɹ (5.16) ɢ (5.17) ɜɢɞɧɨ, ɱɬɨ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɹ

(

)

0ɤ

II ≅

0

ɬɪɟɛɭɟɬɫɹ ɱɬɨɛɵ

R

S S

Σ

Θ

>> +

1

0 0 0

cos

.

γ

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɱɟɬ ɰɟɩɢ ɫɦɟɳɟɧɢɹ ɫɥɟɞɭɟɬ ɧɚɱɚɬɶ ɫ ɜɵɛɨɪɚ ɫɭɦɦɚɪɧɨɝɨ

ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɜɬɨɫɦɟɳɟɧɢɹ:

(

)

( )

»

¼

º

«

¬

ª

+=

Σ

Ĭ

S

R

00

γ

cos

1

53

.

Ɂɚɬɟɦ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɧɚɩɪɹɠɟɧɢɟ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɫɦɟɳɟɧɢɹ:

U E I R

ɛ ɫɦ ɤ0 0

=

+

⋅

Σ

.

Ⱦɚɥɟɟ ɢɡ ɨɱɟɜɢɞɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɜɫɟ ɷɥɟɦɟɧɬɵ ɰɟɩɢ

ɫɦɟɳɟɧɢɹ.

Ɋɚɫɱɟɬ ɰɟɩɢ ɩɢɬɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɪɚɫɱɟɬɟ ɷɥɟɦɟɧɬɨɜ

R

ɮ

ɢ

C

ɛɥ

. Ɉɱɟɜɢɞɧɨ

ɫɨɨɬɧɨɲɟɧɢɟ ɞɥɹ ɪɚɫɱɟɬɚ

R

ɮ

:

R

ɮ

≈ (5…10)

R

ɤ

. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɟɦɤɨɫɬɢ

(5.15)

(5.16)

(5.17)

(5.18)

(5.19)

60

ɛɥɨɤɢɪɨɜɨɱɧɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ

C

ɛɥ

ɧɚ ɪɚɛɨɱɟɣ ɱɚɫɬɨɬɟ ɞɨɥɠɧɨ ɛɵɬɶ ɩɨ ɜɨɡɦɨɠ-

ɧɨɫɬɢ ɦɚɥɵɦ. ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ ɧɭɠɧɨ ɭɱɟɫɬɶ

ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɢ

R

ɮ

:

E

ɉ

= U

ɤ

0

+ I

Ʉ

0

R

ɮ

.

5.6. Ʉɜɚɪɰɟɜɚɹ ɫɬɚɛɢɥɢɡɚɰɢɹ ɱɚɫɬɨɬɵ

ɋɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬɵ ȺȽ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɞɨɛɪɨɬɧɨɫɬɢ ɤɨɧɬɭɪɚ. Ɉɞɧɚɤɨ

ɞɨɛɪɨɬɧɨɫɬɢ ɨɛɵɱɧɵɯ LC ɤɨɧɬɭɪɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɜɟɥɢɤɢ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ

ɛɨɥɶɲɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ȺȽ ɫ ɤɜɚɪɰɟɜɵɦɢ ɪɟɡɨɧɚɬɨɪɚɦɢ.

ɉɨɜɟɞɟɧɢɟ ɪɟɡɨɧɚɬɨɪɚ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ ɨɩɢɫɵɜɚɟɬɫɹ ɟɝɨ

ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɨɣ (ɪɢɫ. 5.10). Ɉɧɚ ɫɨɫɬɨɢɬ ɢɡ ɩɚɪɚɥɥɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ

ɫɬɚɬɢɱɟɫɤɨɣ ɟɦɤɨɫɬɢ ɤɜɚɪɰɚ

C

0

ɢ ɛɟɫɤɨɧɟɱɧɨɝɨ ɪɹɞɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ

ɤɨɧɬɭɪɨɜ

L

n

, C

n

, r

n

(n =1, 3, 5,...), ɤɨɬɨɪɵɟ ɦɨɞɟɥɢɪɭɸɬ ɢɡɦɟɧɟɧɢɟ ɩɶɟɡɨɬɨɤɚ

ɤɜɚɪɰɚ ɨɬ ɱɚɫɬɨɬɵ ɜɛɥɢɡɢ ɟɝɨ ɪɟɡɨɧɚɧɫɧɵɯ ɱɚɫɬɨɬ.

ȿɦɤɨɫɬɶ

C

0

≈ 3...10 ɩɎ ɫɤɥɚɞɵ-

ɜɚɟɬɫɹ ɢɡ ɟɦɤɨɫɬɟɣ ɤɜɚɪɰɟɞɟɪɠɚɬɟɥɹ

ɢ ɜɵɜɨɞɨɜ. Ⱦɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ

ɤɨɧɬɭɪɨɜ ɤɜɚɪɰɟɜɨɝɨ ɪɟɡɨɧɚɬɨɪɚ

ɯɚɪɚɤɬɟɪɧɵ ɨɱɟɧɶ ɛɨɥɶɲɢɟ ɯɚɪɚɤɬɟ-

ɪɢɫɬɢɱɟɫɤɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ρ

n

L

C

= =10 10

4 7



Ɉɦ.

ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨɬɟɪɶ

r

n

ɜ ɡɚɜɢ-

ɫɢɦɨɫɬɢ ɨɬ ɜɢɞɚ ɤɨɥɟɛɚɧɢɣ ɢ ɱɚɫɬɨ-

ɬɵ ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɨɬ ɟɞɢɧɢɰ ɞɨ

ɧɟɫɤɨɥɶɤɢɯ ɬɵɫɹɱ Ɉɦ, ɞɨɛɪɨɬɧɨɫɬɢ ɤɨɧɬɭɪɨɜ ɜɵɫɨɤɢɟ

Q

ɤɜ

n

=

ρ

n

/r

n

= 10

4

...10

7

.

ɇɚ ɥɸɛɨɣ ɝɚɪɦɨɧɢɤɟ ɤɨɥɟɛɚɬɟɥɶɧɵɣ ɤɨɧɬɭɪ ɢɦɟɟɬ ɞɜɟ ɫɨɛɫɬɜɟɧɧɵɟ

ɱɚɫɬɨɬɵ. ɉɟɪɜɚɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɱɚɫɬɨɬɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɪɟɡɨɧɚɧɫɚ ɞɢɧɚ-

ɦɢɱɟɫɤɨɣ ɜɟɬɜɢ

ω

ɤɜn n n

L C=1 ,

ɚ ɜɬɨɪɚɹ

ω

ɉ

n

>

ω

ɤɜ

n

— ɱɚɫɬɨɬɟ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɪɟɡɨɧɚɬɨɪɚ ɜɫɟɝɨ ɤɨɧɬɭɪɚ

ω ω

ɉn

n

ɤɜn

n

L

C C

C

=

+

= +

1

0

.

ɉɨɫɤɨɥɶɤɭ

C

n

/

C

0

<< 1, ɢɧɬɟɪɜɚɥ (

ω

ɉ

n

–

ω

ɤɜ

n

)/

ω

ɤɜ

n

≈ 10

-3

...10

-4

.

Ʉɜɚɪɰ ɷɤɜɢɜɚɥɟɧɬɟɧ ɤɨɧɬɭɪɭ ɫ ɨɱɟɧɶ ɦɚɥɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɜɤɥɸɱɟɧɢɹ,

ɩɨɷɬɨɦɭ ɢɡɦɟɧɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɜɧɟɲɧɟɣ ɫɯɟɦɵ ɫɥɚɛɨ ɜɥɢɹɸɬ ɧɚ ɫɬɚɛɢɥɶɧɨɫɬɶ

ɱɚɫɬɨɬ

ω

ɉ

n

ɢ

ω

ɤɜ

n

. ɇɚ ɪɢɫ. 5.11 ɩɨɤɚɡɚɧɚ ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɯɨɞɧɨɝɨ

ɫɨɩɪɨɬɢɜɥɟɧɢɹ

Z

ɤɜ

=

X

ɤɜ

+ j R

ɤɜ

.

L

1

L

3

C

0

C

1

C

3

r

1

r

3

Ɋɢɫ. 5.10. ɗɤɜɢɜɚɥɟɧɬɧɚɹ ɫɯɟɦɚ

ɤɜɚɪɰɟɜɨɝɨ ɪɟɡɨɧɚɬɨɪɚ

(5.20)

(5.21)

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