Воробьев М.С. Устройства генерирования радиосигналов

111

K

I

C

U

ɇ

B

2

1

2

1

4

= = =

+

′

Ω

γ

.

ɍɱɢɬɵɜɚɹ (11.20), ɩɨɥɭɱɚɟɦ

K

k

ɇ

Ⱦ

B

2

0

1

2

1

= ⋅

+

⋅

∆

ω

γ

.

ɋɨɨɬɧɨɲɟɧɢɟ (11.23) ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɬɪɟɛɨɜɚɧɢɹ ɤ ɱɚɫɬɨɬɧɨɦɭ ɦɨɞɭɥɹɬɨɪɭ

ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɨɝɨ

K

ɇ

2

: 1) ɩɪɢɦɟɧɹɬɶ ɜɚɪɢɤɚɩɵ ɫ ɜɨɡɦɨɠɧɨ ɛɨɥɶɲɢɦɢ

ɡɧɚɱɟɧɢɹɦɢ

γ

(ɪɟɡɤɢɟ ɢ ɫɜɟɪɯɪɟɡɤɢɟ p-n ɩɟɪɟɯɨɞɵ); 2) ɭɜɟɥɢɱɢɜɚɬɶ ɤɨɷɮɮɢɰɢɟɧɬ

ɜɤɥɚɞɚ ɜɚɪɢɤɚɩɚ ɜ ɫɭɦɦɚɪɧɭɸ ɟɦɤɨɫɬɶ ɤɨɧɬɭɪɚ; 3) ɭɦɟɧɶɲɚɬɶ ɞɟɜɢɚɰɢɸ ɱɚɫɬɨɬɵ.

ɍɦɟɧɶɲɟɧɢɟ ɞɟɜɢɚɰɢɢ ɱɚɫɬɨɬɵ ɦɨɠɟɬ ɛɵɬɶ ɤɨɦɩɟɧɫɢɪɨɜɚɧɨ ɩɨɫɥɟɞɭɸɳɢɦ

ɭɦɧɨɠɟɧɢɟɦ ɱɚɫɬɨɬɵ.

11.4. ɑɚɫɬɨɬɧɚɹ ɦɨɞɭɥɹɰɢɹ ɜ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚɯ ɋȼɑ

ɑɆ ɤɨɥɟɛɚɧɢɹ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ ɜ ɞɢɚɩɚɡɨɧɟ

ɋȼɑ. Ɋɚɫɫɦɨɬɪɢɦ ɫɩɨɫɨɛɵ ɩɨɥɭɱɟɧɢɹ ɑɆ ɜ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚɯ ɋȼɑ.

ȼ ɨɬɪɚɠɚɬɟɥɶɧɨɦ ɤɥɢɫɬɪɨɧɟ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɑɆ ɢɫɩɨɥɶɡɭɸɬ ɦɨɞɭɥɹɰɢɸ

ɩɨ ɧɚɩɪɹɠɟɧɢɸ ɧɚ ɨɬɪɚɠɚɬɟɥɟ

U

ɨɬɪ

. ɋɆɏ

∆

f

(

U

ɨɬɪ

) ɹɜɥɹɟɬɫɹ ɩɪɢɧɰɢɩɢɚɥɶɧɨ

ɧɟɥɢɧɟɣɧɨɣ. Ɉɞɧɚɤɨ ɜɛɥɢɡɢ ɰɟɧɬɪɨɜ ɡɨɧ ɝɟɧɟɪɚɰɢɢ ɟɟ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɥɢɧɟɣɧɨɣ ɫ

ɤɪɭɬɢɡɧɨɣ [9]

(

)

( )

ɨɬɪ

UUQ

n

fS

AH

f

−

=

25,0

0

π

, (11.24)

ɝɞɟ

f

0

— ɱɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ ɜ ɰɟɧɬɪɟ ɡɨɧɵ ɝɟɧɟɪɚɰɢɢ;

Q

H

— ɧɚɝɪɭɠɟɧɧɚɹ ɞɨɛ-

ɪɨɬɧɨɫɬɶ ɪɟɡɨɧɚɬɨɪɚ;

U

A

— ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɚɧɨɞɟ. Ⱦɢɚɩɚɡɨɧ ɷɥɟɤɬɪɨɧɧɨɣ

ɩɟɪɟɫɬɪɨɣɤɢ 2

∆

f

max

ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɫɧɢɠɟɧɢɟɦ ɦɨɳɧɨɫɬɢ ɧɚ ɤɪɚɹɯ ɡɨɧɵ

ɝɟɧɟɪɚɰɢɢ. Ⱦɨɩɭɫɬɢɦɵɦ ɫɱɢɬɚɟɬɫɹ ɭɦɟɧɶɲɟɧɢɟ ɦɨɳɧɨɫɬɢ ɧɟ ɛɨɥɟɟ ɱɟɦ ɜ 2 ɪɚɡɚ.

ȼ ɷɬɨɦ ɫɥɭɱɚɟ

2 12

0

∆

f

f Q

H

max

,

.=

Ɉɪɢɟɧɬɢɪɨɜɨɱɧɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ Q

H

= 150 ... 200, ɬ.ɟ. 2

∆

f

max

/

f

0

= (0,6...0,8)%.

Ɂɧɚɱɟɧɢɟ ɤɪɭɬɢɡɧɵ ɫɨɫɬɚɜɥɹɟɬ

S

f

= (0,5...1) ɆȽɰ/ȼ ɞɥɹ ɩɪɢɛɨɪɨɜ, ɪɚɛɨɬɚɸɳɢɯ ɫ

ɞɥɢɧɨɣ ɜɨɥɧɵ ɩɪɢɦɟɪɧɨ ɪɚɜɧɨɣ 10 ɫɦ, ɢ

S

f

≈ 0,5 ɆȽɰ/ȼ, ɟɫɥɢ ɞɥɢɧɚ ɜɨɥɧɵ ɪɚɜɧɚ

3 ɫɦ. ɇɚɢɛɨɥɶɲɢɟ ɧɟɥɢɧɟɣɧɵɟ ɢɫɤɚɠɟɧɢɹ ɧɚɛɥɸɞɚɸɬɫɹ ɩɨ ɬɪɟɬɶɟɣ ɝɚɪɦɨɧɢɤɟ.

¸

¹

·

¨

©

§

∆

=

0

3

max

3

1

f

Q

K

H

. (11.26)

Ɉɞɧɨɜɪɟɦɟɧɧɨ ɫ ɑɆ ɜɨɡɧɢɤɚɟɬ ɩɚɪɚɡɢɬɧɚɹ ɚɦɩɥɢɬɭɞɧɚɹ ɦɨɞɭɥɹɰɢɹ. Ⱦɥɹ

ɛɨɪɶɛɵ ɫ ɧɟɣ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɦɨɞɭɥɹɰɢɟɣ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɨɬɪɚɠɚɬɟɥɟ

U

ɨɬɪ

(11.22)

(11.23)

(11.25)

112

ɦɨɞɭɥɢɪɭɸɬ ɢ ɭɫɤɨɪɹɸɳɟɟ ɧɚɩɪɹɠɟɧɢɟ

U

0

(ɪɢɫ. 11.2, ɚ). Ⱦɥɹ ɩɨɹɫɧɟɧɢɹ ɷɬɨɝɨ

ɩɪɨɰɟɫɫɚ ɪɚɫɫɦɨɬɪɢɦ ɪɢɫ. 11.2, ɛ, ɝɞɟ ɩɨɫɬɪɨɟɧɵ ɥɢɧɢɢ ɩɨɫɬɨɹɧɧɨɣ ɦɨɳɧɨɫɬɢ ɢ

ɱɚɫɬɨɬɵ ɨɬɪɚɠɚɬɟɥɶɧɨɝɨ ɤɥɢɫɬɪɨɧɚ.

ɋ

ȻɅ

U

0

B

E

ɈɌɊ

U

Ω

0

f

1

t

U

Ω

ɨɬɪ

f

2

P

3

U

Ω

A

U

Ω

0

f

3

P

2

E

0

f

4

P

1

ɋ

ȻɅ

U

Ω

ɨɬɪ

U

ɨɬɪ

ɚ) ɛ)

t

Ɋɢɫ. 11.2. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɱɚɫɬɨɬɧɨɝɨ ɦɨɞɭɥɹɬɨɪɚ ɧɚ ɨɬɪɚɠɚɬɟɥɶɧɨɦ

ɤɥɢɫɬɪɨɧɟ (ɚ) ɢ ɟɝɨ ɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (ɛ)

ɂɡ ɪɢɫɭɧɤɚ ɜɢɞɧɨ, ɱɬɨ ɟɫɬɶ ɨɬɪɟɡɤɢ ɥɢɧɢɣ ɩɨɫɬɨɹɧɧɨɣ ɦɨɳɧɨɫɬɢ ɛɥɢɡɤɢɟ ɤ

ɩɪɹɦɵɦ, ɤɨɝɞɚ ɫɜɹɡɶ ɦɟɠɞɭ ɧɚɩɪɹɠɟɧɢɹɦɢ

U

0

ɢ

U

ɨɬɪ

ɛɥɢɡɤɚ ɤ ɥɢɧɟɣɧɨɣ. ȼɵɛɪɚɜ

ɢɡɦɟɧɟɧɢɟ ɪɟɠɢɦɚ ɜɞɨɥɶ ɭɱɚɫɬɤɚ Ⱥȼ ɧɚ ɥɢɧɢɢ ɩɨɫɬɨɹɧɧɨɣ ɦɨɳɧɨɫɬɢ

P

1

, ɦɨɠɧɨ

ɩɨɥɭɱɢɬɶ ɢɡɦɟɧɟɧɢɟ ɱɚɫɬɨɬɵ ɛɟɡ ɡɚɦɟɬɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɦɨɳɧɨɫɬɢ. ɉɪɢ ɷɬɨɦ

ɦɨɞɭɥɹɰɢɹ ɧɚɩɪɹɠɟɧɢɣ

U

0

ɢ

U

ɨɬɪ

ɞɨɥɠɧɚ ɛɵɬɶ ɩɪɨɬɢɜɨɮɚɡɧɨɣ.

ȼ ɚɜɬɨɝɟɧɟɪɚɬɨɪɚɯ ɧɚ ɦɢɬɪɨɧɚɯ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɚɧɨɞɧɵɦ ɧɚɩɪɹ-

ɠɟɧɢɟɦ

U

Ⱥ

ɢ ɱɚɫɬɨɬɨɣ ɝɟɧɟɪɚɰɢɢ

f

ɥɢɧɟɣɧɚ:

( )

Brr

NU

f

KA

A

22

2 −

=

π

, (11.27)

ɝɞɟ

N

— ɱɢɫɥɨ ɲɬɵɪɟɣ ɡɚɦɟɞɥɹɸɳɟɣ ɫɢɫɬɟɦɵ;

r

A

, r

K

— ɪɚɞɢɭɫɵ ɚɧɨɞɚ ɢ ɤɚɬɨɞɚ

ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ;

ȼ

— ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɨɛɥɚɫɬɢ ɜɡɚɢɦɨ-

ɞɟɣɫɬɜɢɹ. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɹɜɥɹɟɬɫɹ ɋɆɏ ɦɢɬɪɨɧɚ. ȿɟ ɤɪɭɬɢɡɧɚ ɫɨɫɬɚɜɥɹɟɬ

0,5…5 ɆȽɰ/ȼ. Ⱦɥɹ ɦɢɬɪɨɧɚ ɧɚɛɥɸɞɚɟɬɫɹ ɫɥɚɛɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɯɨɞɧɨɣ

ɦɨɳɧɨɫɬɢ ɨɬ ɧɚɩɪɹɠɟɧɢɹ

U

Ⱥ

. Ɉɞɧɚɤɨ, ɟɫɥɢ ɩɚɪɚɡɢɬɧɚɹ ȺɆ ɜɫɟ ɠɟ ɩɪɟɜɵɲɚɟɬ

ɞɨɩɭɫɬɢɦɭɸ ɜɟɥɢɱɢɧɭ, ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɦɨɞɭɥɹɰɢɸ

ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɭɩɪɚɜɥɹɸɳɟɦ ɷɥɟɤɬɪɨɞɟ, ɤɚɤ ɷɬɨ ɫɞɟɥɚɧɨ ɞɥɹ ɨɬɪɚɠɚɬɟɥɶɧɨɝɨ

ɤɥɢɫɬɪɨɧɚ.

ȼ ɦɚɝɧɟɬɪɨɧɧɵɯ ɢ ɫɬɚɛɢɥɨɬɪɨɧɧɵɯ ɝɟɧɟɪɚɬɨɪɚɯ ɩɨɥɭɱɟɧɢɟ ɑɆ ɫɨɩ-

ɪɨɜɨɠɞɚɟɬɫɹ ɝɥɭɛɨɤɨɣ ɩɚɪɚɡɢɬɧɨɣ ȺɆ. ɉɪɢɦɟɧɟɧɢɟ ɞɜɨɣɧɨɣ ɦɨɞɭɥɹɰɢɢ ɡɞɟɫɶ ɧɟ

ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ, ɩɨɫɤɨɥɶɤɭ ɨɬɫɭɬɫɬɜɭɟɬ ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ. ȼ

ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɑɆ ɩɭɬɟɦ ɫɢɧɯɪɨɧɢɡɚɰɢɢ (ɪɢɫ. 7.4).

ɋɢɧɯɪɨɧɢɡɢɪɭɸɳɢɣ ɝɟɧɟɪɚɬɨɪ G1 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɦɚɥɨɦɨɳɧɵɣ ɝɟɧɟɪɚɬɨɪ

113

ɑɆ ɤɨɥɟɛɚɧɢɣ. Ɇɨɳɧɵɣ ɝɟɧɟɪɚɬɨɪ G2, ɧɚɯɨɞɹɳɢɣɫɹ ɜ ɫɢɧɯɪɨɧɢɡɦɟ ɫ ɝɟɧɟ-

ɪɚɬɨɪɨɦ G1, ɬɚɤɠɟ ɜɵɪɚɛɚɬɵɜɚɟɬ ɑɆ ɤɨɥɟɛɚɧɢɹ, ɧɨ ɛɟɡ ɫɭɳɟɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ

ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ. ȼɵɪɚɠɟɧɢɟ (7.13) ɨɩɪɟɞɟɥɹɟɬ ɞɟɜɢɚɰɢɸ ɱɚɫɬɨɬɵ

ɫɢɧɯɪɨɧɢɡɢɪɭɟɦɨɝɨ ɝɟɧɟɪɚɬɨɪɚ.

ȼ ɞɢɨɞɧɵɯ ɝɟɧɟɪɚɬɨɪɚɯ (ɧɚ ɞɢɨɞɚɯ Ƚɚɧɧɚ ɢɥɢ ɅɉȾ) ɩɨɥɭɱɟɧɢɟ ɑɆ ɤɨɥɟ-

ɛɚɧɢɣ ɜɨɡɦɨɠɧɨ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ: ɢɡɦɟɧɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɢɥɢ ɬɨɤɚ ɩɢɬɚɧɢɹ ɢ

ɩɪɢɦɟɧɟɧɢɟɦ ɜɚɪɢɤɚɩɚ ɜ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɟ [10]. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ

ɢɫɩɨɥɶɡɭɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ ɪɟɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɢɨɞɚ X

Ⱦ

ɨɬ

ɜɨɡɛɭɠɞɚɸɳɟɝɨ ɬɨɤɚ

I

0

. Ɇɨɞɭɥɹɰɢɨɧɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɛɥɢɡɤɚ ɤ ɥɢɧɟɣɧɨɣ, ɚ

ɤɪɭɬɢɡɧɚ ɡɚɜɢɫɢɬ ɨɬ ɞɨɛɪɨɬɧɨɫɬɢ ɤɨɧɬɭɪɚ ɢ ɩɚɪɚɦɟɬɪɨɜ ɞɢɨɞɚ. ɇɟɞɨɫɬɚɬɤɨɦ

ɷɬɨɝɨ ɦɟɬɨɞɚ ɹɜɥɹɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɚɹ ɞɟɜɢɚɰɢɹ ɱɚɫɬɨɬɵ (0,15...0,3 % ɨɬ

ɫɪɟɞɧɟɣ ɱɚɫɬɨɬɵ) ɢ ɜɵɫɨɤɢɣ ɭɪɨɜɟɧɶ ɩɚɪɚɡɢɬɧɨɣ ȺɆ. ȼ ɫɥɭɱɚɟ ɩɪɢɦɟɧɟɧɢɹ

ɜɚɪɢɤɚɩɚ ɩɨɥɭɱɚɸɬɫɹ ɡɧɚɱɢɬɟɥɶɧɨ ɥɭɱɲɢɟ ɩɚɪɚɦɟɬɪɵ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɑɆ

ɤɨɥɟɛɚɧɢɣ ɫɥɟɞɭɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟɩɨɥɧɨɟ ɜɤɥɸɱɟɧɢɟ ɜɚɪɢɤɚɩɚ ɜ ɤɨɥɟɛɚɬɟɥɶɧɭɸ

ɫɢɫɬɟɦɭ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɫɨɯɪɚɧɢɬɶ ɜɵɫɨɤɭɸ ɞɨɛɪɨɬɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥɶɧɨɣ ɫɢɫɬɟɦɵ

ɩɪɢ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɞɟɜɢɚɰɢɢ (1...5 %).

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɱɚɫɬɨɬɧɵɯ ɦɨɞɭɥɹɬɨɪɨɜ ɜ ɞɢɚɩɚɡɨɧɟ ɋȼɑ ɠɟɥɚɬɟɥɶɧɨ

ɨɛɟɫɩɟɱɢɜɚɬɶ ɞɨɫɬɚɬɨɱɧɨ ɯɨɪɨɲɟɟ ɫɨɝɥɚɫɨɜɚɧɢɟ ɫ ɧɚɝɪɭɡɤɨɣ. ȼ ɩɪɨɬɢɜɧɨɦ

ɫɥɭɱɚɟ ɜ ɤɨɥɟɛɚɬɟɥɶɧɭɸ ɫɢɫɬɟɦɭ ɝɟɧɟɪɚɬɨɪɚ ɛɭɞɟɬ ɜɧɨɫɢɬɶɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ

ɪɟɚɤɬɢɜɧɨɫɬɶ b

H

, ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɦɟɧɹɬɶɫɹ ɫ ɢɡɦɟɧɟɧɢɟɦ ɱɚɫɬɨɬɵ. ȼɨɡɧɢɤɚɸɬ

ɞɨɜɨɥɶɧɨ ɫɥɨɠɧɵɟ ɷɮɮɟɤɬɵ, ɜɥɢɹɸɳɢɟ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɦɨɞɭɥɹɬɨɪɚ [10].

11.5. Ɇɟɬɨɞɵ ɩɨɜɵɲɟɧɢɹ ɥɢɧɟɣɧɨɫɬɢ ɱɚɫɬɨɬɧɵɯ

ɦɨɞɭɥɹɬɨɪɨɜ

Ɍɪɟɛɨɜɚɧɢɹ ɤ ɤɚɱɟɫɬɜɭ ɩɟɪɟɞɚɜɚɟɦɵɯ ɫɢɝɧɚɥɨɜ ɜ ɫɢɫɬɟɦɚɯ ɪɚɞɢɨɫɜɹɡɢ ɢ

ɜɟɳɚɧɢɹ ɩɨɫɬɨɹɧɧɨ ɜɨɡɪɚɫɬɚɸɬ. ɗɬɨ ɩɨɜɵɲɚɟɬ ɬɪɟɛɨɜɚɧɢɹ ɤ ɥɢɧɟɣɧɨɫɬɢ ɋɆɏ

ɱɚɫɬɨɬɧɵɯ ɦɨɞɭɥɹɬɨɪɨɜ. Ɇɨɠɧɨ ɭɤɚɡɚɬɶ ɧɟɫɤɨɥɶɤɨ ɧɚɩɪɚɜɥɟɧɢɣ ɪɟɲɟɧɢɹ ɭɤɚ-

ɡɚɧɧɨɣ ɩɪɨɛɥɟɦɵ.

1. ȼ ɱɚɫɬɨɬɧɵɯ ɦɨɞɭɥɹɬɨɪɚɯ ɧɚ ɜɚɪɢɤɚɩɚɯ ɧɟɨɛɯɨɞɢɦɨ ɪɚɰɢɨɧɚɥɶɧɨ

ɜɵɛɢɪɚɬɶ ɪɟɠɢɦ ɟɝɨ ɪɚɛɨɬɵ, ɱɬɨ ɭɠɟ ɨɛɫɭɠɞɚɥɨɫɶ ɜ ɩ. 11.3.

2. Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɥɢɧɟɣɧɨɫɬɢ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɢɦɟɧɹɬɶ ɧɟɥɢɧɟɣɧɵɟ

ɩɪɟɞɵɫɤɚɠɟɧɢɹ ɦɨɞɭɥɢɪɭɸɳɟɝɨ ɫɢɝɧɚɥɚ. ɉɨɫɤɨɥɶɤɭ ɨɬɤɥɨɧɟɧɢɹ ɟɦɤɨɫɬɢ

ɜɚɪɢɤɚɩɚ (ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɚɫɬɨɬɵ) ɜ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɩɨɥɭɩɟɪɢɨɞ ɦɨɞɭɥɹɰɢɢ

ɩɪɟɜɵɲɚɸɬ ɬɟ ɠɟ ɜɟɥɢɱɢɧɵ ɜ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɩɨɥɭɩɟɪɢɨɞ, ɬɨ ɦɨɞɭɥɢɪɭɸɳɢɣ

ɫɢɝɧɚɥ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɨɞɜɟɪɝɧɭɬɶ ɩɪɟɞɵɫɤɚɠɟɧɢɸ ɜ ɚɦɩɥɢɬɭɞɧɨɦ ɤɨɪɪɟɤɬɨɪɟ.

3. Ʉɨɪɪɟɤɰɢɹ ɋɆɏ ɦɨɠɟɬ ɛɵɬɶ ɨɫɭɳɟɫɬɜɥɟɧɚ ɩɨɞɤɥɸɱɟɧɢɟɦ ɤ ɜɚɪɢɤɚɩɭ

RLC-ɰɟɩɟɣ ɫ ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɱɚɫɬɨɬɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ. ɏɨɬɹ RLC-ɰɟɩɢ

ɹɜɥɹɸɬɫɹ ɥɢɧɟɣɧɵɦɢ ɞɥɹ ɩɟɪɟɦɟɧɧɵɯ ɬɨɤɨɜ ɧɚ ɮɢɤɫɢɪɨɜɚɧɧɨɣ ɱɚɫɬɨɬɟ, ɧɨ ɞɥɹ

ɑɆ ɤɨɥɟɛɚɧɢɹ ɷɬɢ ɰɟɩɢ ɧɟɥɢɧɟɣɧɵ, ɬɚɤ ɤɚɤ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɯ ɡɚɜɢɫɹɬ ɨɬ

ɱɚɫɬɨɬɵ. Ɍɚɤɢɟ ɰɟɩɢ ɩɪɢɦɟɧɹɸɬɫɹ ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɞɟɜɢɚɰɢɹɯ ɱɚɫɬɨɬɵ ɢ ɪɚɫ-

ɫɱɢɬɵɜɚɸɬɫɹ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɢɫɤɚɠɟɧɢɣ ɜɬɨɪɨɝɨ ɢɥɢ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɨɜ.

114

4. Ɇɨɞɭɥɹɬɨɪɵ ɫ ɛɨɥɶɲɨɣ ɞɟɜɢɚɰɢɟɣ ɱɚɫɬɨɬɵ ɫɬɪɨɹɬ ɩɨ ɫɯɟɦɟ, ɤɨɬɨɪɚɹ

ɩɨɥɭɱɢɥɚ ɧɚɡɜɚɧɢɟ ɞɜɭɯɬɚɤɬɧɨɣ. Ⱦɜɭɯɬɚɤɬɧɵɣ ɱɚɫɬɨɬɧɵɣ ɦɨɞɭɥɹɬɨɪ ɫɨɫɬɨɢɬ ɢɡ

ɞɜɭɯ ɨɛɵɱɧɵɯ ɦɨɞɭɥɹɬɨɪɨɜ

ɑɆȽ1 ɢ ɑɆȽ2 (ɪɢɫ. 11.3) ɢ ɫɦɟ-

ɫɢɬɟɥɹ ɋɆ. Ɇɨɞɭɥɹɬɨɪɵ ɪɚɛɨ-

ɬɚɸɬ ɧɚ ɫɪɟɞɧɢɯ ɱɚɫɬɨɬɚɯ

f

01

ɢ

f

02

.

ɇɚ ɜɵɯɨɞɟ ɫɦɟɫɢɬɟɥɹ ɜɵɞɟ-

ɥɹɟɬɫɹ ɫɢɝɧɚɥ ɩɪɨɦɟɠɭɬɨɱɧɨɣ

ɪɚɡɧɨɫɬɧɨɣ ɱɚɫɬɨɬɵ

f

ɉ

=f

01

– f

02

.

ɇɚ ɜɯɨɞɵ ɨɛɨɢɯ ɦɨɞɭɥɹɬɨɪɨɜ

ɩɨɞɚɟɬɫɹ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɦɨɞɭ-

ɥɢɪɭɸɳɢɣ ɫɢɝɧɚɥ

U

Ω

.

ȼ ɦɨɞɭ-

ɥɹɬɨɪɚɯ ɜɚɪɢɤɚɩɵ ɜɤɥɸɱɟɧɵ ɩɪɨɬɢɜɨɮɚɡɧɨ, ɩɨɷɬɨɦɭ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɧɚɩ-

ɪɹɠɟɧɢɹ ɫɢɝɧɚɥɚ ɜ ɨɞɧɨɦ ɦɨɞɭɥɹɬɨɪɟ ɱɚɫɬɨɬɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɜ ɞɪɭɝɨɦ

ɭɦɟɧɶɲɚɟɬɫɹ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɨɬɤɥɨɧɟɧɢɹ ɱɚɫɬɨɬɵ ɜ ɦɨɞɭɥɹɬɨɪɚɯ ɦɨɠɧɨ

ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɢɯ ɦɨɞɭɥɹɰɢɨɧɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ:

∆

f

1

(

ξ

) =

f

01

[S

′

1

⋅ξ

+

S

′

2

⋅ξ

2

+ S

′

3

⋅ξ

3

+...],

(11.28)

∆

f

2

(

ξ

) =

f

02

[S

″

1

⋅

(−

ξ

)

+

S

″

2

⋅

(−

ξ

)

2

+ S

″

3

⋅

(−

ξ

)

3

+...].

(11.29)

ȿɫɥɢ ɬɚɤ ɩɨɞɨɛɪɚɬɶ ɩɚɪɚɦɟɬɪɵ ɦɨɞɭɥɹɬɨɪɨɜ, ɱɬɨɛɵ ɜɵɩɨɥɧɢɥɨɫɶ ɭɫɥɨɜɢɟ

f

01

S

′

2

=

f

02

S

″

2

,

ɬɨ ɩɪɨɢɡɨɣɞɟɬ ɤɨɦɩɟɧɫɚɰɢɹ ɢɫɤɚɠɟɧɢɣ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ, ɚ ɢɫɤɚɠɟɧɢɹ ɛɨɥɟɟ

ɜɵɫɨɤɢɯ ɱɟɬɧɵɯ ɩɨɪɹɞɤɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɫɧɢɠɚɸɬɫɹ. Ʉɨɦɩɟɧɫɚɰɢɹ ɢɫɤɚɠɟɧɢɣ

ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɤɨɪɪɟɤɬɢɪɭɸɳɢɯ ɰɟɩɟɣ.

Ʉɪɨɦɟ ɷɬɨɝɨ, ɦɨɠɧɨ ɨɬɦɟɬɢɬɶ ɫɥɟɞɭɸɳɢɟ ɞɨɫɬɨɢɧɫɬɜɚ ɞɜɭɯɬɚɤɬɧɨɣ ɫɯɟɦɵ:

1) ɟɫɥɢ ɜɵɛɪɚɬɶ ɱɚɫɬɨɬɵ

f

01

ɢ

f

02

ɜɵɫɨɤɢɦɢ, ɬɨ ɭɦɟɧɶɲɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ

ɞɟɜɢɚɰɢɹ ɱɚɫɬɨɬɵ ɜ ɤɚɠɞɨɦ ɦɨɞɭɥɹɬɨɪɟ ɢ ɜɫɥɟɞɫɬɜɢɟ ɷɬɨɝɨ ɩɪɨɢɫɯɨɞɢɬ ɭɦɟɧɶ-

ɲɟɧɢɟ ɢɫɤɚɠɟɧɢɣ ɜɫɟɯ ɩɨɪɹɞɤɨɜ; 2) ɜɞɜɨɟ ɫɧɢɠɚɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɚɹ ɬɪɟɛɭɟɦɚɹ

ɞɟɜɢɚɰɢɹ ɱɚɫɬɨɬɵ ɜ ɤɚɠɞɨɦ ɦɨɞɭɥɹɬɨɪɟ, ɱɬɨ ɬɚɤɠɟ ɭɦɟɧɶɲɚɟɬ ɢɫɤɚɠɟɧɢɹ ɜɫɟɯ

ɩɨɪɹɞɤɨɜ.

11.6. ɋɬɚɛɢɥɢɡɚɰɢɹ ɫɪɟɞɧɟɣ ɱɚɫɬɨɬɵ ɱɚɫɬɨɬɧɵɯ

ɦɨɞɭɥɹɬɨɪɨɜ

Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɫɬɚɛɢɥɶɧɨɫɬɢ ɫɪɟɞɧɟɣ ɱɚɫɬɨɬɵ ɱɚɫɬɨɬɧɵɯ ɦɨɞɭɥɹɬɨɪɨɜ

ɩɪɢɦɟɧɹɸɬ ɫɥɟɞɭɸɳɢɟ ɦɟɬɨɞɵ.

1. ɉɪɢɦɟɧɹɸɬ ɤɨɫɜɟɧɧɵɟ ɦɟɬɨɞɵ ɩɨɥɭɱɟɧɢɹ ɑɆ ɤɨɥɟɛɚɧɢɣ. ɉɪɢ ɷɬɨɦ

ɱɚɫɬɨɬɚ ɜ ɡɚɞɚɸɳɟɦ ɝɟɧɟɪɚɬɨɪɟ ɮɚɡɨɜɨɝɨ ɦɨɞɭɥɹɬɨɪɚ ɫɬɚɛɢɥɢɡɢɪɭɟɬɫɹ ɤɜɚɪɰɟɦ.

2. ȼ ɤɚɱɟɫɬɜɟ ɱɚɫɬɨɬɧɨɝɨ ɦɨɞɭɥɹɬɨɪɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɭɩɪɚɜɥɹɟɦɵɣ ɩɨ ɱɚɫɬɨɬɟ

ɤɜɚɪɰɟɜɵɣ ɚɜɬɨɝɟɧɟɪɚɬɨɪ [10]. ɍɩɪɚɜɥɟɧɢɟ ɱɚɫɬɨɬɨɣ ɞɨɫɬɢɝɚɟɬɫɹ ɡɚ ɫɱɟɬ

ɜɤɥɸɱɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɤɜɚɪɰɟɜɵɦ ɪɟɡɨɧɚɬɨɪɨɦ ɜɚɪɢɤɚɩɚ. ɑɚɫɬɨɬɭ ɦɨɠɧɨ

ɜɚɪɶɢɪɨɜɚɬɶ ɜ ɩɪɟɞɟɥɚɯ ɨɬ

ω

ɤɜ

n

ɞɨ

ω

ɉ

n

(ɪɢɫ. 5.11). ɗɬɨɬ ɞɢɚɩɚɡɨɧ ɡɚɜɢɫɢɬ ɨɬ

f

01

U

Ω

f

ɉɑ

=f

01

−

f

02

f

02

Ɋɢɫ. 11.3 Ⱦɜɭɯɬɚɤɬɧɵɣ ɱɚɫɬɨɬɧɵɣ

ɦɨɞɭɥɹɬɨɪ

ɑɆȽ1

ɑɆȽ2

ɋɆ

115

ɨɬɧɨɲɟɧɢɹ

m

=

C

n

/

C

0

. Ⱦɥɹ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɨɝɨ ɫɪɟɡɚ ȺɌ

m

= (4...5)10

–3

.

ɉɪɟɞɟɥɶɧɚɹ ɞɟɜɢɚɰɢɹ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ,

∆ω

max

, .

ω

ɤɜn

m= 0 25

Ɉɫɧɨɜɧɵɦ ɧɟɞɨɫɬɚɬɤɨɦ ɞɚɧɧɨɝɨ ɦɟɬɨɞɚ ɩɨɥɭɱɟɧɢɹ ɑɆ ɤɨɥɟɛɚɧɢɣ ɹɜɥɹɸɬɫɹ

ɫɭɳɟɫɬɜɟɧɧɵɟ ɧɟɥɢɧɟɣɧɵɟ ɢɫɤɚɠɟɧɢɹ, ɜɨɡɪɚɫɬɚɸɳɢɟ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ

∆ω

max

.

ɉɨɷɬɨɦɭ ɱɚɫɬɨ ɩɪɢɦɟɧɹɸɬ ɪɚɡɥɢɱɧɵɟ ɦɟɬɨɞɵ ɥɢɧɟɚɪɢɡɚɰɢɢ ɦɨɞɭɥɹɰɢɨɧɧɵɯ

ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɧɚɩɪɢɦɟɪ, ɩɨɞɤɥɸɱɚɹ ɩɚɪɚɥɥɟɥɶɧɨ ɤɜɚɪɰɭ ɢɥɢ ɜɚɪɢɤɚɩɭ ɤɚɬɭɲɤɭ

ɢɧɞɭɤɬɢɜɧɨɫɬɢ. ɉɪɢ ɷɬɨɦ ɞɨɫɬɢɝɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɞɟɜɢɚɰɢɹ ɱɚɫɬɨɬɵ

∆ω

/

ω

ɤɜ

n

=3⋅10

–4

ɩɪɢ ɤɨɷɮɮɢɰɢɟɧɬɟ ɧɟɥɢɧɟɣɧɨɫɬɢ ɦɟɧɟɟ 6 %. ɋɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫ-

ɬɨɬɵ ɤɜɚɪɰɟɜɨɝɨ ɦɨɞɭɥɢɪɭɟɦɨɝɨ ȺȽ ɯɭɠɟ, ɱɟɦ ɧɟɭɩɪɚɜɥɹɟɦɨɝɨ, ɧɨ ɞɨɫɬɚɬɨɱɧɨ

ɜɵɫɨɤɚɹ.

3. ɑɚɫɬɨɬɧɚɹ ɦɨɞɭɥɹɰɢɹ ɩɪɨɜɨɞɢɬɫɹ ɧɚ ɩɨɧɢɠɟɧɧɨɣ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɱɚɫɬɨɬɟ

f

1

. Ɂɚɬɟɦ ɫ ɩɨɦɨɳɶɸ ɫɦɟɫɢɬɟɥɹ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɟɪɟɧɨɫ ɫɩɟɤɬɪɚ ɑɆ ɤɨɥɟɛɚɧɢɣ ɜ

ɛɨɥɟɟ ɜɵɫɨɤɨɱɚɫɬɨɬɧɭɸ ɨɛɥɚɫɬɶ:

f = f

1

+ f

2

, ɝɞɟ

f

2

— ɱɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ ɝɟɬɟɪɨ-

ɞɢɧɚ, ɫɬɚɛɢɥɢɡɢɪɨɜɚɧɧɨɝɨ ɤɜɚɪɰɟɦ. ȿɫɥɢ

f

2

>> f

1

, ɬɨ ɨɛɳɚɹ ɫɬɚɛɢɥɶɧɨɫɬɶ

ɫɭɦɦɚɪɧɨɣ ɱɚɫɬɨɬɵ

f

ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɬɚɛɢɥɶɧɨɫɬɶɸ

f

2

.

1. ɉɪɢɦɟɧɹɟɬɫɹ ɫɢɫɬɟɦɚ ɱɚɫɬɨɬɧɨɣ ɚɜɬɨɩɨɞɫɬɪɨɣɤɢ ɱɚɫɬɨɬɵ (ɑȺɉɑ).

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɑȺɉɑ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 11.4. ɑɚɫɬɨɬɧɨ ɦɨɞɭɥɢɪɨɜɚɧɧɵɣ

ɝɟɧɟɪɚɬɨɪ ɑɆȽ ɢɦɟɟɬ ɜ ɫɜɨɟɦ ɫɨɫɬɚɜɟ ɞɜɚ

ɜɚɪɢɤɚɩɚ: ɨɞɢɧ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ

ɩɨɥɭɱɟɧɢɹ ɑɆ ɤɨɥɟɛɚɧɢɣ, ɚ ɞɪɭɝɨɣ — ɞɥɹ

ɚɜɬɨɩɨɞɫɬɪɨɣɤɢ. ȼɵɯɨɞɧɵɟ ɤɨɥɟɛɚɧɢɹ

ɑɆȽ ɩɨɫɬɭɩɚɸɬ ɜ ɩɨɫɥɟɞɭɸɳɢɟ ɭɫɢɥɢ-

ɬɟɥɶɧɵɟ ɤɚɫɤɚɞɵ, ɚ ɬɚɤɠɟ ɜ ɱɚɫɬɨɬɧɵɣ

ɞɢɫɤɪɢɦɢɧɚɬɨɪ ɑȾ. ȼɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ

ɑȾ

U

ɑȾ

ɱɟɪɟɡ Ɏɇɑ ɩɨɞɚɟɬɫɹ ɧɚ

ɭɩɪɚɜɥɹɸɳɢɣ ɜɚɪɢɤɚɩ ɑɆȽ. Ⱦɚɧɧɚɹ

ɫɢɫɬɟɦɚ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɨɛɵɱɧɨɣ ɑȺɉɑ

ɩɚɪɚɦɟɬɪɚɦɢ Ɏɇɑ. ɉɨɫɥɟɞɧɢɣ ɢɦɟɟɬ ɨɱɟɧɶ

ɭɡɤɭɸ ɩɨɥɨɫɭ ɩɪɨɩɭɫɤɚɧɢɹ ɢ ɡɚɞɟɪɠɢɜɚɟɬ ɜɫɟ ɱɚɫɬɨɬɵ, ɫɨɞɟɪɠɚɳɢɟɫɹ ɜ ɫɩɟɤɬɪɟ

ɦɨɞɭɥɢɪɭɸɳɟɝɨ ɫɢɝɧɚɥɚ U

Ω

. ɉɨɷɬɨɦɭ ɫɢɫɬɟɦɚ ɑȺɉɑ ɪɟɚɝɢɪɭɟɬ ɬɨɥɶɤɨ ɧɚ ɨɱɟɧɶ

ɧɢɡɤɢɟ ɱɚɫɬɨɬɵ, ɫ ɤɚɤɢɦɢ ɦɨɠɟɬ ɦɟɧɹɬɶɫɹ ɱɚɫɬɨɬɚ ɩɨɞɫɬɪɚɢɜɚɟɦɨɝɨ ɝɟɧɟɪɚɬɨɪɚ

ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɮɚɤɬɨɪɨɜ. Ⱥɧɚɥɨɝɢɱɧɨ ɦɨɠɟɬ ɛɵɬɶ

ɢɫɩɨɥɶɡɨɜɚɧɚ ɢ ɛɨɥɟɟ ɬɨɱɧɚɹ ɫɢɫɬɟɦɚ ɎȺɉɑ.

11.7. Ɏɚɡɨɜɚɹ ɦɨɞɭɥɹɰɢɹ

Ɏɚɡɨɜɭɸ ɦɨɞɭɥɹɰɢɸ ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɨ ɨɫɭɳɟɫɬɜɢɬɶ, ɩɪɨɩɭɫɬɢɜ ɧɟɫɭɳɟɟ

ɤɨɥɟɛɚɧɢɟ ɱɟɪɟɡ ɪɟɡɨɧɚɧɫɧɭɸ ɫɢɫɬɟɦɭ, ɱɚɫɬɨɬɭ ɧɚɫɬɪɨɣɤɢ ɤɨɬɨɪɨɣ ɦɨɠɧɨ

ɢɡɦɟɧɹɬɶ, ɧɚɩɪɢɦɟɪ, ɦɟɧɹɹ ɫɦɟɳɟɧɢɟ ɧɚ ɜɚɪɢɤɚɩɟ, ɜɯɨɞɹɳɟɦ ɜ ɫɨɫɬɚɜ ɤɨɧɬɭɪɚ.

ɇɚ ɪɢɫ. 11.5 ɩɨɤɚɡɚɧɚ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɬɚɤɨɝɨ ɦɨɞɭɥɹɬɨɪɚ.

(11.30)

ɑɆȽ

U

Ω

ȼɵɯ

Ɏɇɑ

U

ɑȾ

Ɋɢɫ. 11.4. ɋɬɚɛɢɥɢɡɚɰɢɹ ɫɪɟɞɧɟɣ

ɱɚɫɬɨɬɵ ɫɢɫɬɟɦɨɣ ɑȺɉɑ

G

ɑȾ

116

ȼɯɨɞɧɨɟ ɢ ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɹ

ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ

U

ɜɵɯ

= U

ɜɯ

Z

ɤ

/(Z

ɤ

+R)

, ɝɞɟ

Z

ɤ

— ɫɨɩ-

ɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭɪɚ. ɉɪɢ

R

>> |

Z

ɤ

|

ɪɚɡɧɨɫɬɶ ɮɚɡ ɧɚɩɪɹɠɟɧɢɣ

U

ɜɵɯ

ɢ

U

ɜɯ

ɩɪɢɦɟɪɧɨ ɪɚɜɧɚ ɮɚɡɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ɤɨɧɬɭɪɚ:

ϕ = ϕ

ɤ

. ȼɛɥɢɡɢ ɪɟɡɨɧɚɧɫɧɨɣ

ɱɚɫɬɨɬɵ

tg Q

f

ɤ ɤ

ϕ ϕ

≈ ≈−2

0

∆

,

ɝɞɟ

Q

— ɞɨɛɪɨɬɧɨɫɬɶ ɤɨɧɬɭɪɚ. ɂɡ (11.31), ɭɱɢɬɵɜɚɹ (11.23), ɩɨɥɭɱɚɟɦ ɡɧɚɱɟɧɢɟ

ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɨɬɤɥɨɧɟɧɢɹ ɱɚɫɬɨɬɵ

∆

f

K K

ȼ H

0

1

2

4

1

= −

+

γ

.

ɉɨɞɫɬɚɜɥɹɹ ɩɨɥɭɱɟɧɧɨɟ ɜɵɪɚɠɟɧɢɟ ɜ (11.31) ɩɨɥɭɱɢɦ

ϕ

γ

ϕ

max

.= =

+

⋅ ⋅M Q K K

B H

4

1

ɇɚ ɩɪɚɤɬɢɤɟ ɩɪɢ

Ʉ

ȼ

=1 ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ ɡɧɚɱɟɧɢɹɦɢ

M

ϕ

= 15...20

o

. ɂɧɞɟɤɫ

ɦɨɞɭɥɹɰɢɢ ɦɨɠɧɨ ɭɜɟɥɢɱɢɬɶ, ɜɤɥɸɱɢɜ ɤɚɫɤɚɞɧɨ ɧɟɫɤɨɥɶɤɨ ɮɚɡɨɜɵɯ ɦɨɞɭɥɹ-

ɬɨɪɨɜ.

ȼ ɋȼɑ ɞɢɚɩɚɡɨɧɟ ɮɚɡɨɜɭɸ ɦɨɞɭɥɹɰɢɸ ɱɚɫɬɨ ɪɟɚɥɢɡɭɸɬ ɧɚ ɭɫɢɥɢɬɟɥɶɧɵɯ

ɩɪɢɛɨɪɚɯ. ɇɚɩɪɢɦɟɪ, ɜ ɅȻȼ-0 ɢ ɩɪɨɥɟɬɧɵɯ ɤɥɢɫɬɪɨɧɚɯ ɪɚɡɧɨɫɬɶ ɮɚɡ ɦɟɠɞɭ

ɜɯɨɞɧɵɦɢ ɢ ɜɵɯɨɞɧɵɦɢ ɤɨɥɟɛɚɧɢɹɦɢ ɪɚɜɧɚ

∆ϕ

ω

ϕ ϕ ϕ

= + = +a

l

V

ɉ ɉe

0

,

ɝɞɟ

a

— ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ (

a

= 1 ɞɥɹ ɤɥɢɫɬɪɨɧɚ,

a

= 0,58 ɞɥɹ

ɅȻȼ);

l

— ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɪɟɡɨɧɚɬɨɪɚɦɢ ɤɥɢɫɬɪɨɧɚ ɢɥɢ ɞɥɢɧɚ ɡɚɦɟɞɥɹɸɳɟɣ

ɫɢɫɬɟɦɵ ɜ ɅȻȼ;

V

0

— ɫɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɨɬɨɤɚ;

ϕ

ɉ

— ɩɨɫɬɨɹɧɧɵɣ ɮɚɡɨɜɵɣ

ɫɞɜɢɝ, ɧɟ ɡɚɜɢɫɹɳɢɣ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɪɢɛɨɪɚ (

ϕ

ɉ

= π/2 ɞɥɹ ɤɥɢɫɬɪɨɧɚ). Ⱦɥɹ

ɤɪɚɬɤɨɫɬɢ ɞɚɥɶɧɟɣɲɢɯ ɡɚɩɢɫɟɣ ɫɨɫɬɚɜɧɚɹ ɱɚɫɬɶ ɮɚɡɨɜɨɝɨ ɫɞɜɢɝɚ, ɡɚɜɢɫɹɳɚɹ ɨɬ

ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɪɢɛɨɪɚ, ɨɛɨɡɧɚɱɟɧɚ ɤɚɤ

ϕ

e

.

ɋɤɨɪɨɫɬɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɩɨɬɨɤɚ ɡɚɜɢɫɢɬ ɨɬ ɭɫɤɨɪɹɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ

U

0

:

V

e

m

U

0 0

2

= ,

ɝɞɟ

e

ɢ

m

— ɡɚɪɹɞ ɢ ɦɚɫɫɚ ɷɥɟɤɬɪɨɧɚ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,

ϕ

e

c U= ⋅

−

0

1

2

,

ɝɞɟ

ɫ

— ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ.

ɇɚɣɞɟɦ ɤɪɭɬɢɡɧɭ ɫɬɚɬɢɱɟɫɤɨɣ ɦɨɞɭɥɹɰɢɨɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

S

ϕ

.

R

U

ɜɯ

U

ɜɵɯ

L VD

L

ȻɅ

C

ȻɅ

U

Ω

Ɋɢɫ. 11.5. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ

ɮɚɡɨɜɨɝɨ ɦɨɞɭɥɹɬɨɪɚ

(11.31)

(11.32)

(11.33)

(11.34)

117

S

U

c U

U

e e

ϕ

∂ϕ

∂

ϕ

= = − ⋅ ⋅ = −

−

0

3

2

0

1

2 2

.

ɋɞɟɥɚɟɦ ɨɰɟɧɤɭ ɤɪɭɬɢɡɧɵ ɞɥɹ ɅȻȼ.

ϕ

ω

π

λ

π

e

l

V

f l

V

l

N

Ɂɋ

= = = = ⋅0 58 0 58

2

0 58

2

0 58 2

0 0

, , , , ,

ɝɞɟ

N

— ɱɢɫɥɨ ɞɥɢɧ ɜɨɥɧ

λ

Ɂɋ

, ɭɤɥɚɞɵɜɚɸɳɢɯɫɹ ɜ ɡɚɦɟɞɥɹɸɳɟɣ ɫɢɫɬɟɦɟ ɅȻȼ. ɂɡ

(11.35) ɢ (11.36) ɢɦɟɟɦ

S

N

U

ϕ

π

= −0 58

0

, .

ɉɨɫɤɨɥɶɤɭ

N

— ɧɟɫɤɨɥɶɤɨ ɞɟɫɹɬɤɨɜ, ɚ

U

0

— ɟɞɢɧɢɰɵ ɤɢɥɨɜɨɥɶɬ, ɬɨ

S

ϕ

=2...4

[ɝɪɚɞɭɫ/ȼɨɥɶɬ]. Ⱦɥɹ ɤɥɢɫɬɪɨɧɚ

S

ϕ

=(5...10)

ɨ

ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ 1 %. ȼ

ɅȻȼ-Ɇ ɡɚɜɢɫɢɦɨɫɬɶ ɮɚɡɵ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɧɨɞɟ

U

A

ɢ ɤɚɬɨɞɟ

U

K

ɢɦɟɟɬ ɜɢɞ

ϕ

ω

e

l

V

ld B

U U

A K

= =

−

0

,

ɝɞɟ

d

— ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ;

ȼ

— ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɜ ɩɪɨɫɬ-

ɪɚɧɫɬɜɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. Ʉɪɭɬɢɡɧɚ ɋɆɏ ɩɨ ɧɚɩɪɹɠɟɧɢɸ

U

A

S

U U U

e e

A A K

ϕ

∂

ϕ

∂

ϕ

= = −

−

.

ɉɪɢ ɷɬɨɦ ɨɧɚ ɡɧɚɱɢɬɟɥɶɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɤɪɭɬɢɡɧɚ ɦɨɞɭɥɹɰɢɨɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

ɅȻȼ-Ɉ.

11.8. ɍɫɢɥɟɧɢɟ ɦɨɳɧɨɫɬɢ ɫɢɝɧɚɥɨɜ ɫ ɭɝɥɨɜɨɣ ɦɨɞɭɥɹɰɢɟɣ

ɇɟɥɢɧɟɣɧɨɫɬɶ ɪɟɠɢɦɨɜ ɢ ɚɦɩɥɢɬɭɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɬɪɚɤɬɚ ɭɫɢɥɟɧɢɹ

ɦɨɳɧɨɫɬɢ ɧɟ ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɤɚɱɟɫɬɜɨ ɭɫɢɥɢɜɚɟɦɵɯ

ɫɢɝɧɚɥɨɜ ɫ ɍɆ, ɬɚɤ ɤɚɤ ɚɦɩɥɢɬɭɞɚ ɷɬɢɯ ɫɢɝɧɚɥɨɜ ɩɨɫɬɨɹɧɧɚ. Ɉɞɧɚɤɨ ɧɟɪɚɜ-

ɧɨɦɟɪɧɨɫɬɶ Ⱥɑɏ ɢ ɧɟɥɢɧɟɣɧɨɫɬɶ Ɏɑɏ ɡɜɟɧɶɟɜ ɬɪɚɤɬɚ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ ɜ

ɩɪɟɞɟɥɚɯ ɩɨɥɨɫɵ ɱɚɫɬɨɬ

ɉ

ɭɫɢɥɢɜɚɟɦɨɝɨ ɫɢɝɧɚɥɚ ɦɨɠɟɬ ɜɵɡɜɚɬɶ ɫɭɳɟɫɬɜɟɧɧɵɟ

ɢɫɤɚɠɟɧɢɹ. ɂɫɤɚɠɟɧɢɹ ɧɟ ɜɨɡɧɢɤɚɸɬ ɥɢɲɶ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɚɦɩɥɢɬɭɞɧɚɹ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ

Ⱥ(

ω

)

ɪɚɜɧɨɦɟɪɧɚɹ, ɚ ɮɚɡɨɜɚɹ

ϕ

(

ω

)

ɥɢɧɟɣɧɚ ɢ ɫɢɦɦɟɬɪɢɱɧɚ

ɨɬɧɨɫɢɬɟɥɶɧɨ

ω

0

( ɪɢɫ. 11.6, ɲɬɪɢɯɨɜɚɹ ɥɢɧɢɹ).

ȼ ɪɟɚɥɶɧɨɦ ɨɞɧɨɤɨɧɬɭɪɧɨɦ ɪɟɡɨɧɚɧɫɧɨɦ ɭɫɢɥɢɬɟɥɟ Ⱥɑɏ ɹɜɥɹɟɬɫɹ

ɧɟɪɚɜɧɨɦɟɪɧɨɣ, ɚ Ɏɑɏ

ϕ

(

ω

)

ɢɦɟɟɬ ɜɢɞ, ɩɨɤɚɡɚɧɧɨɣ ɫɩɥɨɲɧɨɣ ɥɢɧɢɟɣ ɧɚ

ɪɢɫ. 11.6. ȿɫɥɢ ɫɪɟɞɧɹɹ ɱɚɫɬɨɬɚ ɍɆ ɤɨɥɟɛɚɧɢɣ ɫɨɜɩɚɞɟɬ ɫ ɪɟɡɨɧɚɧɫɧɨɣ ɱɚɫɬɨɬɨɣ

f

0

ɭɫɢɥɢɬɟɥɹ, ɬɨ ɨɬɫɭɬɫɬɜɭɸɬ ɢɫɤɚɠɟɧɢɹ ɱɟɬɧɵɯ ɩɨɪɹɞɤɨɜ, ɚ ɢɡ ɧɟɱɟɬɧɵɯ

ɦɚɤɫɢɦɚɥɶɧɵɦɢ ɹɜɥɹɸɬɫɹ ɢɫɤɚɠɟɧɢɹ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ:

(11.35)

(11.36)

(11.37)

(11.38)

(11.39)

118

K F f ɉ

ɇ3

2 3

2≈

∆

/ ,

ɝɞɟ

∆

f

— ɞɟɜɢɚɰɢɹ ɱɚɫɬɨɬɵ;

F

— ɱɚɫ-

ɬɨɬɚ ɦɨɞɭɥɢɪɭɸɳɟɝɨ ɫɢɝɧɚɥɚ. Ɉɬɫɸɞɚ

ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧɚ ɧɟɨɛɯɨɞɢɦɚɹ

ɩɨɥɨɫɚ ɩɪɨɩɭɫɤɚɧɢɹ ɭɫɢɥɢɬɟɥɹ (ɩɨ

ɭɪɨɜɧɸ −3 ɞȻ):

ɉ F M K

H

≥ 2 2

2

3

max

.

ȿɫɥɢ ɬɪɚɤɬ ɭɫɢɥɟɧɢɹ ɫɨɞɟɪɠɢɬ

ɧɟɫɤɨɥɶɤɨ ɤɚɫɤɚɞɨɜ, ɬɨ ɢɯ ɢɫɤɚɠɟɧɢɹ

ɫɭɦɦɢɪɭɸɬɫɹ. ȼ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚɯ

ɨɛɵɱɧɨ ɤɨɧɬɭɪɧɵɟ ɫɢɫɬɟɦɵ ɢɦɟɸɬ

ɪɚɛɨɱɟɟ ɡɧɚɱɟɧɢɟ ɞɨɛɪɨɬɧɨɫɬɢ

Q

< 10...15 ɢɡ-ɡɚ ɛɨɥɶɲɢɯ ɜɧɨɫɢɦɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨɬɟɪɶ, ɱɬɨ ɫɩɨɫɨɛɫɬɜɭɟɬ

ɩɨɥɭɱɟɧɢɸ ɧɟɛɨɥɶɲɢɯ ɢɫɤɚɠɟɧɢɣ.

ɉɪɢ ɭɫɢɥɟɧɢɢ ɦɨɳɧɨɫɬɢ ɑɆ ɢɥɢ ɎɆ ɤɨɥɟɛɚɧɢɣ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɢɦɟɧɹɬɶ

ɤɪɢɬɢɱɟɫɤɢɣ ɢɥɢ ɩɟɪɟɧɚɩɪɹɠɟɧɧɵɣ ɪɟɠɢɦɵ, ɬɚɤ ɤɚɤ ɚɦɩɥɢɬɭɞɚ ɭɫɢɥɢɜɚɟɦɵɯ

ɤɨɥɟɛɚɧɢɣ ɩɨɫɬɨɹɧɧɚ, ɚ ɜɵɲɟɭɩɨɦɹɧɭɬɵɟ ɪɟɠɢɦɵ ɨɛɟɫɩɟɱɢɜɚɸɬ ɜɵɫɨɤɢɣ ɄɉȾ ɢ

ɧɚɢɥɭɱɲɟɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɭɫɢɥɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ ɩɨ ɦɨɳɧɨɫɬɢ. ɉɪɢɦɟɧɟɧɢɟ

ɷɬɢɯ ɪɟɠɢɦɨɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢ ɟɳɟ ɩɨ ɞɜɭɦ ɫɨɨɛɪɚɠɟɧɢɹɦ:

1. ȼ ɭɤɚɡɚɧɧɵɯ ɪɟɠɢɦɚɯ ɭɫɢɥɢɬɟɥɶ ɨɤɚɡɵɜɚɟɬɫɹ ɛɥɢɠɟ ɤ ɝɟɧɟɪɚɬɨɪɭ

ɧɚɩɪɹɠɟɧɢɹ, ɬɚɤ ɤɚɤ ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɦɚɥɨ ɡɚɜɢɫɢɬ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

ɧɚɝɪɭɡɤɢ, ɬ.ɟ. ɝɟɧɟɪɚɬɨɪ ɢɦɟɟɬ ɦɚɥɨɟ ɜɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɢ ɩɨɷɬɨɦɭ

ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɪɟɡɨɧɚɧɫɧɨɝɨ ɭɫɢɥɢɬɟɥɹ ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɟɟ ɪɚɜɧɨ-

ɦɟɪɧɨɣ ɢ ɲɢɪɨɤɨɩɨɥɨɫɧɨɣ, ɚ ɫɜɹɡɚɧɧɵɟ ɫ ɷɬɢɦ ɮɚɤɬɨɪɨɦ ɢɫɤɚɠɟɧɢɹ ɑɆ

ɭɦɟɧɶɲɚɸɬɫɹ.

2. ȼ ɭɤɚɡɚɧɧɵɯ ɪɟɠɢɦɚɯ ɚɦɩɥɢɬɭɞɚ ɜɵɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɦɚɥɨ ɡɚɜɢɫɢɬ ɨɬ

ɜɯɨɞɧɨɝɨ, ɬ.ɟ. ɭɫɢɥɢɬɟɥɶ ɩɪɢɨɛɪɟɬɚɟɬ ɫɜɨɣɫɬɜɨ ɚɦɩɥɢɬɭɞɧɨɝɨ ɨɝɪɚɧɢɱɢɬɟɥɹ ɢ

ɭɦɟɧɶɲɚɟɬ ɜɨɡɧɢɤɲɭɸ ɩɨ ɤɚɤɢɦ-ɥɢɛɨ ɩɪɢɱɢɧɚɦ ɩɚɪɚɡɢɬɧɭɸ ɚɦɩɥɢɬɭɞɧɭɸ

ɦɨɞɭɥɹɰɢɸ.

Ɇɧɨɝɨɤɪɚɬɧɨɟ ɭɦɧɨɠɟɧɢɟ ɱɚɫɬɨɬɵ ɜ ɬɪɚɤɬɟ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɦɨɠɟɬ

ɩɪɢɜɨɞɢɬɶ ɤ ɧɟɠɟɥɚɬɟɥɶɧɵɦ ɪɟɡɭɥɶɬɚɬɚɦ:

ɚ) ɩɪɢ ɤɚɠɞɨɦ ɭɦɧɨɠɟɧɢɢ ɫɩɟɤɬɪ ɫɢɝɧɚɥɚ ɩɪɢɨɛɪɟɬɚɟɬ ɩɨɛɨɱɧɵɟ ɢ

ɜɧɟɩɨɥɨɫɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ — ɤɚɤ ɜɵɫɲɢɟ ɝɚɪɦɨɧɢɤɢ, ɬɚɤ ɢ ɧɢɡɲɢɟ (ɫɭɛɝɚɪ-

ɦɨɧɢɤɢ); ɩɪɨɛɥɟɦɚ ɮɢɥɶɬɪɚɰɢɢ ɢɯ ɞɨ ɬɪɟɛɭɟɦɨɝɨ ɭɪɨɜɧɹ ɭɫɥɨɠɧɹɟɬɫɹ;

ɛ) ɜ ɭɦɧɨɠɢɬɟɥɹɯ, ɪɚɛɨɬɚɸɳɢɯ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɚɥɵɯ ɭɝɥɨɜ ɨɬɫɟɱɤɢ ɢɥɢ

ɧɚ ɧɟɥɢɧɟɣɧɵɯ ɟɦɤɨɫɬɹɯ, ɜɨɡɧɢɤɚɸɬ ɮɥɭɤɬɭɚɰɢɢ ɮɚɡɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ

ɭɜɟɥɢɱɟɧɢɸ ɭɪɨɜɧɹ ɲɭɦɨɜ ɜ ɫɩɟɤɬɪɟ ɩɨɥɟɡɧɨɝɨ ɫɢɝɧɚɥɚ, ɬ.ɟ. ɤ ɫɧɢɠɟɧɢɸ

ɤɚɱɟɫɬɜɚ.

A

ϕ

A

ϕ

f

Ɋɢɫ.11.6 Ⱥɦɩɥɢɬɭɞɧɚɹ ɢ ɮɚɡɨɜɵɟ

ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɡɨɧɚɧɫɧɨɝɨ

ɭɫɢɥɢɬɟɥɹ

(11.40)

(11.41)

119

ɉɊɂɅɈɀȿɇɂȿ

Ƚɚɪɦɨɧɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ

Ɋɚɫɫɱɢɬɚɟɦ ɝɚɪɦɨɧɢɤɢ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ ɜ ɮɨɪɦɟ ɛɟɫɤɨɧɟɱɧɨɣ ɩɨɫɥɟɞɨɜɚ-

ɬɟɥɶɧɨɫɬɢ ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ ɫ ɭɝɥɨɦ ɨɬɫɟɱɤɢ

Θ

. ɗɬɚ ɩɨɫɥɟɞɨ-

ɜɚɬɟɥɶɧɨɫɬɶ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɱɟɬɧɭɸ ɮɭɧɤɰɢɸ. ɉɨɷɬɨɦɭ ɟɟ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ

ɜ ɜɢɞɟ ɛɟɫɤɨɧɟɱɧɨɝɨ ɪɹɞɚ

i

ɜɵɯ

(t) = I

0

+ I

1

cos

τ

+ I

2

cos 2

τ

+ …, (ɉ.1)

ɝɞɟ

τ

=

ω

1

t

— ɧɨɪɦɢɪɨɜɚɧɧɨɟ ɜɪɟɦɹ. Ⱦɥɹ ɛɟɡɵɧɟɪɰɢɨɧɧɨɝɨ Ⱥɗ ɜɵɯɨɞɧɨɣ ɬɨɤ

ɦɨɠɧɨ ɬɚɤɠɟ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ

S

⋅

U

ɜɯ

:

( )

Ĭ

ĬSUi

ɜɯɜɵɯ

coscos

>

−=

τ

. (ɉ.2)

ɉɨ ɮɨɪɦɭɥɚɦ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɹɞɚ Ɏɭɪɶɟ ɱɟɬɧɨɣ ɮɭɧɤɰɢɢ ɧɚɯɨɞɢɦ

( ) ( )

³

=−=

Ĭ

ĬSUdĬSUI

ɜɯɜɯ

0

00

coscos

1

γττ

π

. (ɉ.3)

ɝɞɟ

( ) ( )

ĬĬĬĬ cossin

1

0

−=

π

γ

. (ɉ.4)

Ⱥɧɚɥɨɝɢɱɧɨ

( ) ( )

³

=−=

Ĭ

n

ĬSUdnĬSUI

nɜɯɜɯ

0

coscoscos

2

γτττ

π

, (ɉ.5)

ɝɞɟ

( )

»

¼

º

«

¬

ª

+

−

=

1

)1(sin

1

)1(sin1

n

Ĭn

n

Ĭn

n

Ĭ

n

π

γ

. (ɉ.6)

Ⱥɦɩɥɢɬɭɞɵ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ ɦɨɠɧɨ

ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɚɦɩɥɢɬɭɞɭ ɢɦɩɭɥɶɫɨɜ

I

max

= S U

ɜɯ

(1– cos

Θ

).

ȼɵɪɚɠɟɧɢɹ (ɉ.3) ɢ (ɉ.5) ɦɨɠɧɨ ɩɟɪɟɩɢɫɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:

I

n

= I

max

α

n

(

Θ

), n =

0, 1, 2,

…

(ɉ.7)

ɝɞɟ

α

n

(

Θ

) =

γ

n

(

Θ

) / (1– cos

Θ

)

(ɉ.8)

— ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɚɡɥɨɠɟɧɢɹ (ɮɭɧɤɰɢɢ Ȼɟɪɝɚ).

Ɏɭɧɤɰɢɢ

γ

n

(

Θ

)

ɢ

α

n

(

Θ

)

ɞɥɹ n = 0, 1, 2, 3 ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. ɉ.1. Ɂɚɦɟɬɢɦ,

ɱɬɨ ɩɪɢ

n

≥

1

ɞɥɹ ɮɭɧɤɰɢɢ

γ

n

(

Θ

)

ɦɚɤɫɢɦɭɦɵ ɢɦɟɸɬ ɦɟɫɬɨ ɩɪɢ

Θ

max n

≈

180

°/

n

, ɚ ɞɥɹ ɮɭɧɤɰɢɢ

α

n

(

Θ

) —

ɩɪɢ

Θ

max n

≈

120

°/

n.

Ɉɬɧɨɲɟɧɢɟ

g

n

=

I

n

/

I

0

ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɮɨɪɦɵ ɬɨɤɚ (ɪɢɫ. ɉ.3).

120

γ

n

(

Θ

)

γ

1

0,8

γ

0

0,6

0,4

0,2

γ

3

γ

2

0 30 60 90 120 150

Θ°

Ɋɢɫ. ɉ.1. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɡɥɨɠɟɧɢɹ

γ

n

ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ

ɢɦɩɭɥɶɫɚ ɨɬ ɭɝɥɚ ɨɬɫɟɱɤɢ

Θ

α

n

(

Θ

)

α

1

0,5

α

0

0,4

0,3

α

2

0,2

α

3

0,1

0 30 60 90 120 150

Θ°

Ɋɢɫ. ɉ.2. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɪɚɡɥɨɠɟɧɢɹ

α

n

ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ

ɢɦɩɭɥɶɫɚ ɨɬ ɭɝɥɚ ɨɬɫɟɱɤɢ

Θ

g

n

(

Θ

)

g

1

1,5

g

3

g

2

1,0

0,5

0

30 60 90 120 150

Θ°

-0,5

Ɋɢɫ. ɉ.3. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɮɨɪɦɵ ɬɨɤɚ

g

n

ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ

ɢɦɩɭɥɶɫɚ ɨɬ ɭɝɥɚ ɨɬɫɟɱɤɢ

Θ

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