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§1. ɉɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɟ ɞɢɨɞɵ
ɉɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɣ ɞɢɨɞ – ɷɬɨ ɩɪɢɛɨɪ ɫ ɞɜɭɯɫɥɨɣɧɨɣ P-N ɫɬɪɭɤɬɭɪɨɣ ɢ ɨɞɧɢɦ P-N ɩɟɪɟɯɨɞɨɦ.
ɋɥɨɣ Ɋ - ɚɤɰɟɩɬɨɪɧɚɹ ɩɪɢɦɟɫɶ ( ɨɫɧɨɜɧɵɟ ɧɨɫɢɬɟɥɢ - ɞɵɪɤɢ ). ɋɥɨɣ N - ɞɨɧɨɪɧɚɹ ɩɪɢɦɟɫɶ (ɨɫɧɨɜɧɵɟ ɧɨɫɢɬɟɥɢ ɷɥɟɤɬɪɨɧɵ).
Ɉɛɨɡɧɚɱɟɧɢɟ ɧɚ ɫɯɟɦɚɯ:
Ʉɚɬɨɞ
V ɢɥɢ VD - ɨɛɨɡɧɚɱɟɧɢɟ ɞɢɨɞɚ
VS – ɨɛɨɡɧɚɱɟɧɢɟ ɞɢɨɞɧɨɣ ɫɛɨɪɤɢ
V7
ɐɢɮɪɚ ɩɨɫɥɟ V, ɩɨɤɚɡɵɜɚɟɬ ɧɨɦɟɪ ɞɢɨɞɚ ɜ ɫɯɟɦɟ
Ⱥɧɨɞ – ɷɬɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤ P-ɬɢɩɚ
Ʉɚɬɨɞ – ɷɬɨ ɩɨɥɭɩɪɨɜɨɞɧɢɤ N-ɬɢɩɚ
Ⱥɧɨɞ
ɉɪɢ ɩɪɢɥɨɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɧɚɩɪɹɠɟɧɢɹ ɤ ɞɢɨɞɭ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ («+» ɧɚ ɚɧɨɞ, ɚ « - » ɧɚ ɤɚɬɨɞ)
ɭɦɟɧɶɲɚɟɬɫɹ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɞɢɮɮɭɡɢɹ – ɞɢɨɞ ɨɬɤɪɵɬ (ɡɚɤɨɪɨɬɤɚ).
ɉɪɢ ɩɪɢɥɨɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ, ɩɪɟɤɪɚɳɚɟɬɫɹ
ɞɢɮɮɭɡɢɹ – ɞɢɨɞ ɡɚɤɪɵɬ (ɪɚɡɪɵɜ).
ȼɨɥɶɬ-ɚɦɩɟɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ (ȼȺɏ) ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɨɝɨ ɞɢɨɞɚ
Uɷɥ.ɩɪɨɛ. = 10 ÷1000 ȼ – ɧɚɩɪɹɠɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɪɨɛɨɹ.
Uɧɚɫ. = 0,3 ÷ 1 ȼ – ɧɚɩɪɹɠɟɧɢɟ ɧɚɫɵɳɟɧɢɹ.
Ia ɢ Ua – ɚɧɨɞɧɵɣ ɬɨɤ ɢ ɧɚɩɪɹɠɟɧɢɟ.
ɍɱɚɫɬɨɤ I:– ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ (ɩɪɹɦɚɹ ɜɟɬɜɶ ȼȺɏ)
ɍɱɚɫɬɤɢ II, III, IV, - ɨɛɪɚɬɧɚɹ ɜɟɬɜɶ ȼȺɏ (ɧɟ ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ)
ɍɱɚɫɬɨɤ II: ȿɫɥɢ ɩɪɢɥɨɠɢɬɶ ɤ ɞɢɨɞɭ ɨɛɪɚɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ – ɞɢɨɞ ɡɚɤɪɵɬ, ɧɨ ɜɫɟ
ɪɚɜɧɨ ɱɟɪɟɡ ɧɟɝɨ ɛɭɞɟɬ ɩɪɨɬɟɤɚɬɶ ɦɚɥɵɣ ɨɛɪɚɬɧɵɣ ɬɨɤ (ɬɨɤ ɞɪɟɣɮɚ, ɬɟɩɥɨɜɨɣ ɬɨɤ), ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɞɜɢɠɟɧɢɟɦ ɧɟ
ɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ.
ɍɱɚɫɬɨɤ III: ɍɱɚɫɬɨɤ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɪɨɛɨɹ. ȿɫɥɢ ɩɪɢɥɨɠɢɬɶ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɧɟɨɫɧɨɜɧɵɟ
ɧɨɫɢɬɟɥɢ ɛɭɞɭɬ ɪɚɡɝɨɧɹɬɶɫɹ ɢ ɩɪɢ ɫɨɭɞɚɪɟɧɢɢ ɫ ɭɡɥɚɦɢ ɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɪɟɲɟɬɤɢ ɩɪɨɢɫɯɨɞɢɬ ɭɞɚɪɧɚɹ
ɢɨɧɢɡɚɰɢɹ, ɤɨɬɨɪɚɹ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɪɢɜɨɞɢɬ ɤ ɥɚɜɢɧɧɨɦɭ ɩɪɨɛɨɸ (ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɟɬ ɬɨɤ)
ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɨɛɨɣ ɹɜɥɹɟɬɫɹ ɨɛɪɚɬɢɦɵɦ, ɩɨɫɥɟ ɫɧɹɬɢɹ ɧɚɩɪɹɠɟɧɢɹ P-N-ɩɟɪɟɯɨɞ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬɫɹ.
ɍɱɚɫɬɨɤ IV: ɍɱɚɫɬɨɤ ɬɟɩɥɨɜɨɝɨ ɩɪɨɛɨɹ. ȼɨɡɪɚɫɬɚɟɬ ɬɨɤ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɦɨɳɧɨɫɬɶ, ɱɬɨ ɩɪɢɜɨɞɢɬ
ɤ ɧɚɝɪɟɜɭ ɞɢɨɞɚ ɢ ɨɧ ɫɝɨɪɚɟɬ.
Ɍɟɩɥɨɜɨɣ ɩɪɨɛɨɣ - ɧɟɨɛɪɚɬɢɦ.
ȼɫɥɟɞ ɡɚ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɪɨɛɨɟɦ, ɨɱɟɧɶ ɛɵɫɬɪɨ ɫɥɟɞɭɟɬ ɬɟɩɥɨɜɨɣ, ɩɨɷɬɨɦɭ ɞɢɨɞɵ ɩɪɢ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɪɨɛɨɟ ɧɟ
ɪɚɛɨɬɚɸɬ.
ȼɨɥɶɬ-ɚɦɩɟɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢɞɟɚɥɶɧɨɝɨ ɞɢɨɞɚ (ɜɟɧɬɢɥɹ)
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɯ ɩɪɢɛɨɪɨɜ
1. Ɇɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɫɪɟɞɧɢɣ ɡɚ ɩɟɪɢɨɞ ɩɪɹɦɨɣ ɬɨɤ (IɉɊ. ɋɊ.)
- ɷɬɨ ɬɚɤɨɣ ɬɨɤ, ɤɨɬɨɪɵɣ ɞɢɨɞ ɫɩɨɫɨɛɟɧ ɩɪɨɩɭɫɬɢɬɶ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ȼɟɥɢɱɢɧɚ ɞɨɩɭɫɬɢɦɨɝɨ ɫɪɟɞɧɟɝɨ ɡɚ ɩɟɪɢɨɞ ɩɪɹɦɨɝɨ ɬɨɤɚ ɪɚɜɧɚ 70% ɨɬ ɬɨɤɚ ɬɟɩɥɨɜɨɝɨ ɩɪɨɛɨɹ.
ɉɨ ɩɪɹɦɨɦɭ ɬɨɤɭ ɞɢɨɞɵ ɞɟɥɹɬɫɹ ɧɚ ɬɪɢ ɝɪɭɩɩɵ:
1) Ⱦɢɨɞɵ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ (IɉɊ.ɋɊ < 0,3 Ⱥ)
2) Ⱦɢɨɞɵ ɫɪɟɞɧɟɣ ɦɨɳɧɨɫɬɢ (0,3 <I ɉɊ.ɋɊ <1 0 Ⱥ)
3) Ⱦɢɨɞɵ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ (IɉɊ.ɋɊ > 10 Ⱥ)
Ⱦɢɨɞɵ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɧɟ ɬɪɟɛɭɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɬɟɩɥɨɨɬɜɨɞɚ (ɬɟɩɥɨ ɨɬɜɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɤɨɪɩɭɫɚ ɞɢɨɞɚ)
Ⱦɥɹ ɞɢɨɞɨɜ ɫɪɟɞɧɟɣ ɢ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ, ɤɨɬɨɪɵɟ ɧɟ ɷɮɮɟɤɬɢɜɧɨ ɨɬɜɨɞɹɬ ɬɟɩɥɨ ɫɜɨɢɦɢ ɤɨɪɩɭɫɚɦɢ, ɬɪɟɛɭɟɬɫɹ
ɞɨɩɨɥɧɢɬɟɥɶɧɵ ɬɟɩɥɨɨɬɜɨɞ (ɪɚɞɢɚɬɨɪ – ɤɭɛɢɤ ɦɟɬɚɥɥɚ, ɜ ɤɨɬɨɪɨɦ ɫ ɩɨɦɨɳɶɸ ɥɢɬɶɹ ɢɥɢ ɮɪɟɡɟɪɨɜɚɧɢɹ ɞɟɥɚɸɬ
ɲɢɩɵ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɜɨɡɪɚɫɬɚɟɬ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɩɥɨɨɬɜɨɞɚ. Ɇɚɬɟɪɢɚɥ - ɦɟɞɶ, ɛɪɨɧɡɚ, ɚɥɸɦɢɧɢɣ, ɫɢɥɭɦɢɧ)
2. ɉɨɫɬɨɹɧɧɨɟ ɩɪɹɦɨɟ ɧɚɩɪɹɠɟɧɢɟ (Uɩɪ.)
ɉɨɫɬɨɹɧɧɨɟ ɩɪɹɦɨɟ ɧɚɩɪɹɠɟɧɢɟ – ɷɬɨ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ ɩɪɢ ɩɪɨɬɟɤɚɧɢɢ
ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɝɨ ɩɪɹɦɨɝɨ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ.
ɉɪɨɹɜɥɹɟɬɫɹ ɨɫɨɛɟɧɧɨ ɩɪɢ ɦɚɥɨɦ ɧɚɩɪɹɠɟɧɢɢ ɩɢɬɚɧɢɹ.
ɉɨɫɬɨɹɧɧɨɟ ɩɪɹɦɨɟ ɧɚɩɪɹɠɟɧɢɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɬɟɪɢɚɥɚ ɞɢɨɞɨɜ (ɝɟɪɦɚɧɢɣ - Ge, ɤɪɟɦɧɢɣ - Si)
Uɩɪ. Si § 0.5÷1 ȼ (Ʉɪɟɦɧɢɟɜɵɟ)
Uɩɪ. Ge § 0.3÷0.5 ȼ (Ƚɟɪɦɚɧɢɟɜɵɟ)
Ƚɟɪɦɚɧɢɟɜɵɟ ɞɢɨɞɵ ɨɛɨɡɧɚɱɚɸɬ – ȽȾ (1Ⱦ)
Ʉɪɟɦɧɢɟɜɵɟ ɞɢɨɞɵ ɨɛɨɡɧɚɱɚɸɬ – ɄȾ (2Ⱦ)
3. ɉɨɜɬɨɪɹɸɳɟɟɫɹ ɢɦɩɭɥɶɫɧɨɟ ɨɛɪɚɬɧɨɟ ɦɚɤɫɢɦɚɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ (Uɨɛɪ. max)
ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɨɛɨɣ ɢɞɟɬ ɩɨ ɚɦɩɥɢɬɭɞɧɨɦɭ ɡɧɚɱɟɧɢɸ (ɢɦɩɭɥɶɫɭ) Uɨɛɪ. max § 0.7Uɗɥ. ɩɪɨɛɨɹ (10÷100 ȼ)
Ⱦɥɹ ɦɨɳɧɵɯ ɞɢɨɞɨɜ Uɨɛɪ. max= 1200 ȼ.
ɗɬɨɬ ɩɚɪɚɦɟɬɪ ɢɧɨɝɞɚ ɧɚɡɵɜɚɸɬ ɤɥɚɫɫɨɦ ɞɢɨɞɚ (12 ɤɥɚɫɫ -Uɨɛɪ. max= 1200 ȼ)
4. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɨɛɪɚɬɧɵɣ ɬɨɤ ɞɢɨɞɚ (Imax ..ɨɛɪ.)
ɋɨɨɬɜɟɬɫɬɜɭɟɬ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɨɛɪɚɬɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ (ɫɨɫɬɚɜɥɹɟɬ ɟɞɢɧɢɰɵ mA).
Ⱦɥɹ ɤɪɟɦɧɢɟɜɵɯ ɞɢɨɞɨɜ ɦɚɤɫɢɦɚɥɶɧɵɣ ɨɛɪɚɬɧɵɣ ɬɨɤ ɜ ɞɜɚ ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɞɥɹ ɝɟɪɦɚɧɢɟɜɵɯ.
5. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ (ɞɢɧɚɦɢɱɟɫɤɨɟ) ɫɨɩɪɨɬɢɜɥɟɧɢɟ.
RȾ
'U
'I
§2 ɋɬɚɛɢɥɢɬɪɨɧɵ
ɋɬɚɛɢɥɢɬɪɨɧ – ɷɬɨ ɪɚɡɧɨɜɢɞɧɨɫɬɶ ɞɢɨɞɚ. ɉɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɨɝɪɚɧɢɱɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɢɝɧɚɥɨɜ ɩɨ ɬɨɤɭ ɢ
ɧɚɩɪɹɠɟɧɢɸ.
ɂɫɩɨɥɶɡɭɸɬɫɹ ɜ ɫɬɚɛɢɥɢɡɚɬɨɪɚɯ ɧɚɩɪɹɠɟɧɢɹ.
Ɉɛɨɡɧɚɱɟɧɢɟ ɧɚ ɫɯɟɦɚɯ:
ȼɨɥɶɬ-ɚɦɩɟɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɬɚɛɢɥɢɬɪɨɧɚ
Ɋɚɛɨɱɢɦ ɭɱɚɫɬɤɨɦ ɹɜɥɹɟɬɫɹ ɭɱɚɫɬɨɤ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɪɨɛɨɹ.
Uɫɬɚɛ. – ɧɚɩɪɹɠɟɧɢɟ ɫɬɚɛɢɥɢɡɚɰɢɢ
Iɫɬɚɛ.min – ɦɢɧɢɦɚɥɶɧɵɣ ɬɨɤ ɫɬɚɛɢɥɢɡɚɰɢɢ
Iɫɬɚɛ.max – ɦɚɤɫɢɦɚɥɶɧɵɣ ɬɨɤ ɫɬɚɛɢɥɢɡɚɰɢɢ
Ɋɚɛɨɱɢɣ ɬɨɤ ɫɬɚɛɢɥɢɬɪɨɧɚ ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ ɨɬ ɦɢɧɢɦɚɥɶɧɨɝɨ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɬɨɤɚ
ɫɬɚɛɢɥɢɡɚɰɢɢ. I ɫɬ. max d I ɪɚɛ . t I ɫɬ. min
ɋɬɟɩɟɧɶ ɧɚɤɥɨɧɚ ɪɚɛɨɱɟɝɨ ɭɱɚɫɬɤɚ, ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɞɢɧɚɦɢɱɟɫɤɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ
RȾ
'U
'I
Ⱦɥɹ ɢɞɟɚɥɶɧɨɝɨ ɫɬɚɛɢɥɢɬɪɨɧɚ RȾ=0. Uɫɬɚɛ. =3 ÷ 200 ȼ
§3 Ɍɢɪɢɫɬɨɪɵ
Ɍɢɪɢɫɬɨɪ – ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɵɣ ɩɪɢɛɨɪ ɫ ɧɟɫɤɨɥɶɤɢɦɢ ɱɟɪɟɞɭɸɳɢɦɢɫɹ ɫɥɨɹɦɢ n-p ɩɪɨɜɨɞɢɦɨɫɬɢ, ɱɚɳɟ
ɱɟɬɵɪɟɯɫɥɨɣɧɨɣ ɫɬɪɭɤɬɭɪɵ p-n-p-n. Ɍɢɪɢɫɬɨɪɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɤɥɸɱɟɜɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɦɢ
ɫɢɝɧɚɥɚɦɢ ɜ ɪɟɠɢɦɟ ɨɬɤɪɵɬ-ɡɚɤɪɵɬ (ɭɩɪɚɜɥɹɟɦɵɣ ɞɢɨɞ).
ɇɚɡɜɚɧɢɟ ɬɢɪɢɫɬɨɪɚ - ɨɬ ɝɪɟɱɟɫɤɨɝɨ ɫɥɨɜɚ thyra (ɬɢɪɚ), ɱɬɨ ɨɡɧɚɱɚɟɬ "ɞɜɟɪɶ" ɢɥɢ "ɜɯɨɞ".
ȼɨɥɶɬɚɦɩɟɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɢɪɢɫɬɨɪɚ.
+
Ⱥ
ɍ
Ʉ
VS1
ɍ - ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ
ȼɵɲɟ ɩɪɢɜɟɞɟɧɨ ɫɯɟɦɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ ɭɩɪɚɜɥɹɟɦɨɝɨ ɬɢɪɢɫɬɨɪɚ (ɬɪɢɨɞɧɵɣ ɬɢɪɢɫɬɨɪ, ɬɪɢɧɢɫɬɨɪ). ɇɚ
ɩɪɚɤɬɢɤɟ ɩɪɢ ɭɩɨɬɪɟɛɥɟɧɢɢ ɬɟɪɦɢɧɚ "ɬɢɪɢɫɬɨɪ" ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɢɦɟɧɧɨ ɷɬɨɬ ɷɥɟɦɟɧɬ.
ɉɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɨɥɹɪɧɨɫɬɢ: 0 d U d U max - ɭɱɚɫɬɨɤ ɈȺ – ɬɢɪɢɫɬɨɪ ɡɚɤɪɵɬ.
U ɜɤɥ - ɧɚɡɵɜɚɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟɦ ɜɤɥɸɱɟɧɢɹ. Ʉɚɤ ɬɨɥɶɤɨ ɧɚɩɪɹɠɟɧɢɟ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɹ, U ɜɤɥ ɨɧɨ ɥɚɜɢɧɨɨɛɪɚɡɧɨ
ɫɧɢɠɚɟɬɫɹ – ɭɱɚɫɬɨɤ Ⱥȼ
ɋɩɨɫɨɛ ɭɩɪɚɜɥɟɧɢɹ ɩɨɜɵɲɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɞɨ U ɜɤɥ ɧɟ ɪɟɤɨɦɟɧɞɭɟɬɫɹ (ɬɢɪɢɫɬɨɪ ɨɬɤɪɵɜɚɟɬɫɹ ɬɨɥɶɤɨ ɨɞɢɧ ɪɚɡ)
ɑɟɦ ɛɨɥɶɲɢɣ ɬɨɤ ɩɨɞɚɧ ɧɚ ɭɩɪɚɜɥɹɸɳɢɣ ɷɥɟɤɬɪɨɞ, ɬɟɦ «ɤɨɥɟɧɨ ɈȺȼ» ɦɟɧɶɲɟ.
ȿɫɥɢ I ɭɩɪ t I ɭ 4 , (I ɭ4 = I ɭɩɪ ɨɩɬ - ɭɩɪɚɜɥɹɸɳɢɣ ɬɨɤ ɨɬɩɢɪɚɧɢɹ), ɬɨ ȼȺɏ ɬɢɪɢɫɬɨɪɚ ɫɨɜɩɚɞɟɬ ɫ ȼȺɏ ɞɢɨɞɚ.
Ʉɨɝɞɚ ɬɢɪɢɫɬɨɪ ɜɵɲɟɥ ɧɚ ɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ ȼɋ, ɦɨɠɧɨ ɨɬɤɥɸɱɢɬɶ ɬɨɤ ɭɩɪɚɜɥɟɧɢɹ. ɑɬɨɛɵ ɡɚɤɪɵɬɶ ɬɢɪɢɫɬɨɪ
ɧɟɨɛɯɨɞɢɦɨ ɫɧɢɡɢɬɶ ɚɧɨɞɧɵɣ ɬɨɤ ɞɨ ɬɨɤɚ ɭɞɟɪɠɚɧɢɹ ɧɚ ɞɨɫɬɚɬɨɱɧɨɟ ɜɪɟɦɹ (ɜɪɟɦɹ ɭɞɟɪɠɚɧɢɹ). ɉɪɢ ɫɦɟɧɟ
ɩɨɥɹɪɧɨɫɬɢ ɬɨɤɚ ɬɢɪɢɫɬɨɪ ɡɚɤɪɵɜɚɟɬɫɹ.
Ɍɢɪɢɫɬɨɪɵ ɛɵɜɚɸɬ ɞɜɭɯ ɜɢɞɨɜ:
1. ɇɟ ɡɚɩɢɪɚɟɦɵɟ – ɷɬɨ ɬɢɪɢɫɬɨɪɵ, ɭɩɪɚɜɥɹɟɦɵɟ ɩɪɢ ɩɨɞɚɱɢ ɧɚɩɪɹɠɟɧɢɹ ɢ ɬɨɤɚ ɧɚ ɭɩɪɚɜɥɹɟɦɵɣ ɷɥɟɤɬɪɨɞ.
2. Ɂɚɩɢɪɚɟɦɵɟ – ɢɯ ɢɫɯɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ – ɨɬɤɪɵɬ. ɑɬɨɛɵ ɡɚɤɪɵɬɶ ɡɚɩɢɪɚɟɦɵɣ ɬɢɪɢɫɬɨɪ ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɚɬɶ ɬɨɤ
ɨɛɪɚɬɧɨɣ ɩɨɥɹɪɧɨɫɬɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɛɨɥɶɲɨɣ ɜɟɥɢɱɢɧɵ.
ɂɡɦɟɧɹɹ ɭɝɨɥ Į, ɦɨɠɧɨ ɪɟɝɭɥɢɪɨɜɚɬɶ ɫɪɟɞɧɟɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɚɝɪɭɡɤɟ, ɱɟɦ ɛɨɥɶɲɟ Į, ɬɟɦ ɦɟɧɶɲɟ ɫɪɟɞɧɟɟ
ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɚɝɪɭɡɤɟ.
ɋɢɦɦɟɬɪɢɱɧɵɟ ɬɢɪɢɫɬɨɪɵ ɢɥɢ ɫɢɦɢɫɬɨɪɵ – ɷɬɨ ɞɜɚ ɬɢɪɢɫɬɨɪɚ ɜɤɥɸɱɟɧɧɵɯ ɜɫɬɪɟɱɧɨ - ɩɚɪɚɥɥɟɥɶɧɨ.
ɋɥɟɜɚ ɞɚɧɨ ɨɛɨɡɧɚɱɟɧɢɟ ɧɟɭɩɪɚɜɥɹɟɦɨɝɨ ɬɢɪɢɫɬɨɪɚ (ɞɢɧɢɫɬɨɪɚ). Ɉɧ ɨɬɤɪɵɜɚɟɬɫɹ ɩɪɢ
ɩɪɢɥɨɠɟɧɢɢ ɦɟɠɞɭ ɚɧɨɞɨɦ ɢ ɤɚɬɨɞɨɦ ɧɚɩɪɹɠɟɧɢɹ ɛɨɥɶɲɟ U ɜɤɥ
ɉɚɪɚɦɟɬɪɵ ɬɢɪɢɫɬɨɪɨɜ
1. ɇɚɩɪɹɠɟɧɢɟ ɜɤɥɸɱɟɧɢɹ ( U ɜɤɥ ) – ɷɬɨ ɬɚɤɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ ɬɢɪɢɫɬɨɪ ɩɟɪɟɯɨɞɢɬ ɜ ɨɬɤɪɵɬɨɟ
ɫɨɫɬɨɹɧɢɟ.
2. ɉɨɜɬɨɪɹɸɳɟɟɫɹ ɢɦɩɭɥɶɫɧɨɟ ɨɛɪɚɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ (Uɨɛɪ.max) – ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ ɧɚɫɬɭɩɚɟɬ
ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɩɪɨɛɨɣ. Ⱦɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɬɢɪɢɫɬɨɪɨɜ Uɜɤɥ.= Uɨɛɪ.max
3. Ɇɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɵɣ ɩɪɹɦɨɣ, ɫɪɟɞɧɢɣ ɡɚ ɩɟɪɢɨɞ ɬɨɤ.
4. ɉɪɹɦɨɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɨɬɤɪɵɬɨɦ ɬɢɪɢɫɬɨɪɟ (Uɩɪ.= 0,5÷1 ȼ)
5. Ɉɛɪɚɬɧɵɣ ɦɚɤɫɢɦɚɥɶɧɵɣ ɬɨɤ – ɷɬɨ ɬɨɤ, ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɞɜɢɠɟɧɢɟɦ ɧɟɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ ɩɪɢ ɩɪɢɥɨɠɟɧɢɢ
ɧɚɩɪɹɠɟɧɢɹ ɨɛɪɚɬɧɨɣ ɩɨɥɹɪɧɨɫɬɢ.
6. Ɍɨɤ ɭɞɟɪɠɚɧɢɹ – ɷɬɨ ɚɧɨɞɧɵɣ ɬɨɤ, ɩɪɢ ɤɨɬɨɪɨɦ ɬɢɪɢɫɬɨɪ ɡɚɤɪɵɜɚɟɬɫɹ
7. ȼɪɟɦɹ ɨɬɤɥɸɱɟɧɢɹ - ɷɬɨ ɜɪɟɦɹ ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɡɚɤɪɵɜɚɟɬɫɹ ɬɢɪɢɫɬɨɪ.
8. ɉɪɟɞɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɧɚɪɚɫɬɚɧɢɹ ɚɧɨɞɧɨɝɨ ɬɨɤɚ dI ɚ . ȿɫɥɢ ɚɧɨɞɧɵɣ ɬɨɤ ɛɭɞɟɬ ɛɵɫɬɪɨ ɧɚɪɚɫɬɚɬɶ, ɬɨ p-n
dt
ɩɟɪɟɯɨɞɵ ɛɭɞɭɬ ɡɚɝɪɭɠɚɬɶɫɹ ɬɨɤɨɦ ɧɟɪɚɜɧɨɦɟɪɧɨ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɛɭɞɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɦɟɫɬɧɵɣ ɩɟɪɟɝɪɟɜ ɢ
ɬɟɩɥɨɜɨɣ ɩɪɨɛɨɣ .
9. ɉɪɟɞɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɧɚɪɚɫɬɚɧɢɹ ɚɧɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ dU a . ȿɫɥɢ ɩɪɟɞɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɧɚɪɚɫɬɚɧɢɹ
dt
ɚɧɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɛɭɞɟɬ ɛɨɥɶɲɟ ɩɚɫɩɨɪɬɧɨɣ, ɬɢɪɢɫɬɨɪ ɦɨɠɟɬ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɨɬɤɪɵɬɶɫɹ ɨɬ
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɩɨɦɟɯɢ.
10.
ɍɩɪɚɜɥɹɸɳɢɣ ɬɨɤ ɨɬɩɢɪɚɧɢɹ – ɷɬɨ ɬɨɤ, ɤɨɬɨɪɵɣ ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɚɬɶ, ɱɬɨɛɵ ɬɢɪɢɫɬɨɪ ɨɬɤɪɵɥɫɹ ɛɟɡ
«ɤɨɥɟɧɚ».
11.
ɍɩɪɚɜɥɹɸɳɟɟ ɧɚɩɪɹɠɟɧɢɟ ɨɬɩɢɪɚɧɢɹ - ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ, ɤɨɬɨɪɨɟ ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɚɬɶ, ɱɬɨɛɵ ɬɢɪɢɫɬɨɪ
ɨɬɤɪɵɥɫɹ ɛɟɡ «ɤɨɥɟɧɚ».
§4 Ɉɞɧɨɮɚɡɧɵɟ ɫɯɟɦɵ ɜɵɩɪɹɦɥɟɧɢɹ
Ɋɚɡɥɢɱɚɸɬ ɞɜɚ ɫɩɨɫɨɛɚ (ɫɯɟɦɵ) ɜɵɩɪɹɦɥɟɧɢɹ:
1. Ɉɞɧɨɩɨɥɭɩɟɪɢɨɞɧɨɟ – ɬɨɤ ɜ ɧɚɝɪɭɡɤɟ ɩɪɨɬɟɤɚɟɬ ɬɨɥɶɤɨ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɨɥɭɜɨɥɧɟ ɩɢɬɚɸɳɟɝɨ
ɧɚɩɪɹɠɟɧɢɹ..
2. Ⱦɜɭɯɩɨɥɭɩɟɪɢɨɞɧɨɟ – ɬɨɤ ɜ ɧɚɝɪɭɡɤɚɯ ɩɪɨɬɟɤɚɟɬ ɩɪɢ ɨɛɟɢɯ ɩɨɥɭɜɨɥɧɚɯ.
Ɉɞɧɨɩɨɥɭɩɟɪɢɨɞɧɚɹ ɫɯɟɦɚ ɜɵɩɪɹɦɥɟɧɢɹ
ɇɚ ɭɱɚɫɬɤɟ 0< Ȧt < ʌ Ud=e2
ɇɚ ɭɱɚɫɬɤɟ ʌ<Ȧt<2ʌ Ud=0
Ⱦɨɫɬɨɢɧɫɬɜɨ ɨɞɧɨɩɨɥɭɩɟɪɢɨɞɧɨɣ ɫɯɟɦɵ ɜɵɩɪɹɦɥɟɧɢɹ: ɩɪɨɫɬɨɬɚ ɢ ɞɟɲɟɜɢɡɧɚ.
ɇɟɞɨɫɬɚɬɤɢ ɨɞɧɨɩɨɥɭɩɟɪɢɨɞɧɨɣ ɫɯɟɦɵ ɜɵɩɪɹɦɥɟɧɢɹ: ɬɨɤɢ ɢ ɧɚɩɪɹɠɟɧɢɹ ɩɪɟɪɵɜɢɫɬɵ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɢɡɤɨɟ
ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɬɨɤɨɜ ɢ ɧɚɩɪɹɠɟɧɢɣ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɫɯɟɦɟ ɜɟɥɢɤ ɭɪɨɜɟɧɶ ɧɚɩɪɹɠɟɧɢɹ ɩɭɥɶɫɚɰɢɣ.
Ⱦɜɭɯɩɨɥɭɩɟɪɢɨɞɧɚɹ ɫɯɟɦɚ ɜɵɩɪɹɦɥɟɧɢɹ
Ɋɚɫɫɦɨɬɪɢɦ ɨɞɧɨɮɚɡɧɭɸ ɞɜɭɯɩɨɥɭɩɟɪɢɨɞɧɭɸ ɫɯɟɦɭ ɜɵɩɪɹɦɥɟɧɢɹ ɫ ɧɭɥɟɜɨɣ ɬɨɱɤɨɣ (ɧɭɥɟɜɚɹ ɫɯɟɦɚ)
Ɋɚɫɫɦɨɬɪɢɦ ɢɧɬɟɪɜɚɥ 0 < Ȧt < ʌ : ɞɢɨɞ V1 – ɨɬɤɪɵɬ; ɞɢɨɞ V2 – ɡɚɤɪɵɬ. Ud=e2 Udm=E2m=
Ɋɚɫɫɦɨɬɪɢɦ ɢɧɬɟɪɜɚɥ ʌ < Ȧt < 2ʌ: ɞɢɨɞ V1 –ɡɚɤɪɵɬ; ɞɢɨɞ V2 – ɨɬɤɪɵɬ.
2E 2
Ɍɨɤɢ ɢ ɧɚɩɪɹɠɟɧɢɹ ɢɦɟɸɬ ɨɞɢɧɚɤɨɜɭɸ ɩɨɥɹɪɧɨɫɬɶ, ɧɨ ɜ ɤɚɠɞɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɢɡɦɟɧɹɸɬ ɫɜɨɸ ɜɟɥɢɱɢɧɭ
(ɬɨɤ ɢ ɧɚɩɪɹɠɟɧɢɟ ɜ ɧɚɝɪɭɡɤɟ ɢɦɟɸɬ ɩɭɥɶɫɢɪɭɸɳɢɣ ɯɚɪɚɤɬɟɪ).
ɇɚɩɪɹɠɟɧɢɟ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɤɚɤ ɩɨɫɬɨɹɧɧɭɸ, ɬɚɤ ɢ ɩɟɪɟɦɟɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ.
u d (t ) U d u (t )
T
ud
ud
1
u d (t )dt
T ³0
2 2
S
E2
1
S
1
S
0
S³
0.9 E 2
E2
S
³ u dm sinwtdwt
2 E 2 sin wtdwt
0
S
2 2
ud
2E2
S
cos wt
S
0
2 2
S
E2
0.9 E 2
1.11U d
U ɩ1max
2ʌ
ʌ
0
ɉɟɪɢɨɞ ɩɢɬɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ T 2S
ɉɟɪɢɨɞ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
T
S
t
Uɩ
U ɩ1
ɇɚɢɛɨɥɶɲɭɸ ɜɟɥɢɱɢɧɭ ɜ ɤɪɢɜɨɣ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢɦɟɟɬ 1-ɚɹ
Z ɉ ɜ 2 ɪɚɡɚ ɜɵɲɟ ɱɚɫɬɨɬɵ ɩɢɬɚɸɳɟɣ
ɝɚɪɦɨɧɢɤɚ, ɱɚɫɬɨɬɚ ɤɨɬɨɪɨɣ
ɫɟɬɢ. ɗɬɭ
ɝɚɪɦɨɧɢɤɭ ɧɚɢɛɨɥɟɟ ɬɪɭɞɧɨ ɩɨɞɚɜɢɬɶ ɮɢɥɶɬɪɚɦɢ,
ɩɨɷɬɨɦɭ ɩɨ ɟɟ ɜɟɥɢɱɢɧɟ ɫɭɞɹɬ ɨɛ ɢɫɤɚɠɟɧɢɢ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɲɬɪɢɯɨɜɨɣ ɥɢɧɢɟɣ
ɩɨɤɚɡɚɧɚ ɩɟɪɜɚɹ ɝɚɪɦɨɧɢɤɚ ɩɭɥɶɫɚɰɢɢ.
ɉɭɥɶɫɚɰɢɹ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɭɥɶɫɚɰɢɢ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɭɥɶɫɚɰɢɣ
2
,
m 1
q
2
q
U n1m
ud
;
ɝɞɟ m – ɤɪɚɬɧɨɫɬɶ ɱɚɫɬɨɬɵ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɤ ɱɚɫɬɨɬɟ ɫɟɬɢ (ɱɢɫɥɨ
ɮɚɡ ɜɵɩɪɹɦɥɟɧɢɹ ɢɥɢ ɩɭɥɶɫɧɨɫɬɶ ɜɵɩɪɹɦɢɬɟɥɹ).
Ɉɩɪɟɞɟɥɢɦ ɤɨɷɮɮɢɰɢɟɧɬ ɩɭɥɶɫɚɰɢɢ ɞɥɹ ɧɚɲɟɝɨ ɪɚɫɫɦɨɬɪɟɧɧɨɝɨ ɫɥɭɱɚɹ
q
2
2 1
2
2
3
0.67
ɑɟɦ ɦɟɧɶɲɟ ɤɨɷɮɮɢɰɢɟɧɬ ɩɭɥɶɫɚɰɢɢ, ɬɟɦ ɦɟɧɶɲɟ ɭɪɨɜɟɧɶ ɩɭɥɶɫɚɰɢɢ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɵɲɟ ɤɚɱɟɫɬɜɨ
ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ.
Ɉɫɧɨɜɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɞɥɹ ɜɵɛɨɪɚ ɞɢɨɞɚ ɹɜɥɹɸɬɫɹ:
1. ɉɪɹɦɨɣ ɫɪɟɞɧɢɣ ɡɚ ɩɟɪɢɨɞ ɦɚɤɫɢɦɚɥɶɧɵɣ ɬɨɤ.
2. Ɉɛɪɚɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ.
Ud
- ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɩɪɨɬɟɤɚɸɳɟɝɨ ɱɟɪɟɡ ɧɚɝɪɭɡɤɭ.
Id
Rɧ
I am
I dm
Ɍɚɤ ɤɚɤ ɞɥɹ ɬɨɤɚ
ɨɞɧɚ ɩɨɥɭɜɨɥɧɚ ɨɬɫɭɬɫɬɜɭɟɬ, ɚ ɞɥɹ ɬɨɤɚ
id
ɧɟɬ ɩɨɥɭɱɚɟɦ:
Id
2
Ia
u ɨɛɪ.m
2 Em2
uɨɛɪ.m Su
Pɧ
ia
U d2
Rɧ
2 2E2
2 2
2 2
Su d
Su d
d
Ud
E2
Pɧ
E 22
Rɧ
- ɩɨɥɧɚɹ ɦɨɳɧɨɫɬɶ.
Ɇɨɳɧɨɫɬɶ, ɜɵɞɟɥɹɟɦɚɹ ɧɚ ɧɚɝɪɭɡɤɟ ɨɬ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ:
Pɧ.ɩɨɫɬ.
u d2
Rɧ
(0.9 E 2 ) 2
Rɧ
0.81E 22
Rɧ
0.81Pɧ
Ɉɤɨɥɨ 20% ɜɫɟɣ ɦɨɳɧɨɫɬɢ ɜ ɧɚɝɪɭɡɤɭ ɩɟɪɟɞɚɟɬɫɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɩɭɥɶɫɚɰɢɢ
(ɭɫɬɪɚɧɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ) ɩɪɢɦɟɧɹɸɬɫɹ ɮɢɥɶɬɪɵ.
Ɋɚɫɱɟɬɧɚɹ ɦɨɳɧɨɫɬɶ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ:
SɌ
1.34 Pd
(ɩɪɢ ɚɤɬɢɜɧɨ - ɢɧɞɭɤɬɢɜɧɨɣ ɧɚɝɪɭɡɤɟ)
§5 Ɉɞɧɨɮɚɡɧɚɹ ɞɜɭɯɩɨɥɭɩɟɪɢɨɞɧɚɹ
ɦɨɫɬɨɜɚɹ ɫɯɟɦɚ ɜɵɩɪɹɦɥɟɧɢɹ
ɬɨɤ
id
ɩɨɜɬɨɪɹɟɬ ɮɨɪɦɭ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɧɚɝɪɭɡɤɟ, ɚ
i1
ɉɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɩɨɥɭɜɨɥɧɟ ɗȾɋ
e 2 (ɢɧɬɟɪɜɚɥ 0- S ) ɢ ɭɤɚɡɚɧɧɨɣ ɧɚ
ɪɢɫɭɧɤɟ ɩɨɥɹɪɧɨɫɬɢ ɜɵɩɪɹɦɥɟɧɧɵɣ
ɬɨɤ ɛɭɞɟɬ ɩɪɨɬɟɤɚɬɶ ɱɟɪɟɡ ɞɢɨɞ V1,
ɧɚɝɪɭɡɤɭ Rɧ Lɧ ɢ ɞɢɨɞ V4. Ⱦɢɨɞɵ V2 ɢ
V3 ɧɚɯɨɞɹɬɫɹ ɩɨɞ ɨɛɪɚɬɧɵɦ
ɧɚɩɪɹɠɟɧɢɟɦ ɢ ɬɨɤɚ ɧɟ ɩɪɨɜɨɞɹɬ
(ɩɥɸɫ ɩɪɢɥɨɠɟɧ ɤ ɤɚɬɨɞɭ, ɚ ɦɢɧɭɫ ɤ
ɚɧɨɞɭ).
ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɹɪɧɨɫɬɢ
Ɇɨɫɬɨɜɚɹ ɫɯɟɦɚ ɦɨɠɟɬ ɪɚɛɨɬɚɬɶ ɢ ɛɟɡ
ɩɟɪɟɦɟɧɧɨɝɨ
ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ,ɧɚɩɪɹɠɟɧɢɹ
ɚ ɫɯɟɦɚ ɫ ɧɭɥɟɜɨɣe 2ɬɨɱɤɨɣ ɧɟɬ
(ɢɧɬɟɪɜɚɥ S y 2S ) ɨɬɤɪɵɜɚɸɬɫɹ V2 ɢ
V3 ɢ ɬɨɤ id ɫɨɯɪɚɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɟ.
ȿɫɥɢ ɧɚɝɪɭɡɤɚ ɚɤɬɢɜɧɚɹ ( Lɧ 0 ), ɬɨ
ɢ i2 ɢɦɟɸɬ ɫɢɧɭɫɨɢɞɚɥɶɧɭɸ ɮɨɪɦɭ (ɲɬɪɢɯɨɜɵɟ ɤɪɢɜɵɟ)
ȿɫɥɢ Lɧ z 0 , ɨɧɚ ɩɪɟɩɹɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɸ ɬɨɤɚ ɢ id ɧɟ ɛɭɞɟɬ ɭɫɩɟɜɚɬɶ ɫɥɟɞɨɜɚɬɶ ɡɚ ɢɡɦɟɧɟɧɢɟɦ u d ɢ ɛɭɞɟɬ
ɫɝɥɚɠɢɜɚɬɶɫɹ (ɫɩɥɨɲɧɚɹ ɥɢɧɢɹ id ).
ɉɪɢ ɡɧɚɱɢɬɟɥɶɧɨɣ ɢɧɞɭɤɬɢɜɧɨɣ ɧɚɝɪɭɡɤɟ ( X L Z ɉ Lɇ > 10 R ɇ ) ɬɨɤ id ɢɡ-ɡɚ ɦɚɥɵɯ ɩɭɥɶɫɚɰɢɣ ɦɨɠɧɨ ɫɱɢɬɚɬɶ
ɩɨɫɬɨɹɧɧɵɦ (ɢɞɟɚɥɶɧɨ ɫɝɥɚɠɟɧɧɵɦ).
ɉɟɪɟɞɚɱɚ ɚɤɬɢɜɧɨɣ ɦɨɳɧɨɫɬɢ ɜ ɧɚɝɪɭɡɤɭ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɬɨɤɚ ɨɬɫɭɬɫɬɜɭɟɬ. Ɍɨɤɢ ia , i2 , i1 ɩɪɢɧɢɦɚɸɬ
ɮɨɪɦɭ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ.
ɉɪɢ R-L ɧɚɝɪɭɡɤɟ, ɤɚɤ ɢ ɩɪɢ ɚɤɬɢɜɧɨɣ, ɮɨɪɦɚ u d ɩɨɜɬɨɪɹɟɬ e2 , ɚ ɟɝɨ ɡɧɚɱɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɢ ɞɥɹ ɦɨɫɬɨɜɨɣ
ɫɯɟɦɵ ɫ ɚɤɬɢɜɧɨɣ ɧɚɝɪɭɡɤɨɣ.
2 2
Ud
S
E2
ɢɥɢ
0. 9 E 2
E2
1.11U d
ɉɪɟɧɟɛɪɟɠɟɦ ɩɨɬɟɪɹɦɢ ɜ
Ɍɨɤ ɜ ɞɢɨɞɟ
U ɨɛɪ.m
U
E2m
2E2
S
ɨɛɪ.m
Ia
2
U
Id
2
Id
2 Rɧ
2
2 2
SU d
Lɧ ,
;ɢ
S
2
ɞɢɨɞɚɯ ɢ ɬɪɚɧɫɮɨɪɦɚɬɨɪɟ ɢ ɩɨɥɨɠɢɦ
I a max
Ud
id
I d (ɢɞɟɚɥɶɧɨ
ɫɝɥɚɠɟɧ)
Id
Ud
Rɧ
Id
SɌ
1.11Pd
d
Ⱦɨɫɬɨɢɧɫɬɜɚ ɫɯɟɦɵ ɫ ɧɭɥɟɜɨɣ ɬɨɱɤɨɣ:
1. Ɇɟɧɶɲɟɟ ɱɢɫɥɨ ɞɢɨɞɨɜ Ÿ ɦɟɧɶɲɚɹ ɫɬɨɢɦɨɫɬɶ.
2. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɨɛɬɟɤɚɟɬɫɹ ɜɫɟɝɞɚ ɬɨɥɶɤɨ ɨɞɢɧ ɞɢɨɞ ɢ ɧɚɝɪɭɡɤɚ
ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɛɭɞɟɬ ɦɟɧɶɲɟ.
Ÿ
ɩɪɢ ɦɚɥɨɦ ɩɢɬɚɸɳɟɦ ɧɚɩɪɹɠɟɧɢɢ,
ɇɟɞɨɫɬɚɬɤɢ ɫɯɟɦɵ ɫ ɧɭɥɟɜɨɣ ɬɨɱɤɨɣ:
1. ɇɟ ɪɚɛɨɬɚɟɬ ɛɟɡ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ.
2. S Ɍ ɛɨɥɶɲɟ ɧɚ 20% Ÿ ɛɨɥɶɲɟ ɝɚɛɚɪɢɬɵ ɢ ɜɵɫɨɤɚɹ ɰɟɧɚ.
3. Ɉɛɪɚɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɛɨɥɶɲɟ ɜ ɞɜɚ ɪɚɡɚ.
ɉɪɢɦɟɧɹɟɬɫɹ ɩɪɢ ɦɚɥɵɯ ɧɚɩɪɹɠɟɧɢɹɯ ɩɢɬɚɧɢɹ.
Ⱦɨɫɬɨɢɧɫɬɜɚ ɦɨɫɬɨɜɨɣ ɫɯɟɦɵ:
1. Ɇɨɠɟɬ ɪɚɛɨɬɚɬɶ ɛɟɡ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ, ɟɫɥɢ ɧɚɫ ɭɫɬɪɚɢɜɚɟɬ ɜɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ.
2. S Ɍ ɧɚ 20% ɦɟɧɶɲɟ Ÿ ɦɟɧɶɲɟ ɝɚɛɚɪɢɬɵ ɢ ɧɢɠɟ ɰɟɧɚ.
3. ȼ ɞɜɚ ɪɚɡɚ ɦɟɧɶɲɟ ɨɛɪɚɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɞɥɹ ɞɢɨɞɨɜ.
ɇɟɞɨɫɬɚɬɤɢ ɦɨɫɬɨɜɨɣ ɫɯɟɦɵ:
1. ȼ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟɟ ɱɢɫɥɨ ɞɢɨɞɨɜ.
2. ɉɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ, ɬɚɤ ɤɚɤ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɧɚɝɪɭɡɤɨɣ ɬɨɤɨɦ ɨɛɬɟɤɚɸɬɫɹ ɞɜɚ ɞɢɨɞɚ.
Ɇɨɫɬɨɜɚɹ ɫɯɟɦɚ ɩɪɢɦɟɧɹɟɬɫɹ ɩɪɢ E2=10÷100 ȼ.
§6 Ɏɢɥɶɬɪɵ ɜɵɩɪɹɦɢɬɟɥɟɣ.
ɇɚɡɧɚɱɟɧɢɟ: ɍɥɭɱɲɟɧɢɟ ɤɚɱɟɫɬɜɚ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ, ɩɭɬɟɦ ɨɫɥɚɛɥɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ:
S
q ɜɯ
q ɜɵɯ
- ɯɚɪɚɤɬɟɪɢɡɭɟɬ (ɤɨɥɢɱɟɫɬɜɟɧɧɨ) ɨɫɥɚɛɥɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ. ɑɟɦ
ɛɨɥɶɲɟ ɤɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ, ɬɟɦ ɥɭɱɲɟ.
S
U n1m
Ud
U ɧn1m
Uɇ
U n1mU ɧ
U d U ɧn1m
ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɞɥɹ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ L ɢ L-C ɮɢɥɶɬɪɚ:
Uɧ
I ɧ Rɧ
r – ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɚɬɭɲɤɢ ɢɧɞɭɤɬɢɜɧɨɫɬɢ.
ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ L ɢ L-C ɮɢɥɶɬɪɚ:
Ȧn= 2Ȧɫɟɬɢ
Z ɩɨɫɥ
Z ɩɚɪ
- ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɮɢɥɶɬɪɚ ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ.
- ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɚɪɚɥɥɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɮɢɥɶɬɪɚ ɞɥɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ.
U ɧɩ1
ɑɟɦ ɛɨɥɶɲɟ
Z ɩɨɫɥ
ɢ ɦɟɧɶɲɟ
I ɩ1m Z ɩɚɪ
Z ɩɚɪ ,
ɬɟɦ ɦɟɧɶɲɟ U ɧɩ1 ɢ ɛɨɥɶɲɟ ɤɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ S.
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ ɞɥɹ L – ɮɢɥɶɬɪɚ:
Z ɩɨɫɥ
Zɩ L
U ɩ1mU ɧ
U ɧɩ1U d
S
S
Z ɩɚɪ
U ɩ1m
(Z ɩ L) 2 Rɧ2
U ɩ1mU d Rɧ (Z ɩ L) 2 Rɧ2
(Z ɩ L) 2 Rɧ2
(r Rɧ )U ɩ1mU d Rɧ
r Rɧ
ZɩL
Rɧ
U ɧɩ1m
Rɧ
S
Rɧ
ɉɪɢɦɟɦ ɞɨɩɭɳɟɧɢɹ: r <<
Rɧ
ɢ Rɧ <<
ZɩL Ÿ
Z ɩɨɫɥ
Z
ɩɚɪ
ɑɟɦ ɦɟɧɶɲɟ Rɧ Ÿ ɬɟɦ ɛɨɥɶɲɟ S
ɂɧɞɭɤɬɢɜɧɵɣ ɮɢɥɶɬɪ ɷɮɮɟɤɬɢɜɟɧ ɜ «ɫɢɥɶɧɨɬɨɱɧɵɯ» ɫɯɟɦɚɯ, ɝɞɟ
Rɧ - ɦɚɥɨ
«ɋɢɥɶɧɨɬɨɱɧɚɹ» ɫɯɟɦɚ – ɷɬɨ ɫɯɟɦɚ, ɝɞɟ ɩɪɨɬɟɤɚɸɬ ɛɨɥɶɲɢɟ (ɫɢɥɶɧɵɟ) ɬɨɤɢ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ ɞɥɹ Lɋ – ɮɢɥɶɬɪɚ:
ȿɦɤɨɫɬɶ ɲɭɧɬɢɪɭɟɬ ɧɚɝɪɭɡɤɭ ɩɨ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ.
ɍɫɥɨɜɢɟ ɷɮɮɟɤɬɢɜɧɨɝɨ ɲɭɧɬɢɪɨɜɚɧɢɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ:
1
ɞɨɥɠɧɨ ɛɵɬɶ < 0.1 Rɧ
Xc
Z ɩɋ
Z ɩɚɪ
S
S
1
Z ɩɋ
Z ɩɨɫɥ
ZɩL
Z ɩɚɪ
1
Z ɩɋ
Z ɩ2 LC
Z ɩ2 LC
- ɂɡ ɱɟɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ LC-ɮɢɥɶɬɪɵ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵ.
ȿɦɤɨɫɬɧɨɣ ɢ R-C-ɮɢɥɶɬɪ
ȿɦɤɨɫɬɧɵɟ ɢ R-C ɮɢɥɶɬɪɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɪɢ ɧɚɝɪɭɡɤɟ ɩɨɬɪɟɛɥɹɸɳɟɣ ɦɚɥɵɟ ɬɨɤɢ ɨɬ ɜɵɩɪɹɦɢɬɟɥɹ
("ɫɥɚɛɨɬɨɱɧɚɹ" ɧɚɝɪɭɡɤɚ, ɬ.ɟ. ɧɚɝɪɭɡɤɚ ɫ ɦɚɥɵɦ ("ɫɥɚɛɵɦ") ɬɨɤɨɦ).
r - ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɢɨɞɨɜ ɢ ɨɛɦɨɬɨɤ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ
Ɋɚɫɫɦɨɬɪɢɦ, ɱɬɨ ɩɪɨɢɫɯɨɞɢɬ ɜ ɫɯɟɦɟ ɜ ɪɚɡɧɵɟ ɩɪɨɦɟɠɭɬɤɢ ɜɪɟɦɟɧɢ:
1. 0 < t <t1 e2 > ud V1 – ɨɬɤɪɵɬ, V2 – ɡɚɤɪɵɬ. Ÿ ɤɨɧɞɟɧɫɚɬɨɪ ɡɚɪɹɠɚɟɬɫɹ ɢɦɩɭɥɶɫɨɦ ɬɨɤɚ i a1
2. t1 < t < t2 e2 < ud Ÿ ɤɨɧɞɟɧɫɚɬɨɪ ɪɚɡɪɹɠɚɟɬɫɹ ɧɚ ɧɚɝɪɭɡɤɭ ( Rɧ ). V1 ɢ V2 – ɡɚɤɪɵɬɵ.
3. t2 < t < t3 e2 > ud V2 – ɨɬɤɪɵɬ, V1 – ɡɚɤɪɵɬ. Ÿ ɤɨɧɞɟɧɫɚɬɨɪ ɡɚɪɹɠɚɟɬɫɹ ɢɦɩɭɥɶɫɨɦ ɬɨɤɚ i a2
Ⱥɦɩɥɢɬɭɞɚ ɜɬɨɪɨɝɨ ɢɦɩɭɥɶɫɚ ɛɭɞɟɬ ɦɟɧɶɲɟ ɩɟɪɜɨɝɨ, ɬ.ɤ. ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ ɜ ɦɨɦɟɧɬ t2 ud > 0
ɉɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ud ɜɪɟɦɹ ɡɚɪɹɞɚ ɤɨɧɞɟɧɫɚɬɨɪɚ ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɜɪɟɦɹ ɪɚɡɪɹɞɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ.
ɑɟɪɟɡ ɧɟɫɤɨɥɶɤɨ ɩɟɪɢɨɞɨɜ ɧɚɫɬɭɩɚɟɬ ɩɨɥɨɠɟɧɢɟ, ɤɨɝɞɚ ud ɢɡɦɟɧɹɟɬɫɹ ɜɨɡɥɟ ɫɜɨɟɝɨ ɫɪɟɞɧɟɝɨ
ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ.
I am (5 y 7)ia ɬ.ɤ. ɬɨɤ i a - ɩɪɟɪɵɜɢɫɬɵɣ, ɫ ɩɚɭɡɚɦɢ. ȼɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜɜɟɞɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ r ɞɥɹ ɬɨɤɨɨɝɪɚɧɢɱɟɧɢɹ.
ɇɚ ɧɺɦ ɩɪɨɢɫɯɨɞɢɬ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ
ɭɦɟɧɶɲɚɟɬɫɹ.
ɑɟɦ ɛɨɥɶɲɟ Rɧ , ɬɟɦ ɛɨɥɶɲɟ ɜɪɟɦɹ ɪɚɡɪɹɞɚ W ɪ ɋRɧ Ÿ p U ɩ1m Ÿn ud Ÿn S
ɉɪɢ ɯɨɥɨɫɬɨɦ ɯɨɞɟ R ɧ = ’, U dxx = E 2m = ¥2•E 2
Ɇɨɠɧɨ ɨɬɦɟɬɢɬɶ ɫɥɟɞɭɸɳɢɟ ɨɬɥɢɱɢɹ ɪɚɛɨɬɵ ɜɵɩɪɹɦɢɬɟɥɟɣ ɫ ɺɦɤɨɫɬɧɨɣ ɧɚɝɪɭɡɤɨɣ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɚɤɬɢɜɧɨɣ
ɧɚɝɪɭɡɤɨɣ:
1. Ȼɨɥɶɲɚɹ ɚɦɩɥɢɬɭɞɚ ɚɧɨɞɧɨɝɨ ɬɨɤɚ ɢ ɦɟɧɶɲɚɹ ɟɝɨ ɞɥɢɬɟɥɶɧɨɫɬɶ.
2. Ȼɨɥɶɲɚɹ ɜɟɥɢɱɢɧɚ u d .
3. Ɇɟɧɶɲɟ ɚɦɩɥɢɬɭɞɚ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ - U ɩ1m
4. Ɋɟɡɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ u d ɨɬ Rɧ .
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɝɥɚɠɢɜɚɧɢɹ R-C ɮɢɥɶɬɪɚ
ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɩɟɪɟɦɟɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ:
ɂɫɬɨɱɧɢɤ ɩɢɬɚɧɢɹ ɛɥɢɠɟ ɤ ɢɫɬɨɱɧɢɤɭ ɗȾɋ, ɬɚɤ ɤɚɤ ɟɝɨ ɜɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɥɨ
Ÿ r ɢ Rɧ ɜɤɥɸɱɟɧɵ ɩɚɪɚɥɥɟɥɶɧɨ.
Ɂɧɚɱɢɬ
S
Z ɩɨɫɥ
Z ɩɚɪ
Z ɩɨɫɥ
r Rɧ
rRɧ
Z ɩɋ
r Rɧ
Ɂɚ ɫɱɟɬ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɢ r ɫɧɢɠɚɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟ
ɦɚɥɵɯ ɬɨɤɚɯ ɧɚɝɪɭɡɤɢ.
ud Ÿ
R-C ɮɢɥɶɬɪ ɷɮɮɟɤɬɢɜɟɧ ɩɪɢ
§7 ɉɚɪɚɦɟɬɪɢɱɟɫɤɢɣ ɫɬɚɛɢɥɢɡɚɬɨɪ ɧɚɩɪɹɠɟɧɢɹ.
ɇɚɡɧɚɱɟɧɢɟ: ɉɨɞɞɟɪɠɢɜɚɟɬ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɧɚɝɪɭɡɤɟ ɩɨɫɬɨɹɧɧɵɦ ɩɪɢ ɢɡɦɟɧɹɸɳɟɦɫɹ ɜɯɨɞɧɨɦ ɧɚɩɪɹɠɟɧɢɢ ɢ
ɬɨɤɟ ɧɚɝɪɭɡɤɢ ɜ ɧɟɤɨɬɨɪɨɦ ɞɢɚɩɚɡɨɧɟ.
Ɍɢɩɵ ɫɬɚɛɢɥɢɡɚɬɨɪɨɜ:
1. ɉɚɪɚɦɟɬɪɢɱɟɫɤɢɣ
2. Ʉɨɦɩɟɧɫɚɰɢɨɧɧɵɟ
3. ɂɦɩɭɥɶɫɧɵɟ (ɫɚɦɵɟ ɫɨɜɪɟɦɟɧɧɵɟ, ɧɨ ɢ ɫɚɦɵɟ ɫɥɨɠɧɵɟ ɢ ɞɨɪɨɝɢɟ)
U ɜɵɯ | const
U ɜɵɯ
ɑɟɦ
I ɧ | const
n U ɜɯ Ÿ ɬɟɦ n I V
(ɬɨɥɶɤɨ ɧɚ ɪɚɛɨɱɟɦ ɭɱɚɫɬɤɟ)
U ɜɯ
- ɧɚ ɪɚɛɨɱɟɦ ɭɱɚɫɬɤɟ - ɭɱɚɫɬɤɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɪɨɛɨɹ.
ɋɬɚɛɢɥɢɬɪɨɧ ɡɚɛɢɪɚɟɬ ɧɚ ɫɟɛɹ ɱɚɫɬɶ ɬɨɤɚ ɧɚɝɪɭɡɤɢ I ɧ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɜɯɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
u ɜɯ
u ɜɯ
Iv
( I ɧ I V ) Rɛ u ɫɬ
Rɛ I ɧ Rɛ I V u ɫɬ
uɜɯ uɫɬ I ɧ Rɛ
Rɛ
Iɧ
uɫɬ
Rɧ
= const
u ɜɯ .
Iv
Rɛ
ɉɪɢ
Rɧ
I V max
ɉɪɢ
ɢ
Iɧ
0
IV
I V max
u ɜɯ max u ɫɬ
Rɛ
Iɧ
I ɧ max
Ⱦɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɭɫɥɨɜɢɟ:
IV
§
Rɛ
u ɜɯ. min u ɫɬ ¨¨1 Rɧ. min
©
Rɛ
I V max d I ɫɬ. max
I V min
·
¸¸
¹
Ⱦɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɭɫɥɨɜɢɟ:
u ɜɯ u ɫɬ
Iɧ
Rɛ
Ɍɨɤɭ
Ɍɨɤɭ
Rɛ
f
Rɧ min z 0
I V . min
IV
§ R ·
uɜɯ uɫɬ ¨¨1 ɛ ¸¸
© Rɧ ¹
Rɛ
Rɛ
Rɧ
uɜɯ uɫɬ uɫɬ
I V . min
I V . max
ɫɨɨɬɜɟɬɫɬɜɭɟɬ u ɜɯ. min ɢ I ɧ. max
ɫɨɨɬɜɟɬɫɬɜɭɟɬ u ɜɯ. max ɢ I ɧ. min
u ɜɯ u ɫɬ
Ÿ Rɛ
I ɧ IV
ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ:
u ɜɯ. max u ɫɬ
u
u ɫɬ
d Rɛ d ɜɯ. min
I ɫɬ. max I ɧ. min
I ɫɬ. min I ɧ. max
I V min d I ɫɬ. min
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɬɚɛɢɥɢɡɚɰɢɢ
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɬɚɛɢɥɢɡɚɰɢɢ ɫɜɨɟɣ ɜɟɥɢɱɢɧɨɣ ɩɨɤɚɡɵɜɚɟɬ, ɧɚ ɫɤɨɥɶɤɨ ɯɨɪɨɲɨ ɫɬɚɛɢɥɢɡɚɬɨɪ ɩɨɞɞɟɪɠɢɜɚɟɬ
ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɜ ɡɚɞɚɧɧɵɯ ɩɪɟɞɟɥɚɯ.
K ɫɬ
'u ɜɯ
'u ɜɵɯ
'u ɜɯ
u ɜɯ
'u ɜɵɯ
u ɜɵɯ
'u ɜɯ u ɜɵɯ
'u ɜɵɯ u ɜɯ
ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɞɥɹ ɩɪɢɪɚɳɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ:
rȾ
- ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɛɢɥɢɬɪɨɧɚ.
'u ɜɵɯ
'u ɜɯ
r Ⱦ Rɧ
R ɛ r Ⱦ Rɧ
ɉɨɫɤɨɥɶɤɭ
Ɂɧɚɱɢɬ
'u ɜɵɯ ˜ R Ȼ
'u ɜɯ ˜ rȾ
r Ⱦ << Rɛ
'uɜɯ
'uɜɯ
ɢ
r Ⱦ << Rɧ Ÿ 'u ɜɵɯ | 'u ɜɯ
rȾ
Rɛ rȾ
| 'u ɜɯ
rȾ
Rɛ
Rɛ
rȾ
Ɍɨɝɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɫɬɚɛɢɥɢɡɚɰɢɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ:
K ɫɬ
K ɫɬ <
'uɜɯ uɜɵɯ
'uɜɯ uɜɯ
20 y 40
Rɛ uɜɵɯ
rȾ uɜɯ
K ɫɬ
Rɛ u ɜɵɯ
rȾ u ɜɯ
Ⱦɥɹ ɭɜɟɥɢɱɟɧɢɹ Ʉ ɫɬ ɭɜɟɥɢɱɢɜɚɬɶ Rɛ , ɧɨ ɩɪɢ ɷɬɨɦ ɛɭɞɟɬ ɭɦɟɧɶɲɚɬɶɫɹ Uɜɵɯ , ɩɨɷɬɨɦɭ ɡɚɞɚɱɚ ɪɟɲɚɟɬɫɹ
ɤɨɦɩɪɨɦɢɫɫɧɵɦ ɩɭɬɟɦ.
ɉɨɬɨɦɭ ɨɛɵɱɧɨ ɫɨɛɥɸɞɚɟɬɫɹ ɭɫɥɨɜɢɟ u ɜɯ | (1.2 y 1.3)u ɜɵɯ
ȼɵɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɬɚɛɢɥɢɡɚɬɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɬɟɨɪɟɦɟ ɨɛ ɷɤɜɢɜɚɥɟɧɬɧɨɦ ɝɟɧɟɪɚɬɨɪɟ.
ɉɪɢ ɷɬɨɦ : ɭ ɢɞɟɚɥɶɧɨɝɨ ɫɬɚɛɢɥɢɡɚɬɨɪɚ ɜɵɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɪɚɜɧɨ ɧɭɥɸ, ɭ ɪɟɚɥɶɧɨɝɨ ɨɧɨ ɫɨɫɬɚɜɥɹɟɬ ɨɬ
ɧɟɫɤɨɥɶɤɢɯ ɟɞɢɧɢɰ ɞɨ ɞɟɫɹɬɤɨɜ Ɉɦ.
ɉɚɪɚɦɟɬɪɢɱɟɫɤɢɣ ɫɬɚɛɢɥɢɡɚɬɨɪ ɢɦɟɟɬ ɞɨɜɨɥɶɧɨ ɛɨɥɶɲɨɟ ɜɵɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
Rɛ rȾ Ÿ ɤɨɷɮɮɢɰɢɟɧɬ ɫɬɚɛɢɥɢɡɚɰɢɢ ɦɚɥ.
Ȼɢɩɨɥɹɪɧɵɟ ɬɪɚɧɡɢɫɬɨɪɵ
ɉɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɭɫɢɥɟɧɢɹ ɫɢɝɧɚɥɨɜ ɢ ɭɩɪɚɜɥɟɧɢɹ ɬɨɤɨɦ ɜ ɫɯɟɦɚɯ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜɨɣ ɷɥɟɤɬɪɨɧɢɤɢ.
ɉɪɟɞɫɬɚɜɥɹɸɬ ɢɡ ɫɟɛɹ ɬɪɟɯɫɥɨɣɧɭɸ ɫɬɪɭɤɬɭɪɭ ɫ ɱɟɪɟɞɭɸɳɢɦɢɫɹ ɫɥɨɹɦɢ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɢɦɟɸɬ ɬɪɢ ɜɵɜɨɞɚ ɞɥɹ
ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɜɧɟɲɧɟɣ ɰɟɩɢ.
Ȼɢɩɨɥɹɪɧɵɟ ɩɨɞɱɟɪɤɢɜɚɸɬ ɬɨ, ɱɬɨ ɭ ɬɚɤɢɯ ɬɪɚɧɡɢɫɬɨɪɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɛɚ ɬɢɩɚ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɨɜ (ɷɥɟɤɬɪɨɧɵ ɢ
ɞɵɪɤɢ).
ɋɭɳɟɫɬɜɭɟɬ ɞɜɚ ɬɢɩɚ ɬɪɚɧɡɢɫɬɨɪɨɜ:
1. ɋ ɩɪɹɦɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ (p-n-p)
2. ɋ ɨɛɪɚɬɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ (n-p-n)
Ʉɪɚɣɧɢɟ ɫɥɨɣ ɧɚɡɵɜɚɸɬɫɹ ɤɨɥɥɟɤɬɨɪɨɦ ɢ ɷɦɢɬɬɟɪɨɦ, ɫɥɨɣ ɦɟɠɞɭ ɧɢɦɢ – ɛɚɡɨɣ.
ɗ-Ȼ – ɷɦɢɬɬɟɪɧɵɣ ɩɟɪɟɯɨɞ.
Ȼ-Ʉ – ɤɨɥɥɟɤɬɨɪɧɵɣ ɩɟɪɟɯɨɞ.
Ɉɫɨɛɟɧɧɨɫɬɢ ɤɨɧɫɬɪɭɤɰɢɢ:
1. Ɍɨɥɳɢɧɚ ɛɚɡɵ ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ ɞɥɢɧɵ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɨɜ.
2. Ʉɨɧɰɟɧɬɪɚɰɢɹ ɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ (ɩɪɢɦɟɫɢ) ɜ ɷɦɢɬɬɟɪɟ ɞɨɥɠɧɚ ɛɵɬɶ ɦɧɨɝɨ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɛɚɡɟ.
naɗ >> nɞȻ - ɞɥɹ p-n-p ɩɟɪɟɯɨɞɚ.
ɗɦɢɬɬɟɪɧɵɣ ɩɟɪɟɯɨɞ ɫɦɟɳɟɧ ɜ ɩɪɹɦɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɤɨɥɥɟɤɬɨɪɧɵɣ ɜ ɨɛɪɚɬɧɨɦ.
ɋɯɟɦɵ ɫ ɨɛɳɢɦ ɷɦɢɬɬɟɪɨɦ (Ɉɗ):
ɋɯɟɦɚ ɫ ɨɛɳɢɦ ɷɦɢɬɬɟɪɨɦ ɧɚɡɵɜɚɟɬɫɹ ɬɚɤ ɩɨɬɨɦɭ, ɱɬɨ ɜɯɨɞɧɚɹ ɢ ɜɵɯɨɞɧɚɹ ɰɟɩɶ ɢɦɟɸɬ ɨɛɳɭɸ ɬɨɱɤɭ ɧɚ ɷɦɢɬɬɟɪɟ.
ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɬɪɚɧɡɢɫɬɨɪɚ
Ɋɚɫɫɦɨɬɪɢɦ ɧɚ ɩɪɢɦɟɪɟ p-n-p ɬɪɚɧɡɢɫɬɨɪɚ.
Ɍɨɤɢ ɱɟɪɟɡ ɩɟɪɟɯɨɞ Ȼɗ ɢ Ʉɗ ɨɬɫɭɬɫɬɜɭɸɬ (ɧɚɥɢɱɢɟ ɡɚɩɢɪɚɸɳɢɯ ɫɥɨɟɜ).
ɉɭɫɬɶ U Ȼɗ 0 , U Ʉɗ 0 ( ȿ Ʉ ɢ
ȼɤɥɸɱɢɦ ɢɫɬɨɱɧɢɤɢ ɗȾɋ
U Ʉɗ ! U Ȼɗ
U ɄȻ
- ɡɚɤɨɪɨɱɟɧɵ).
ȿɄ ɢ ȿȻ .
ȿȻ
naɗ
>>
nɞȻ
U Ʉɗ U Ȼɗ
ɉɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɧɚ ɷɦɢɬɬɟɪɧɨɦ ɩɟɪɟɯɨɞɟ ɭɦɟɧɶɲɢɬɫɹ, ɬɚɤ ɤɚɤ ɩɨɥɹɪɧɨɫɬɶ ɩɪɢɥɨɠɟɧɧɨɝɨ ɤ ɧɟɦɭ
ɧɚɩɪɹɠɟɧɢɹ – ɩɪɹɦɚɹ Ÿ ɬɨɤ ɞɢɮɮɭɡɢɢ ɱɟɪɟɡ ɷɦɢɬɬɟɪɧɵɣ ɩɟɪɟɯɨɞ ɭɜɟɥɢɱɢɬɫɹ.
ɇɚ ɤɨɥɥɟɤɬɨɪɧɨɦ ɩɟɪɟɯɨɞɟ ɩɨɥɹɪɧɨɫɬɶ ɨɛɪɚɬɧɚɹ Ÿ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɭɜɟɥɢɱɢɬɫɹ.
ɉɨɱɬɢ ɜɫɟ ɞɵɪɤɢ ɩɨɞɨɲɥɢ ɤ ɤɨɥɥɟɤɬɨɪɧɨɦɭ ɩɟɪɟɯɨɞɭ Ÿ ɞɵɪɤɢ ɛɭɞɭɬ ɜɬɹɝɢɜɚɬɶɫɹ ɜ ɤɨɥɥɟɤɬɨɪ (ɬɚɤ ɤɚɤ
ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɛɭɞɟɬ «ɜɬɹɝɢɜɚɸɳɟɣ»).
'I Ʉ
- ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɬɨɤɚ ɷɦɢɬɬɟɪɚ. ( D 0.9 y 0.99 )
'I Ʉ D'I ɗ , ɝɞɟ D
'I ɗ
ɑɚɫɬɶ ɞɵɪɨɤ ɪɟɤɨɦɛɢɧɢɪɭɟɬ ɜ ɛɚɡɟ
ɛɚɡɭ.
IȻ
I ɪɟɤɨɦ .
Iɗ IɄ
I ɗ DI ɗ
Ÿ
ɧɟɣɬɪɚɥɶɧɨɫɬɶ ɛɚɡɵ ɧɚɪɭɲɚɟɬɫɹ
Ÿ
ɜɨɡɧɢɤɚɟɬ ɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɜ
(1 D ) I ɗ
Ɉɫɧɨɜɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɬɨɤɚɦɢ ɜ ɬɪɚɧɡɢɫɬɨɪɟ.
P
Ⱦɵɪɤɢ (ɧɟ ɨɫɧɨɜɧɵɟ) ɢɡ Ȼ
o
Ʉ.
I ɄȻ
n
ɗɥɟɤɬɪɨɧɵ (ɧɟ ɨɫɧɨɜɧɵɟ) ɢɡ Ʉ
o
- ɨɛɪɚɬɧɵɣ (ɬɟɩɥɨɜɨɣ)
Ȼ.
ɉɨɥɧɵɣ ɬɨɤ ɱɟɪɟɡ ɤɨɥɥɟɤɬɨɪ:
I Ʉ .ɩɨɥɧɵɣ DI ɗ I ɄȻɈ (1)
(2)
ȼɵɪɚɠɟɧɢɹ (1) ɢ (2) ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɬɨɤɢ ɜ ɬɪɚɧɡɢɫɬɨɪɟ ɫɜɹɡɚɧɵ ɥɢɧɟɣɧɨ.
IȻ
Iɗ IɄ
I ɗ DI ɗ I ɄȻɈ
(1 D ) I ɗ I ɄȻɈ
Ʌɟɤɰɢɹ 6
ɂɡ ɭɪɚɜɧɟɧɢɹ (2) ɫɥɟɞɭɟɬ, ɱɬɨ
Iɗ
I Ȼ I ɄȻɈ
(3)
1 Į
ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ (3) ɜ (1) ɩɨɥɭɱɚɟɦ
IɄ
Į
Į
˜ IȻ ˜ I ɄȻɈ I ɄȻɈ (4)
1 Į
1 Į
ȕ
IɄ
- ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɬɨɤɚ ɛɚɡɵ
IȻ
ȕ
(1)
(2)
Į ˜ I ɗ I ɄȻɈ
Į
| | ɩɪɟɧɟɛɪɟɝɚɟɦ IɄȻɈ | |
(1 Į) ˜ I ɗ I ɄȻɈ
1 Į
I Ʉ ȕ ˜ I Ȼ ȕ ˜ I ɄȻɈ I ɄȻɈ ȕ ˜ I Ȼ (1 ȕ) ˜ I ɄȻɈ
Iɗ
IȻ Iɗ
Iɗ
IȻ ȕ ˜ IȻ
(1 ȕ) ˜ I Ȼ ;
ȕ ˜ I Ȼ I ɄɗɈ | ȕ ˜ I Ȼ
(1 ȕ) ˜ I Ȼ
h 21
ȕ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɬɪɚɧɡɢɫɬɨɪɨɜ
ȼɵɯɨɞɧɚɹ (ɤɨɥɥɟɤɬɨɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ)
IɄ=f(UɄɗ) ɩɪɢ IȻ = const
ɍɱɚɫɬɤɢ: I – ɤɪɭɬɨɣ, II – ɩɨɥɨɝɢɣ, III – ɭɱɚɫɬɨɤ ɬɟɩɥɨɜɨɝɨ ɩɪɨɛɨɹ.
Ɉɫɧɨɜɧɵɦ ɹɜɥɹɟɬɫɹ II (ɭɫɢɥɢɬɟɥɶɧɵɣ) ɭɱɚɫɬɨɤ. ɇɚ ɧɺɦ ɬɪɚɧɡɢɫɬɨɪ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
ɭɩɪɚɜɥɹɟɦɵɣ ɢɫɬɨɱɧɢɤ ɬɨɤɚ.
ɇɚɤɥɨɧ ɩɨɥɨɝɨɝɨ ɭɱɚɫɬɤɚ: ɩɪɢ ĹUɄɗ => Ĺij0 => Ĺ ɨɛɴɺɦɧɵɣ ɡɚɪɹɞ => Ĺ ɲɢɪɢɧɚ ɞɜɨɣɧɨɝɨ ɫɥɨɹ => Ļ
ɷɮɮɟɤɬɢɜɧɚɹ ɲɢɪɢɧɚ ɛɚɡɵ => Ļ ɜɟɪɨɹɬɧɨɫɬɶ ɪɟɤɨɦɛɢɧɚɰɢɢ => Ĺ IɄ.
I Ʉ E ˜ I Ȼ I ɄȻɈ , I Ȼ I ɗ ˜ (1 E) , I Ʉ D ˜ I ɗ E ˜ I Ȼ
Ⱦɥɹ ɭɜɟɥɢɱɟɧɢɹ IȻ ɧɚɞɨ ɭɜɟɥɢɱɢɬɶ UȻɗ:
I-ɭɱɚɫɬɨɤ U ɄȻ U Ʉɗ U Ȼɗ , U Ʉɗ ! U Ȼɗ
ɉɭɫɬɶ ɦɵ ɛɭɞɟɦ ɭɦɟɧɶɲɚɬɶ UɄɗ ɩɪɢ UȻɗ = const, ɤɨɝɞɚ UɄɗ = UȻɗ = UɄɗ ɇȺɋ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ
ɭɦɟɧɶɲɟɧɢɢ UɄɗ, UɄȻ ɫɦɟɧɢɬ ɡɧɚɤ – ɤɨɥɥɟɤɬɨɪɧɵɣ ɩɟɪɟɯɨɞ ɜɫɬɚɥ ɩɨɞ ɩɪɹɦɨɟ ɧɚɩɪɹɠɟɧɢɟ.
ȼɨɡɧɢɤɚɟɬ ɞɢɮɮɭɡɢɹ ɞɵɪɨɤ ɢɡ ɤɨɥɥɟɤɬɨɪɚ ɜ ɛɚɡɭ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɬɨɤ IɄ, ɬɪɚɧɡɢɫɬɨɪ
ɬɟɪɹɟɬ ɭɫɢɥɢɬɟɥɶɧɵɟ ɫɜɨɣɫɬɜɚ.
I ɭɱɚɫɬɨɤ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɤɥɸɱɟɜɨɦ ɪɟɠɢɦɟ ɬɪɚɧɡɢɫɬɨɪɚ. UɄɗɇ § 0.2 ÷ 1 ȼ
III ɭɱɚɫɬɨɤ – ɭɱɚɫɬɨɤ ɬɟɩɥɨɜɨɝɨ ɩɪɨɛɨɹ. ȿɫɥɢ ɭɜɟɥɢɱɢɬɫɹ UɄɗ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫɬɚɧɟɬ
ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɭɞɚɪɧɨɣ ɢɨɧɢɡɚɰɢɢ, ɧɟɪɚɛɨɱɢɣ ɭɱɚɫɬɨɤ.
ȼɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɋɟɦɟɣɫɬɜɨ ɤɪɢɜɵɯ IȻ = f(UȻɗ) ɩɪɢ UɄɗ = const
IȻ = IɄ + Iɗ
ȼɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ - ȼȺɏ ɞɜɭɯ ɩɚɪɚɥɥɟɥɶɧɨ ɜɤɥɸɱɟɧɧɵɯ p-n ɩɟɪɟɯɨɞɨɜ.
ɉɪɢ UɄɗ = 0 ɧɚ ɗȻ ɢ ȻɄ UɉɊəɆɈȿ.
ɉɪɢ UɄɗ > UɄɗɇ ɧɚ ɗȻ – UɉɊəɆɈȿ, ɧɚ ȻɄ – UɈȻɊȺɌɇɈȿ.
ɉɪɢ UȻɗ = 0 IȻ = IɄȻɈ
IȻ = IɄ - Iɗ = (1-Į) ˜ Iɗ - IɄȻɈ ɢɡ (2)
'U Ȼɗ
- ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɛɚɡɵ – ɜɯɨɞɧɨɟ ɞɢɩɨɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɬɪɚɧɡɢɫɬɨɪɚ
rȻ
'I Ȼ
rȻ h 11ɗ
Ɍɪɚɧɡɢɫɬɨɪɧɵɟ ɭɫɢɥɢɬɟɥɢ
ɍɫɬɪɨɣɫɬɜɚ, ɤɨɬɨɪɵɟ ɫ ɩɨɦɨɳɶɸ ɢɡɦɟɧɟɧɢɹ ɫɢɝɧɚɥɚ ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ ɭɩɪɚɜɥɹɸɬ ɢɡɦɟɧɟɧɢɟɦ ɛɨɥɶɲɨɣ
ɦɨɳɧɨɫɬɢ ɧɚ ɧɚɝɪɭɡɤɟ
1. ɍɫɢɥɢɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ.
2. ɍɫɢɥɢɬɟɥɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ.
ɍɫɢɥɢɬɟɥɢ ɱɚɳɟ ɜɫɟɝɨ ɭɫɢɥɢɜɚɸɬ ɧɚɩɪɹɠɟɧɢɟ.
ɍɫɢɥɢɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɩɟɪɟɦɟɧɧɨɝɨ ɫɢɝɧɚɥɚ ɧɟ ɞɨɥɠɟɧ ɜɨɫɩɪɢɧɢɦɚɬɶ ɩɨɫɬɨɹɧɧɭɸ
ɫɨɫɬɚɜɥɹɸɳɭɸ, ɞɥɹ ɷɬɨɝɨ ɧɚ ɜɯɨɞɟ ɫɬɚɜɹɬ ɤɨɧɞɟɧɫɚɬɨɪ. ȼɥɢɹɧɢɟ ɤɨɧɞɟɧɫɚɬɨɪɚ ɭɧɢɱɬɨɠɚɟɬ ɞɪɟɣɮ ɧɭɥɹ.
ɍɫɢɥɢɬɟɥɶ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɩɪɨɳɟ, ɱɟɦ ɭɫɢɥɢɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɬ.ɤ. ɭɫɢɥɢɬɟɥɶ ɞɨɥɠɟɧ
ɜɨɫɩɪɢɧɢɦɚɬɶ ɩɨɫɬɨɹɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ, ɩɨɷɬɨɦɭ ɧɟɥɶɡɹ ɫɬɚɜɢɬɶ ɤɨɧɞɟɧɫɚɬɨɪ ɢ ɛɨɪɨɬɶɫɹ ɫ ɞɪɟɣɮɨɦ ɧɭɥɹ
ɞɪɭɝɢɦɢ ɫɩɨɫɨɛɚɦɢ, ɤɨɬɨɪɵɟ ɩɪɢɜɨɞɹɬ ɤ ɭɫɥɨɠɧɟɧɢɸ ɫɯɟɦɵ ɭɫɢɥɢɬɟɥɹ.
ɍɫɢɥɢɬɟɥɶɧɵɣ ɤɚɫɤɚɞ ɫ ɨɛɳɢɦ ɷɦɢɬɬɟɪɨɦ
ɉɨɫɬɪɨɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɤɚɫɤɚɞɚ.
Ɋɟɠɢɦ ɤɥɚɫɫɚ Ȼ
I ɍɱɚɫɬɨɤ:
IȻ § 0, ɬɪɚɧɡɢɫɬɨɪ ɡɚɤɪɵɬ, IȻ = IɄȻɈ, IɄ = ȕ ˜ IȻ = 0, UɄɗ=EɄ - IɄ ˜ RɄ, ɬ.ɤ. IɄ=0,
UɄɗ = EɄ.
II ɍɱɚɫɬɨɤ:
IȻ ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ (ɢɡ ɜɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ) ɧɟɪɚɜɧɨɟ ɧɭɥɸ. IɄ = ȕ ˜ IȻ  0 ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ UȻɗ,
ɭɜɟɥɢɱɢɜɚɸɬɫɹ IȻ, IɄ ɢ ɭɦɟɧɶɲɚɟɬɫɹ UɄɗ.
III ɍɱɚɫɬɨɤ
ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ UȻɗ; UɄɗ ɨɫɬɚɺɬɫɹ ɩɨɫɬɨɹɧɧɵɦ ɢ ɪɚɜɟɧ UɄɗɇ = (0.2÷1) ȼ
E Ʉ U Ʉɗɇ
IɄ
RɄ
ɉɪɟɞɟɥ ɢɡɦɟɪɟɧɢɹ:
E Ʉ U Ʉɗɇ
; UɄɗɇ ” ( UɄɗ = Uȼɕɏ ) ”EɄ
RɄ
Ɂɧɚɤɢ ¨Uȼɏ ɢ ¨Uȼɕɏ – ɪɚɡɧɵɟ, ɬɚɤɨɣ ɤɚɫɤɚɞ ɧɚɡɵɜɚɟɬɫɹ ɢɧɜɟɪɬɢɪɭɸɳɢɦ.
IɄȻɈ ” IɄ ”
Ʌɟɤɰɢɹ 7
Ɋɟɠɢɦ ɤɥɚɫɫɚ ȼ
ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɜɵɯɨɞɟ ɧɟ ɦɟɧɹɟɬɫɹ.
ɇɟɞɨɫɬɚɬɨɤ: ɩɨɬɟɪɹ ɢɧɮɨɪɦɚɰɢɢ ɧɚ ɜɬɨɪɨɦ ɩɨɥɭɩɟɪɢɨɞɟ.
ɑɬɨɛɵ ɞɨɛɢɬɶɫɹ ɩɨɫɬɨɹɧɧɨɝɨ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɫɢɝɧɚɥɚ, ɧɟɨɛɯɨɞɢɦɨ ɫɦɟɫɬɢɬɶ ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ (ɗȾɋ
ɫɦɟɳɟɧɢɹ).
Ɋɟɠɢɦ ɤɥɚɫɫɚ Ⱥ
ɉɪɢ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ ɩɨɫɬɨɹɧɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɭɛɢɪɚɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɤɥɸɱɺɧɧɵɦ
ɤɨɧɞɟɧɫɚɬɨɪɨɦ, ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɬɨɤɟ – ɩɨɫɬɨɹɧɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ Uȼɕɏ ɭɛɢɪɚɟɬɫɹ ɩɭɬɺɦ ɜɤɥɸɱɟɧɢɹ
ɩɪɨɬɢɜɨɗȾɋ ɧɚ ɜɵɯɨɞɟ.
Ʉɥɸɱɟɜɨɣ ɪɟɠɢɦ
Ɋɟɠɢɦ ɫ ɛɨɥɶɲɨɣ ɚɦɩɥɢɬɭɞɨɣ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ, ɩɪɢ ɷɬɨɦ ɡɚɯɜɚɬɵɜɚɸɬɫɹ ɜɫɟ ɬɪɢ ɭɱɚɫɬɤɚ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ. ɇɚ ɤɪɢɜɨɣ ɜɬɨɪɨɣ ɫɢɝɧɚɥ ɨɛɪɚɡɭɟɬɫɹ ɩɨ ɦɢɧɢɦɚɥɶɧɨɦɭ ɭɪɨɜɧɸ.
Ɏɨɪɦɚ ɜɵɯɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɢɫɤɚɡɢɥɚɫɶ, ɬ.ɟ. ɩɪɨɢɡɨɲɥɨ ɨɝɪɚɧɢɱɟɧɢɟ ɩɨ ɚɦɩɥɢɬɭɞɟ. ɑɟɦ ɛɨɥɶɲɟ
ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɩɨ ɧɚɩɪɹɠɟɧɢɸ, ɬɟɦ ɛɨɥɶɲɟ ɜɵɯɨɞɧɨɣ ɫɢɝɧɚɥ ɩɨɯɨɠ ɧɚ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɢɦɩɭɥɶɫ.
ɉɪɢɦɟɧɹɟɬɫɹ ɜ ɢɦɩɭɥɶɫɧɨɣ ɬɟɯɧɢɤɟ, ɝɞɟ ɜɚɠɧɚ ɧɟ ɚɦɩɥɢɬɭɞɚ ɫɢɝɧɚɥɚ, ɚ ɜɡɚɢɦɧɵɣ ɮɚɡɨɜɵɣ ɫɞɜɢɝ
ɦɟɠɞɭ Uȼɏ ɢ Uȼɕɏ.
Ɇɨɳɧɨɫɬɶ, ɜɵɞɟɥɹɟɦɚɹ ɜ ɬɪɚɧɡɢɫɬɨɪɚɯ
T
1
P
U Ʉɗ t Ʉ dt
T ³0
Ɋɚɡɨɝɪɟɜɚɟɬ p-n ɩɟɪɟɯɨɞ ɢ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɬɟɩɥɨɜɨɦɭ ɩɪɨɛɨɸ. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɦɨɳɧɨɫɬɢ ɧɚɞɨ ɪɚɛɨɬɚɬɶ ɜ
ɤɥɸɱɟɜɨɦ ɪɟɠɢɦɟ.
Ɋɟɠɢɦ ɩɨɤɨɹ
ȼɜɨɞɢɬɫɹ ɤɚɤ ɩɪɢɺɦ ɞɥɹ ɪɚɫɱɺɬɚ ɢ ɚɧɚɥɢɡɚ ɷɥɟɤɬɪɨɧɧɵɯ ɫɯɟɦ. Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɪɟɠɢɦɚ ɩɨɤɨɹ ɜɫɟ ɗȾɋ
ɜɤɥɸɱɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ (EɄ, EɋɆ, EɄɈɆɉ)
EɄɈɆɉ ɜɤɥɸɱɺɧ ɞɥɹ ɭɫɬɪɚɧɟɧɢɹ ɩɨɫɬɨɹɧɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ Uȼɕɏ ɜ ɤɥɚɫɫɟ Ⱥ.
1) ɉɭɫɬɶ Uȼɏ = 0, ɬ.ɤ. ɟɫɬɶ EɋɆ, ɩɨɷɬɨɦɭ ɬɪɚɧɡɢɫɬɨɪ ɨɬɤɪɵɬ, ɩɪɨɬɟɤɚɸɬ ɬɨɤɢ IȻɉ, IɄɉ, Iɗɉ  0, UɄɗɉ  0,
EɄɈɆɉ = UɄɗɉ. ɉɪɢ ɜɤɥɸɱɟɧɢɢ ɢɫɬɨɱɧɢɤɨɜ ɩɢɬɚɧɢɹ ɜ ɫɯɟɦɟ ɩɪɨɬɟɤɚɸɬ ɬɨɤɢ ɩɨɤɨɹ ɢ ɟɫɬɶ UɄɗɉ, ɱɬɨɛɵ
ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɟ ɛɵɥɨ ɪɚɜɧɨ ɧɭɥɸ, ɧɚɞɨ ɜɜɟɫɬɢ UɄɈɆɉ = UɄɗɉ.
ɇɟɞɨɫɬɚɬɨɤ: ɡɚɜɢɫɢɦɨɫɬɶ ɬɨɤɚ ɢ ɧɚɩɪɹɠɟɧɢɹ ɬɪɚɧɡɢɫɬɨɪɚ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ.
ɉɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ 10° ɋ ɬɨɤ IɄȻɈ ɩɨɜɵɲɚɟɬɫɹ ɜ 2 ɪɚɡɚ. Ɍɚɤɠɟ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ,
ɢɡɦɟɧɹɟɬɫɹ ɬɨɤ, ɨɛɭɫɥɨɜɥɟɧɧɵɣ ɨɫɧɨɜɧɵɦɢ ɧɨɫɢɬɟɥɹɦɢ: ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ 20-30° ɋ IɄ
ɩɨɜɵɲɚɟɬɫɹ ɧɚ ɞɟɫɹɬɤɢ ɩɪɨɰɟɧɬɨɜ, ɬ.ɤ. ɡɚɩɨɥɧɹɸɬɫɹ ɰɟɧɬɪɵ ɪɟɤɨɦɛɢɧɚɰɢɢ (ɞɟɮɟɤɬɵ ɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ
ɪɟɲɺɬɤɢ), ɩɨɷɬɨɦɭ ɢɯ ɱɢɫɥɨ ɢ ɜɟɪɨɹɬɧɨɫɬɶ ɪɟɤɨɦɛɢɧɚɰɢɢ ɭɦɟɧɶɲɚɸɬɫɹ ɢ ȕ ɭɜɟɥɢɱɢɜɚɟɬɫɹ.
ɉɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɤɨɝɞɚ IȻɉ = const, ɭɜɟɥɢɱɢɜɚɟɬɫɹ IɄɉ, ɬ.ɤ.
IɄɉ = ȕ ˜ IȻɉ, ɭɦɟɧɶɲɚɟɬɫɹ UɄɗɉ, ɬ.ɤ. UɄɗɉ = EɄ - IɄɉ ˜ RɄ, ɩɨɷɬɨɦɭ Uȼɕɏ ɧɟ ɛɭɞɟɬ ɩɨɫɬɨɹɧɧɵɦ. Ⱦɥɹ ɭɫɬɪɚɧɟɧɢɹ
ɷɬɨɝɨ ɷɮɮɟɤɬɚ ɩɪɢɦɟɧɹɸɬɫɹ ɫɯɟɦɵ ɤɨɦɩɟɧɫɚɰɢɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ.
Ɉɛɪɚɬɧɵɟ ɫɜɹɡɢ
ɉɟɪɟɞɚɱɚ ɜɵɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɧɚ ɜɯɨɞ ɭɫɬɪɨɣɫɬɜɚ. ȿɫɥɢ ɫɤɥɚɞɵɜɚɸɬɫɹ ɬɨɤɢ – ɫɜɹɡɶ ɩɚɪɚɥɥɟɥɶɧɚɹ, ɟɫɥɢ
ɧɚɩɪɹɠɟɧɢɹ – ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɚɹ. ȿɫɥɢ ɡɧɚɤɢ ɫɤɥɚɞɵɜɚɟɦɵɯ ɫɢɝɧɚɥɨɜ ɨɞɢɧɚɤɨɜɵ – ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɨɛɪɚɬɧɚɹ
ɫɜɹɡɶ (ɉɈɋ), ɩɪɢ ɪɚɡɧɵɯ ɡɧɚɤɚɯ – ɨɬɪɢɰɚɬɟɥɶɧɚɹ (ɈɈɋ). ɉɈɋ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɭɫɤɨɪɟɧɢɹ ɩɭɧɤɬɚ ɩɢɬɚɧɢɹ ,
ɬ.ɟ. ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ ɛɵɫɬɪɨɞɟɣɫɬɜɢɹ ɭɫɬɪɨɣɫɬɜɚ, ɧɨ ɛɨɥɟɟ ɧɟɫɬɚɛɢɥɶɧɚ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɈɈɋ ɩɨɜɵɲɚɟɬ
ɫɬɚɛɢɥɶɧɨɫɬɶ ɭɫɬɪɨɣɫɬɜɚ, ɜɜɨɞɢɬɫɹ ɩɭɬɺɦ ɜɤɥɸɱɟɧɢɹ ɜ ɰɟɩɶ ɷɦɢɬɬɟɪɚ.
ɇɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɩɨ ɜɬɨɪɨɦɭ ɡɚɤɨɧɭ Ʉɢɪɯɝɨɮɚ ɞɥɹ ɜɯɨɞɧɨɣ ɰɟɩɢ:
Uȼɏ + EɋɆ = UȻɗ + Iɗ ˜ Rɗ
UȻɗ = Uȼɏ + EɋɆ - Iɗ ˜ Rɗ § Uȼɏ + EɋɆ - IɄ ˜ Rɗ
Iɗ § IɄ, ɬ.ɤ. Į = 0.99 ÷ 0.9
Ɍ.ɟ Rɗ ɭɦɟɧɶɲɚɟɬ ɈɈɋ ɩɨ ɬɨɤɭ.
Ⱦɨɫɬɨɢɧɫɬɜɨ: ɩɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɢ IȻɉ = const => Ĺ ȕ => Ĺ IɄɉ => Ĺ IɄ ˜ Rɗ => Ļ UȻɗ => Ļ IȻ
=> Ļ IɄ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ IɄ ɢ ɫɥɟɞɨɜɚɬɟɥɶɧɨ UɄɗ ɨɫɬɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ.
ɇɟɞɨɫɬɚɬɨɤ: ɭɦɟɧɶɲɚɟɬɫɹ Uȼɕɏ, ɡɚ ɫɱɺɬ ɭɦɟɧɶɲɟɧɢɹ UȻɗ, ɩɨɷɬɨɦɭ ɭɦɟɧɶɲɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ
ɭɫɢɥɟɧɢɹ Ʉɍ,
Iɗɉ ˜ Rɗ ” 0.1 ˜ EɄ – ɤɪɢɬɟɪɢɣ ɜɵɛɨɪɚ Rɗ. Ɍɚɤɨɟ Rɗ ɨɛɟɫɩɟɱɢɜɚɟɬ ɞɨɫɬɚɬɨɱɧɭɸ ɬɟɦɩɟɪɚɬɭɪɧɭɸ ɫɬɚɛɢɥɢɡɚɰɢɸ
ɢ ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɩɨɧɢɠɟɧɢɟ Uȼɕɏ.
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɤɚɫɤɚɞɚ ɫ ɨɛɳɢɦ ɷɦɢɬɬɟɪɨɦ
Rȼɏ, Rȼɕɏ, Kɍɏ.ɏ..
Ⱦɨɩɭɳɟɧɢɹ: ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɬɨɥɶɤɨ ɩɟɪɟɦɟɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ (ɩɪɢɪɚɳɟɧɢɹ) i, u. ȼɧɭɬɪɟɧɧɟɟ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢɫɬɨɱɧɢɤɨɜ ɩɨɫɬɨɹɧɧɨɝɨ ɗȾɋ ɞɥɹ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɛɭɞɟɬ ɪɚɜɧɨ ɧɭɥɸ.
1) RȼɇɍɌ
'u
, ¨i  0, ¨u = 0, ɬ.ɤ. EɄ ɩɨɫɬɨɹɧɧɨ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, RɄ ɜɟɪɯɧɢɦ ɤɨɧɰɨɦ ɩɪɢɫɨɟɞɢɧɟɧɨ ɤ ɡɟɦɥɟ, ɬ.ɤ.
R
'i
U ȼɏ
Uȼɏ = ¨IȻ ˜ rȻ + ¨Iɗ ˜ Rɗ
Rȼɇ = 0, R ȼɏ
I ȼɏ
'U Ȼɗ
- ɞɢɧɚɦɢɱɟɫɤɨɟ ɜɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɬɪɚɧɡɢɫɬɨɪɚ rȻ=h11ɗɄȼ.
rȻ
'I Ȼ
¨Iɗ = ¨IȻ + ¨IɄ = ¨IȻ + ȕ ˜ ¨IȻ = ¨IȻ ˜ (1+ȕ)
Uȼɏ = ¨IȻ ˜ [rȻ + (1+ȕ) ˜ Rɗ]
'I Ȼ ˜ [rȻ (1 E) ˜ R ɗ ]
R ȼɏ
rȻ (1 E) ˜ R ɗ
'I Ȼ
Rȼɏ § 1000 ɈɆ (ɱɬɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɚɥɨ, ɞɥɹ ɢɞɟɚɥɶɧɨɝɨ Rȼɏ = ’)
Ʌɟɤɰɢɹ 8
2) KUɏɏ – ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɜ ɪɟɠɢɦɟ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ.
U ȼɕɏ
'I Ʉ ˜ R Ʉ
'I Ȼ ˜ E ˜ R Ʉ
E˜RɄ
Rɇ = ’; K U
U ȼɏ
'I Ȼ ˜ R ȼɏ 'I Ȼ ˜ >rȻ (E 1) ˜ R ɗ @ rȻ (E 1) ˜ R ɗ
ɩɪɟɧɟɛɪɟɝɚɟɦ rȻ,
E˜RɄ
RɄ
rȻ + (ȕ + 1) ˜ Rɗ § (ȕ + 1) ˜ Rɗ; K U |
§KUXX
(E 1) ˜ R ɗ R ɗ
ɉɪɢ ɜɤɥɸɱɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɤ IɄ ɞɨɛɚɜɢɬɫɹ Iɇ, ɬ.ɨ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɭɦɟɧɶɲɢɬɫɹ (KUɊȺȻ<KUɏ.ɏ.)
ɢɡ-ɡɚ ɭɜɟɥɢɱɟɧɢɹ ɩɨɬɟɪɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ RɄ.
3) Ⱦɥɹ ɜɵɜɨɞɚ Rȼɕɏ ɩɪɢɦɟɧɹɟɦ ɬɟɨɪɟɦɭ ɨɛ ɷɤɜɢɜɚɥɟɧɬɧɨɦ ɝɟɧɟɪɚɬɨɪɟ, ɗȾɋ ɡɚɤɨɪɚɱɢɜɚɸɬɫɹ,
ɧɚɝɪɭɡɤɚ ɡɚɦɟɧɹɟɬɫɹ ɨɦɦɟɬɪɨɦ.
Uȼɕɏ = 0, ɫɥɟɞɨɜɚɬɟɥɶɧɨ IȻ = 0; IɄ ɢ Iɗ = 0; Rȼɕɏ = RɄ § 1000 ɈɆ
ɇɟɞɨɫɬɚɬɤɢ: ɩɨ ɜɯɨɞɧɵɦ ɢ ɜɵɯɨɞɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɤɚɫɤɚɞ ɫ ɨɛɳɢɦ ɷɦɢɬɬɟɪɨɦ ɢɦɟɟɬ
ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ (’/0 ɜ ɢɞɟɚɥɶɧɨɦ ɫɥɭɱɚɟ).
ɋɩɨɫɨɛɵ ɩɨɫɬɪɨɟɧɢɹ ɍɉɌ (ɭɫɢɥɢɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ)
3 ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ ɡɚɦɟɧɹɸɬ ɨɞɧɢɦ. R1 ɢ R2 ɫɨɡɞɚɸɬ ɗȾɋ ɫɦɟɳɟɧɢɹ; R3 ɢ R4 – ɗȾɋ ɤɨɦɩɟɧɫɚɰɢɢ.
ɇɟɞɨɫɬɚɬɤɢ: ɢɫɬɨɱɧɢɤ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɢ ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɟ ɢɦɟɸɬ ɨɛɳɟɣ ɬɨɱɤɢ, ɬ.ɟ. ɢɫɩɨɥɶɡɨɜɚɬɶ
ɬɚɤɭɸ ɫɯɟɦɭ ɧɟɭɞɨɛɧɨ. Ⱦɥɹ ɢɫɤɥɸɱɟɧɢɹ ɷɬɨɝɨ ɧɟɞɨɫɬɚɬɤɚ ɧɚɞɨ ɩɪɢɦɟɧɢɬɶ ɞɜɭɯɩɨɥɹɪɧɵɣ ɢɫɬɨɱɧɢɤ ɩɢɬɚɧɢɹ.
R1 ɢ R2 ɫɨɡɞɚɺɬ UɄɈɆɉ. Ɍ.ɤ. ɬɨɱɤɚ 0 ɭ Uȼɏ ɢɦɟɟɬ ij1 = 0, ɚ ɬ. –ȿɄ ij2 = - ȿɄ, ɡɧɚɱɢɬ
ij1 > ij2, ɬ.ɟ. ɜ ɫɯɟɦɭ ɧɟɹɜɧɨ ɜɜɨɞɢɬɫɹ (ɜɨ ɜɯɨɞɧɭɸ ɰɟɩɶ) ɢɫɬɨɱɧɢɤ ɗȾɋ.
ɍɫɢɥɢɬɟɥɶ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ
C1 ɢ C2 ɨɬɫɟɤɚɸɬ ɩɨɫɬɨɹɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ ɜ Uȼɏ ɢ Uȼɕɏ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. C1 ɨɞɧɨɜɪɟɦɟɧɧɨ ɮɢɥɶɬɪ
ɜɵɫɨɤɢɯ ɱɚɫɬɨɬ.
Ʉɚɫɤɚɞ ɫ ɨɛɳɢɦ ɤɨɥɥɟɤɬɨɪɨɦ (ɷɦɢɬɬɟɪɧɵɣ ɩɨɜɬɨɪɢɬɟɥɶ)
ɇɚɡɧɚɱɟɧɢɟ: ɢɫɩɨɥɶɡɭɟɬɫɹ ɤɚɤ ɫɨɝɥɚɫɭɸɳɢɣ ɤɚɫɤɚɞ ɦɟɠɞɭ ɭɫɢɥɢɬɟɥɶɧɵɦ ɤɚɫɤɚɞɨɦ ɫ ɨɛɳɢɦ
ɷɦɢɬɬɟɪɨɦ ɢ ɦɚɥɨɦɨɳɧɵɦ ɢɫɬɨɱɧɢɤɨɦ ɧɚɩɪɹɠɟɧɢɹ Uȼɏ, ɚ ɬɚɤɠɟ ɫ ɜɵɫɨɤɨɣ ɧɚɝɪɭɡɤɨɣ.
ȿɫɥɢ ɛɵ ɈɄ ɧɟ ɛɵɥɨ: RȼɏɈɗ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɚɥɨ, ɚ RȼɕɏɈɗ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɥɢɤɨ, ɩɨɷɬɨɦɭ Iɇ ɛɨɥɶɲɨɣ
=> Ļ Uȼɏ (Uȼɏ < ɟȽ) => Ĺ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɜɵɯɨɞɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ; Uȼɕɏ < Uȼɕɏɏ.ɏ. RȼɏɈɄ > RȼɏɈɗ, RȼɕɏɈɄ <
RȼɕɏɈɗ. Ɍ.ɨ. ɥɟɜɵɣ ɈɄ ɩɨɜɵɲɚɟɬ Rȼɏ ɢ Uȼɏ, ɩɨɧɢɠɚɟɬ ¨Uȼɏ ɫɯɟɦɵ. ɉɨɧɢɠɚɟɬɫɹ, Iȼɏ => Ļ RȽ ˜ Iȼɏ =>
Ĺ Uɇ.
ɇɟɞɨɫɬɚɬɤɢ: ɤɚɫɤɚɞ ɫ ɈɄ ɧɟ ɭɫɢɥɢɜɚɟɬ ɧɚɩɪɹɠɟɧɢɟ, ɄUXX § 1 (0.9÷0.99) Uȼɕɏ = Uȼɏ - UȻɗ, UȻɗ > 0 §
0.5 ÷ 0.7 ȼ.
ɋɯɟɦɚ ɧɚɡɵɜɚɟɬɫɹ ɫ ɈɄ, ɬ.ɤ. ɨɛɳɟɣ ɬɨɱɤɨɣ ɹɜɥɹɟɬɫɹ ɡɟɦɥɹ, ɚ EK ɡɚɡɟɦɥɺɧ, ɜɬɨɪɨɟ ɧɚɡɜɚɧɢɟ – ɷɦɢɬɬɟɪɧɵɣ
ɩɨɜɬɨɪɢɬɟɥɶ, ɹɜɥɹɟɬɫɹ ɧɟɢɧɜɟɪɬɢɪɭɸɳɢɦ.
ɉɭɫɬɶ ɜɨɡɪɚɫɬɚɟɬ ¨Uȼɏ; ɡɧɚɱɢɬ ɜɨɡɪɚɫɬɚɟɬ ¨IȻ, ¨Iɗ, ¨IɗRɗ.
ɉɚɪɚɦɟɬɪɵ ɤɚɫɤɚɞɚ ɫ ɈɄ
1) Rȼɏ
R ȼɏ
U ȼɏ
K UXX
'I Ȼ ˜ rȻ 'I ɗ ˜ (R ɗ || R ɇ )
U ȼɏ
'I ȼɏ
rȻ (E 1) ˜ (R ɗ || R ɇ ) § 104 ɈɆ
'I Ȼ ˜ rȻ 'I Ȼ ˜ (E 1) ˜ (R ɗ || R ɇ )
'I Ȼ ˜ >rȻ (E 1) ˜ (R ɗ || R ɇ )@ 2)
U ȼɕɏ
, Rɇ = ’
U ȼɏ
Uȼɏ = ¨IȻ ˜ [rȻ + (ȕ+1) ˜ Rɗ || Rɇ], Uȼɕɏ = ¨Iɗ ˜ Rɗ = ¨IȻ ˜ (1 + ȕ) ˜ Rɗ
(E 1) ˜ R ɗ
(1 E) ˜ R ɗ
1
| 0.9 ÷ 0.99
K UXX
rȻ (E 1) ˜ R ɗ rȻ ˜ (1 E) ˜ R ɗ rȻ
Ʌɟɤɰɢɹ 9
3) Rȼɕɏ ɤɚɫɤɚɞɚ ɫ ɈɄ
ɬ.ɤ. eȽ = 0 => ¨IȻ = 0, => ¨Iɗ = 0; Rȼɕɏ = Rɗ.
Ɂɚɞɚɱɚ:
Ʉ – ɡɚɦɤɧɭɬ – ɈɄ
Ʉ – ɪɚɡɨɦɤɧɭɬ – Ɉɗ
RɄ = 2000 ɈɆ
Rɗ = 400 ɈɆ
ȿɄ = 10 ȼ
ȿɋɆ = 0.4 ȼ
ȕ = 100
~UȼɏM = 1 ȼ
Ɉɩɪɟɞɟɥɢɬɶ 3 ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɚ ɞɥɹ ɫɯɟɦɵ ɫ ɈɄ ɢ Ɉɗ.
Rȼɏ, Rȼɕɏ, KUXX ɞɥɹ Ɉɗ ɢ ɈɄ, ɧɚɪɢɫɨɜɚɬɶ ɨɫɰɢɥɥɨɝɪɚɦɦɵ Uȼɏ, Uȼɕɏ1, Uȼɕɏ2.
1. Ʉɚɫɤɚɞ ɫ Ɉɗ (Ʉ - ɪɚɡɨɦɤɧɭɬ)
R K 2000
K UXX
5
Rɗ
400
Rȼɏ = rȻ + (ȕ + 1) ˜ Rɗ = 100 + (100 + 1) ˜ 400 = 40.5 ɤɈɆ,
Rȼɏ = 40.4 ɤɈɆ ɩɪɢ rȻ = 0
Rȼɕɏ = RK = 2000 ɈɆ
ȿCM ˜ KUXX = 0.4 ˜ 5 = 2 ȼ
UȼɏɆ ˜ KUXX = 1 ˜ 5 = 5 ȼ
2. Ʉɚɫɤɚɞ ɫ ɈɄ
KUXX = 1
Rȼɏ = rȻ + (ȕ + 1) ˜ (Rɗ||Rɇ) = 100 + (100 + 1) ˜ 400 = 40.5 ɤɈɆ
Rȼɕɏ = Rɗ = 400 ɈɆ
Ɉɫɰɢɥɥɨɝɪɚɦɦɵ Uȼɏ, Uȼɕɏ1, Uȼɕɏ2.
Ⱦɪɟɣɮ ɧɭɥɹ
Ⱦɪɟɣɮ ɧɭɥɹ – ɯɚɪɚɤɬɟɪɧɚɹ ɱɟɪɬɚ ɍɉɌ. ɉɨɞ ɞɪɟɣɮɨɦ ɧɭɥɹ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɢɡɦɟɧɟɧɢɟ Uȼɕɏ ɩɪɢ
ɩɨɫɬɨɹɧɧɨɦ Uȼɏ. ɉɪɢɱɢɧɵ: ɧɟɫɬɚɛɢɥɶɧɨɫɬɶ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ, ɜɥɢɹɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ, ɢɡɦɟɧɟɧɢɟ
ɩɚɪɚɦɟɬɪɨɜ ɩɭɧɤɬɚ ɩɢɬɚɧɢɹ ɩɪɢɛɨɪɨɜ ɫ ɬɟɱɟɧɢɟɦ ɜɪɟɦɟɧɢ (ɜɫɥɟɞɫɬɜɢɟ ɫɬɚɪɟɧɢɹ).
1) ɇɟɫɬɚɛɢɥɶɧɨɫɬɶ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ.
ɉɭɫɬɶ EK ɭɜɟɥɢɱɢɬɫɹ => ĹEɋɆ => ĹIȻ => ĹIɄ => ĹURK => Uȼɕɏ ɭɦɟɧɶɲɢɬɫɹ, ɬ.ɤ. KU > 1, ɡɧɚɱɢɬ ɢɡɦɟɧɟɧɢɟ
Uȼɕɏ ɛɭɞɟɬ ɛɨɥɶɲɟ, ɱɟɦ ɢɡɦɟɧɟɧɢɟ EK.
2) ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ.
ɉɪɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ȕ => ĹIɄ => ĹURK, ɢ ɩɨɧɢɠɚɟɬɫɹ Uȼɕɏ.
UȾɊ.ȼɕɏ.MAX – ɦɚɤɫɢɦɚɥɶɧɵɣ Uȼɕɏ ɞɪɟɣɮɚ ɧɭɥɹ.
U ȾɊ.ȼɕɏ.MAX
U ȾɊ.MAX
KU
Ⱦɨɥɠɧɨ ɛɵɬɶ Uȼɏ >> UȾɊ.ȼɏ.MAX; ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɦɵ ɧɚ ɜɵɯɨɞɟ ɧɟ ɨɬɥɢɱɢɦ ɞɪɟɣɮ ɧɭɥɹ ɨɬ ɩɨɥɟɡɧɨɝɨ
ɫɢɝɧɚɥɚ. ɗɮɮɟɤɬɢɜɧɨɟ ɫɪɟɞɫɬɜɨ ɛɨɪɶɛɵ ɫ ɞɪɟɣɮɨɦ ɧɭɥɹ – ɩɪɢɦɟɧɟɧɢɟ ɭɫɢɥɢɬɟɥɶɧɵɯ ɤɚɫɤɚɞɨɜ ɧɚ ɛɚɡɟ
ɭɪɚɜɧɨɜɟɲɟɧɧɵɯ ɦɨɫɬɨɜ.
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɣ ɤɚɫɤɚɞ (ȾɄ)
4 ɩɥɟɱɚ ɨɛɪɚɡɨɜɚɧɵ RK1, RK2, VT1, VT2. ɉɟɪɜɚɹ ɞɢɚɝɨɧɚɥɶ – ɩɢɬɚɧɢɹ EK, -EK. ȼɬɨɪɚɹ ɞɢɚɝɨɧɚɥɶ –
ɧɚɝɪɭɡɤɢ RK1, RH. ȾɄ ɭɫɢɥɢɜɚɟɬ ɪɚɡɧɨɫɬɶ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ. ɂɦɟɟɬ ɯɨɪɨɲɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɭɫɥɨɜɢɢ
ɨɞɢɧɚɤɨɜɨɫɬɢ ɟɝɨ ɷɥɟɦɟɧɬɨɜ, ɬ.ɟ. RK1 = RK2, VT1 = VT2, ɱɬɨ ɞɨɫɬɢɝɚɟɬɫɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɧɚ ɨɞɧɨɦ
ɤɪɢɫɬɚɥɥɟ ɧɚ ɛɚɡɟ ɦɢɤɪɨɫɯɟɦɵ.
Ɋɟɠɢɦ ɩɨɤɨɹ
ȼɤɥɸɱɚɟɦ EK1 ɢ –ȿɄ2; Uȼɏ1 = Uȼɏ2 = 0, UȻɗɉ1 = UȻɗɉ2 > 0, UȻɗ = - Uɗɉ.
Uɗɉ = [- ȿɄ1 + (Iɗɉ1 + Iɗɉ2) ˜ Rɗ] ” 0
ɬ.ɟ. UȻɗ = EɋɆ = - Uɗɉ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɪɨɬɟɤɚɸɬ IȻɉ1 = IȻɉ2;
UɄɗɉ1 = UɄɗɉ2 = EK1 – IɄɉ1 ˜ RK1 – Uɗɉ = EK1 – IɄɉ2 ˜ RɄ2 - Uɗɉ
Uȼɕɏ = UɄɗɉ2 – UɄɗɉ1 = 0
ɉɭɫɬɶ ɭɜɟɥɢɱɢɥɚɫɶ ɬɟɦɩɟɪɚɬɭɪɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ Ĺ ȕ => ĹIɄɉ1 = IɄɉ2 => ĹIɗɉ1 = Iɗɉ2 => ĹUɗɉ => ĻUȻɗɉ1,
UȻɗɉ2 => ĻIȻɉ1, IȻɉ2 => ĻIɄɉ1, IɄɉ2 => Ļ Iɗɉ1, Iɗɉ2, ɬ.ɟ Iɗɉ1 + Iɗɉ2 = const, ɬ.ɤ. Rɗ ɜɟɥɢɤɨ, ɩɨɷɬɨɦɭ ɫɬɚɛɢɥɢɡɚɰɢɹ
ɯɨɪɨɲɚɹ. ȿɫɥɢ ɱɟɪɟɡ Rɗ ɩɪɨɬɟɤɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ Rɗ ɦɨɠɧɨ ɡɚɦɟɧɢɬɶ ɢɫɬɨɱɧɢɤɨɦ ɬɨɤɚ ɫ
RȼɇɍɌ = ’.
Ʌɟɤɰɢɹ 10
¨Uɗ – ɫɢɝɧɚɥ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ, ɫɬɚɛɢɥɢɡɢɪɭɸɳɢɣ ɫɭɦɦɭ Iɗ1 + Iɗ2 = const
Ⱦɪɟɣɮ ɧɭɥɹ
ɉɭɫɬɶ E1 ɜɨɡɪɚɫɬɚɟɬ => ĹUɄɗ1 = UɄɗ2, Uȼɕɏ = UɄɗ2 – UɄɗ1 = 0
Ʌɸɛɵɟ ɫɢɦɦɟɬɪɢɱɧɵɟ ɢɡɦɟɧɹɸɳɢɟɫɹ ɫɢɝɧɚɥɵ ɜ ɫɯɟɦɟ ɧɟ ɩɪɢɜɨɞɹɬ ɤ ɞɪɟɣɮɭ ɧɭɥɹ.
ɉɪɢɥɨɠɢɦ ɩɟɪɟɦɟɧɧɵɣ 2-ɨɣ ɫɢɝɧɚɥ.
1) Ɇɟɠɞɭ ɛɚɡɚɦɢ ɬɪɚɧɡɢɫɬɨɪɨɜ.
e
ɉɭɫɬɶ U ȼɏ1
ɛɭɞɟɬ ɩɨɥɨɠɢɬɟɥɶɧɵɦ, ɡɧɚɱɢɬ
2
¨UȻɗ1 > 0 => ¨IȻ1 > 0 => ¨IɄ1 > 0 => ¨Iɗ1 > 0 => ¨UɄɗ1 < 0.
e
ɛɭɞɟɬ ɨɬɪɢɰɚɬɟɥɶɧɵɦ, ɡɧɚɱɢɬ
U ȼɏ 2
2
¨UȻɗ2 = 0 => ¨IȻ2 < 0 => ¨IɄ2 = 0 => ¨Iɗ2 < 0 => ¨UɄɗ2 > 0.
Uȼɕɏ = ¨UɄɗ2 - ¨UɄɗ1 = 2 ˜ ¨UɄɗ
ȿɫɥɢ Uȼɏ1 = -Uȼɏ2, ɫɥɟɞɨɜɚɬɟɥɶɧɨ ¨Iɗ1 = -¨Iɗ2
ɬ.ɤ. ɩɟɪɜɵɣ ɬɨɤ ɜɨɡɪɚɫɬɚɟɬ, ɚ ɜɬɨɪɨɣ ɭɦɟɧɶɲɚɟɬɫɹ, ɡɧɚɱɢɬ Iɗ1 + Iɗ2 = const
Ɂɧɚɱɢɬ ¨Uɗ = 0, ɩɨɷɬɨɦɭ:
ɚ) Ɉɛɪɚɬɧɚɹ ɫɜɹɡɶ ɧɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɟ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɤɚɫɤɚɞɚ.
ɛ) ȼ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɦ ɤɚɫɤɚɞɟ ɩɪɟɨɞɨɥɟɜɚɸɬɫɹ ɩɪɨɬɢɜɨɪɟɱɢɟ ɦɟɠɞɭ ɧɟɨɛɯɨɞɢɦɨɫɬɶɸ
ɫɬɚɛɢɥɢɡɚɰɢɢ ɪɟɠɢɦɚ ɡɚ ɫɱɺɬ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ ɢ ɜɥɢɹɧɢɟɦ Rɗ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɤɚɫɤɚɞɚ.
2)Ɍɟɩɟɪɶ ɩɪɢɥɨɠɢɦ ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ ɤ ɛɚɡɟ ɩɟɪɜɨɝɨ ɬɪɚɧɡɢɫɬɨɪɚ, ɡɚɤɨɪɨɬɢɜ ɩɪɢ ɷɬɨɦ ɜɬɨɪɨɣ ɜɯɨɞ.
Uȼɏ1 = e > 0; Uȼɏ2 = 0.
Ɂɧɚɱɢɬ ¨UȻɗ1 > 0 =>¨IȻ1 > 0 => ¨IɄ1 > 0 => ¨Iɗ1 > 0 => ¨UɄɗ1 < 0;
ɉɪɢ ɪɨɫɬɟ IȻ1, => ĹIɗ1, ɬ.ɤ. Iɗ1 + Iɗ2 = const; Iɗ2 ɭɦɟɧɶɲɚɟɬɫɹ ɢ
¨Iɗ2 = -¨Iɗ1.
Iɗ
IȻ
, ¨IȻ2 = -¨IȻ1, ¨IK2 = -¨IK1, ¨UɄɗ2 = -¨UɄɗ1,
E 1
Uȼɕɏ = ¨UɄɗ2 - ¨UɄɗ1 > 0
ȼɵɜɨɞ: ɜɯɨɞ 1 ɧɟɢɧɜɟɪɬɢɪɭɸɳɢɣ, ɬ.ɤ ¨Uȼɏ>0 ɢ ¨Uȼɕɏ>0.Ɂɧɚɱɢɬ ɢɡ ɚɧɚɥɨɝɢɱɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ
ɜɯɨɞ 2 ɹɜɥɹɟɬɫɹ ɢɧɜɟɪɬɢɪɭɸɳɢɣ. ɉɪɢ ɩɪɢɥɨɠɟɧɢɢ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɤ ɨɞɧɨɦɭ ɬɪɚɧɡɢɫɬɨɪɭ ɛɭɞɭɬ
ɢɡɦɟɧɹɬɶɫɹ ɬɨɤɢ ɢ ɧɚɩɪɹɠɟɧɢɹ ɜ ɨɛɨɢɯ ɬɪɚɧɡɢɫɬɨɪɚɯ.
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɣ ɤɚɫɤɚɞ ɭɫɢɥɢɜɚɟɬ ɪɚɡɧɨɫɬɶ ɜɯɨɞɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɬɨɝɞɚ, ɤɨɝɞɚ Uȼɏ1 = Uȼɏ2,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ Uȼɕɏ = (Uȼɏ1 – Uȼɏ2) ˜ KU = 0 ɍɫɢɥɢɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɫɢɧɮɚɡɧɵɯ ɫɢɝɧɚɥɨɜ. Ɂɚ ɫɱɺɬ
ɧɟɤɨɬɨɪɨɣ ɧɟɨɞɢɧɚɤɨɜɨɫɬɢ ɩɚɪɚɦɟɬɪɨɜ: Uȼɕɏ = kɋ ˜ Uȼɏ, ɝɞɟ kɋ – ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɫɢɧɮɚɡɧɨɝɨ
ɫɢɝɧɚɥɚ. ɑɟɦ ɦɟɧɶɲɟ kɋ, ɬɟɦ ɤɚɱɟɫɬɜɟɧɧɟɟ ɭɫɢɥɢɬɟɥɶ.
ɇɟɞɨɫɬɚɬɤɢ: ɨɬɫɭɬɫɬɜɢɟ ɨɛɳɟɣ ɬɨɱɤɢ ɦɟɠɞɭ ɜɯɨɞɧɵɦ ɢ ɜɵɯɨɞɧɵɦ ɫɢɝɧɚɥɨɦ. Ⱦɥɹ ɭɫɬɪɚɧɟɧɢɹ
ɩɪɢɧɢɦɚɟɬɫɹ ɫɯɟɦɚ ɧɟɫɢɦɦɟɬɪɢɱɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɤɚɫɤɚɞɚ (ȾɄ).
Ɉɛɳɚɹ ɬɨɱɤɚ – ɡɟɦɥɹ.
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ȾɄ
Uȼɕɏ = 2 ˜ ¨UɄɗ, ɬ.ɤ. Iɗ1 + Iɗ2 = const, ɡɧɚɱɢɬ ɢɫɬɨɱɧɢɤ ɬɨɤɚ Rɗ = ’
I Ȼ1 I Ȼ 2
I ɗ1 I ɗ 2
E 1
const , ɫɥɟɞɨɜɚɬɟɥɶɧɨ 'I Ȼ1
U ȼɕɏ 2 ˜ 'U Ʉɗ 2 ˜ 'I Ʉ ˜ R Ʉ
U ȼɏ
Uȼ ɏ
Uȼ ɏ
2) ȼɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɚɫɤɚɞɚ
1) K UXX
'I Ȼ 2
2 ˜ 'I Ȼ ˜ E ˜ R Ʉ
U ȼɏ
U ȼɏ
;
2 ˜ rȻ
U
2 ˜ ȼɏ ˜ E ˜ R Ʉ
2 ˜ rȻ
U ȼɏ
E˜
RɄ
rȻ
U ȼɏ
2 ˜ rȻ ; Rȼɏ = 2 ˜ rȻ ,
I ȼɏ
3) ȼɵɯɨɞɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɚɫɤɚɞɚ
Ɂɚɤɨɪɨɬɢɥɢ Uȼɏ, ɢ ɜɫɟ ɗȾɋ, ɧɚ ɧɚɝɪɭɡɤɟ ɩɨɞɤɥɸɱɚɟɦ ɨɦɦɟɬɪ.¨IȻ=0; ¨IɄ=0; ¨Iɗ=0; Rȼɕɏ = 2 ˜ RɄ
Ɉɩɟɪɚɰɢɨɧɧɵɟ ɭɫɢɥɢɬɟɥɢ
R ȼɏ
ɍɫɢɥɢɬɟɥɶ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɛɨɥɶɲɢɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɫɢɥɟɧɢɹ ɢ ɜɵɫɨɤɢɦ Rȼɏ.
ɗɉ – ɷɦɢɬɬɟɪɧɵɣ ɩɨɜɬɨɪɢɬɟɥɶ.
Ȼɥɚɝɨɞɚɪɹ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɫɢɦɦɟɬɪɢɱɧɵɯ ȾɄ ɢɦɟɟɦ ɫɥɚɛɵɣ ɞɪɟɣɮ ɧɭɥɹ. ɇɟɫɢɦɦɟɬɪɢɱɧɵɣ ȾɄ ɞɚɺɬ
ɨɛɳɭɸ ɬɨɱɤɭ ɦɟɠɞɭ Uȼɏ ɢ Uȼɕɏ. Ʉɚɫɤɚɞ ɫ ɈɄ ɞɚɺɬ ɭɦɟɧɶɲɟɧɢɟ Rȼɕɏ. ɂɡ-ɡɚ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ȾɄ ɧɚɩɪɹɠɟɧɢɟ
ɩɢɬɚɧɢɹ Ɉɍ ɞɜɭɯɩɨɥɹɪɧɨ. Ɉɛɨɡɧɚɱɟɧɢɟ: ȾȺ3.2 ɢɥɢ Ⱥ3.2, ɝɞɟ 3 – ɧɨɦɟɪ ɜ ɫɯɟɦɟ, 2 – ɧɨɦɟɪ Ɉɍ ɜ ɤɨɪɩɭɫɟ,
ɟɫɥɢ ɢɯ ɜ ɤɨɪɩɭɫɟ ɧɟɫɤɨɥɶɤɨ.
Uȼɕɏ = KU ˜ (Uȼɏ1 - Uȼɏ2)
Ƚɨɜɨɪɹɬ, ɱɬɨ Ɉɍ ɢɦɟɟɬ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɣ ɜɯɨɞ, ɬ.ɟ. ɭɫɢɥɢɜɚɟɬ ɪɚɡɧɨɫɬɶ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ.
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ Ɉɍ
1) KUXX § 50000
2) Rȼɏ = 300 ɤɈɆ (ɛɢɩɨɥɹɪɧɵɣ ɬɪɚɧɡɢɫɬɨɪ)
= 10 ɆɈɆ (ɩɨɥɟɜɵɟ ɬɪɚɧɡɢɫɬɨɪɵ)
3) RɇȺȽ.MIN § 3 ɤɈɆ (ɨɫɧɨɜɧɚɹ ɦɚɫɫɚ)
Eɉ
15ȼ
| 7.5 ɦȺ,
I ȼɕɏ
R ɇȺȽ.MIN 2ɤɈɦ
ȼ ɦɨɳɧɵɯ Ɉɍ Iȼɕɏ § 300 ɦȺ
4) ɇɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ ɧɭɥɹ UɋɆ = 5 ɦȼ
5) ɇɚɩɪɹɠɟɧɢɟ ɩɢɬɚɧɢɹ Eɉ = r 15 ȼ (ɟɫɬɶ r 12,6; r 6,3; r 5 ÷ 15)
Ʌɟɤɰɢɹ 11
Uȼɕɏ.Ɉɍ.MAX = (0.9 ÷ 0.95) ˜ Eɉ = (0.9 ÷ 0.95) ˜ 15 = 13.5 ÷ 14.25 ȼ
ɉɪɢɛɥɢɡɢɬɟɥɶɧɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɜɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ ɧɚɩɪɹɠɟɧɢɸ ɩɢɬɚɧɢɹ. Ɉɍ ɭɫɢɥɢɜɚɟɬ (Uȼɏ
– Uȼɏ2) = EȾɂɎ (ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɣ ɗȾɋ)
KU.Ɉɍ § 50000 (ɜ ɫɪɟɞɧɟɦ)
U
15
ɉɭɫɬɶ Uȼɏ2 = 0 (ɬ.ɟ ɡɚɡɟɦɥɟɧɨ), ɫɥɟɞɨɜɚɬɟɥɶɧɨ Uȼɏ1.MAX = EȾɂɎ.MAX = ȼɕɏ.MAX |
3.10 4 ȼ = 300 ɦɤȼ
K U.Ɉɍ
50000
§0ȼ
ɋɜɨɣɫɬɜɚ ɢɞɟɚɥɶɧɨɝɨ Ɉɍ
1) ɉɨɬɟɧɰɢɚɥ ɩɪɹɦɨɝɨ ɜɯɨɞɚ = ɩɨɬɟɧɰɢɚɥ ɢɧɜɟɪɬɢɪɭɸɳɟɝɨ ɜɵɯɨɞɚ ijɉɊəɆ.ȼɏ = ijɂɇȼ.ȼɏ ɢɥɢ Uȼɏ – Uȼɏ2
=0
2) Rȼɕɏ.Ɉɍ = ’ ( § 300 ɤɈɆ ), ɩɨɷɬɨɦɭ Iȼɏ = 0
3) KU = 50000, ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɫɱɢɬɚɬɶ KU = ’
ȼ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɺɬɨɜ ɦɨɠɧɨ ɪɟɚɥɶɧɵɣ Ɉɍ ɫɱɢɬɚɬɶ ɤɚɤ ɢɞɟɚɥɶɧɵɣ. ɇɟɫɦɨɬɪɹ ɧɚ ɷɬɨ Ɉɍ ɤɚɤ ɭɫɢɥɢɬɟɥɶ
ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɱɟɧɶ ɪɟɞɤɨ.
ɇɚɪɢɫɭɟɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ Uȼɕɏ(Uȼɏ).
Uȼɕɏ = 0 ɩɪɢ Uȼɏ = UCM
ɇɟɞɨɫɬɚɬɤɢ:
1)Ʌɢɧɟɣɧɵɣ ɭɫɢɥɢɬɟɥɶɧɵɣ ɞɢɚɩɚɡɨɧ Ɉɍ ɨɱɟɧɶ ɦɚɥ.
2)Ɂɚɜɢɫɢɦɨɫɬɶ ɄU ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ.
3)ɇɟɨɞɢɧɚɤɨɜɨɫɬɶ KU ɨɬ ɤɨɪɩɭɫɚ ɤ ɤɨɪɩɭɫɭ.
ɉɨɷɬɨɦɭ Ɉɍ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɤɚɱɟɫɬɜɟ ɫɯɟɦɵ ɫ ɨɛɪɚɬɧɵɦɢ ɫɜɹɡɹɦɢ.
ɇɟɢɧɜɟɪɬɢɪɭɸɳɢɣ ɭɫɢɥɢɬɟɥɶ ɧɚ ɛɚɡɟ Ɉɍ
Ɉɬɪɢɰɚɬɟɥɶɧɚɹ ɨɛɪɚɬɧɚɹ ɫɜɹɡɶ (ɈɈɋ)
Uȼɕɏ = (Uȼɏ - UOC) ˜ KU = Uȼɏ – UOC =
ɉɪɢ KU ĺ ’, Uȼɏ – UOC = 0, Uȼɏ = UOC;
U ȼɕɏ
;
KU
U OC
U ȼɕɏ ˜
R1
;
R 1 R OC
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ (ɉ) ɫɯɟɦɵ ɫ ɨɛɪɚɬɧɨɣ ɫɜɹɡɹɦɢ
R 1 R OC
U ȼɕɏ U ȼɕɏ
U ȼɕɏ
;
ɉ
R1
R1
U ȼɏ
U OC
U ȼɕɏ ˜
R 1 R OC
ɉ ɫɯɟɦɵ ɫ Ɉɋ ɧɟ ɡɚɜɢɫɢɬ ɨɬ KU , ɢɫɤɥɸɱɚɟɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɪɚɡɛɪɨɫ KU.
ɂɧɜɟɪɬɢɪɭɸɳɢɣ ɭɫɢɥɢɬɟɥɶ ɧɚ ɛɚɡɟ Ɉɍ
U2 = 0 ɬ.ɤ ɡɚɡɟɦɥɟɧɨ.
U1
300 ˜ 10 6 ȼ
i ȼɏ
10 9 Ⱥ = 1 ɧȺ § 0
3
R ȼɏ.Ɉɍ 300 ˜ 10 Ɉɦ
U1 = 300 ɦɤȼ
i1 + i2 = iȼɏ = 0, ɡɧɚɱɢɬ i1 = -i2
i2
U ȼɏ
R1
U ȼɕɏ
; i1
R OC
U ȼɕɏ
; U ȼɕɏ
R OC
ɉ
U ȼɏ
R1
U ȼɏ ˜
R OC
R1
R OC
R1
ɋɜɹɡɶ ɩɚɪɚɥɥɟɥɶɧɚɹ, ɬ.ɤ. ɫɤɥɚɞɵɜɚɸɬɫɹ ɧɟ ɧɚɩɪɹɠɟɧɢɹ, ɚ ɬɨɤɢ. ɗɬɨ ɥɢɲɶ ɬɟɨɪɟɬɢɱɟɫɤɚɹ ɫɯɟɦɚ ɜ ɧɟɣ
ɨɬɫɭɬɫɬɜɭɸɬ ɰɟɩɢ ɤɨɪɪɟɤɰɢɢ.
ɂɧɜɟɪɬɢɪɭɸɳɢɣ ɫɭɦɦɚɬɨɪ ɧɚ ɛɚɡɟ Ɉɍ
i OC
i1 + i2 + … + in = iOC
U ȼɕɏ U ȼɏ1 U ȼɏ 2
U
... ȼɏn
R OC
R1
R2
Rn
R OC
R
R
U ȼɏ 2 ˜ OC ... U ȼɏn ˜ OC )
R1
R2
Rn
Ɉɬɧɨɲɟɧɢɟ ROC ɤ R ɜɯɨɞɚ ɦɨɠɧɨ ɧɚɡɜɚɬɶ ɜɟɫɨɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ. ȿɫɥɢ ROC = R1 = R2 = … = Rn,
ɡɧɚɱɢɬ ɫɭɦɦɚɬɨɪ ɜ ɱɢɫɬɨɦ ɜɢɞɟ, ɢɧɚɱɟ ɩɨɥɭɱɚɟɦ ɫɭɦɦɚɬɨɪ ɫ ɜɟɫɨɜɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.
U ȼɕɏ
( U ȼɏ1 ˜
ɗɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ
Ʉɨɦɩɟɧɫɚɬɨɪ ɜɯɨɞɧɵɯ ɬɨɤɨɜ ɢ ɧɚɩɪɹɠɟɧɢɹ ɫɦɟɳɟɧɢɹ ɧɭɥɹ
ȼ ɪɟɠɢɦɟ ɩɨɤɨɹ:
Iȼɏ1 ɢ Iȼɏ2 - ɷɬɨ Iȼɇ1 ɢ IȻɉ2 ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɤɚɫɤɚɞɚ.
Iȼɏ1 ɩɪɨɬɟɤɚɟɬ ɱɟɪɟɡ R1 ɢ RɈɋ
Uȼɏ = 0, ɡɧɚɱɢɬ Uȼɕɏ = 0
R ˜R
U 1 I ȼɏ1 ˜ 1 OC ; ɬ.ɤ. ɄU ɜɟɥɢɤ => U1  0, ɩɨɥɭɱɢɦ Uȼɕɏ  0.
R 1 R OC
ɑɬɨɛɵ ɜ ɪɟɠɢɦɟ ɩɨɤɨɹ Uȼɕɏ = 0, U1 = U2 =>
R 1 ˜ R OC
; ɬ.ɨ. ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɜɥɢɹɧɢɟ ɜɯɨɞɧɵɯ ɬɨɤɨɜ.
R
R 1 R OC
U BIX
0 ɩɪɢ U BX
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ
U BX
U CM
0
o U BIX
z0
ɑɬɨɛɵ ɢɫɤɥɸɱɢɬɶ «ɜɪɟɞɧɨɟ» ɧɚɩɪɹɠɟɧɢɟ ɫɦɟɳɟɧɢɹ, ɩɪɢɦɟɧɹɸɬ ɫɥɟɞɭɸɳɢɟ ɫɯɟɦɵ:
ɉɭɬɟɦ ɩɟɪɟɦɟɳɟɧɢɹ ɞɜɢɠɤɚ ɩɨɬɟɧɰɢɨɦɟɬɪɚ ɞɨɛɢɜɚɟɦɫɹ, ɱɬɨɛɵ ɩɪɢ Uɜɯ = 0, Uɜɵɯ ɬɨɠɟ ɞɨɥɠɧɨ ɛɵɬɶ ɪɚɜɧɨ ɧɭɥɸ.
ɂɧɬɟɝɪɢɪɭɸɳɢɣ ɭɫɢɥɢɬɟɥɶ. ɂɧɬɟɝɪɚɬɨɪ ɧɚ ɛɚɡɟ ɨɩɟɪɚɰɢɨɧɧɨɝɨ ɭɫɢɥɢɬɟɥɹ.
1) ɧɚ ɛɚɡɟ ɢɞɟɚɥɶɧɨɝɨ Ɉɍ (ɢɧɬɟɝɪɚɬɨɪɚ) ɛɟɡ r
2) c r , ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɟɝɨ ɜɤɥɸɱɟɧɢɹ
1
iC (t ) dt
C³
UC
U BIX
UC
U BIX
1
iC (t )dt
C³
i BX
i C
i BX
U BX
R
1
i BX (t )dt
C³
U BIX
UC
1 U BX (t )
˜ dt
C³ R
1
U BX (t )dt
RC ³
;
ɩɟɪɟɣɞɟɦ ɨɬ ɧɟɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ ɤ ɨɩɪɟɞɟɥɟɧɧɵɦ:
t
1
U BIX (0) U BX (t )dt
RC ³0
U BIX
, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
U BIX ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ:
ɉ
z OC
1
ZC
z BX
R
1
ZR , ɝɞɟ z OC - ɤɨɷɮɮɢɰɢɟɧɬ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ;
z BX - ɤɨɷɮɮɢɰɢɟɧɬ ɜɯɨɞɚ
ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɱɚɫɬɨɬɵ, ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ.
ɂɧɬɟɝɪɚɬɨɪ ɹɜɥɹɟɬɫɹ ɭɫɢɥɢɬɟɥɟɦ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ (ɍɍɇ).
ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ:
ɉ1=ɉ2
ɉ1 , ɉ 2 - ɩɥɨɳɚɞɢ
ȿɫɥɢ
ɉ 1z ɉ 2 , ɬɨ ɧɚ ɜɵɯɨɞɟ ɧɟ ɛɭɞɟɬ ɧɭɥɹ.
³ sin Ztdt
1
Z
cos Zt
;
U BIX
Um sin Zt
U
1
Um cos Zt
ZRC
.
ȿɫɥɢ BX
, ɬɨ
ɉɨɞɚɥɢ ɧɚ ɜɯɨɞ «ɩɢɥɨɨɛɪɚɡɧɵɣ» ɫɢɝɧɚɥ, ɧɚ ɜɵɯɨɞɟ ɩɨɥɭɱɢɥɢ ɤɨɫɢɧɭɫɨɢɞɭ (ɮɚɡɨɜɵɣ ɫɞɜɢɝ ɧɚ 90 ɝɪɚɞɭɫɨɜ).
ɉɨɞɚɞɢɦ ɧɚ ɜɯɨɞ ɫɢɝɧɚɥ ɜ ɮɨɪɦɟ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ:
ɇɚɡɧɚɱɟɧɢɟ r: ɩɪɢ ɜɤɥɸɱɟɧɢɢ r || C ɭɫɬɪɚɧɹɟɬ ɧɚɤɚɩɥɢɜɚɧɢɟ ɫɢɝɧɚɥɚ
ɧɚ ɜɵɯɨɞɟ ɡɚ ɫɱɟɬ ɬɨɤɚ ɜɯɨɞɚ ɢ ɧɚɩɪɹɠɟɧɢɹ ɫɦɟɳɟɧɢɹ ɧɭɥɹ.
Ⱦɢɮɮɟɪɟɧɰɢɪɭɸɳɢɣ ɭɫɢɥɢɬɟɥɶ. Ⱦɢɮɮɟɪɟɧɰɢɚɬɨɪ ɧɚ ɛɚɡɟ Ɉɍ.
iC
C
dUc
dt ;
iC
iR ; U C
U BX ;
iC
C
dU BX
dt
;
iR
U BIX
R ,
ɩɪɢɪɚɜɧɹɟɦ ɩɪɚɜɵɟ ɱɚɫɬɢ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ:
CdU BX (t )
dt
U BIX
ɉ
U BIX
R
dU BX (t )
RC
dt
z OC
z BX
R
1
ZC
ZRC
; ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ, ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ.
Ⱦɢɮɮɟɪɟɧɰɢɚɬɨɪ ɹɜɥɹɟɬɫɹ ɭɫɢɥɢɬɟɥɟɦ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ (ɍȼɑ).
sin` cos
(sin Zt )` Z cos Zt
U
Um sin Zt o U BIX
ȿɫɥɢ BX
ZRCUm cos Zt .
ɇɚɪɢɫɭɟɦ ɷɩɸɪɵ:
ɞɥɹ ɞɢɮɮɟɪɟɧɰɢɚɬɨɪɚ ɩɭɧɤɬɢɪɧɚɹ ɤɪɢɜɚɹ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɧɚ ɛɚɡɟ ɪɟɚɥɶɧɨɝɨ Ɉɍ;
ɨɛɵɱɧɚɹ ɤɪɢɜɚɹ - ɧɚ ɛɚɡɟ ɢɞɟɚɥɶɧɨɝɨ Ɉɍ.
ɋɯɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɬɨɪɚ ɫɤɥɨɧɧɚ ɤ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɸ. ɉɨɞ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɩɨɧɢɦɚɟɬɫɹ ɧɚɥɢɱɢɟ
U BX
U BIX z 0 ɩɪɢ
0
ɉɪɢɱɢɧɚ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ - ɢɧɟɪɰɢɨɧɧɨɫɬɶ ɬɪɚɧɡɢɫɬɨɪɚ. ɂɧɟɪɰɢɨɧɧɨɫɬɶ ɬɪɚɧɡɢɫɬɨɪɚ ɜɜɢɞɭ ɬɨɝɨ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ
ɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ ɧɟ ɛɟɫɤɨɧɟɱɧɚ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɩɪɢɪɚɳɟɧɢɹ ɜɵɯɨɞɧɵɯ ɬɨɤɨɜ ɬɪɚɧɡɢɫɬɨɪɚ ɨɬɫɬɚɸɬ
ɨɬ ɜɯɨɞɧɵɯ ɬɨɤɨɜ.
Ɉɫɨɛɟɧɧɨ ɷɬɨ ɫɤɚɡɵɜɚɟɬɫɹ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ.
ɗɩɸɪɵ:
ɉɪɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɨɦ ɫɢɝɧɚɥɟ ɧɚɛɥɸɞɚɟɬɫɹ ɨɬɫɬɚɸɳɢɣ ɮɚɡɨɜɵɣ ɫɞɜɢɝ ɢ ɫɧɢɠɟɧɢɟ ɚɦɩɥɢɬɭɞɵ
«ɨɬɫɥɟɞɢɬɶ» ɧɚ Ⱥɑɏ (ɚɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ):
Ɏɑɏ
M
U BIX . ɗɬɨ ɦɨɠɧɨ
180 q ; ɈɈɋ ɩɪɟɜɪɚɬɢɥɚɫɶ ɜ ɉɈɋ. ɗɬɨ
U BX (ɩɨɦɟɯɚ), ɩɪɢɜɨɞɢɬ ɤ ɥɚɜɢɧɨɨɛɪɚɡɧɨɦɭ ɧɚɪɚɫɬɚɧɢɸ U BIX ,
ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɥɸɛɨɟ ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ
15 ȼ. ɗɬɨ ɢ ɟɫɬɶ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟ.
U
ɞɨ BIXMAX
ɑɬɨ ɦɨɠɟɬ ɩɪɨɢɡɨɣɬɢ: ɩɪɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ ɡɚ ɫɱɟɬ ɮɚɡɨɜɨɝɨ ɫɞɜɢɝɚ
ɋ ɷɬɢɦ ɹɜɥɟɧɢɟɦ ɧɚɞɨ ɛɨɪɨɬɶɫɹ: ɨɝɪɚɧɢɱɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ.
ɇɚɪɢɫɭɟɦ ɫɯɟɦɭ:
ɉ
z OC
z BX
ɜɜɟɞɟɧɢɟ
C1 op z OC ;
ɜɜɟɞɟɧɢɟ Rɛ on z BX .
Ɋɚɫɫɦɨɬɪɢɦ ɬɚɤɭɸ ɫɯɟɦɭ:
i 2 i1
U BIX
i1
C
UC2
dU C1
dt
1
i2 (t )dt
C2 ³
C1
1
C2
³ i (t )dt
1
dU BX (t )
1
˜ dt
C1
³
dt
C2
C1
C2
³
dU BX (t )
˜ dt
dt
C1
UBX
C2
dU BX (t )
dt .
Ʉɨɦɩɚɪɚɬɨɪɵ.
U
Ʉɨɦɩɚɪɚɬɨɪɵ - ɷɬɨ ɩɨɪɨɝɨɜɵɣ ɷɥɟɦɟɧɬ, ɭ ɤɨɬɨɪɨɝɨ BIX ɢɡɦɟɧɹɟɬɫɹ ɫɤɚɱɤɨɨɛɪɚɡɧɨ ɢɡ ɨɞɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ.
ɗɬɨ ɩɨ ɫɭɬɢ ɝɪɚɧɢɱɧɵɣ ɷɥɟɦɟɧɬ ɦɟɠɞɭ ɚɧɚɥɨɝɨɜɵɦɢ ɢ ɢɦɩɭɥɶɫɧɵɦɢ (ɰɢɮɪɨɜɵɦɢ) ɫɯɟɦɚɦɢ.
Ʉɨɦɩɚɪɚɬɨɪɵ ɦɨɠɧɨ ɜɵɩɨɥɧɹɬɶ ɧɚ ɨɫɧɨɜɟ ɨɩɟɪɚɰɢɨɧɧɵɯ ɭɫɢɥɢɬɟɥɟɣ (ɫ ɧɚɜɟɫɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ), ɧɨ ɫɭɳɟɫɬɜɭɸɬ
ɨɬɞɟɥɶɧɵɟ ɢɧɬɟɝɪɚɥɶɧɵɟ ɦɢɤɪɨɫɯɟɦɵ ɤɨɦɩɚɪɚɬɨɪɨɜ.
Ȼɵɫɬɪɨɞɟɣɫɬɜɢɟ ɢɧɬɟɝɪɚɥɶɧɵɯ ɤɨɦɩɚɪɚɬɨɪɨɜ ɜɵɲɟ.
ɇɚɩɪɢɦɟɪ, S54 CA3 - ɢɧɬɟɝɪɚɥɶɧɵɣ ɤɨɦɩɚɪɚɬɨɪ,
ɋȺ- ɫɟɥɟɤɬɨɪ ɚɦɩɥɢɬɭɞɧɵɣ, ɪɚɡɥɢɱɚɟɬ ɜɯɨɞɧɵɟ ɫɢɝɧɚɥɵ.
Ʉɨɦɩɚɪɚɬɨɪ - ɚɧɚɥɨɝ ɪɟɥɟ.
Ɉɩɟɪɚɰɢɨɧɧɵɣ ɭɫɢɥɢɬɟɥɶ ɭɫɢɥɢɜɚɟɬ ɪɚɡɧɨɫɬɶ ɫɢɝɧɚɥɨɜ ɞɜɭɯ ɜɢɞɨɜ: ɨɞɧɨ ɨɩɨɪɧɨɟ, ɞɪɭɝɨɟ - ɜɯɨɞɧɨɟ:
U BIX
0 o U BIX
U BX
(U OP U BX ) ˜ K U K U | 50000
,
U BIXMAX | 13 ȼ
U BIX | E ɉ
U % 0 U BIX ɧɟ ɢɡɦɟɧɢɬɫɹ;
ɉɪɢ BX
U
0ɢ U OP U BIX ɢɡɦɟɧɢɬɫɹ ɫɤɚɱɤɨɦ ɞɨ -13ȼ.
ɉɪɢ BX
U
U
,U BIX 0 , ɧɨ ɷɬɨ ɨɱɟɧɶ ɧɟɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ.
OP
ɉɪɢ BX
ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ:
ɉɪɢ
n U OP o W 1 p,W 2 n
.
Ɇɟɧɹɹ ɡɧɚɤ U OP ɢ ɩɨɞɚɜɚɹ ɟɝɨ ɧɚ ɪɚɡɧɵɟ ɜɯɨɞɵ ɨɩɟɪɚɰɢɨɧɧɨɝɨ ɭɫɢɥɢɬɟɥɹ, ɦɨɠɧɨ ɦɟɧɹɬɶ ɡɧɚɤ
ɫɨɫɬɨɹɧɢɢ ɢ ɩɪɢ ɫɪɚɛɚɬɵɜɚɧɢɢ. ɉɪɢ ɷɬɨɦ
U BIX ɜ ɢɫɯɨɞɧɨɦ
U BX , ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ «ɫɪɚɛɚɬɵɜɚɧɢɟ» ɤɨɦɩɚɪɚɬɨɪɚ (ɢɡɦɟɧɟɧɢɟ U
BIX
U CPK , ɚ U , ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ ɨɛɪɚɬɧɵɣ ɩɪɨɰɟɫɫ «ɜɨɡɜɪɚɬ» - U BZK . Ⱦɥɹ
BX
U BZK
|1
ɨɛɵɱɧɨɝɨ ɤɨɦɩɚɪɚɬɨɪɚ U CPK | U BZK ɢ. K B
U CPK
U BX o t ɂɆɉ .
Ʉɨɦɩɚɪɚɬɨɪ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ
Sin o
ɢɥɢ
ɨɬ +13ȼ ɞɨ -13ȼ) ɦɨɠɧɨ ɧɚɡɜɚɬɶ
ȼ ɪɹɞɟ ɫɥɭɱɚɟɜ ɬɚɤɨɣ ɤɨɦɩɚɪɚɬɨɪ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɨɠɧɨ, ɬɚɤ ɤɚɤ:
U BX ɦɨɠɟɬ ɛɵɬɶ ɬɚɤɢɦ ɤɚɤ ɧɚ ɪɢɫɭɧɤɟ, ɛɭɞɟɬ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ «ɞɪɟɛɟɡɝ». ɑɬɨɛɵ ɷɬɨɝɨ
ɢɡɛɟɠɚɬɶ, ɜɜɨɞɹɬ ɉɈɋ. Ʉɨɦɩɚɪɚɬɨɪ ɫ ɉɈɋ ɧɚɡɵɜɚɟɬɫɹ ɤɨɦɩɚɪɚɬɨɪ ɫɨ ɫɦɟɳɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɢɥɢ «ɬɪɢɝɝɟɪ
ɒɦɢɬɬɚ».
Ɉɩɪɟɞɟɥɢɦ
U 1 ɜ ɪɟɠɢɦɟ ɩɨɤɨɹ:
U1
R2
R1
U BIX
R1 R2
R1 R2
U OP
U BIX 0
ɉɪɢ
U BX
ɉɪɢ
U BX
U OP 0
ɪɟɲɚɥɢ ɦɟɬɨɞɨɦ ɫɭɩɟɪɩɨɡɢɰɢɢ (ɧɚɥɨɠɟɧɢɹ);
0 - ɤɨɦɩɚɪɚɬɨɪ ɧɟ ɫɪɚɛɨɬɚɟɬ,
0 ɢ U 1 ɤɨɦɩɚɪɚɬɨɪ ɢɡɦɟɧɢɬ ɫɜɨɟ ɫɨɫɬɨɹɧɢɟ ɢ U BIX ɫɬɚɧɟɬ % 0 .
U 1 ɫɬɚɧɟɬ ɪɚɜɧɨ ɫɥɟɞɭɸɳɟɦɭ ɜɵɪɚɠɟɧɢɸ:
R1
R1
U 1 U OP
U BIX
U1 `
R1 R2
R1 R2
U `% U 1 ɢɫɱɟɡɧɟɬ «ɞɪɟɛɟɡɝ» ɤɨɧɬɚɤɬɚ.
ɬɚɤ ɤɚɤ 1
Ɍɟɩɟɪɶ ɛɭɞɟɦ ɭɦɟɧɶɲɚɬɶ
U BX . ɉɪɢ ɢɫɯɨɞɧɨɦ UBIXɤɨɦɩɚɪɚɬɨɪ ɧɟ ɩɟɪɟɤɥɸɱɢɬɫɹ, ɬɚɤ ɤɚɤ
U 1 p . ɉɟɪɟɤɥɸɱɟɧɢɟ ɛɭɞɟɬ ɩɪɢ ɦɟɧɶɲɟɦ U BX .
ɂɡɨɛɪɚɡɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ:
ɑɟɦ > ɝɥɭɛɢɧɚ ɉɈɋ, ɬ.ɟ.
R1
R2 , ɬɟɦ ɲɢɪɟ ɩɟɬɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
Ɂɚɞɚɱɢ ɧɚ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ:
Ɂɚɞɚɱɚ ʋ1
Ⱦɚɧɨ:
U1
U2
R1
8 cos 314t ȼ
1ȼ
R2
33 ɤɈɦ
39 ɤɈɦ
C1
0.15 ɦɤɎ
Ⱦɚɧɚ ɫɯɟɦɚ:
Ep
15 ȼ
ª
º
R
« (U 1 )` 2 U 2 »
R1
¬
¼
U BIX
Ɋɟɲɟɧɢɟ:
ɉ
ª
39 º
«8 R 2 C ˜ 314 ˜( ) ˜ sin 314 t 1 »
33 »
«¬
¼
8 ˜ 39 ˜ 10 3 ˜ 0.15 ˜ 10 6 ˜ 314 ˜ sin 314t 1.18 14.7 ˜ sin 314t 1.18
U BIX
RC
Z
2Sf
T
1
f
dU BX (t )
dt
314
1
50
2Sf
RC (sin Zt )
f
314
2S
0 . 02 c
RC cos Zt
50
Ƚɰ
20 mc
ɇɚɪɢɫɭɟɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ:
Ɂɚɞɚɱɚ ʋ 2
Ⱦɚɧɨ:
U1
U2
R1
2ȼ
62.8 sin 3140t
10 ɤɈɦ
R2
20 ɤɈɦ
C 1 ɦɤɎ
Ⱦɚɧɚ ɫɯɟɦɚ:
Ɋɟɲɟɧɢɟ:
³ sin Zt
f
3140
2S
1
cos Zt
ZRC
T
500
Ƚɰ
1
500
0.02
ɫ
1
1
U BIX ( ³ U 1 dt ³ U 2dt ) (
˜ ³ 2dt 62.8 sin 3140tdt )
R1C
R2 C ³
2
62.8
(
t
cos 3140t 200t 1 cos 3140t
3
6
3
10 ˜ 10 ˜ 1 ˜ 10
20 ˜ 10 ˜ 1 ˜ 10 6 ˜ 3140
n
200*T*n
1
0.4
2
0.8
ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ:
3
1.2
4
1.6
5
2
ɂɦɩɭɥɶɫɧɵɟ ɭɫɬɪɨɣɫɬɜɚ.
ɒɢɪɨɤɨ ɩɪɢɦɟɧɹɟɦɵɦɢ ɭɡɥɚɦɢ ɷɥɟɤɬɪɨɧɧɨɣ ɬɟɯɧɢɤɢ ɢ ɫɢɫɬɟɦ ɨɛɪɚɛɨɬɤɢ ɢɧɮɨɪɦɚɰɢɢ ɹɜɥɹɸɬɫɹ
ɢɦɩɭɥɶɫɧɵɟ ɭɫɬɪɨɣɫɬɜɚ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɵ ɤɚɤ ɧɚ ɚɧɚɥɨɝɨɜɵɯ, ɬɚɤ ɢ ɧɚ ɰɢɮɪɨɜɵɯ ɦɢɤɪɨɫɯɟɦɚɯ (Ɇɋ).
Ɉɧɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɚɧɚɥɨɝɨɜɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɦɚɲɢɧɚɯ (ȺȼɆ), ɜ ɛɥɨɤɚɯ ɭɩɪɚɜɥɟɧɢɹ, ɜɜɨɞɚ ɢ ɜɵɜɨɞɚ ɰɢɮɪɨɜɵɯ
ɗȼɆ, ɜ ɬɟɥɟɦɟɬɪɢɱɟɫɤɨɣ, ɪɚɞɢɨɧɚɜɢɝɚɰɢɨɧɧɨɣ ɚɩɩɚɪɚɬɭɪɟ, ɜ ɫɢɫɬɟɦɚɯ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ.
ɂɦɩɭɥɶɫɧɵɟ ɭɫɬɪɨɣɫɬɜɚ (ɂɍ) ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɫɢɝɧɚɥɨɜ, ɢɦɟɸɳɢɯ ɯɚɪɚɤɬɟɪ ɢɦɩɭɥɶɫɨɜ ɢ ɩɟɪɟɩɚɞɨɜ ɧɚɩɪɹɠɟɧɢɣ (ɩɨɬɟɧɰɢɚɥɨɜ)
ɢɥɢ ɬɨɤɚ, ɚ ɬɚɤɠɟ ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɟɣ, ɩɪɟɞɨɫɬɚɜɥɟɧɧɨɣ ɭɩɨɦɹɧɭɬɵɦɢ ɫɢɝɧɚɥɚɦɢ.
ɉɪɢɦɟɧɟɧɢɟ ɢɦɩɭɥɶɫɧɨɝɨ ɫɩɨɫɨɛɚ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ ɨɛɭɫɥɨɜɥɟɧɨ ɪɹɞɨɦ ɩɪɢɱɢɧ: ɛɨɥɶɲɢɧɫɬɜɨ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɢɦɟɸɬ ɞɢɫɤɪɟɬɧɵɣ (ɬɚɤɬɨɜɵɣ) ɯɚɪɚɤɬɟɪ (ɩɭɫɤ, ɨɫɬɚɧɨɜ, ɫɪɚɛɚɬɵɜɚɧɢɟ ɡɚɳɢɬɵ ɢ ɬ.ɞ.),
ɩɟɪɟɞɚɱɚ ɢɧɮɨɪɦɚɰɢɢ ɜ ɜɢɞɟ ɢɦɩɭɥɶɫɨɜ ɩɨɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɦɨɳɧɨɫɬɶ; ɩɨɜɵɲɚɟɬɫɹ ɩɨɦɟɯɨɭɫɬɨɣɱɢɜɨɫɬɶ, ɬɨɱɧɨɫɬɶ ɢ ɧɚɞɟɠɧɨɫɬɶ ɷɥɟɤɬɪɨɧɧɵɯ ɭɫɬɪɨɣɫɬɜ, ɬ.ɤ. ɢɧɮɨɪɦɚɰɢɹ ɩɟɪɟɞɚɟɬɫɹ ɜ ɜɢɞɟ ɤɨɞɨɜɨɝɨ ɧɚɛɨɪɚ ɢɦɩɭɥɶɫɨɜ
ɢ ɫɭɳɟɫɬɜɟɧɧɵɦ ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɧɚɥɢɱɢɟ ɢɥɢ ɨɬɫɭɬɫɬɜɢɟ ɢɦɩɭɥɶɫɚ.
ɇɚɢɛɨɥɟɟ ɱɚɫɬɨ ɩɪɢɦɟɧɹɸɬɫɹ ɢɦɩɭɥɶɫɵ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɮɨɪɦɵ (ɪɢɫ.1).
0.9 Um
Tɩ
tɩ
Um
0.1Um
tɢ
tɮ
tɫ
Ɋɢɫ.1 Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɢɦɩɭɥɶɫɨɜ
Ɉɧɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɫɥɟɞɭɸɳɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ:
Um- ɚɦɩɥɢɬɭɞɚ ɢɦɩɭɥɶɫɚ;
tɂ - ɞɥɢɬɟɥɶɧɨɫɬɶ ɢɦɩɭɥɶɫɚ;
tɉ - ɞɥɢɬɟɥɶɧɨɫɬɶ ɩɚɭɡ ɦɟɠɞɭ ɢɦɩɭɥɶɫɚɦɢ;
Ɍɉ- ɩɟɪɢɨɞ ɩɨɜɬɨɪɟɧɢɹ ɢɦɩɭɥɶɫɨɜ;
f = 1/ Ɍɉ - ɱɚɫɬɨɬɚ ɩɨɜɬɨɪɟɧɢɹ ɢɦɩɭɥɶɫɨɜ;
Q = Ɍɉ / tɉ - ɫɤɜɚɠɧɨɫɬɶ ɢɦɩɭɥɶɫɨɜ.
Ɋɟɚɥɶɧɵɣ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɢɦɩɭɥɶɫ ɢɦɟɟɬ ɨɩɪɟɞɟɥɟɧɧɭɸ ɞɥɢɬɟɥɶɧɨɫɬɶ ɮɪɨɧɬɚ tɎ (ɜɪɟɦɹ ɧɚɪɚɫɬɚɧɢɹ ɨɬ 0,1 ɞɨ
0,9 Um) ɢ ɫɪɟɡɚ tC. Ɉɛɵɱɧɨ tɎ ɢ tC << tɂ , ɩɨɷɬɨɦɭ ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ tɎ = tɎ = 0.
Ɍ.ɤ. ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɢɦɩɭɥɶɫ ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɟɪɟɩɚɞ ɧɢɡɤɨɝɨ ɢ ɜɵɫɨɤɨɝɨ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɭɪɨɜɧɟɣ, ɟɝɨ ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɢɡɦɟɧɟɧɢɟɦ ɞɜɨɢɱɧɨɝɨ ɱɢɫɥɚ 0 ɢ 1 ɢɥɢ ɥɨɝɢɱɟɫɤɨɝɨ ɭɪɨɜɧɹ ɇ (ɧɢɡɤɢɣ) ɢ ȼ (ɜɵɫɨɤɢɣ). Ⱦɥɹ ɪɚɛɨɬɵ ɫ
ɬɚɤɢɦɢ ɞɢɫɤɪɟɬɧɵɦɢ ɫɢɝɧɚɥɚɦɢ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɰɢɮɪɨɜɵɟ ɢɧɬɟɝɪɚɥɶɧɵɟ ɦɢɤɪɨɫɯɟɦɵ (ɐɂɆɋ). Ɉɫɧɨɜɨɣ ɞɥɹ ɢɯ
ɩɨɫɬɪɨɟɧɢɹ ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɤɥɸɱɢ. Ɉɧɢ ɦɨɝɭɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɨɞɧɨɦ ɢɡ ɞɜɭɯ ɫɨɫɬɨɹɧɢɢ: ȼ(1) ɢ ɇ(0). ɂɯ ɞɟɣɫɬɜɢɟ
ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɩɟɪɟɯɨɞɟ ɢɡ ɨɞɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɜɯɨɞɧɵɯ ɥɨɝɢɱɟɫɤɢɯ ɫɢɝɧɚɥɨɜ. ɉɨ
ɮɭɧɤɰɢɨɧɚɥɶɧɨɦɭ ɧɚɡɧɚɱɟɧɢɸ ɐɂɆɋ ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɩɨɞɝɪɭɩɩɵ: ɥɨɝɢɱɟɫɤɢɟ ɷɥɟɦɟɧɬɵ (Ʌɗ), ɬɪɢɝɝɟɪɵ, ɨɞɧɨ
ɜɢɛɪɚɬɨɪɵ, ɦɭɥɶɬɢɜɢɛɪɚɬɨɪɵ, ɷɥɟɦɟɧɬɵ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ ɢ ɞɢɫɤɪɟɬɧɵɯ ɭɫɬɪɨɣɫɬɜ ɢ ɞɪ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
ɫɯɟɦɨɬɟɯɧɢɱɟɫɤɨɣ ɪɟɚɥɢɡɚɰɢɢ ɐɂɆɋ ɞɟɥɹɬɫɹ ɧɚ ɫɥɟɞɭɸɳɢɟ ɬɢɩɵ: ɬɪɚɧɡɢɫɬɨɪɧɨɣ ɥɨɝɢɤɢ (ɌɅ), ɞɢɨɞɧɨ-ɬɪɚɧɡɢɫɬɨɪɧɨɣ
ɥɨɝɢɤɢ (ȾɌɉ), ɬɪɚɧɡɢɫɬɨɪɧɨ-ɬɪɚɧɡɢɫɬɨɪɧɨɣ ɥɨɝɢɤɢ (ɌɌɅ), ɬɪɚɧɡɢɫɬɨɪɧɨɣ ɥɨɝɢɤɢ ɧɚ ɆɈɉ-ɬɪɚɧɡɢɫɬɨɪɚɯ (ɆɈɉ ɌɅ). Ʉ
ɨɫɧɨɜɧɵɦ ɩɚɪɚɦɟɬɪɚɦ ɐɂɆɋ ɨɬɧɨɫɹɬɫɹ:
0
0
- ɜɯɨɞɧɨɟ U BX ɢ ɜɵɯɨɞɧɨɟ U BɕX ɧɚɩɪɹɠɟɧɢɹ ɥɨɝɢɱɟɫɤɨɝɨ 0;
1
1
- ɜɯɨɞɧɨɟ U BX ɢ ɜɵɯɨɞɧɨɟ U Bɕɏ ɧɚɩɪɹɠɟɧɢɹ ɥɨɝɢɱɟɫɤɨɣ 1;
1, 0
- ɜɪɟɦɹ ɡɚɞɟɪɠɤɢ ɩɪɢ ɜɤɥɸɱɟɧɢɢ t ɁȾ – ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɜɯɨɞɧɵɦ ɢ ɜɵɯɨɞɧɵɦ ɢɦɩɭɥɶɫɚɦɢ ɩɪɢ
1
0
ɩɟɪɟɯɨɞɟ U BɕX ɨɬU BɕX ɤ U BɕX ɢ ɞɪɭɝɢɟ.
ɑɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɡɚɜɢɫɹɬ ɨɬ ɬɢɩɚ ɢɫɩɨɥɶɡɭɟɦɵɯ ɫɟɪɢɣ ɐɂɆɋ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɫɟɪɢɢ Ʉ155
0
1
0
1
U BɕX
ɛɨɥɟɟ 0,4 ȼ, U Bɕɕ ɧɟ ɦɟɧɟɟ 2,4 ȼ, I BX ɧɟ ɛɨɥɟɟ 1,6 ɦȺ, I BX ɧɟ ɛɨɥɟɟ 0,04 ɦȺ.
Ⱦɥɹ ɚɧɚɥɢɡɚ ɢ ɫɢɧɬɟɡɚ ɐɂɆɋ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɬɫɹ ɚɩɩɚɪɚɬ ɚɥɝɟɛɪɵ ɥɨɝɢɤɢ. Ɉɫɧɨɜɧɵɦ ɩɨɧɹɬɢɟɦ ɩɨɫɥɟɞɧɟɣ
ɹɜɥɹɟɬɫɹ ɩɨɧɹɬɢɟ "ɜɵɫɤɚɡɵɜɚɧɢɟ" - ɧɟɤɨɬɨɪɨɟ ɩɪɟɞɥɨɠɟɧɢɟ, ɨ ɤɨɬɨɪɨɦ ɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɨɧɨ ɢɫɬɢɧɧɨ ɢɥɢ
ɥɨɠɧɨ. Ʌɸɛɨɟ ɜɵɫɤɚɡɵɜɚɧɢɟ ɦɨɠɧɨ ɨɛɨɡɧɚɱɢɬɶ ɫɢɦɜɨɥɨɦ ɏ ɢ ɫɱɢɬɚɬɶ, ɱɬɨ ɏ=1, ɟɫɥɢ ɜɵɫɤɚɡɵɜɚɧɢɟ ɢɫɬɢɧɧɨ ɢ ɏ=0
ɟɫɥɢ ɜɵɫɤɚɡɵɜɚɧɢɟ ɥɨɠɧɨ. Ʌɨɝɢɱɟɫɤɚɹ ɩɟɪɟɦɟɧɧɚɹ - ɬɚɤɚɹ ɜɟɥɢɱɢɧɚ X, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɬɨɥɶɤɨ ɞɜɚ ɡɧɚɱɟɧɢɹ:
0 ɢɥɢ 1. Ʌɨɝɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ ɭ = f (ɏ1, ɏ2,…,ɏn) ɤɚɤ ɢ ɟɟ ɚɪɝɭɦɟɧɬɵ (ɏ1, ɏ2,…,ɏn) ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɡɧɚɱɟɧɢɹ 0 ɢɥɢ 1.
ɉɪɢ ɬɟɯɧɢɱɟɫɤɨɣ ɪɟɚɥɢɡɚɰɢɢ ɥɨɝɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ ɥɨɝɢɱɟɫɤɢɟ ɩɟɪɟɦɟɧɧɵɟ ɏ1, ɏ2,…,ɏn ɨɬɨɠɞɟɫɬɜɥɹɸɬɫɹ ɫ ɜɯɨɞɧɵɦɢ
ɫɢɝɧɚɥɚɦɢ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ, ɚ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɭ = f (ɏ1, ɏ2,…,ɏn) - ɫ ɜɵɯɨɞɧɵɦɢ ɫɢɝɧɚɥɚɦɢ.
x1
x
y=x
1
x1
y= x1 x2 = x1+ x2
x2
ɚ) "ɇȿ"
ɢɧɜɟɪɫɢɹ
x1
1
&
y= x1 x2 =
= x1 x2
x2
ɛ) "ɂɅɂ" ɥɨɝɢɱɟɫɤɨɟ
ɜ) "ɂ" ɥɨɝɢɱɟɫɤɨɟ
ɫɥɨɠɟɧɢɟ, ɞɢɡɴɸɧɤɰɢɹ
ɭɦɧɨɠɟɧɢɟ, ɤɨɧɴɸɧɤɰɢɹ
y= x1 x2 =x1
= x1+x2
x2 =
x2
x1
&
x2
y= x1 x2 =x1 x2 = x1 x2
ɞ) "ɂ-ɇȿ" ɲɬɪɢɯ ɒȿɎɎȿɊȺ,
ɨɬɪɢɰɚɧɢɟ ɤɨɧɴɸɧɤɰɢɢ
ɝ) "ɂɅɂ - ɇȿ" ɮɭɧɤɰɢɹ
ɉɂɊɋȺ, ɨɬɪɢɰɚɧɢɟ
ɞɢɡɴɸɧɤɰɢɢ
Ɋɢɫ.2 Ɉɛɨɡɧɚɱɟɧɢɟ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ
Ɏɭɧɤɰɢɹ ɭ = f1 (X), ɩɨɜɬɨɪɹɸɳɚɹ ɡɧɚɱɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ - ɬɨɠɞɟɫɬɜɟɧɧɚɹ, ɚ ɮɭɧɤɰɢɹ ɭ = f2 (X),
ɩɪɨɬɢɜɨɩɨɥɨɠɧɚɹ ɡɧɚɱɟɧɢɹɦ ɏ -ɥɨɝɢɱɟɫɤɨɟ ɨɬɪɢɰɚɧɢɟ (ɇȿ) f2(X)= X . Ɉɧɚ ɪɟɚɥɢɡɭɟɬɫɹ ɥɨɝɢɱɟɫɤɢɦ ɷɥɟɦɟɧɬɨɦ ɇȿ
(ɪɢɫ.2ɚ), ɩɪɟɞɫɬɚɜɥɹɸɳɢɦ ɫɨɛɨɣ ɢɧɜɟɪɬɢɪɭɸɳɢɣ ɤɥɸɱ. Ⱦɢɡɴɸɧɤɰɢɹ (ɥɨɝɢɱɟɫɤɨɟ ɫɥɨɠɟɧɢɟ "ɂɅɂ") - ɮɭɧɤɰɢɹ ɭ = f3
(ɏ1, ɏ2) = X 1vX 2 (ɦɨɠɟɬ ɬɚɤɠɟ ɨɛɨɡɧɚɱɚɬɶɫɹ ɭ = f3 (ɏ1, ɏ2) = X1 +X2 ɢɫɬɢɧɧɨ, ɤɨɝɞɚ ɢɫɬɢɧɧɵ ɢɥɢ ɏ1 ɢɥɢ ɏ2, ɢɥɢ ɨɛɟ
ɩɟɪɟɦɟɧɧɵɟ. Ɉɛɨɡɧɚɱɟɧɢɟ ɫɦ. ɪɢɫ.2ɛ).
Ʉɨɧɴɸɧɤɰɢɹ (ɥɨɝɢɱɟɫɤɨɟ ɫɥɨɠɟɧɢɟ, "ɂ") - ɭ = f4 (ɏ1, ɏ2) = X1 / X2 (ɦɨɠɟɬ ɬɚɤɠɟ ɨɛɨɡɧɚɱɚɬɶɫɹ ɭ = f4 (ɏ1, ɏ2) =
X1 ˜ X2 ɢɫɬɢɧɧɚ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ ɢɫɬɢɧɧɵ ɏ1 ɢ ɏ2. Ɉɛɨɡɧɚɱɟɧɢɟ ɪɢɫ. 2ɜ).
Ʌɨɝɢɱɟɫɤɢɟ ɷɥɟɦɟɧɬɵ "ɂ" ɢɥɢ "ɂɅɂ" ɨɛɥɚɞɚɸɬ ɫɜɨɣɫɬɜɨɦ ɞɜɨɣɫɬɜɟɧɧɨɫɬɢ, ɬ.ɟ. ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɷɥɟɦɟɧɬ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɢɫɩɨɥɶɡɭɟɦɨɣ ɥɨɝɢɤɢ (ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɢɥɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ) ɦɨɠɟɬ ɜɵɩɨɥɧɹɬɶ ɮɭɧɤɰɢɢ ɥɢɛɨ ɷɥɟɦɟɧɬɚ
"ɂ", ɥɢɛɨ "ɂɅɂ" ɬ.ɟ. ɟɫɥɢ ɥɨɝɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ ɪɟɚɥɢɡɭɟɬ ɮɭɧɤɰɢɸ "ɂɅɂ" ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɣ ɥɨɝɢɤɟ, ɬɨ ɨɧ
ɨɞɧɨɜɪɟɦɟɧɧɨ ɦɨɠɟɬ ɪɟɚɥɢɡɨɜɚɬɶ ɮɭɧɤɰɢɸ "ɂ" ɩɪɢ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɥɨɝɢɤɟ.
Ɏɭɧɤɰɢɹ ɉɢɪɫɚ (ɨɬɪɢɰɚɧɢɟ ɞɢɡɴɸɧɤɰɢɢ, "ɂɅɂ / ɇȿ") - ɭ = f5 (ɏ1, ɏ2) = X1pX2 =
X 1vX 2
X 1 X 2 ɢɫɬɢɧɧɚ
ɬɨɝɞɚ, ɤɨɝɞɚ ɏ1 ɢɥɢ X2 ɥɨɠɧɵ. Ɉɛɨɡɧɚɱɟɧɢɟ – ɪɢɫ.2ɝ).
ɒɬɪɢɯ ɒɟɮɮɟɪɚ - (ɨɬɪɢɰɚɧɢɟ ɤɨɧɴɸɧɤɰɢɢ) ɮɭɧɤɰɢɹ ɭ = f6(ɏ1, ɏ2) = X1 ¨X2 = X 1/X 2
X 1 x X 2 ɢɫɬɢɧɧɚ
ɬɨɝɞɚ, ɤɨɝɞɚ ɏ1 ɢ ɏ2 ɥɨɠɧɵ. Ɉɛɨɡɧɚɱɟɧɢɟ – ɪɢɫ.2ɞ).
ȼ ɬɚɛɥɢɰɟ 1 ɩɪɟɞɫɬɚɜɥɟɧɵ ɫɨɫɬɨɹɧɢɹ ɩɟɪɟɤɥɸɱɚɬɟɥɶɧɨɣ ɮɭɧɤɰɢɢ ɭ = f (ɏ1, ɏ2) ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɨɱɟɬɚɧɢɹɯ
ɡɧɚɱɟɧɢɣ ɥɨɝɢɱɟɫɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ɏ1 X2. ɗɬɚ ɬɚɛɥɢɰɚ ɧɚɡɵɜɚɟɬɫɹ ɬɚɛɥɢɰɟɣ ɢɫɬɢɧɧɨɫɬɢ.
Ɍɚɛɥɢɰɚ 1
ɋɨɫɬɨɹɧɢɟ ɮɭɧɤɰɢɢ ɭ = fK(ɏ1, ɏ2)
ɭ = fK(ɏ 1, ɏ 2)
ɏ
ɏ
1
"ɇȿ"
2
x1
"ɂɅɂ"
y
1
"ɂ"
0
1
1
1
x1
x2
1
1
0
0
0
1
0
1
0
0
1
1
y
"ɂ-ɇȿ"
&
"ɂɅɂ-ɇȿ"
1
0
0
0
1
1
0
0
0
1
1
1
0
&
ɉɟɪɟɤɥɸɱɚɬɟɥɶɧɚɹ ɮɭɧɤɰɢɹ ɭ ɫɨɫɬɚɜɥɹɟɬɫɹ ɧɚ ɨɫɧɨɜɚɧɢɢ ɬɚɛɥɢɰɵ ɢɫɬɢɧɧɨɫɬɢ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɮɭɧɤɰɢɢ "ɂɇȿ" ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɨɜɟɫɧɨ: "Ɏɭɧɤɰɢɹ ɭ ɢɫɬɢɧɧɚ (ɪɚɜɧɚ 1), ɤɨɝɞɚ ɢɫɬɢɧɧɵ ɧɟ ɏ1 ɢ ɧɟ ɏ2 (1-ɹ ɫɬɪɨɤɚ), ɢɥɢ ɧɟ
ɏ1 ɢ ɏ2 (2-ɹ ɫɬɪɨɤɚ) ɢɥɢ ɏ1 ɢ ɧɟ X2 (3-ɹ ɫɬɪɨɤɚ). Ɂɚɦɟɧɢɜ ɫɥɨɜɚ ɧɟ, ɢ, ɢɥɢ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɤɢ ɥɨɝɢɱɟɫɤɢɯ
ɨɩɟɪɚɰɢɣ ɩɨɥɭɱɢɦ:
(1)
ȿɫɥɢ
ɫɨɡɞɚɜɚɬɶ
ɭɫɬɪɨɣɫɬɜɨ
ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ
ɪɟɚɥɢɡɭɸɳɟɟ
ɷɬɭ
ɮɭɧɤɰɢɸ,
ɩɨɬɪɟɛɭɟɬɫɹ
ɫɬɪɭɤɬɭɪɚ,
y= x1 x2 + x1 x2 +x1 x2
ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɧɚ ɪɢɫ. 3. Ɉɞɧɚɤɨ ɷɬɭ ɫɬɪɭɤɬɭɪɭ ɦɨɠɧɨ ɭɩɪɨɫɬɢɬɶ, ɦɢɧɢɦɢɡɢɪɨɜɚɜ ɜɵɪɚɠɟɧɢɟ (1) ɧɚ ɨɫɧɨɜɟ ɬɨɠɞɟɫɬɜ
x1
x1
x1 x2
&
x2
x2
1
x1 x2
x1 x2 + x1 x2 + x1 x2
&
&
x1 x2
Ɋɢɫ.3 ɋɯɟɦɚ ɪɟɚɥɢɡɚɰɢɢ ɮɭɧɤɰɢɢ
y= x1 x2 + x1 x2 +x1 x2
ɚɥɝɟɛɪɵ ɥɨɝɢɤɢ:
Ⱥ+Ⱥ = Ⱥ (2)
Ⱥ˜Ⱥ = Ⱥ (6)
Ⱥ+ A = 1 (3)
Ⱥ˜ A = 0 (7)
A
A (10)
Ⱥ+Ⱥȼ+Ⱥɋ = Ⱥ (11)
Ⱥ+0 = Ⱥ (4)
Ⱥ˜0 = 0 (8)
Ⱥ+ A ˜ B = Ⱥ+ȼ (12)
Ⱥ+1 = 1 (5)
Ⱥ˜1 = Ⱥ (9)
A B C
A ˜ B ˜C
ȼɵɧɨɫɢɦ
y=
A ˜ B ˜ C (13)
A B C (14)
X 1 ɜ ɜɵɪɚɠɟɧɢɢ ( 1) ɡɚ ɫɤɨɛɤɢ ɢ ɢɫɩɨɥɶɡɭɟɦ ɬɨɠɞɟɫɬɜɨ (3) ɢ (9):
X 1 ˜ X 2 + X 1 ˜ X 2 + X 1 ˜ X 2 = X 1 ( X 2 + X 2 )+ X 1 ˜ X 2 = X 2 ˜1+ X 1 ˜ X 2 = X 1 + X 1 X 2
Ɉɛɨɡɧɚɱɢɦ X 1 = Ⱥ ɢ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɨɠɞɟɫɬɜɨɦ (12), (13):
Ⱥ+ A ˜ X =A+ X 2 = X 1 + X 2 = X 1 ˜ X 2
ɉɨɥɭɱɢɥɨɫɶ, ɱɬɨ ɜɵɪɚɠɟɧɢɟ (1) ɪɟɚɥɢɡɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɨɞɧɨɝɨ ɷɥɟɦɟɧɬɚ ɂ-ɇȿ. ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ
ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɫɬɪɟɦɹɬɫɹ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɝɪɚɧɢɱɟɧɧɭɸ ɧɨɦɟɧɤɥɚɬɭɪɭ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ. ȼ ɱɚɫɬɧɨɫɬɢ ɥɸɛɨɟ
ɭɫɬɪɨɣɫɬɜɨ ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧɨ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɧɚ ɷɥɟɦɟɧɬɚɯ "ɂ-ɇȿ" (ɢɥɢ "ɂɅɂ/ɇȿ"). Ɍɚɤ ɨɩɟɪɚɰɢɹ "ɇȿ" ɦɨɠɟɬ
ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧɚ ɷɥɟɦɟɧɬɨɦ "ɂ-ɇȿ", ɜ ɤɨɬɨɪɨɦ ɧɚ ɤɚɠɞɨɦ ɢɡ ɜɯɨɞɨɜ ɩɟɪɟɦɟɧɧɚɹ X. Ɍɨɝɞɚ ɭ =
ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ.4ɚ. Ɉɩɟɪɚɰɢɹ "ɂɅɂ" ɪɟɚɥɢɡɭɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: X 1
ɭɫɬɪɨɣɫɬɜɚ - ɧɚ ɪɢɫ.4ɛ. Ɉɩɟɪɚɰɢɹ "ɂ" ɪɟɚɥɢɡɭɟɬɫɹ: ɏ1˜ɏ2 =
x
&
x
ɚ) Ɉɩɟɪɚɰɢɹ "ɇȿ"
&
x1
x2
&
x2
X1X2
X 1 ˜ X 2 . ɋɯɟɦɚ
X 1 ˜ X 2 . ɂɫɩɨɥɶɡɨɜɚɧɨ ɬɨɠɞɟɫɬɜɨ (10). ɋɯɟɦɚ – ɪɢɫ.4ɜ.
x1
x1
X2
X ˜ X = X . ɋɯɟɦɚ
& x x =x +x x2
1 2
1 2
&
&
x1 x2
x1 x2
ɜ) Ɉɩɟɪɚɰɢɹ "ɂ"
ɛ) Ɉɩɟɪɚɰɢɹ "ɂɅɂ"
Ɋɢɫ.4 Ɋɟɚɥɢɡɚɰɢɹ ɪɚɡɥɢɱɧɵɯ ɮɭɧɤɰɢɣ ɧɚ ɷɥɟɦɟɧɬɚɯ ɂ-ɇȿ
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɯɨɞɧɨɣ ɫɢɝɧɚɥ ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɥɨɝɢɱɟɫɤɢɦ ɷɥɟɦɟɧɬɨɦ ɧɚ ɭɪɨɜɧɟ 0 ɬɨɥɶɤɨ ɜ ɬɨɦ
ɫɥɭɱɚɟ, ɟɫɥɢ ɩɪɨɬɟɤɚɟɬ ɬɨɤ ɫ ɜɯɨɞɚ Ɇɋ ɜɨ ɜɧɟɲɧɸɸ ɰɟɩɶ. ȿɫɥɢ ɤ ɜɯɨɞɭ ɧɢɱɟɝɨ ɧɟ ɩɨɞɤɥɸɱɟɧɨ ("ɜɢɫɢɬ ɜ ɜɨɡɞɭɯɟ"), ɧɟɬ
ɩɭɬɢ ɞɥɹ ɩɪɨɬɟɤɚɧɢɹ ɬɨɤɚ ɱɟɪɟɡ ɜɯɨɞ ɢ ɞɚɧɧɨɟ ɩɨɥɨɠɟɧɢɟ ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɬɚɤɠɟ, ɤɚɤ ɟɫɥɢ ɛɵ ɧɚ ɜɯɨɞ ɛɵɥ ɩɨɞɚɧ
ɫɢɝɧɚɥ 1. ɋɯɟɦɚ ɜɧɭɬɪɟɧɧɢɯ ɷɥɟɦɟɧɬɨɜ ɥɨɝɢɱɟɫɤɨɣ ɹɱɟɣɤɢ ɂ-ɇȿ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ.5.
R1
+ȿɩ
V1
x1
x2
x3
V3
V2
y
V4
Ɋɢɫ.5 Ʌɨɝɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ "ɂ-ɇȿ" ɌɌɅ-ɥɨɝɢɤɢ
2. ɌɊɂȽȽȿɊɕ
Ɍɪɢɝɝɟɪɨɦ ɧɚɡɵɜɚɟɬɫɹ ɭɫɬɪɨɣɫɬɜɨ, ɢɦɟɸɳɟɟ ɞɜɚ ɭɫɬɨɣɱɢɜɵɯ ɫɨɫɬɨɹɧɢɹ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɢɯ
ɜɨɡɞɟɣɫɬɜɢɣ ɬɪɢɝɝɟɪ ɦɨɠɟɬ ɫɤɨɥɶ ɭɝɨɞɧɨ ɧɚɯɨɞɢɬɶɫɹ ɜ ɨɞɧɨɦ ɢɡ ɭɫɬɨɣɱɢɜɵɯ ɫɨɫɬɨɹɧɢɣ. ȼɯɨɞɧɨɣ ɫɢɝɧɚɥ ɦɨɠɟɬ
ɩɟɪɟɜɟɫɬɢ ɬɪɢɝɝɟɪ ɢɡ ɨɞɧɨɝɨ ɭɫɬɨɣɱɢɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ. Ɍɪɢɝɝɟɪɵ ɦɨɝɭɬ ɜɵɩɨɥɧɹɬɶ ɮɭɧɤɰɢɢ ɪɟɥɟ, ɩɟɪɟɤɥɸɱɚɬɟɥɟɣ, ɷɥɟɦɟɧɬɨɜ ɩɚɦɹɬɢ. Ɉɛɵɱɧɨ ɬɪɢɝɝɟɪɵ ɢɦɟɸɬ ɨɞɢɧ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɭɩɪɚɜɥɹɸɳɢɯ ɜɯɨɞɨɜ ɢ ɞɜɚ ɜɵɯɨɞɚ: ɨɫɧɨɜɧɨɣ (
Q ) ɢ ɢɧɜɟɪɫɧɵɣ ( Q ).
Ɍɪɢɝɝɟɪɵ ɦɨɝɭɬ ɛɵɬɶ ɚɫɢɧɯɪɨɧɧɵɦɢ ɢ ɫɢɧɯɪɨɧɧɵɦɢ (ɬɚɤɬɢɪɭɟɦɵɦɢ). ȼ ɚɫɢɧɯɪɨɧɧɨɦ ɬɪɢɝɝɟɪɟ ɢɧɮɨɪɦɚɰɢɹ
ɧɚ ɜɵɯɨɞɟ ɢɡɦɟɧɹɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɜɯɨɞɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. ȼ ɫɢɧɯɪɨɧɧɵɯ - ɬɨɥɶɤɨ ɜ ɦɨɦɟɧɬɵ ɞɟɣɫɬɜɢɹ
ɬɚɤɬɨɜɨɝɨ (ɫɢɧɯɪɨɧɢɡɢɪɭɸɳɟɝɨ) ɢɦɩɭɥɶɫɚ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ ɫɨɫɬɨɹɧɢɟ ɬɪɢɝɝɟɪɚ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɵɦ ɧɟɫɦɨɬɪɹ ɧɚ ɢɡɦɟɧɟɧɢɟ ɢɧɮɨɪɦɚɰɢɢ ɧɚ ɜɯɨɞɟ.
Ɍɪɢɝɝɟɪɵ ɜɵɩɨɥɧɹɸɬɫɹ ɧɚ ɨɬɞɟɥɶɧɵɯ ɫɬɚɧɞɚɪɬɧɵɯ (ɛɚɡɨɜɵɯ) ɢɧɬɟɝɪɚɥɶɧɵɯ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɚɯ ɨɞɧɨɣ ɢ
ɬɨɣ ɠɟ ɫɟɪɢɢ. ɉɨ ɷɬɨɦɭ ɩɪɢɧɰɢɩɭ ɨɛɵɱɧɨ ɫɬɪɨɹɬ RS -ɬɪɢɝɝɟɪɵ ɢ ɩɪɨɫɬɵɟ D - ɬɪɢɝɝɟɪɵ. Ȼɨɥɟɟ ɫɥɨɠɧɵɟ JɄ- ɬɪɢɝɝɟɪɵ,
Ɍ-ɬɪɢɝɝɟɪɵ ɢɡɝɨɬɨɜɥɹɸɬ ɜ ɜɢɞɟ ɨɬɞɟɥɶɧɨɣ Ɇɋ, ɜɤɥɸɱɚɸɳɟɣ ɜ ɫɟɛɹ ɨɬ ɨɞɧɨɝɨ ɞɨ ɱɟɬɵɪɟɯ ɨɬɞɟɥɶɧɵɯ ɬɪɢɝɝɟɪɨɜ.
2.1. Ⱥɫɢɧɯɪɨɧɧɵɣ RS-ɬɪɢɝɝɟɪ
Ɂɚɤɨɧ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ RS -ɬɪɢɝɝɟɪɚ ɩɨɹɫɧɹɟɬɫɹ ɬɚɛɥɢɰɟɣ ɢɫɬɢɧɧɨɫɬɢ (ɬɚɛɥ.2). S ɢ R - ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ
ɫɢɝɧɚɥɵ ɧɚ ɜɯɨɞɚɯ ɬɪɢɝɝɟɪɚ. ɋɨɤɪɚɳɟɧɢɹ ɞɚɧɵ ɨɬ ɫɥɨɜ S ( set - ɭɫɬɚɧɨɜɤɚ) ɢ R(reset - ɫɛɪɨɫ). Qn - ɜɵɯɨɞɧɨɣ
ɥɨɝɢɱɟɫɤɢɣ ɫɢɝɧɚɥ ɞɨ ɩɨɫɬɭɩɥɟɧɢɹ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ, Qn+1- ɬɨ ɠɟ ɩɨɫɥɟ ɜɨɡɞɟɣɫɬɜɢɹ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ.
Ɍɚɛɥɢɰɚ 2
Ɍɚɛɥɢɰɚ ɢɫɬɢɧɧɨɫɬɢ R-S ɬɪɢɝɝɟɪɚ
S
R
Qn+1
0
0
Qn
0
1
0
1
0
1
1
1
ɇɟɨɩɪɟɞɟɥɺɧɧɨɫɬɶ
ɉɪɢ ɩɨɞɚɱɟ ɫɢɝɧɚɥɚ 1 ɧɚ ɜɯɨɞ S(set - ɭɫɬɚɧɨɜɤɚ "ɜɤɥɸɱɢɬɶ") ɬɪɢɝɝɟɪ ɩɟɪɟɯɨɞɢɬ ɜ ɫɨɫɬɨɹɧɢɟ Qn+1 = 1. ɉɪɢ
ɩɨɫɬɭɩɥɟɧɢɢ 1 ɧɚ ɜɯɨɞ R (reset - ɫɛɪɨɫ, "ɨɬɤɥɸɱɢɬɶ") ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ Qn+1 = 0. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɬɪɢɝɝɟɪ ɹɜɥɹɟɬɫɹ
ɚɧɚɥɨɝɨɦ ɪɟɥɟ. ɇɚɪɹɞɭ ɫ ɷɬɢɦ ɨɧ ɫɥɭɠɢɬ ɷɥɟɦɟɧɬɨɦ ɩɚɦɹɬɢ, ɬ.ɟ. ɫɨɯɪɚɧɹɟɬ ɢɧɮɨɪɦɚɰɢɸ ɨ ɩɨɫɥɟɞɧɟɣ ɢɡ ɩɨɫɬɭɩɢɜɲɢɯ
ɤɨɦɚɧɞ ɢ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɧɨɜɵɯ ɤɨɦɚɧɞ ɧɚ ɜɯɨɞɚɯ. ɉɪɢ S=R=0 ɫɨɫɬɨɹɧɢɟ ɬɪɢɝɝɟɪɚ ɧɟ ɦɟɧɹɟɬɫɹ. ɋɨɜɩɚɞɟɧɢɟ ɤɨɦɚɧɞ S
= R= 1 ("ɜɤɥɸɱɢɬɶ" - "ɨɬɤɥɸɱɢɬɶ") ɧɟɞɨɩɭɫɬɢɦɨ. ɉɪɢ ɬɚɤɨɦ ɫɨɱɟɬɚɧɢɢ ɜɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ ɫɨɫɬɨɹɧɢɟ ɜɵɯɨɞɚ
R
S
R T
S
Q
S
Q
R
Ɋɢɫ.6 Ɉɛɨɡɧɚɱɟɧɢɟ
RS - ɬɪɢɝɝɟɪɚ.
Q
Q
Ɋɢɫ.7 ȼɪɟɦɟɧɧɚɹ
ɞɢɚɝɪɚɦɦɚ RS - ɬɪɢɝɝɟɪɚ.
S
&
S
&
Q
R
&
R
&
Q
Ɋɢɫ.8 Ɋɟɚɥɢɡɚɰɢɹ RS -ɬɪɢɝɝɟɪɚ ɧɚ ɷɥɟɦɟɧɬɚɯ ɂ - ɇȿ.
ɧɟɨɩɪɟɞɟɥɟɧɧɨ ɢ ɷɬɨ ɫɨɱɟɬɚɧɢɟ ɧɟ ɢɫɩɨɥɶɡɭɟɬɫɹ.
ɇɚ ɪɢɫ.6 ɩɪɢɜɟɞɟɧɨ ɨɛɨɡɧɚɱɟɧɢɟ Ɋ-ɬɪɢɝɝɟɪɚ, ɚ ɧɚ ɪɢɫ.7 ɜɪɟɦɟɧɧɵɟ ɞɢɚɝɪɚɦɦɵ, ɢɥɥɸɫɬɪɢɪɭɸɳɢɟ ɟɝɨ ɪɚɛɨɬɭ.
ɇɚ ɪɢɫ.8 ɩɨɤɚɡɚɧɚ ɪɟɚɥɢɡɚɰɢɹ RS -ɬɪɢɝɝɟɪɚ ɧɚ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɚɯ ɂ-ɇȿ. Ɉɫɨɛɟɧɧɨɫɬɶɸ ɬɪɢɝɝɟɪɚ ɹɜɥɹɸɬɫɹ
ɨɛɪɚɬɧɵɟ ɫɜɹɡɢ, ɩɨɡɜɨɥɹɸɳɢɟ ɭɱɢɬɵɜɚɬɶ ɩɪɟɞɵɞɭɳɟɟ ɫɨɫɬɨɹɧɢɟ.
RS -ɬɪɢɝɝɟɪ ɦɨɠɟɬ ɢɦɟɬɶ ɢɧɜɟɪɫɧɵɟ ɜɯɨɞɵ R ɢ S. Ɍɚɤɨɣ ɬɪɢɝɝɟɪ ɡɚɩɭɫɤɚɟɬɫɹ ɩɟɪɟɯɨɞɨɦ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ
ɫɢɝɧɚɥɚ ɨɬ 1 ɤ 0 (ɧɢɡɤɢɣ ɚɤɬɢɜɧɵɣ ɭɪɨɜɟɧɶ).
ȼ ɪɹɞɟ ɫɟɪɢɣ ɐɂɆɋ ɢɦɟɸɬɫɹ ɝɨɬɨɜɵɟ ɫɯɟɦɵ RS ɬɪɢɝɝɟɪɨɜ.
2.2. ɋɢɧɯɪɨɧɧɵɣ
JɄ – ɬɪɢɝɝɟɪ
ȼ ɨɬɥɢɱɢɟ ɨɬ ɚɫɢɧɯɪɨɧɧɨɝɨ ɬɪɢɝɝɟɪɚ, ɤɨɬɨɪɵɣ ɩɟɪɟɤɥɸɱɚɟɬɫɹ ɦɝɧɨɜɟɧɧɨ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ,
ɫɢɧɯɪɨɧɧɵɣ ɬɪɢɝɝɟɪ ɜɨɫɩɪɢɧɢɦɚɟɬ ɢɧɮɨɪɦɚɰɢɸ ɬɨɥɶɤɨ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɦ (ɨɬ 0 ɤ 1) ɩɟɪɟɯɨɞɟ ɢɦɩɭɥɶɫɨɜ ɧɚ
ɬɚɤɬɨɜɨɦ ɜɯɨɞɟ ɢ ɩɟɪɟɯɨɞɢɬ ɜ ɧɨɜɨɟ ɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ ɜ ɦɨɦɟɧɬ ɫɪɟɡɚ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ (ɬɪɢɝɝɟɪ ɹɜɥɹɟɬɫɹ
ɞɜɭɯɫɬɭɩɟɧɱɚɬɵɦ). Ɍɚɤɚɹ ɨɫɨɛɟɧɧɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɫɢɧɯɪɨɧɢɡɢɪɨɜɚɬɶ ɜɨ ɜɪɟɦɟɧɢ ɢɡɦɟɧɟɧɢɟ ɫɨɫɬɨɹɧɢɹ ɦɧɨɝɢɯ ɹɱɟɟɤ
ɨɞɧɨɝɨ ɭɫɬɪɨɣɫɬɜɚ ɬɟɦ ɫɚɦɵɦ ɢɫɤɥɸɱɚɹ ɟɝɨ ɧɟɩɪɟɞɭɫɦɨɬɪɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ. ɇɚɡɧɚɱɟɧɢɟ ɜɯɨɞɨɜ Ʉ ɢ J ɚɧɚɥɨɝɢɱɧɵ R ɢ
S (ɫɛɪɨɫ ɢ ɭɫɬɚɧɨɜɤɚ). Ɇɢɤɪɨɫɯɟɦɚ Ʉ155Ɍȼ1 ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɢɧɯɪɨɧɧɵɣ
JɄ-ɬɪɢɝɝɟɪ ɫ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦɢ
ɚɫɢɧɯɪɨɧɧɵɦɢ ɭɫɬɚɧɨɜɨɱɧɵɦɢ ɢɧɜɟɪɫɧɵɦɢ ɜɯɨɞɚɦɢ R ɢ S . ɋɯɟɦɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ.9, ɜɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɧɚ
ɪɢɫ. 10, ɚ ɬɚɛɥɢɰɚ ɢɫɬɢɧɧɨɫɬɢ - ɬɚɛɥ. 3.
1 2
113
3
3
4
5
112
2
9
10
111
1
2
3 4 5
6 7 8 9 10 11
C
R
T
J1
6
Q
J
J2
t1 t2
K
J3
Q
C
K1
K2
K3
Q
8
Q
S
Ɋɢɫ.10 ȼɪɟɦɟɧɧɚɹ
Ɋɢɫ.9 JK - ɬɪɢɝɝɟɪ
ɞɢɚɝɪɚɦɦɚ ɍɄ - ɬɪɢɝɝɟɪɚ
Ʉ 155 Ɍȼ 1.
Ʉ 155 Ɍȼ 1.
Ɍɚɛɥɢɰɚ 3
Ɍɚɛɥɢɰɚ ɢɫɬɢɧɧɨɫɬɢ JɄ-ɬɪɢɝɝɟɪɚ Ʉ155Ɍȼ1
Ɋɟɠɢɦ ɪɚɛɨɬɵ
ȼɯɨɞ
ȼɵɯɨɞ
S
R
C
J
K
Q
Q
Ⱥɫɢɧɯɪɨɧɧɚɹ ɭɫɬɚɧɨɜɤɚ
0
1
H
H
H
1
0
Ⱥɫɢɧɯɪɨɧɧɵɣ ɫɛɪɨɫ
1
0
H
H
H
0
1
ɇɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ
0
0
H
H
H
1
1
ɉɟɪɟɤɥɸɱɟɧɢɟ
1
1
1
1
Q n-1
Q n-1
Ɂɚɝɪɭɡɤɚ 1 (ɭɫɬɚɧɨɜɤɚ)
1
1
0
1
1
0
Ɂɚɝɪɭɡɤɚ 0 ( ɫɛɪɨɫ)
1
1
1
0
0
1
ɏɪɚɧɟɧɢɟ (ɧɟɬ ɢɡɦɟɧɟɧɢɣ)
1
1
0
0
Q n-1
Q n-1
ȼ ɬɚɛɥ.3 ɇ - ɧɟɨɩɪɟɞɟɥɟɧɧɨɟ (ɥɸɛɨɟ) ɫɨɫɬɨɹɧɢɟ. ɂɧɮɨɪɦɚɰɢɸ ɦɨɠɧɨ ɡɚɝɪɭɠɚɬɶ ɨɬ ɜɯɨɞɨɜ
ɡɚɞɟɪɠɢɜɚɬɶ ɟɟ ɬɨɥɶɤɨ ɩɪɢ R = S = 1. ȿɫɥɢ R = S =0 ɫɨɫɬɨɹɧɢɟ
J ɢ Ʉ ɢɥɢ
Q ɢ Q ɧɟɨɩɪɟɞɟɥɟɧɧɨɟ. ɂɡ ɜɪɟɦɟɧɧɨɣ ɞɢɚɝɪɚɦɦɵ
ɪɢɫ.10 ɜɢɞɧɨ, ɱɬɨ ɧɚ ɢɧɬɟɪɜɚɥɟ ɜɪɟɦɟɧɢ (ɨɬɫɭɬɫɬɜɢɟ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ) ɢɧɮɨɪɦɚɰɢɹ ɩɨ ɜɯɨɞɚɦ
J ɢ Ʉ ɧɟ
ɜɨɫɩɪɢɧɢɦɚɟɬɫɹ ɢ ɫɨɫɬɨɹɧɢɟ ɬɪɢɝɝɟɪɚ ɧɟ ɦɟɧɹɟɬɫɹ.
2.3. ɋɱɟɬɧɵɣ Ɍ-ɬɪɢɝɝɟɪ
ɗɬɨɬ ɬɪɢɝɝɟɪ ɩɨɥɭɱɚɟɬɫɹ ɢɡ JɄ/ɬɪɢɝɝɟɪɚ ɩɭɬɟɦ ɩɪɢɫɨɟɞɢɧɟɧɢɹ J ɢ Ʉ ɜɯɨɞɨɜ ɤ ɩɨɬɟɧɰɢɚɥɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦɭ
ɥɨɝɢɱɟɫɤɨɣ 1 (ɦɨɠɧɨ ɨɫɬɚɜɢɬɶ ɢɯ "ɜɢɫɹɳɢɦɢ ɜ ɜɨɡɞɭɯɟ"). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɨɫɬɚɥɫɹ ɬɨɥɶɤɨ ɨɞɢɧ ɬɚɤɬɨɜɵɣ ɜɯɨɞ - Ɍ. ȼ
ɦɨɦɟɧɬ ɫɪɟɡɚ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ ɬɪɢɝɝɟɪ ɩɟɪɟɤɥɸɱɚɟɬɫɹ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨɟ ɫɨɫɬɨɹɧɢɟ. Ɉɛɨɡɧɚɱɟɧɢɟ Ɍ-ɬɪɢɝɝɟɪɚ
ɩɪɢɜɟɞɟɧɨ ɧɚ ɪɢɫ. II, ɚ ɜɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɧɚ ɪɢɫ. 12. ɂɡ ɞɢɚɝɪɚɦɦɵ ɜɢɞɧɨ, ɱɬɨ ɱɚɫɬɨɬɚ ɩɨɜɬɨɪɟɧɢɹ ɫɢɝɧɚɥɚ Q ɜ 2
ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɫɢɝɧɚɥɚ Ɍ, ɬ.ɟ. Ɍ-ɬɪɢɝɝɟɪ ɞɟɥɢɬ ɱɚɫɬɨɬɭ ɢɦɩɭɥɶɫɨɜ ɧɚ 2. Ɍ-ɬɪɢɝɝɟɪ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɞɟɥɢɬɟɥɹɯ
ɱɚɫɬɨɬɵ, ɫɱɟɬɱɢɤɚɯ ɢ ɞɪ.
T
T
Q
T
Q
Q
T
Ɋɢɫ.11 ɋɱɟɬɧɵɣ Ɍ ɬɪɢɝɝɟɪ.
Ɋɢɫ.12 ȼɪɟɦɟɧɧɚɹ
ɞɢɚɝɪɚɦɦɚ Ɍ - ɬɪɢɝɝɟɪɚ.
2.4.
D-ɬɪɢɝɝɟɪ
Ⱦ - ɬɪɢɝɝɟɪ ɢɥɢ ɬɪɢɝɝɟɪ ɡɚɞɟɪɠɤɢ (delay) ɩɟɪɟɞɚɟɬ ɧɚ ɜɵɯɨɞ ɢɧɮɨɪɦɚɰɢɸ, ɩɨɫɬɭɩɚɸɳɭɸ ɧɚ ɜɯɨɞ ɩɪɢ
ɩɨɹɜɥɟɧɢɢ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ, ɩɨɷɬɨɦɭ ɦɨɦɟɧɬ ɫɦɟɧɵ ɜɵɯɨɞɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɧɟɫɤɨɥɶɤɨ ɡɚɞɟɪɠɢɜɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɦɨɦɟɧɬɚ ɫɦɟɧɵ ɜɯɨɞɧɨɣ ɢɧɮɨɪɦɚɰɢɢ. Ʌɨɝɢɤɚ ɪɚɛɨɬɵ Ⱦ-ɬɪɢɝɝɟɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ Qt+1=D. Ⱦ - ɬɪɢɝɝɟɪ
ɩɨɦɢɦɨ ɬɚɤɬɨɜɨɝɨ ɜɯɨɞɚ ɢɦɟɟɬ ɬɨɥɶɤɨ ɨɞɢɧ ɜɯɨɞ Ⱦ=J= K . ɋɢɝɧɚɥ ɧɚ ɜɯɨɞɟ Ⱦ ɡɚɩɨɦɢɧɚɟɬɫɹ ɜ ɦɨɦɟɧɬ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ ɢ ɯɪɚɧɢɬɫɹ ɞɨ ɫɥɟɞɭɸɳɟɝɨ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ. ɉɨɷɬɨɦɭ Ⱦ-ɬɪɢɝɝɟɪ ɹɜɥɹɟɬɫɹ ɷɥɟɦɟɧɬɨɦ ɩɚɦɹɬɢ, ɧɚɯɨɞɢɬ
ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɪɟɝɢɫɬɪɚɯ.
Ɇɢɤɪɨɫɯɟɦɚ Ʉ155ɌɆ2 ɫɨɞɟɪɠɢɬ ɜ ɤɨɪɩɭɫɟ ɞɜɚ Ⱦ-ɬɪɢɝɝɟɪɚ. Ɉɛɨɡɧɚɱɟɧɢɟ ɧɚ. ɪɢɫ.1Ɂ, ɬɚɛɥɢɰɚ ɢɫɬɢɧɧɨɫɬɢ ɬɚɛɥ.4, ɜɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ - ɪɢɫ. 14.
1
2
3
4
13
12
11
10
R
T
D
C
S
R
D
C
S
T
5
Q
6
Q
9
Q
8
Q
C
D
Q
Ɋɢɫ.13 Ⱦɜɚ D - ɬɪɢɝɝɟɪɚ
Ʉ 155 ɌɆ 1.
Ɋɢɫ.14 ȼɪɟɦɟɧɧɚɹ
ɞɢɚɝɪɚɦɦɚ D - ɬɪɢɝɝɟɪɚ.
Ɍɚɛɥɢɰɚ 4
Ɍɚɛɥɢɰɚ ɢɫɬɢɧɧɨɫɬɢ Ⱦ-ɬɪɢɝɝɟɪɚ Ʉ155ɌɆ2
Ɋɟɠɢɦ ɪɚɛɨɬɵ
ȼɯɨɞ
ȼɵɯɨɞ
S
R
ɋ
D
Q
Q
Ⱥɫɢɧɯɪɨɧɧɚɹ ɭɫɬɚɧɨɜɤɚ
0
1
H
H
1
0
Ⱥɫɢɧɯɪɨɧɧɵɣ ɫɛɪɨɫ
1
0
H
H
0
1
ɇɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ
0
0
H
H
1
1
Ɂɚɝɪɭɡɤɚ 1 (ɭɫɬɚɧɨɜɤɚ)
1
1
1
1
0
Ɂɚɝɪɭɡɤɚ 0 (ɫɛɪɨɫ)
1
1
0
0
1
Ɉɛɨɡɧɚɱɟɧɢɟ: ɇ - ɧɟɨɩɪɟɞɟɥɟɧɧɨɟ (ɥɸɛɨɟ) ɫɨɫɬɨɹɧɢɟ,
- ɮɪɨɧɬ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ.
ȼɯɨɞɵ S ɢ R - ɚɫɢɧɯɪɨɧɧɵɟ ɭɫɬɚɧɨɜɨɱɧɵɟ ɫ ɧɢɡɤɢɦ ɚɤɬɢɜɧɵɦ ɭɪɨɜɧɟɦ. ɋɛɪɚɫɵɜɚɸɬ ɫɨɫɬɨɹɧɢɟ ɬɪɢɝɝɟɪɚ
ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɫɢɝɧɚɥɚ ɧɚ ɬɚɤɬɨɜɨɦ ɜɯɨɞɟ. ȿɫɥɢ ɫɨɫɬɨɹɧɢɟ S = R = 0, ɫɨɫɬɨɹɧɢɟ Q ɢ Q ɧɟɨɩɪɟɞɟɥɟɧɧɨ. ɂɧɮɨɪɦɚɰɢɹ
ɧɚ ɜɵɯɨɞ Q ɢ Q ɩɪɢ ɧɚɥɢɱɢɢ ɜɯɨɞɧɨɝɨ Ⱦ ɢ ɬɚɤɬɨɜɨɝɨ ɋ ɫɢɝɧɚɥɚ ɩɟɪɟɞɚɟɬɫɹ ɬɨɥɶɤɨ ɩɪɢ S = R =1. ɋɢɝɧɚɥ Ⱦ ɩɟɪɟɞɚɟɬɫɹ
ɧɚ ɜɵɯɨɞɵ Q ɢ Q ɩɨ ɮɪɨɧɬɭ ɬɚɤɬɨɜɨɝɨ ɢɦɩɭɥɶɫɚ.
3. ɆɍɅɖɌɂȼɂȻɊȺɌɈɊɕ
ȿɫɥɢ ɜ ɬɪɢɝɝɟɪɟ ɪɢɫ.8 ɨɞɧɭ ɢɥɢ ɨɛɟ ɨɛɪɚɬɧɵɟ ɫɜɹɡɢ ɡɚɦɟɧɢɬɶ ɟɦɤɨɫɬɧɵɦɢ, ɬɨ ɨɞɧɨ ɢɥɢ ɨɛɚ ɭɫɬɨɣɱɢɜɵɯ
(ɫɬɚɬɢɱɟɫɤɢɯ) ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɧɟɭɫɬɨɣɱɢɜɨɟ, ɞɥɢɬɟɥɶɧɨɫɬɶ ɤɨɬɨɪɵɯ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ
ɩɪɨɰɟɫɫɚɦɢ ɪɟɥɚɤɫɚɰɢɢ ɡɚɪɹɞɨɦ ɢɥɢ ɪɚɡɪɹɞɨɦ ɤɨɧɞɟɧɫɚɬɨɪɨɜ ɜ ɰɟɩɹɯ ɫɜɹɡɢ. Ɍ.ɤ. ɷɬɢ ɧɟɭɫɬɨɣɱɢɜɵɟ ɫɨɫɬɨɹɧɢɹ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɟɞɥɟɧɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ ɬɨɤɨɜ ɢ ɧɚɩɪɹɠɟɧɢɣ, ɢɯ ɧɚɡɵɜɚɸɬ ɜɪɟɦɟɧɧɨ ɧɟɭɫɬɨɣɱɢɜɵɦɢ
(ɤɜɚɡɢɫɬɚɬɢɱɟɫɤɢɦɢ). Ƚɟɧɟɪɚɬɨɪɵ ɢɦɩɭɥɶɫɨɜ ɫ ɪɟɡɢɫɬɢɜɧɨ-ɟɦɤɨɫɬɧɵɦɢ ɦɟɠɤɚɫɤɚɞɧɵɦɢ ɫɜɹɡɹɦɢ, ɨɛɥɚɞɚɸɳɢɟ ɨɞɧɢɦ
ɢɥɢ ɧɟɫɤɨɥɶɤɢɦɢ ɤɜɚɡɢɫɬɚɬɢɱɟɫɤɢɦɢ ɫɨɫɬɨɹɧɢɹɦɢ ɧɚɡɵɜɚɸɬɫɹ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪɚɦɢ (Ɇȼ). Ɇȼ ɦɨɝɭɬ ɪɚɛɨɬɚɬɶ ɜ
ɫɥɟɞɭɸɳɢɯ ɪɟɠɢɦɚɯ: ɠɞɭɳɟɦ, ɚɜɬɨɤɨɥɟɛɚɬɟɥɶɧɨɦ. ȼ ɠɞɭɳɟɦ ɪɟɠɢɦɟ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ (ɠɞɭɳɢɣ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ
(ɀɆ), ɡɚɬɨɪɦɨɠɟɧɧɵɣ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ, ɨɞɧɨ ɜɢɛɪɚɬɨɪ (ɈȾ)- ɷɬɨ ɜɫɟ ɫɢɧɨɧɢɦɵ) ɨɛɥɚɞɚɟɬ ɨɞɧɢɦ ɞɥɢɬɟɥɶɧɨ ɭɫɬɨɣɱɢɜɵɦ ɫɨɫɬɨɹɧɢɟɦ ɪɚɜɧɨɜɟɫɢɹ, ɜ ɤɨɬɨɪɨɦ ɨɧ ɧɚɯɨɞɢɬɫɹ ɞɨ ɩɨɞɚɱɢ ɡɚɩɭɫɤɚɸɳɟɝɨ ɢɦɩɭɥɶɫɚ. ȼɬɨɪɨɟ ɜɨɡɦɨɠɧɨɟ
ɫɨɫɬɨɹɧɢɟ ɹɜɥɹɟɬɫɹ ɜɪɟɦɟɧɧɨ ɭɫɬɨɣɱɢɜɵɦ. ȼ ɷɬɨ ɫɨɫɬɨɹɧɢɟ Ɇȼ ɩɟɪɟɯɨɞɢɬ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɡɚɩɭɫɤɚɸɳɟɝɨ ɢɦɩɭɥɶɫɚ ɢ
ɧɚɯɨɞɢɬɫɹ ɜ ɧɟɦ ɤɨɧɟɱɧɨɟ ɜɪɟɦɹ W , ɩɨɫɥɟ ɱɟɝɨ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɢɫɯɨɞɧɨɟ.
ȼ ɪɟɠɢɦɟ ɚɜɬɨɤɨɥɟɛɚɬɟɥɶɧɨɦ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ (ɱɚɫɬɨ ɩɨɞ ɩɨɧɹɬɢɟɦ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪɚ ɩɨɧɢɦɚɟɬɫɹ ɢɦɟɧɧɨ ɷɬɨɬ
ɪɟɠɢɦ) ɨɛɥɚɞɚɟɬ ɞɜɭɦɹ ɜɪɟɦɟɧɧɨ ɭɫɬɨɣɱɢɜɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ, ɤɨɬɨɪɵɟ ɩɟɪɢɨɞɢɱɟɫɤɢ ɱɟɪɟɞɭɸɬɫɹ. ɉɟɪɢɨɞ ɤɨɥɟɛɚɧɢɣ
Ɍ=W01+W02, ɝɞɟW01 ɢ W02- ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ ɜ ɩɟɪɜɨɦ ɢ ɜɬɨɪɨɦ ɧɟɭɫɬɨɣɱɢɜɵɯ ɫɨɫɬɨɹɧɢɹɯ.
Ɇȼ ɦɨɠɧɨ ɪɟɚɥɢɡɨɜɚɬɶ ɧɚ ɬɪɚɧɡɢɫɬɨɪɚɯ, ɨɩɟɪɚɰɢɨɧɧɵɯ ɭɫɢɥɢɬɟɥɹɯ, ɐɂɆɋ.
3.1. ɀɞɭɳɢɣ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ
ɋɯɟɦɭ ɀɆ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ ɫɯɟɦɵ RS -ɬɪɢɝɝɟɪɚ (ɪɢɫ.8), ɡɚɦɟɧɢɜ ɨɞɧɭ ɢɡ ɞɜɭɯ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɯ ɫɜɹɡɟɣ
ɟɦɤɨɫɬɧɨɣ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 15. Ɂɚɩɭɫɤɚɸɳɢɟ ɢɦɩɭɥɶɫɵ ɧɢɡɤɨɝɨ ɭɪɨɜɧɹ ɩɨɞɚɸɬɫɹ ɧɚ ɫɜɨɛɨɞɧɵɣ ɜɯɨɞ Ⱦ1. ȼ
ɢɫɯɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ Ⱦ2 ɢɦɟɟɬ ɧɚ ɜɵɯɨɞɟ 1, ɬ.ɟ. ɱɟɪɟɡ R ɩɪɨɬɟɤɚɟɬ ɜɯɨɞɧɨɣ ɬɨɤ ɫ ɜɯɨɞɚ. Ⱦ2. ɇɚ ɜɵɯɨɞɟ Ⱦ1 ɩɪɢɫɭɬɫɬɜɭɟɬ
0, ɬ.ɤ. ɩɨ ɨɛɨɢɦ ɜɯɨɞɚɦ ɩɨɞɚɟɬɫɹ 1. ɉɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɡɚɩɭɫɤɚɸɳɟɝɨ ɢɦɩɭɥɶɫɚ ɧɚ ɜɵɯɨɞɟ Ⱦ1 ɩɨɹɜɥɹɟɬɫɹ 1,
ɤɨɧɞɟɧɫɚɬɨɪ ɋ ɧɚɱɢɧɚɟɬ ɡɚɪɹɠɚɬɶɫɹ ɱɟɪɟɡ ɜɵɯɨɞ Ⱦ1 ɢ R. ɇɚɩɪɹɠɟɧɢɟ UBX.D2
ɩɨ ɦɟɪɟ ɡɚɪɹɞɚ ɤɨɧɞɟɧɫɚɬɨɪɚ
ɭɦɟɧɶɲɚɟɬɫɹ ( ɫɦ. ɪɢɫ. 16).
ɉɪɢ ɞɨɫɬɢɠɟɧɢɢ UBX.D2 ɡɧɚɱɟɧɢɹ U0BX. (ɭɪɨɜɟɧɶ ɧɚɩɪɹɠɟɧɢɹ ɥɨɝɢɱɟɫɤɨɝɨ ɧɭɥɹ) UBɕX.D2 ɫɤɚɱɤɨɦ ɩɟɪɟɯɨɞɢɬ ɧɚ
Uɜɯ
Uɜɯ
&
Uɜɵɯ
C
Uɜɯ2
R
&
Ɋɢɫ.15 ɀɞɭɳɢɣ
ɦɭɥɶɬɢɜɢɛɪɚɬɨɪ
ɧɚ ɛɚɡɟ RS ɬɪɢɝɝɟɪɚ.
Uɜɯ2
1
Uɜɯ
W
Ɋɢɫ.16 ȼɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ
ɀɆ ɩɨ ɫɯɟɦɟ ɪɢɫ. 15.
ɭɪɨɜɟɧɶ 1 ɢ ɩɨɞɚɟɬɫɹ ɧɚ ɜɬɨɪɨɣ ɜɯɨɞ Ⱦ1. ɇɚ ɩɟɪɜɨɦ ɜɯɨɞɟ Ⱦ1 ɤ ɷɬɨɦɭ ɦɨɦɟɧɬɭ ɫɢɝɧɚɥ ɬɨɠɟ ɢɦɟɟɬ ɭɪɨɜɟɧɶ 1,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɧɚ ɜɵɯɨɞɟ Ⱦ1 ɩɨɹɜɢɬɫɹ 0. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɦɩɭɥɶɫɚ ɡɚɤɨɧɱɢɬɫɹ. ɀɆ ɩɪɢɞɟɬ ɜ ɢɫɯɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɜ
ɤɨɬɨɪɨɦ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɞɨ ɩɪɢɯɨɞɚ ɫɥɟɞɭɸɳɟɝɨ ɡɚɩɭɫɤɚɸɳɟɝɨ ɢɦɩɭɥɶɫɚ.
Ⱦɪɭɝɚɹ ɫɯɟɦɚ ɜɵɩɨɥɧɟɧɢɹ ɀɆ ɧɚ ɨɫɧɨɜɟ ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɂ-ɇȿ ɪɚɫɫɦɨɬɪɟɧɚ ɧɚ ɪɢɫ. 17. ȼɪɟɦɟɧɧɚɹ
ɞɢɚɝɪɚɦɦɚ ɷɬɨɝɨ ɭɫɬɪɨɣɫɬɜɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ.18.
Uɜɯ
Uɜɯ5 D 9.2
Uɜɵɯ D 9.1
2
Uɜɯ 3
ɤɩɢ1
D9.1
&
D9.2
R4
ɋ3
xs2
6
&
ɤɩɢ4
D9.3
8,9 & Uɜɵɯ
5
Uɜɯ6 D 9.2
0
Uɜɯ
ɤɩɢ5
Uɜɵɯ
tɢ
11,12
Ɋɢɫ.17 ɀɆ ɧɚ ɨɫɧɨɜɟ
ɥɨɝɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ.
Ɋɢɫ.18 ȼɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ
ɀɆ ɩɨ ɫɯɟɦɟ ɪɢɫ. 17.
Ɂɞɟɫɶ ɞɥɢɬɟɥɶɧɨɫɬɶ ɢɦɩɭɥɶɫɚ tɂ ɨɛɭɫɥɨɜɥɟɧɚ ɜɪɟɦɟɧɟɦ ɫɨɜɩɚɞɟɧɢɹ ɫɢɝɧɚɥɨɜ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ ɧɚ ɜɯɨɞɚɯ ɷɥɟɦɟɧɬɚ Ⱦ9.2. Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɫɢɝɧɚɥɚ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ (ɛɨɥɟɟ U0BX.)ɧɚ ɜɬɨɪɨɦ ɜɯɨɞɟ Ⱦ9.2 (ɜɵɜɨɞ 5) ɨɩɪɟɞɟɥɹɟɬɫɹ
ɩɨɫɬɨɹɧɧɨɣ ɪɚɡɪɹɞɚ
WɊȺɁ = ɋ3˜R4
ɋɭɳɟɫɬɜɭɸɬ ɀɆ ɜ ɢɧɬɟɝɪɚɥɶɧɨɦ ɢɫɩɨɥɧɟɧɢɢ, ɧɚɩɪɢɦɟɪ Ʉ155ȺȽ1 (ɫɦ. ɫɯ. ɪɢɫ. 19).
+ȿɩ
Ⱥ1 3
4
Ⱥ2
& G1
1
ɤɩɢ 2
6
ɤɩɢ8
Q
ȼ
ɨɬ ɤɧ. 14 5
xs14
W
R
7 10 11
ɋ
W
Ɋɢɫ.19 ɀɆ Ʉ 155 ȺȽ 1.
Ɇɋ ɫɨɞɟɪɠɢɬ ɜɧɭɬɪɟɧɧɸɸ ɹɱɟɣɤɭ ɩɚɦɹɬɢ-ɬɪɢɝɝɟɪ ɫ ɞɜɭɦɹ ɜɵɯɨɞɚɦɢ Q ɢ
Q . Ɍɪɢɝɝɟɪ ɢɦɟɟɬ ɬɪɢ ɢɦɩɭɥɶɫɧɵɯ
ɜɯɨɞɚ ɥɨɝɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ (ɭɫɬɚɧɨɜɤɢ ɜ ɢɫɯɨɞɧɨɟ ɫɨɫɬɨɹɧɢɟ). ȼɯɨɞ ȼ ɞɚɟɬ ɩɪɹɦɨɣ ɡɚɩɭɫɤ ɬɪɢɝɝɟɪɚ (ɚɤɬɢɜɧɵɣ
ɩɟɪɟɩɚɞ - ɩɨɥɨɠɢɬɟɥɶɧɵɣ), ɜɯɨɞɵ A1 , A2 - ɢɧɜɟɪɫɧɵɟ (ɚɤɬɢɜɧɵɣ ɩɟɪɟɩɚɞ - ɨɬɪɢɰɚɬɟɥɶɧɵɣ). ɋɢɝɧɚɥ ɫɛɪɨɫɚ, ɬ.ɟ.
ɨɤɨɧɱɚɧɢɹ ɢɦɩɭɥɶɫɚ ɮɨɪɦɢɪɭɟɬɫɹ ɫ ɩɨɦɨɳɶɸ Ɋɋ -ɡɜɟɧɚ: ɜɪɟɦɹɡɚɞɚɸɳɢɣ ɤɨɧɞɟɧɫɚɬɨɪ ɋ
ɩɨɞɤɥɸɱɚɟɬɫɹ ɦɟɠɞɭ
ɜɵɜɨɞɚɦɢ 10 ɢ 11, ɪɟɡɢɫɬɨɪ RW ɜɤɥɸɱɚɟɬɫɹ ɦɟɠɞɭ ɜɵɜɨɞɚɦɢ 11 ɢ 14. Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɜɵɯɨɞɧɨɝɨ ɢɦɩɭɥɶɫɚ ɦɨɠɧɨ
ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɜɵɪɚɠɟɧɢɸ: Wȼɕɏ = ɋW ˜RW ˜ln2 | 0,7˜ ɋW ˜RW
˜Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɜɵɯɨɞɧɵɯ ɢɦɩɭɥɶɫɨɜ ɦɨɠɧɨ ɦɟɧɹɬɶ ɨɬ 30 ɦɫ ɞɨ 0,28 ɫ. ȼ ɬɚɛɥ.5 ɞɚɧɚ ɫɜɨɞɤɚ ɫɢɝɧɚɥɨɜ
ɥɨɝɢɱɟɫɤɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɦɭɥɶɬɢɜɢɛɪɚɬɨɪɨɦ Ʉ155ȺȽ1. ɉɟɪɜɵɟ ɱɟɬɵɪɟ ɫɬɪɨɤɢ ɩɨɤɚɡɵɜɚɸɬ ɡɚɜɢɫɢɦɨɫɬɶ ɫɬɚɬɢɱɟɫɤɢɯ
ɜɵɯɨɞɧɵɯ ɭɪɨɜɧɟɣ ɜɵɯɨɞɚɦɢ Q ɢ
Q ɨɬ ɥɨɝɢɱɟɫɤɢɯ ɭɪɨɜɧɟɣ ɧɚ ɜɯɨɞɚɯ A1 , A2 , ȼ (ɭɫɬɚɧɨɜɤɚ ɬɪɢɝɝɟɪɚ ɜ ɢɫɯɨɞɧɨɟ
ɫɨɫɬɨɹɧɢɟ). ɇɢɠɧɹɹ ɱɚɫɬɶ ɬɚɛɥɢɰɵ (ɫɬɪɨɤɢ 5-9) ɫɨɞɟɪɠɢɬ ɩɹɬɶ ɭɫɥɨɜɢɣ ɝɟɧɟɪɚɰɢɢ ɨɞɧɨɝɨ ɜɵɯɨɞɧɨɝɨ ɢɦɩɭɥɶɫɚ ɢ
ɭɤɚɡɵɜɚɟɬ ɮɚɡɭ ɫɢɝɧɚɥɨɜ ɧɚ ɜɵɯɨɞɚɯ Q ɢ
Q . Ɉɬɤɥɢɤ ɫ ɞɥɢɬɟɥɶɧɨɫɬɶɸ Wȼɕɏ ɩɨɥɭɱɚɟɬɫɹ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɩɟɪɟɩɚɞɟ
ɧɚ ɜɯɨɞɟ ȼ ɢɥɢ ɨɬɪɢɰɚɬɟɥɶɧɨɦ ɧɚ ɜɯɨɞɟ A1 (ɢɥɢ Ⱥ2).
Ɍɚɛɥɢɰɚ 5
ɍɩɪɚɜɥɟɧɢɟ ɢ ɫɢɝɧɚɥɵ ɀɆ Ʉ155ȺȽ1
ȼɯɨɞ
ȼɵɯɨɞ
A1
A2
ȼ
Q
Q
0
ɇ
1
0
1
ɇ
0
1
0
1
ɇ
ɇ
0
0
1
1
ɇ
ɇ
0
1
1
1
1
1
1
0
ɇ
ɇ
0
Ɂɞɟɫɶ: ɇ - ɧɟɨɩɪɟɞɟɥɟɧɧɨɟ (ɥɸɛɨɟ) ɫɨɫɬɨɹɧɢɟ,
- ɮɪɨɧɬ ɢɦɩɭɥɶɫɚ,
-
ɫɪɟɡ ɢɦɩɭɥɶɫɚ
3.2. Ⱥɜɬɨɤɨɥɟɛɚɬɟɥɶɧɵɣ Ɇȼ
ɉɨɜɬɨɪɢɦ ɟɳɟ ɪɚɡ, ɱɬɨ ɨɛɵɱɧɨ ɩɨɞ ɬɟɪɦɢɧɨɦ ɆȻ ɩɨɧɢɦɚɸɬ ɢɦɟɧɧɨ ɚɜɬɨɤɨɥɟɛɚɬɟɥɶɧɵɣ ɪɟɠɢɦ. ɋɯɟɦɧɨ ɆȻ
ɦɨɠɟɬ ɛɵɬɶ ɪɟɚɥɢɡɨɜɚɧ ɬɚɤɠɟ ɧɚ ɛɚɡɟ ɫɯɟɦɵ RS -ɬɪɢɝɝɟɪɚ (ɪɢɩ.8) ɚɧɚɥɨɝɢɱɧɨ ɟɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɸ ɜ ɀɆ (ɪɢɫ. 15).
Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɜɯɨɞ ɀɆ ɩɨ ɫɯɟɦɟ ɪɢɫ. 15 ɩɪɢɫɨɟɞɢɧɢɬɶ ɤ ɜɵɯɨɞɭ ɷɥɟɦɟɧɬɚ Ⱦ2, ɚ ɪɟɡɢɫɬɨɪ Ɋ ɜɤɥɸɱɢɬɶ ɦɟɠɞɭ
ɜɯɨɞɚɦɢ ɢ ɜɵɯɨɞɨɦ Ⱦ2 (ɫɯɟɦɚ ɷɬɨɝɨ ɭɫɬɪɨɣɫɬɜɚ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ.20).
ȿɫɥɢ ɜ ɢɫɯɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ ɧɚ ɜɵɯɨɞɟ Ⱦ1 ɭɫɬɚɧɨɜɢɥɚɫɶ 1, ɚ ɧɚ ɜɵɯɨɞɟ Ⱦ2 0, ɬɨ ɤɨɧɞɟɧɫɚɬɨɪ ɋ ɡɚɪɹɠɚɟɬɫɹ ɩɨ
ɰɟɩɢ: ɜɵɯɨɞ Ⱦ1, ɋ, R, ɜɵɯɨɞ Ⱦ2. ɉɨ ɦɟɪɟ ɡɚɪɹɞɚ UBX.D2 ɛɭɞɟɬ ɫɧɢɠɚɬɶɫɹ ɢ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t1 ɞɨɫɬɢɝɧɟɬ
D1
&
Uɜɵɯ
D2
& 1
R
Ɋɢɫ. 20 Ⱥɜɬɨɤɨɥɟɛɚɬɟɥɶɧɵɣ Ɇȼ
ɧɚ ɛɚɡɟ RS - ɬɪɢɝɝɟɪɚ.
ɜɟɥɢɱɢɧɵ U0BX, ɧɚ ɜɵɯɨɞɟ Ⱦ2 ɩɨɹɜɢɬɫɹ 1, ɤɨɬɨɪɚɹ ɩɪɢɥɨɠɢɬɫɹ ɤ ɜɯɨɞɭ Ⱦ1. ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɧɚ ɜɵɯɨɞɟ Ⱦ1 ɩɨɹɜɢɬɫɹ 0 ɢ
ɧɚɱɧɟɬɫɹ ɩɟɪɟɡɚɪɹɞ ɋ ɜ ɨɛɪɚɬɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ. ȼ ɦɨɦɟɧɬ t1
UBX.D2 Ⱦ2 ɫɦɟɧɢɬ ɡɧɚɤ ɢ ɧɚɱɧɟɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ ɩɨ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɦɭ ɡɚɤɨɧɭ. ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t2 UBX.D2 ɞɨɫɬɢɝɧɟɬ
ɜɟɥɢɱɢɧɵ UBX1. ɉɪɢ ɷɬɨɦ ɧɚ ɜɵɯɨɞɟ Ⱦ2 ɩɨɹɜɢɬɫɹ 0 ɢ ɩɪɨɰɟɫɫ ɧɚɱɧɟɬ ɩɨɜɬɨɪɹɬɶɫɹ. ȼɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ ɩɪɟɞɫɬɚɜɥɟɧɚ
ɧɚ ɪɢɫ.21.
ȼ ɪɚɛɨɬɟ ɢɫɫɥɟɞɭɟɬɫɹ ɫɯɟɦɚ Ɇȼ ɧɟɫɤɨɥɶɤɨ ɢɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ (ɪɢɫ. 22), ɤɨɬɨɪɚɹ ɜɵɩɨɥɧɟɧɚ ɧɚ ɷɥɟɦɟɧɬɚɯ
"ɇȿ". ɉɪɢɧɰɢɩ ɪɚɛɨɬɵ ɫɯɟɦɵ ɚɧɚɥɨɝɢɱɟɧ ɫɯɟɦɟ ɩɨ ɪɢɫ .20.
U ɜɯ D2
1
U ɜɯ
ɨ
U ɜɯ
R1
D7.2
D7.1
U ɜɵɯ D1
1
2
3
1
D7.3
4
5
1
U ɜɵɯ D2
C2
t1
t2
Ɋɢɫ. 21. ȼɪɟɦɟɧɧɚɹ ɞɢɚɝɪɚɦɦɚ
Ɇȼ ɩɨ ɫɯɟɦɟ ɪɢɫ. 20.
XS1
Ʉɉɂ 10 ɜɯ.1
Ʉɉɂ 7
Ɋɢɫ. 22. ɋɯɟɦɚ Ɇȼ ɧɚ
ɷɥɟɦɟɧɬɚɯ ɇȿ.
6
U ɜɵɯ
Ʉɉɂ 1
Ɍɪɟɯɮɚɡɧɵɟ ɫɯɟɦɵ ɜɵɩɪɹɦɥɟɧɢɹ.
Ɉɛɳɢɟ ɩɪɟɢɦɭɳɟɫɬɜɚ ɬɪɟɯɮɚɡɧɵɯ ɫɯɟɦ ɜɵɩɪɹɦɥɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɨɞɧɨɮɚɡɧɵɦɢ: ɦɟɧɶɲɟ ɭɪɨɜɟɧɶ
ɩɭɥɶɫɚɰɢɢ; ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɟɧɶɲɢɟ ɝɚɛɚɪɢɬɵ.
ɋɭɳɟɫɬɜɭɸɬ ɞɜɟ ɫɯɟɦɵ ɜɵɩɪɹɦɥɟɧɢɹ:
1) ɬɪɟɯɮɚɡɧɚɹ ɫɯɟɦɚ ɫ ɧɭɥɟɜɨɣ ɬɨɱɤɨɣ (ɬɪɟɯɮɚɡɧɚɹ ɧɭɥɟɜɚɹ ɫɯɟɦɚ),
2) ɬɪɟɯɮɚɡɧɚɹ ɦɨɫɬɨɜɚɹ ɫɯɟɦɚ.
Ɍɪɟɯɮɚɡɧɚɹ ɦɨɫɬɨɜɚɹ ɫɯɟɦɚ ɜɵɩɪɹɦɥɟɧɢɹ (ɫɯɟɦɚ Ʌɚɪɢɨɧɨɜɚ).
ȼ ɫɯɟɦɟ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɨɬɤɪɵɬɨ ɬɨɥɶɤɨ 2 ɞɢɨɞɚ.
ɇɚɝɪɭɡɤɚ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɨɠɟɬ ɛɵɬɶ ɚɤɬɢɜɧɨ-ɢɧɞɭɤɬɢɜɧɨɣ.
ɇɚɪɢɫɭɟɦ ɷɩɸɪɵ ɫɢɝɧɚɥɨɜ:
6 ɞɢɨɞɨɜ ɧɚ ɫɯɟɦɟ ɨɛɴɟɞɢɧɟɧɵ ɜ ɞɜɟ ɝɪɭɩɩɵ: ɟɫɬɶ ɤɚɬɨɞɧɚɹ ɝɪɭɩɩɚ (VD1, VD3,VD5), ɢ ɚɧɨɞɧɚɹ ɝɪɭɩɩɚ (VD2,
VD4, VD6).
ɉɪɚɜɢɥɨ: ɜ ɤɚɬɨɞɧɨɣ ɝɪɭɩɩɟ ɨɬɤɪɵɬ ɬɨɬ ɞɢɨɞ, ɱɟɣ ɩɨɬɟɧɰɢɚɥ ɚɧɨɞɚ ɛɨɥɟɟ «ɩɨɥɨɠɢɬɟɥɟɧ»;
ɜ ɚɧɨɞɧɨɣ ɝɪɭɩɩɟ ɨɬɤɪɵɬ ɬɨɬ ɞɢɨɞ, ɭ ɤɨɬɨɪɨɝɨ ɩɨɬɟɧɰɢɚɥ ɤɚɬɨɞɚ ɛɨɥɟɟ «ɨɬɪɢɰɚɬɟɥɟɧ».
ɉɭɫɬɶ
eA
t
0
t1
eB
eC
eB % 0
VD1 ɨɬɤɪɵɬ, VD2 ɡɚɤɪɵɬ
eC % 0
ɜ ɚɧɨɞɧɨɣ ɝɪɭɩɩɟ ɨɬɤɪɵɬ VD4 (ɮɚɡɚ ȼ), ɬɚɤ ɤɚɤ e B
eC
ɮɚɡɚ ȼ ɧɚɢɛɨɥɟɟ «ɨɬɪɢɰɚɬɟɥɶɧɚ».
ȼ ɚɧɨɞɧɨɣ ɝɪɭɩɩɟ ɨɬɤɪɵɬ VD6.
ȿɫɥɢ ɛɵ L H %% RH , ɬɨ ɫɦɨɬɪɢ ɪɢɫɭɧɨɤ.
,
Ɋɚɫɫɦɨɬɪɢɦ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ t ɤɨɝɞɚ ɨɬɤɪɵɬ VD1, VD4
Ud
e A eB
Ɋɚɫɫɦɨɬɪɢɦ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ t, ɤɨɝɞɚ ɨɬɤɪɵɬ VD1, VD6
Ud
Udm
e A eC
2 3E 2
Ɉɫɧɨɜɧɚɹ ɝɚɪɦɨɧɢɤɚ ɲɟɫɬɚɹ.
ɑɚɫɬɨɬɚ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɜ 6 ɪɚɡ ɛɨɥɶɲɟ ɱɚɫɬɨɬɵ ɫɟɬɢ.
q
2
m 1
2
2
35
0.06 (ɩɪɚɤɬɢɱɟɫɤɢ ɡɞɟɫɶ ɧɟ ɧɭɠɟɧ ɮɢɥɶɬɪ ɧɚ ɜɵɯɨɞɟ).
ɱɟɦ q<, ɬɟɦ ɤɚɱɟɫɬɜɟɧɧɟɟ ɜɵɩɪɹɦɥɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ.
T
Ud
1
U dm cos Ztdt
T ³0
S / 6
1
U dm cos ZtdZt
S / 3 S³/ 6
3
S / 6
S S³/ 6
2 3E 2
3 2 3
S
S / 6
E 2 sin Zt
³
S / 6
3 3 2
Ia
Ud
E2
S
Id
3
E2
3 3 2
2.34 E 2
E2
S
S
Ud
3 3 2
2.34 E 2 ;
0.4275U d .
ɇɚɝɪɭɡɤɚ ɧɚ ɬɪɚɧɫɮɨɪɦɚɬɨɪ ɜɨ ɜɪɟɦɹ «+» ɢ «-» ɩɨɥɭɜɨɥɧ ɜ ɫɯɟɦɟ ɨɞɢɧɚɤɨɜɚ.
e2 A e2 B ɧɚ ɢɧɬɟɪɜɚɥɟ (t3;t4)
e2 A e2C ɧɚ ɢɧɬɟɪɜɚɥɟ (t4;t5)
U OBR
U OBR
U OBR m
2 3E 2
2 3
S
3 2 3
Ud
S
3
Ud
1.05U d .
ȼɦɟɫɬɨ ɞɢɨɞɨɜ ɜ ɫɯɟɦɟ ɦɨɝɭɬ ɫɬɨɹɬɶ ɬɢɪɢɫɬɨɪɵ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɯɟɦɚ ɭɩɪɚɜɥɹɟɦɨɝɨ ɬɪɟɯɮɚɡɧɨɝɨ ɜɵɩɪɹɦɢɬɟɥɹ
(ɫɯɟɦɚ Ʌɚɪɢɨɧɨɜɚ).
ȿɫɥɢ ɭɝɨɥ ɭɩɪɚɜɥɟɧɢɹ D 0 Ÿ ɬɢɪɢɫɬɨɪɵ { ɞɢɨɞɵ ɢ ɨɬɤɪɵɜɚɸɬɫɹ ɜ ɦɨɦɟɧɬɵ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɨɬɩɢɪɚɧɢɹ.
Ɇɨɦɟɧɬɵ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɨɬɩɢɪɚɧɢɹ – ɦɨɦɟɧɬɵ ɩɟɪɟɫɟɱɟɧɢɹ ɫɢɧɭɫɨɢɞ ɞɜɭɯ ɫɨɫɟɞɧɢɯ ɮɚɡ.
ȿɫɥɢ ɭɝɨɥ ɭɩɪɚɜɥɟɧɢɹ D z 0 , ɬɨ ɬɢɪɢɫɬɨɪɵ ɜ ɷɬɢ ɦɨɦɟɧɬɵ ɟɳɟ ɧɟ ɨɬɤɪɵɬɵ, ɬɨɝɞɚ ɤɪɢɜɚɹ ɧɚɩɪɹɠɟɧɢɹ
ɢɫɤɚɡɢɬɫɹ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɢɪɢɫɬɨɪɨɜ ɜɦɟɫɬɨ ɞɢɨɞɨɜ:
S / 6 D
Ud
1
2 3E 2 cos ZtdZt
2S / 3 S /³6D
U do cos D ,
ɝɞɟ U do - ɧɚɩɪɹɠɟɧɢɟ ɧɚɝɪɭɡɤɢ ɩɪɢ ɧɭɥɟɜɨɦ ɭɝɥɟ ɭɩɪɚɜɥɟɧɢɹ (ɢɥɢ ɩɪɢ ɞɢɨɞɚɯ).
U do
3 3 2 E2
S
2.34 E 2
Ɍɪɟɯɮɚɡɧɵɣ ɜɵɩɪɹɦɢɬɟɥɶ ɫ ɧɭɥɟɜɨɣ ɬɨɱɤɨɣ.
ɇɚɪɢɫɭɟɦ ɷɩɸɪɵ ɫɢɝɧɚɥɨɜ:
ɉɪɢ t  (t1, t2)
eA 0 , eA
e B ɨɬɤɪɵɬ VD1
eA
eC
Ud
e2 A
ɉɪɢ t  (t2,t3)
eB 0 , eB
e A ɨɬɤɪɵɬ VD2
eB
Ud
eC
e2 B .
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɭɥɶɫɚɰɢɢ:
q
2
m 1
2
2
3 1
2
0.25 , ɬ.ɟ. ɤɚɱɟɫɬɜɨ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɛɭɞɟɬ ɯɭɠɟ, ɬɚɤ ɤɚɤ q ɛɨɥɶɲɨɣ.
ɇɚɣɞɟɦ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚɝɪɭɡɤɢ:
S /3
Ud
1
2 E 2 cos ZtdZt
2S / 3 S³/ 3
3
2S
2E2 (
Ud
E2
3
3
)
2
2
3 3 2
E2
2 S
1.17 E 2
3 2 3
E 2 1.17 E 2
2 S
2S
U d 0.855U d .
3 3 2
ɉɪɢ t  (t1;t2) VD1 ɡɚɤɪɵɬ, VD2 ɨɬɤɪɵɬ
U AKVD1
e2 B e2 A
U OBRm
2 3E 2
2 3
S
3 2 3
Ud
ɫɯɟɦɟ, ɞɢɨɞ ɢɫɩɵɬɵɜɚɸɬ ɧɚ ɩɪɨɛɨɣ.
2S
Ud
3
2.09U d . ɇɚɩɪɹɠɟɧɢɟ ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɦɨɫɬɨɜɨɣ
ɉɪɢ E 2
100 ȼ
U OBRm
2 3 ˜ 100 24 ȼ
Id
Ia
- ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɱɟɪɟɡ ɞɢɨɞ, ɬɚɤ ɠɟ, ɤɚɤ ɢ ɜ ɦɨɫɬɨɜɨɣ ɫɯɟɦɟ ɜ ɬɪɢ ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɧɚɝɪɭɡɤɟ.
3
ɨɛɦɨɬɤɢ ɮɚɡ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ ɧɚɝɪɭɠɟɧɵ ɧɟɪɚɜɧɨɦɟɪɧɨ.
i1 A
2i1C
2i1B
Ɉɫɧɨɜɧɨɣ ɧɟɞɨɫɬɚɬɨɤ ɞɚɧɧɨɣ ɫɯɟɦɵ: ɜɬɨɪɢɱɧɵɣ ɬɨɤ ɢɦɟɟɬ ɩɨɫɬɨɹɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ. ɉɨɫɬɨɹɧɧɚɹ
ɫɨɫɬɚɜɥɹɸɳɚɹ ɧɟ ɬɪɚɧɫɮɨɪɦɢɪɭɟɬɫɹ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢɞɟɬ ɧɚ ɩɨɞɦɚɝɧɢɱɢɜɚɧɢɟ ɫɟɪɞɟɱɧɢɤɚ, ɬ.ɟ. ɬɨɤ
ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɭɜɟɥɢɱɢɜɚɸɬɫɹ ɩɨɬɟɪɢ, ɷɬɨ ɜɟɞɟɬ ɤ ɧɚɝɪɟɜɚɧɢɸ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ. ȼɜɢɞɭ ɷɬɢɯ
ɩɪɢɱɢɧ, ɦɵ ɜɵɧɭɠɞɟɧɵ ɭɜɟɥɢɱɢɬɶ ɝɚɛɚɪɢɬɵ ɫɟɪɞɟɱɧɢɤɚ ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ. ɉɨɷɬɨɦɭ ɜ ɱɢɫɬɨɦ ɜɢɞɟ ɷɬɚ ɫɯɟɦɚ
ɩɪɢɦɟɧɹɟɬɫɹ ɨɱɟɧɶ ɪɟɞɤɨ, ɱɚɳɟ, ɤɚɤ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɨɫɬɨɜɵɯ ɫɯɟɦ.