Лекции по электронике
.pdfUȼɏ = 0, ɡɧɚɱɢɬ Uȼɕɏ = 0
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R1 ROC |
; ɬ.ɤ. ɄU ɜɟɥɢɤ => U1 0, ɩɨɥɭɱɢɦ Uȼɕɏ 0. |
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R1 ROC |
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ɑɬɨɛɵ ɜ ɪɟɠɢɦɟ ɩɨɤɨɹ Uȼɕɏ = 0, U1 = U2 => |
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R1 ROC |
; ɬ.ɨ. ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɜɥɢɹɧɢɟ ɜɯɨɞɧɵɯ ɬɨɤɨɜ. |
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UBX UCM |
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ɩɪɢ |
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ UBX 0 o UBIX z 0
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
UC |
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³iC (t)dt |
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iBX iC |
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UBIX UC |
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C |
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UBIX |
UC |
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iBX |
UBX |
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UBX (t) |
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UBIX |
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³iC (t)dt |
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³iBX (t)dt |
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³ |
dt |
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³UBX (t)dt ; |
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C |
C |
C |
R |
RC |
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ɩɟɪɟɣɞɟɦ ɨɬ ɧɟɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ ɤ ɨɩɪɟɞɟɥɟɧɧɵɦ:
UBIX U BIX (0) |
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t UBX (t)dt |
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³0 |
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, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, |
BIX |
ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ. |
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Ʉɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ: |
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zOC |
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ɉ |
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ZC |
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zBX |
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R |
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ZR , ɝɞɟ zOC - ɤɨɷɮɮɢɰɢɟɧɬ ɨɛɪɚɬɧɨɣ ɫɜɹɡɢ; |
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zBX - ɤɨɷɮɮɢɰɢɟɧɬ ɜɯɨɞɚ
ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɱɚɫɬɨɬɵ, ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. ɂɧɬɟɝɪɚɬɨɪ ɹɜɥɹɟɬɫɹ ɭɫɢɥɢɬɟɥɟɦ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ (ɍɍɇ). ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ:
ɉ1=ɉ2
ɉ1, ɉ2 - ɩɥɨɳɚɞɢ
ȿɫɥɢ ɉ1z ɉ2 , ɬɨ ɧɚ ɜɵɯɨɞɟ ɧɟ ɛɭɞɟɬ ɧɭɥɹ.
³sinZtdt 1 cosZt |
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ȿɫɥɢ UBX UmsinZt , ɬɨ |
U BIX |
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UmcosZt . |
ZRC |
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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 |
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iR ; |
iC |
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dUBX |
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iR |
UBIX |
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dt |
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dt ; |
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UC UBX ; |
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ɩɪɢɪɚɜɧɹɟɦ ɩɪɚɜɵɟ ɱɚɫɬɢ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ: |
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CdUBX (t) |
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UBIX |
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dt |
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UBIX |
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RC |
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dt |
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ɉ |
zOC |
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R |
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ZRC |
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zBX |
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ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ, ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. |
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ZC |
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Ⱦɢɮɮɟɪɟɧɰɢɚɬɨɪ ɹɜɥɹɟɬɫɹ ɭɫɢɥɢɬɟɥɟɦ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ (ɍȼɑ).
sin` cos
(sinZt)` |
ZcosZt |
ȿɫɥɢ UBX |
UmsinZt oUBIX ZRCUmcosZt . |
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 UBIX z 0 ɩɪɢ
UBX 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 UBIX . ɗɬɨ ɦɨɠɧɨ «ɨɬɫɥɟɞɢɬɶ» ɧɚ Ⱥɑɏ (ɚɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ):
Ɏɑɏ
ɑɬɨ ɦɨɠɟɬ ɩɪɨɢɡɨɣɬɢ: ɩɪɢ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ ɡɚ ɫɱɟɬ ɮɚɡɨɜɨɝɨ ɫɞɜɢɝɚ M 180q; ɈɈɋ ɩɪɟɜɪɚɬɢɥɚɫɶ ɜ ɉɈɋ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɥɸɛɨɟ ɧɟɡɧɚɱɢɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ UBX (ɩɨɦɟɯɚ), ɩɪɢɜɨɞɢɬ ɤ ɥɚɜɢɧɨɨɛɪɚɡɧɨɦɭ ɧɚɪɚɫɬɚɧɢɸUBIX ,
ɞɨUBIXMAX 15 ȼ. ɗɬɨ ɢ ɟɫɬɶ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟ.
ɋ ɷɬɢɦ ɹɜɥɟɧɢɟɦ ɧɚɞɨ ɛɨɪɨɬɶɫɹ: ɨɝɪɚɧɢɱɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɩɟɪɟɞɚɱɢ ɧɚ ɜɵɫɨɤɢɯ ɱɚɫɬɨɬɚɯ. ɇɚɪɢɫɭɟɦ ɫɯɟɦɭ:
ɉzOC
zBX ɜɜɟɞɟɧɢɟ C1 op zOC ;
ɜɜɟɞɟɧɢɟ Rɛ on zBX . Ɋɚɫɫɦɨɬɪɢɦ ɬɚɤɭɸ ɫɯɟɦɭ:
i2 i1
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dU BX |
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UBIX UC2 |
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Ʉɨɦɩɚɪɚɬɨɪɵ. |
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UBIX |
ɢɡɦɟɧɹɟɬɫɹ ɫɤɚɱɤɨɨɛɪɚɡɧɨ ɢɡ ɨɞɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ ɜ |
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Ʉɨɦɩɚɪɚɬɨɪɵ - ɷɬɨ ɩɨɪɨɝɨɜɵɣ ɷɥɟɦɟɧɬ, ɭ ɤɨɬɨɪɨɝɨ |
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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,
ɋȺɫɟɥɟɤɬɨɪ ɚɦɩɥɢɬɭɞɧɵɣ, ɪɚɡɥɢɱɚɟɬ ɜɯɨɞɧɵɟ ɫɢɝɧɚɥɵ. Ʉɨɦɩɚɪɚɬɨɪ - ɚɧɚɥɨɝ ɪɟɥɟ.
Ɉɩɟɪɚɰɢɨɧɧɵɣ ɭɫɢɥɢɬɟɥɶ ɭɫɢɥɢɜɚɟɬ ɪɚɡɧɨɫɬɶ ɫɢɝɧɚɥɨɜ ɞɜɭɯ ɜɢɞɨɜ: ɨɞɧɨ ɨɩɨɪɧɨɟ, ɞɪɭɝɨɟ - ɜɯɨɞɧɨɟ:
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UBIX (UOP |
UBX ) KU |
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UBX 0 oUBIX UBIXMAX |13 ȼ |
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U BIX | Eɉ |
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ɉɪɢ UBX |
% 0 UBIX ɧɟ ɢɡɦɟɧɢɬɫɹ; |
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ɉɪɢ |
U BX |
0ɢ UOP U |
BIX ɢɡɦɟɧɢɬɫɹ ɫɤɚɱɤɨɦ ɞɨ -13ȼ. |
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ɉɪɢ U BX |
UOP ,U BIX 0, ɧɨ ɷɬɨ ɨɱɟɧɶ ɧɟɭɫɬɨɣɱɢɜɨɟ ɫɨɫɬɨɹɧɢɟ. |
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ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ: |
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ɉɪɢ nUOP oW1 p,W2 n.
Ɇɟɧɹɹ ɡɧɚɤ UOP ɢ ɩɨɞɚɜɚɹ ɟɝɨ ɧɚ ɪɚɡɧɵɟ ɜɯɨɞɵ ɨɩɟɪɚɰɢɨɧɧɨɝɨ ɭɫɢɥɢɬɟɥɹ, ɦɨɠɧɨ ɦɟɧɹɬɶ ɡɧɚɤ UBIX ɜ ɢɫɯɨɞɧɨɦ ɫɨɫɬɨɹɧɢɢ ɢ ɩɪɢ ɫɪɚɛɚɬɵɜɚɧɢɢ. ɉɪɢ ɷɬɨɦ UBX , ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ «ɫɪɚɛɚɬɵɜɚɧɢɟ» ɤɨɦɩɚɪɚɬɨɪɚ (ɢɡɦɟɧɟɧɢɟ UBIX
ɨɬ +13ȼ ɞɨ -13ȼ) ɦɨɠɧɨ ɧɚɡɜɚɬɶ UCPK , ɚ UBX , ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ ɨɛɪɚɬɧɵɣ ɩɪɨɰɟɫɫ «ɜɨɡɜɪɚɬ» - UBZK . Ⱦɥɹ
ɨɛɵɱɧɨɝɨ ɤɨɦɩɚɪɚɬɨɪɚ U |
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U BZK |
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CPK |
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UBX otɂɆɉ . |
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Ʉɨɦɩɚɪɚɬɨɪ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ Sin o |
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ȼ ɪɹɞɟ ɫɥɭɱɚɟɜ ɬɚɤɨɣ ɤɨɦɩɚɪɚɬɨɪ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɨɠɧɨ, ɬɚɤ ɤɚɤ: |
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UBX 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 U1 ɜ ɪɟɠɢɦɟ ɩɨɤɨɹ:
U |
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UBIX 0 |
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UOP |
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ɪɟɲɚɥɢ ɦɟɬɨɞɨɦ ɫɭɩɟɪɩɨɡɢɰɢɢ (ɧɚɥɨɠɟɧɢɹ); |
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ɉɪɢ UBX |
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0 - ɤɨɦɩɚɪɚɬɨɪ ɧɟ ɫɪɚɛɨɬɚɟɬ, |
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ɉɪɢ UBX |
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U1 ɤɨɦɩɚɪɚɬɨɪ ɢɡɦɟɧɢɬ ɫɜɨɟ ɫɨɫɬɨɹɧɢɟ ɢ UBIX ɫɬɚɧɟɬ % 0 . |
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U1 |
ɫɬɚɧɟɬ ɪɚɜɧɨ ɫɥɟɞɭɸɳɟɦɭ ɜɵɪɚɠɟɧɢɸ: |
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ɬɚɤ ɤɚɤ U1`%U1 |
ɢɫɱɟɡɧɟɬ «ɞɪɟɛɟɡɝ» ɤɨɧɬɚɤɬɚ. |
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Ɍɟɩɟɪɶ ɛɭɞɟɦ ɭɦɟɧɶɲɚɬɶ UBX . ɉɪɢ ɢɫɯɨɞɧɨɦ UBIX ɤɨɦɩɚɪɚɬɨɪ ɧɟ ɩɟɪɟɤɥɸɱɢɬɫɹ, ɬɚɤ ɤɚɤ
U1 p . ɉɟɪɟɤɥɸɱɟɧɢɟ ɛɭɞɟɬ ɩɪɢ ɦɟɧɶɲɟɦ UBX .
ɂɡɨɛɪɚɡɢɦ ɩɟɪɟɞɚɬɨɱɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ:
R1
ɑɟɦ > ɝɥɭɛɢɧɚ ɉɈɋ, ɬ.ɟ. R2 , ɬɟɦ ɲɢɪɟ ɩɟɬɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.
Ɂɚɞɚɱɢ ɧɚ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ:
Ɂɚɞɚɱɚ ʋ1
Ⱦɚɧɨ:
U1 8cos314t ȼ U2 1 ȼ
R1 33 ɤɈɦ
R2 39 ɤɈɦ
C1 0.15 ɦɤɎ
Ⱦɚɧɚ ɫɯɟɦɚ:
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15 ȼ |
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U BIX |
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(U 1 )` |
U 2 » |
«8R 2 C 314 ( ) sin 314 t 1 |
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33 » |
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Ɋɟɲɟɧɢɟ: |
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8 39 103 0.15 10 6 314 sin 314t 1.18 14.7 sin 314t 1.18 |
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UBIX |
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dUBX |
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RC(sinZt) |
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2Sf 314 2Sf |
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ɇɚɪɢɫɭɟɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ: 
Ɂɚɞɚɱɚ ʋ 2
Ⱦɚɧɨ:
U1 |
2 ȼ |
U2 |
62.8sin3140t |
R1 |
10 ɤɈɦ |
R2 |
20 ɤɈɦ |
C1 ɦɤɎ
Ⱦɚɧɚ ɫɯɟɦɚ:
Ɋɟɲɟɧɢɟ: |
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U BIX |
(³U1dt ³U 2dt) |
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cos3140t |
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10 103 1 10 6 |
20 103 1 106 3140 |
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ɉɨɫɬɪɨɢɦ ɷɩɸɪɵ ɜɯɨɞɧɵɯ ɢ ɜɵɯɨɞɧɵɯ ɫɢɝɧɚɥɨɜ: