Superposisi di Sirkuit AC

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We have already studied the superposition theorem for DC circuits. In this chapter we will show its application for AC circuits.

Grafikteorema superposisi states that in a linear circuit with several sources, the current and voltage for any element in the circuit is the sum of the currents and voltages produced by each source acting independently. The theorem is valid for any linear circuit. The best way to use superposition with AC circuits is to calculate the complex effective or peak value of the contribution of each source applied one at a time, and then to add the complex values. This is much easier than using superposition with time functions, where one has to add the individual time functions.

To calculate the contribution of each source independently, all the other sources must be removed and replaced without affecting the final result.

When removing a voltage source, its voltage must be set to zero, which is equivalent to replacing the voltage source with a short circuit.

When removing a current source, its current must be set to zero, which is equivalent to replacing the current source with an open circuit.

Sekarang mari kita telusuri contoh.

Di sirkuit yang ditunjukkan di bawah ini

R_i = 100 ohm, R₁= 20 ohm, R₂ = 12 ohm, L = 10 uH, C = 0.3 nF, v_S(t) = 50cos (wt) V, i_S(t) = 1cos (wt+30°) A, f=400 kHz.

Notice that both sources have the same frequency: we will only work in this chapter with sources all having the same frequency. Otherwise, superposition must be handled differently.

Temukan arus i (t) dan i₁(t) menggunakan teorema superposisi.

Mari kita gunakan TINA dan perhitungan tangan secara paralel untuk menyelesaikan soal.

First substitute an open circuit for the current source and calculate the complex phasors I ', I1 ′ karena kontribusi hanya dari VS.

Arus dalam kasus ini sama:

I'= I₁'= V_S/ (R_i + R₁ + j* w* L) = 50 / (120+j2* p* 4 * 10⁵* 10^-5) = 0.3992-j0.0836

I'= 0.408 e^{j 11.83 °}A

Selanjutnya gantilah korsleting untuk sumber tegangan dan hitung fasa kompleks I ”, I1” karena kontribusi hanya dari AKU S.

Dalam hal ini kita dapat menggunakan rumus pembagian saat ini:

Saya ”= -0.091 - j Para 0.246

dan

I₁^" = 0.7749 + j Para 0.2545

Jumlah dari dua langkah:

I = I'+ I”= 0.3082 - j 0.3286 = 0.451 e^{- j46.9 °}A

I₁ = I₁^" + I₁'= 1.174 + j 0.1709 = 1.1865 e^{j 8.28 °}A

Fungsi waktu dari arus:

i (t) = 0.451 cos ( wx t - 46.9 ° )A

i₁(t) = 1.1865 cos ( wx t + 8.3 ° )A

As we said in the DC chapter on superposition, it gets pretty complicated using the superposition theorem for circuits containing more then two sources. While the superposition theorem can be useful for solving simple practical problems, its main use is in the theory of circuit analysis, where it is employed in proving other theorems.