APPLICATION FOR SIMULATING AND ANALYSIS OF A SERIAL R-L-C CIRCUIT
C. Hațiegan, Department of Engineering Science, Babeș-Bolyai University, Reșița, ROMANIA
M.D. Stroia, Department of Engineering Science, Babeș-Bolyai University, Reșița, ROMANIA, Corresponding author
C.Popescu, “Constantin Brȃncuşi” University of Tȃrgu Jiu, ROMANIA
C.M. Muscai, Polytechnic University of Bucharest, Faculty of Electrical Engineering, Bucuresti, Department of Engineering Science, Babeș-Bolyai University, Reșița, ROMANIA
ABSTRACT: In present paper we describe an application designed and built in order to obtain a simulator for a serial R-L-C circuit. The program for the application was developed using Visual Basic software. It allows generating circuit signals for current or voltage when supplied by an AC or DC source and comes with a few more options implemented in order to facilitate signal analysis. In fact, the application is an improved version of a he length of a previously existing one.
KEY WORDS: simulation, application, circuit, RLC, software.
A serial circuit of RLC type becomes more complicated to analyze when we want to describe second law of Kirchhoff for circuit supplied by a source of voltage Ɛ, case in which we have to consider as well the voltage induced in reel having L inductance [1-3]:
𝜀 − 𝑖𝑅 − 𝐿𝑑𝑖
= 0 (1) Capacity accumulated on capacitor, q(t), and current, i(t) will be solutions for a system of two first order differential equations.
with initial conditions q(t0
. Substituting first equation in the second one of the system we obtain a second order differential equation:
𝐿 𝑑𝑞 𝑑𝑡
Applying a continuous voltage, Ɛ=Ɛ0
, to serial RLC circuit, a particular solution for equation 3 is constant CƐ0
. Solution for homogenous equation can be written by means of similarities between equation 3 and damped linear oscillator equation. Thus, solution for equation 3 can be written as:
cos(Ωt-θ) for 𝑅 ≤𝐿
(4) where constants A and θ will be determined from initial conditions.
When voltage Ɛ0
is applied, at t0
=0 initial conditions are q0
=0 and i0
=0, due to presence of inductance. For an adequate period of time, when t→∞, load C on capacitor reaches value CƐ0,
when current decreases to 0.
If at a certain moment of time, t0
, load on capacitor is q0
, supply Ɛ is disconnected, thus equation 3 becomes homogenous.
Both load on capacitor as well as current in
circuit decrease to zero for high time values,
in shape of damped oscillations .
21 In stationary regime, difference of phase between voltage and current is zero with condition that resonance circuit frequency ω=
Application program actually calculates the solution of a second order differential equation[2-5]:
𝑞 − 𝑅𝑑𝑞