Electronics/RCL

RLC Series An RLC series circuit consists of a resistor, inductor, and capacitor connected in series: left|100px By Kirchhoff's voltage law the differential equation for the circuit is: or Leading to: ± with and There are three cases to consider, each giving different circuit behavior, . . = Equation above has only one real root s = -α = , > Equation above has only two real roots ± . Equation above has only two complex roots + j - j Circuit Analysis R = 0 If R = 0 then the RLC circuit will reduce to LC series circuit . LC circuit will generate a standing wave when it operates in resonance; At Resonance the conditions rapidly convey in a steady functional method. R = 0 ZL = ZC If R = 0 and circuit above operates in resonance then the total impedance of the circuit is Z = R and the current is V / R At Resonance Or At Frequency I = 0 . Capacitor opens circuit . I = 0 I = 0 Inductor opens circuit . I = 0 Plot the three value of I at three I above we have a graph I - 0 At Resonance frequency the value of current is at its maximum . If the value of current is half then circuit has a stable current does not change with frequency over a Bandwidth of frequencies É1 - É2 . When increase current above circuit has stable current over a Narrow Bandwidth . When decrease current below circuit has stable current over a Wide Bandwidth Thus the circuit has the capability to select bandwidth that the circuit has a stable current when circuit operates in resonance therefore the circuit can be used as a Resonance Tuned Selected Bandwidth Filter Further Reading RCL circuit analysed in the time domain RCL circuit analysed in the frequency domain