Introduction

Series RLC circuits consist of a resistance, a capacitance and an inductance connected in series across an alternating supply. Series RLC circuits are classed as second-order circuits because they contain two energy storage elements, an inductance L and a capacitance C. Consider the RLC circuit below. In this experiment a circuit(Fig 1) will be provided. A p-p sinusoidal signal of amplitude 3V will be applied to it and its frequency response would be verified .

Figure 1:Circuit diagram

The above R, L, C series circuit forms a second order system.The transfer function of this circuit is given by,

$$H(s)=\frac{\frac{1}{LC}}{s^2+(\frac{R}{L})s+\frac{1}{LC}}$$

can be compared with general equation.

$$H(s)=\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}where{\omega }_n=\frac{1}{\sqrt{LC}}$$

The gain and phase response against frequency will be typical of second order system. The expected maximum gain for each ζ can be observed from the plot in the experiment. Theoretical expression for obtaining maximum gain is,

$$M_m=\frac{1}{2\omega \sqrt{1-{\zeta }^2}}$$

$$Occurringat{\omega }_m={\omega }_n\sqrt{1-2{\zeta }^2}$$