Complete Response of Second Order Circuits Gutierrez, Marian Joice Ateneo de Manila University III BS Electronics and Communications Engineering Loyola Heights, Quezo n City, Phil ippines [email protected] Abstract – The aim of the experiment is to study the complete response of second order circuits I. I NTRODUCTION The laboratory activity examines how does the complete response of second order circuits behaves. A second order circuit has two independent energy-storage elements: capacitor and inductor. In this experiment, two capacitors were used. The analysis of second order circuits yields to second order differential equations. II. METHODOLOGY A. Materials and Equipments The electronic materials and equipment needed for this laboratory activity are fundamental components of a second order circuit. The materials needed are as follows: a 1 kΩ resistor, two 2 kΩ resistors, a 1µF capacitor, a 0.125µF capacitor and a LM741 op-amp. The equipment needed is function generator which represents the V s and oscilloscope. B.Proce dures After gathering all the required electronic materials and equipment, the experiment is started by constructing the circuit in fig. 1 having V s =318 Hz. The oscilloscope will be used to show the input (V s ) and output (V out ) signals of the circuit in channel 1 and channel 2 respectively. After this, the value of V s will change to 2 kHz, as seen in fig. 2. Then, as seen in fig. 3, square wave is used to show both sinusoids; and now follows by fig. 4 and fig. 5, where the value of V s will become 100 kHz and 200 kHz, respectively. The oscilloscope will be used again to be able to show the input and output signals of the circuit. C.Theories Solving a second order circuit is usually done through the use of differential equations; however, it is tedious and has the high risk of committing mistakes in the middle of solution. In this experiment, the traditional method is still used for the natural response; consequently, another method is used in solving the theoretical complete response of the circuit: the phasor for m. It is mostly appli cable if the given input voltage is sinusoidal. Moreover, capacitors with capacitance C are Maceren, Armond Royce R. Ateneo de Manila University III BS Electronics and Communications Engineering Loyola Heights, Quezo n City, Phil ippines [email protected] converted to as its phasor equivalent; and inductors with inductance L are converted to as its phasor equivalent. Last principle is Kirchhoff’s Circuit Law (KCL). It states that at any node (junction) in an electrical circuit, the sum of the currents flowing into that node is equal to the sum of currents flowing out of that node. [1] The analysis of the natural response of the second order circuit yields second order differential equation which has the form: . (1) In finding natural response, set the forcing function f(t) to zero, . (2) Substituting the general form of the solution Ae st yields the characteristic equation: (3) Finding the roots through quadratic equation, . (4) The roots of the quadratic equation above may be real and distinct, repeated or complex. Thus, the natural response to a second order circuit has 3 possible forms: a. Overdamped response- two real distinct roots (5) b. Critically damped response- one real root (6) b. Underdamped response- 2 complex roots [ ]. (7)