1. L C V1V1 + -R1R1 R2R2 Example 3.1: Current in the resistor R 1 = V 1 : Input q ve q 2 : Gen. charges QqQq Q q2 L=3.4 mH, C=286 µF, R 1 =3.2 Ω, R 2 =4.5 Ω D(s)=0.02618s 3 +26.288s 2 +11188.81s=0 Eigenvalues: 0, -502.06±418.70i (ξ=0.768) Modeling of Electrical Circuits

2. C1C1 - + V1V1 V2V2 R1R1 R2R2 R3R3 C2C2 Also, in op-amp: V + =V - =0 Example3.2 Input : V 1 Generalized charges: q 1, q 2, q 3 In op-amp input, resistance is too high

3. R 1 =15.9 kΩ, R 2 =837 Ω, R 3 =318 kΩ, C 1 =C 2 =0.005 µF Eigenvalues: 0, -628.93±12561.76i (ξ=0.05)

4. V2V2 R2R2 - + V1V1 R1R1 C - + V1V1 V2V2 R R - + V1V1 V2V2 C

5. - + V1V1 VcVc R R R V2V2 V3V3 R R V2V2 R R V1V1 - + VcVc R R - + + - V1V1 V2V2 VcVc

6. R2R2 - + R1R1 R4R4 - + C4C4 C3C3 - + R3R3 R R R R - + V1V1 V2V2 PID control circuit