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# Problem 05 In R Out For the circuit above, answer the following questions. 1. Derive the formula ...

Problem 05 In R Out For the circuit above, answer the following questions. 1. Derive the formula for the transfer function angular resonant frequency omega_res (enter the right hand side part of the formula only) Use exactly same notations for L,C and R as in the circuit diagram. Hints for solving the problem. (1) Ignore trivial solution omega_res 0 (2) In case obtaining the resonant frequency using the condition imag(H)0 fails, try finding the resonant frequency using impedance resonance: imag(Z)0 Hints for entering formula 1) use multiplication symbol * explicitly; do not write LC for L*C 2) to enter square root of variable X, use either sqrt(X) or X(1/2) omega-res = Submit Answer Tries 0/5 2. Find the value of the resonant frequency fr (NOT the angular frequency) if the circut parameters are R=155 Ohm, C=1 uF ("u"-micro), L= 2 mH; (Unit: Hz) Submit Answer Tries 0/3
Problem 06 し2 R3 V The circuit above has the folloiwng prameters: R= 195 Ohm, C=0.5 uF ("u"-micro), L1 = 5 mH, L2-3 mH; 1. Find the resonant frequency fr (Unit: Hz; note: NOT the angular frequency) Hint: you can find the fr using the folloiwng steps (1) find the transfer function H using any technique (nodal analysis or SPICE simulation) (2) plot the imaginary part of H or the phase of H as a function of frequency (3) find the frequency at which im(H) 0 or angle(H)-0 As an alternative, you can derive the formula for the resonant frequency, either manually or using MATLAb symbolic calculations Submit Answer Tries 0/5 2. Find the magnitude M (in dB) of the transfer function at the resonant frequency fr Hint: you can find M using similar steps as in part 1. As an alternative, you can derive the formula for M and substitute om with om_res in it; then calculate M Submit Answer Tries 0/5 Submit All

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