Find the transfer function and deduce the type of filter

Question

CIRCUIT & NETWORK THEORY III ASSIGNMENT I

1. For the circuit shown in Figure 1 below, find the transfer function and deduce the type of filter represented.

i). Find Q, ω₀ and the DC gain H.

ii). Find the sensitivity of Q, ω₀ and H with R₁, R₃, C₂, C₄, R_A and R_B.

iii). Find the sensitivity of magnitude of the transfer function |T(jω)| with R₁, R₃, C₂, C₄, R_A and R_B.

iv). Given that R₁ = 10k?, R₃ = 10k?, C₂ = 16nF, C₄ = 16nF, R_A = 10k? and R_B = 10k?, simplify the transfer function and determine the actual values of Q, f₀, ω₀ and K.

v). For values of Rb from 1k? to 21k? in steps of 2k? plot in MATLAB the gain A in dB against f in kHz on a semilog scale. Axes specification:
-40dB ≤ A(dB) ≤ 50dB and 100 ≤ f ≤ 10k?.

2. For the three circuits shown in Figure 2 below, derive the transfer function and simplify them to the form
T(s) =( K/ (s² +s/Q+1))

i). For each of the circuit, determine S^Q_R1, S^Q_R2, S^Q_C1, S^Q_C2, S^Q_K, S^Q_RA, S^Q_RB, S^K_RAand S^Q_{RB .}

ii). If the three circuits were prototypes, which of the three would you chose for implementation and why?