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Q. The model of an elemental length of a lossy transmission line is shown in Figure
(a), along with its parameters, where R is series resistance per unit length, L is series inductance per unit length, G is shunt conductance per unit length, and C is shunt capacitance per unit length.
The characteristic impedance ¯ Z0 of the line is given by
where α is the attenuation constant (nepers per unit length) and β is the phase constant (radians per unit length). The ac steady-state solution for the uniform line reveals the voltage on a matched line ( ¯ ZL = ¯ Z0) to be ¯ E(x) = ¯ ES e-¯ γx= ¯ ES e-αx e-jβx , where ¯ ES is the sending-end voltage and x is distance along the line from the sending end.
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A feedback control system with the configuration of Figure has the following parameters: K p = 0.5 V/rad, K a = 100 V/V, K m = 2.7 × 10 -4 N·m/V, J = 1.5 × 10 -5 kg·m 2 , and
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