Solid-state integrated electronic circuits are composed of distributed R and C elements. Therefore, feedback electronic circuits in integrated circuit form must be investigated by obtaining the transfer function of the distributed RC networks. It has been shown that the slope of the attenuation curve of a distributed RC network is 10n dB/decade, where n is the order of the RC filter [13]. This attenuation is in contrast with the normal 20n dB/decade for the lumped parameter circuits. (The concept of the slope of an attenuation curve is considered in Chapter 8. If it is unfamiliar reexamine this problem after studying Chapter 8.) An interesting case arises when the distributed RC network occurs in a series-to-shunt feedback path of a transistor amplifier. Then the loop transfer function may be written as

(a) Using the root locus method, determine the locus of roots as K varies from zero to infinity.
(b) Calculate the gain at borderline stability and the frequency of oscillation for this gain.

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K (s (s 3)1/2 (s + 1)(s + 2)1,2 L(s) = Gc(s)G(s) =