The s-domain circuit below has a number of impedance configurations seen between the various ports 1-6 which can be solved for with the switch open or closed. Please calculate the following impedances in a form that has a common denominator (simple, unfactored form is fine): a) With the switch open, solve the impedance seen between ports 1 and 2, that is Zız(s). b) With the switch open, solve the impedance seen between ports 3 and 4, that is Zu4(s). With the switch open, solve the impedance seen between ports 5 and 6, that is Zso(s). with the switch closed, solve the impedance seen between ports 1 and 2, that is new Ziz(s). With the switch closed, solve the impedance seen between ports 3 and 4, that is new Zu(s). With the switch closed, solve the impedance seen between ports 5 and 6, that is new Zx(s). e) d) e)

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Thevenin Theorem

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.