52 Ch 10 RC _ RL - Making sense of EE 2nd ed Transients in...

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Quite often, the voltage applied to a circuit abruptly changes. It happens when we flip a switch or send a digital signal: in your computer, such abrupt changes occur billions of times every second! In response to the changed input voltage, the currents and voltages in the circuit will change: gradually they will reach new steady-state conditions, but before then, some transient changes will occur that exist only for a certain amount of time. Transient responses occur in all circuits. Their parameters depend on resistances, capacitances, and inductances; their features are described with differential equations. Of course, the simplest differential equations are of the first order: they look like dx dt + k " x = 0 or dx dt + k " x = f ( t ) The circuits, whose responses can be described (accurately enough) with such equations, are called the First-Order Circuits. They include circuits with sources, resistors, and one energy-storing element – a capacitor or an inductor. We call them RC and RL circuits. The time-dependent x in the equations above can be a current or a voltage. In this course, we consider the simplest case where f ( t ) is a constant or a step function. The solutions to these differential equations above have been known for at least 200 years. They are exponential: x ( t ) = A " e # k " t + B = A " e # t $ + B , where k > 0
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