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7 Transient Analysis

# 7 Transient Analysis - Transient Analysis We are still...

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4-1 Transient Analysis We are still using DC power supplies. But we switch them on or off and study the transients. AC power supplies is discussed in AC analysis Switches and Operations Charging Capacitors with Current Source Capacitors in Parallel and in Series Charging Capacitors with Voltage Source (RC Circuit Response) First Order Linear Differential Equations Continuity of Capacitor Voltage Capacitor as Open Circuit in DC Analysis Charging Inductors with Voltage Source Inductors in Series and in Parallel Charging Inductors with Current Source (RL Circuit Response) Continuity of Inductor Current * 2nd Order ODE and RLC Circuit Response * RLC Circuits

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4-2 A resistive network has trivial circuit dynamics: all voltages and currents are linear functions of (that is, proportional to) input sources. However, many applications need energy storing elements , such as capacitors and inductors, along with switching actions that has specific circuit dynamics to achieve useful functions. The study of circuit dynamics is also known as transient analysis . 10V t=0 5k 5k + V o (t) V a t 0 V a (t) 10V t 0 V o (t) 10V Example 4-1 : The output voltage of a resistor divider circuit follows the input voltage exactly. Resistive Networks have Trivial Circuit Dynamics
4-3 Applications of Circuit Dynamics Transients are unavoidable when one switches on or off a circuit. Sometimes we deliberately induce transients, e.g. in pulse power circuits to generate a current or voltage pulse We can also use transients to provide timing circuits. Example: in an alarm system, a sensor may set off an alarm after 30 seconds. Very often, transients and RC or LC resonances are used together. A timer consists of an RC (resistor + capacitor) circuit: an RC timer. LC resonances are used for frequency generation.

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4-4 Transients are used to generate high voltage and high current pulsed used in camera flashlamp, lasers, automobile engines, bombs etc. Make use of dv/dt or di/dt Capacitive energy storage (E-field) or inductive energy storage (H-field) Pulse power 2 L C LI 1 U CV
4-5 Switches and Operations A switch has two states: open and closed . For an ideal switch , when it is closed, the resistance is zero; and when it is open, the resistance is infinite. switch open switch closed switch closed at t=0: for t<0, S 1 open; for t 0, S 1 closed. S 1 S 1 S 1 t=0

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4-6 Electronic switches Mechanical switches such as the toggle switch are slow (microseconds) and have mechanical bounces – good for turning on/off power but not good for precision applications Electrical switches are better: e.g. simple transistors (bipolar and field effect), silicon-controlled rectifier (SCR), thyristor, krytrons, thyratrons, spark gap etc. Different switches have different voltage and current ratings and speed Typical electronic switch has about 1 ns switching time Switches are also used in switching-mode power supplies Two types of switches: opening switches (for inductors) and closing switches (for capacitors, more common) Fuse switch is used in power lines as circuit breakers
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7 Transient Analysis - Transient Analysis We are still...

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