Lesson 16Inductors Transient Analysis

Learning ObjectivesCalculate inductor voltage and current as a function of time.Explain inductor DC characteristics.

Inductor Charging Inductor: Oppose Changes (Choking effects) Inductor is initially fully dischargedacts like a open circuitWhen switch is closed, the changing current across the inductor immediately induces a voltage that opposes that change, which keeps the current near zero:

Inductor charging

As current iL builds up, the voltage across the R1 resistor increases.

Inductor Charging EquationsVoltages and currents in a charging circuit change exponentially over time

Steady State ConditionsCircuit is at steady state: voltage and current reach their final values and stop changing

There is no change in current in the circuit, so the inductor has zero voltage induced across it. Inductor current will be steady:

Inductor then looks like a short circuit

The Time ConstantRate at which an inductor charges depends on R and L, which is called the TIME CONSTANT:

Transients can be considered to last for five time constants

In the circuit below, the switch is initially open and conditions are at steady-state.

After the switch is shut, determine:how long it will take for the inductor to reach a steady-state condition (>99% of final current). Write the equation for the VL(t) & iL(t). Sketch the transient. Find the Energy stored in the Inductor.Example Problem 1

Interrupting Current in an Inductive CircuitWhen switch opens in an RL circuitEnergy is released in a short timeThis may create a large voltageInduced voltage is called an inductive kickOpening of inductive circuit may cause voltage sparks of thousands of volts

Interrupting a Circuit Switch flashovers are generally undesirableThey can be controlled with proper engineering design

These large voltages can be usefulSuch as in automotive ignition systems

Inductor DischargingInductor is initially fully charged with constant 100 ma current through it. It acts like a short circuit When switch is opened, the inductor will immediately induce a voltage to keep the 100 mA current constant. KVL can be used to calculate this induced voltageNotice the polarity of the induced voltage!

Inductor Discharging

As stored energy is released, the induced voltage across the inductor drops.

This makes the voltage drop across the resistor drop, so current in the circuit drops

Inductor Discharging EquationsVoltages and currents in a discharging circuit also change exponentially over time

The Time ConstantRate at which an inductor discharges depends on R and L, which is called the TIME CONSTANT:

Transients can be considered to last for five time constants

The circuit shown below has been in operation with the switch shut for a long time. The switch opens at time t = 0, determine:

how long it will take for the inductor to discharge. Write the equation for the VL, iL,. Sketch the transient.

Example Problem 2

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