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RL Circuit and Ripple Reduction

 

RL Circuit and Ripple Reduction

RL Circuit and Ripple Reduction

RL Circuit Basics

For an RL series circuit:

V(t) = VR + VL = IR + L(dI/dt)

Impedance Approach (for Ripple)

For ripple frequency ω:

ZR = R
ZL = jωL
Z = R + jωL
|Z| = √(R² + (ωL)²)

Ripple Current

If ripple voltage is Vr:

Iripple = Vr / √(R² + (ωL)²)

Key Insight

1. Low Frequency Ripple

ωL ≪ R
Iripple ≈ Vr / R

Inductor has little effect.

2. High Frequency Ripple

ωL ≫ R
Iripple ≈ Vr / (ωL)

Strong ripple reduction.

Ripple Reduction Factor

Ripple Reduction = R / √(R² + (ωL)²)
  • Larger L → less ripple
  • Higher frequency → less ripple
  • Larger R → more ripple

Physical Meaning

  • Resistor affects both DC and ripple
  • Inductor resists only changing current

RL smooths current but wastes power in R

Time-Domain View

Ï„ = L / R
  • Large Ï„ → smoother output
  • Small Ï„ → more ripple passes

Summary

  • RL reduces ripple using inductive reactance
  • Effectiveness depends on ωL / R
  • Works better at high frequency
  • Less efficient than LC filters

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