Multiple Resonance

MULTIPLE RESONANCE

Circuits which exhibit more than one resonant frequency are called multiple resonant circuits.

L₁ C₁ series resonant at f₁. Inductive at f₂.

F₂ > f₁

L₁ C₁ in parallel with C₂ is parallel resonant at ƒ₂.

ω₁ = 2π f₁; ω₂ = 2π f₂; 0 = 2π f

Where ƒ is any frequency.

At ω₂, Reactance of L₁ C₁ arm = Reactance of C₂ arm

Here, pole is greater than zero.

ω₁ < ω₁ : ω₂ : z is capacitive

ω₁ < ω < ω₂ : z is inductive

ω₁ < ω₂ < ω : z is capacitive

Example: Zero at 1296 KHz

Pole at 1476 KHz

Capacitive at all other frequencies

Reactance of: 936 KHz 1296 KHz 1350 KHz

L₁ || C₁ is capacitive for ω > ω₁

L₀ in series with L₁ || C₁ is series resonant at ω₂ ω₂ : Zero ω₂ > ω₁

Domain of ω :

Z: ω < ω₂ inductive

ω₁ < ω < ω₂ capacitive

ω₁ < ω₂ < ω inductive

Practical Problem:

Z_AB = Z Ohms

f = Working frequency in KHz

L₁, L₂ : μH ; C₁: pF

L₁ || C₁ : Parallel resonant at 2 f

L₂ in series with L₁ || C₁ series resonant at 3 f.

Z_AB = Z at f (inductive)