Coupled LC Resonators

Two identical LC tanks coupled by mutual inductance M split into two resonant modes: an even mode (lower frequency f₋) and an odd mode (upper frequency f₊). The coupling coefficient k = M/L determines the mode splitting and passband bandwidth. Critical coupling (k = 1/Q) maximises the transfer response with a flat passband.

Equations & Parameters ▸

\(f_{\pm} = \dfrac{f_0}{\sqrt{1\mp k}} \quad \text{BW} \approx k\cdot f_0 \quad k_{\rm crit} = \dfrac{1}{Q}\)

k	Coupling coefficient (dimensionless, 0 < k < 1). Enter directly or derive from M.
M	Mutual inductance between the two coils. k = M/L for identical resonators.
Q	Unloaded quality factor of each resonator; set R = 0 for lossless (Q → ∞).
k_crit	Critical coupling: flat-top passband at k = k_crit = 1/Q.

Resonator Parameters

Inductance, L

Capacitance, C

Series resistance, R (loss, optional)

Coupling (enter k or M)

Coupling coefficient, k

Mutual inductance, M (alternative)

Results

Diagram