Microstrip Meander Line Inductor Synthesizer
Synthesize compact serpentine/meander line planar inductors, account for negative mutual coupling between anti-parallel segments, and evaluate self-resonant frequencies (SRF).
Microstrip Meander Line Inductor Design
In planar microwave integrated circuits (MICs), straight transmission line inductors consume excessive board length. Folding the conductor into a periodic serpentine (meander) shape compacts the layout by up to 75%.
1. Grover Formulation & Negative Mutual Coupling
Because adjacent parallel vertical segments carry currents in opposing directions, their mutual electromagnetic coupling is negative ((M < 0)), which reduces total net inductance:
$$L_{\text{net}} = \sum L_{\text{self}} - 2 \sum |M_{\text{negative}}| + 2 \sum M_{\text{positive}}$$
To maximize inductance per unit board area, the spacing (S) between adjacent turns should be kept wide enough ((S \ge 2W)) to avoid canceling out too much positive self-inductance.
2. Self-Resonant Frequency (SRF) & Inter-Turn Capacitance
Fringing electric fields across the narrow gaps between adjacent meander traces create parasitic inter-turn capacitance (C_p). At the Self-Resonant Frequency, inductive reactance equals capacitive reactance:
$$\text{SRF} = \frac{1}{2\pi \sqrt{L_{\text{net}} \cdot C_p}}$$
Above the SRF, the component ceases to behave as an inductor and turns purely capacitive. For reliable RF chokes and filters, operate at frequencies below 50% of the SRF.
Frequently Asked Questions
Why does increasing the number of turns beyond a certain point fail to increase inductance?
As turns are packed closer together, negative mutual coupling between opposing currents accelerates faster than self-inductance accumulates. Widening the turn spacing or lengthening the meander height is required to restore inductive growth.
How does meander Q-factor compare to a spiral inductor?
Planar spiral inductors generally achieve higher Q-factors (50-80) because all current segments circle in the same direction with positive mutual coupling. Meanders have lower Q (25-45) due to negative mutual cancellation, but require zero center underpass vias.