Microstrip Meander Line Inductor Synthesizer

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.