The Slot Line Conversion Calculator computes the effective dielectric constant (εeff) and guide wavelength (λg) for a slot line based on the operating frequency and substrate dielectric constant. It helps engineers analyze signal propagation characteristics and design high-frequency planar circuits with accurate wavelength control.
Formula
εeff = (εr + 1) / 2
λg = λo / √(εeff)
where λo = c / f and c = 3 × 108 m/s
Formula Explanation
- εr = Relative dielectric constant of the substrate.
- εeff = Effective dielectric constant representing the propagation medium for the slot line mode.
- λo = Wavelength in free space determined by the frequency.
- λg = Guide wavelength, which indicates how the signal travels within the slot line.
Uses of this calculator
- Designing and analyzing microwave slot line components.
- Determining wavelength shortening effects due to the substrate.
- Optimizing slot line filters, couplers, and antennas.
- Evaluating dielectric effects in hybrid and monolithic RF circuits.
What is the guide wavelength for a 10 GHz slot line on a substrate with εr = 4.4?
Input: f = 10 GHz, εr = 4.4
Output:
- εeff = (4.4 + 1) / 2 = 2.7
- λo = 3 × 108 / 10 × 109 = 0.03 m
- λg = 0.03 / √2.7 = 0.03 / 1.643 = 0.0183 m
- Guide wavelength (λg) ≈ 18.3 mm