Band-Pass Filters Overview
A band-pass filter allows transmission within a specific wavelength range, bounded by rejection regions on either side. For broad band-pass filters, combining longwave-pass and shortwave-pass filters is effective.
However, for narrower band-pass filters, achieving precision in edge steepness and positioning becomes challenging, necessitating other methods like thin-film **Fabry–Perot filters** or multiple-cavity filters.
The Fabry–Perot filter uses a spacer (cavity) layer to act as a resonant cavity, and the simplest configuration is a single-cavity filter. For improved performance, coupling multiple simple filters in series creates multiple-cavity filters, a development similar to tuned circuits. Historically, these were referred to as “multiple half-wave filters,” with terms like DHW filter (double half-wave) and THW filter (triple half-wave) for two- and three-cavity filters.
Broad Band-Pass Filters
Band-pass filters can be categorized into broadband-pass filters and narrowband-pass filters.
Broadband filters typically have bandwidths exceeding 20%. These filters are constructed by combining longwave-pass and shortwave-pass filters, often on opposite sides of a single substrate to maximize transmission.
Key Design Considerations:
1. Matching Substrate and Medium:
– Each edge filter must match the substrate to its surrounding medium.
– This ensures high transmission in the pass band.
2. Combining Edge Filters:
– Placing both filters on the same side of the substrate introduces challenges in transmission peaks and matching layers.
– Matching involves balancing equivalent admittances and may require **quarter-wave matching layers** or advanced techniques.
Example Design:
In the visible spectrum:
– Longwave-Pass Section: [(H/2)L(H/2)]S, where equivalent admittance near the pass region approaches unity.
– Shortwave-Pass Section: [(L/2)H(L/2)]S, with slightly lower equivalent admittance than the longwave-pass filter.
These sections can be combined without matching layers between them, but a matching layer is required between the shortwave-pass section and the substrate.
Final Design Example:
– Table 8.1 details the design.
– Figure 8.2a: Equivalent admittances for the sections.
– Figure 8.2b: Transmittance of the final design.
Avoiding Transmission Peaks in Rejection Zones:
– Overlap of high-reflectance zones between components should be avoided.
– Second-order reflection peaks, typically missing in normal shortwave-pass filters, may appear due to thickness errors and interfere with rejection zones.
Maximum Transmission Expression:
The maximum transmission is given by:
\[
T_{\text{max}} = \left[ T_a T_b / \left( 1 – R_a R_b \right) \right]
\]
This holds only if phase conditions are met.
This tutorial provides an understanding of broadband-pass filters, detailing design considerations and methods for optimizing their performance. The principles discussed here are extensions of those outlined in previous tutorials, with specific attention to combining edge filters for enhanced functionality.
