Chamfered Bend
Understanding Chamfered Bend
Impedance Discontinuities in Transmission Line Corners
When routing RF and microwave signals in microstrip, stripline, or waveguide structures, the path must often make 90-degree turns. A simple, square 90-degree bend introduces a significant physical discontinuity. In a microstrip line, the corner adds extra conductor area, creating a localized parasitic capacitance to ground. In a waveguide, the sharp corner disturbs the electromagnetic field distribution, causing reflection waves that travel back to the source.
This impedance mismatch degrades the return loss (VSWR) and increases insertion loss. At higher frequencies (such as Ku, Ka, and mmWave bands), these reflections can cause severe ripple in the passband and degrade the performance of filters, couplers, and amplifiers. To resolve this, the outer corner of the bend is cut away (chamfered or mitered), removing the excess capacitance and restoring the characteristic impedance of the line.
Optimum Mitering Calculations and Waveguide Applications
The fraction of the corner that is removed is defined by the mitering percentage. For microstrips, the optimum chamfer removes approximately 50% to 70% of the corner width, depending on the substrate's dielectric constant ($\epsilon_r$) and the line width to substrate height ratio ($w/h$). An under-mitered corner retains excess capacitance, while an over-mitered corner introduces parasitic inductance by narrowing the line too much.
In rectangular metal waveguides, a mitered bend is constructed by inserting a flat metal plate at a 45-degree angle across the outer corner of the 90-degree bend. The position of this flat plate is calculated to balance the inductive and capacitive discontinuities at the corner. This mitered design provides a much wider bandwidth and lower reflection profile than a simple sharp corner, while being far more compact and easier to manufacture than a swept, curved waveguide bend.
Key Mathematical Relations
Technical Specifications Comparison
| Bend Geometry | Parasitic Effect | Return Loss (VSWR) | Physical Size Profile | Manufacturing Complexity | Optimal Frequency Band |
|---|---|---|---|---|---|
| Right-Angle Bend (Unmitered) | High capacitive loading | Poor (high reflections) | Very Compact | Extremely Low | < 2 GHz |
| Chamfered / Mitered Bend | Balanced (parasitics canceled) | Good (low reflections) | Very Compact | Low-Moderate (requires precision cut) | 2 GHz - 40 GHz |
| Swept / Curved Bend | Minimal (smooth transition) | Excellent (lowest reflections) | Large (requires sweep radius $R > 3w$) | High (requires bending tooling) | All bands (including mmWave) |
Frequently Asked Questions
Why does a square corner introduce parasitic capacitance?
A square 90-degree corner has a larger surface area than a straight trace of the same width. Since capacitance is directly proportional to the conductor area ($C = \epsilon A / d$), this extra area acts as a local capacitor, lowering the impedance of the line at the corner ($Z = \sqrt{L/C}$), which creates a signal reflection.
What is the miter percentage and how is it measured?
The miter percentage ($M$) is the ratio of the diagonal length of the cut to the original diagonal length of the square corner, expressed as a percentage. A 60% miter means that 60% of the diagonal dimension of the corner has been cut away. The optimum percentage varies based on the substrate material and trace width.
When should a swept bend be used instead of a chamfered bend?
A swept (curved) bend provides the lowest possible reflections and is preferred in ultra-high-frequency mmWave circuits or high-power applications where sharp edges can cause dielectric breakdown or arcing. However, swept bends require significantly more board space than chamfered bends, making chamfered bends the default choice for compact PCB routing.