TE10 Mode Wavelength Calculator for a Specific Frequency

Historical Background

The TE10 mode is the dominant mode of propagation in rectangular waveguides, meaning it is the lowest frequency mode that can propagate. This mode is widely used in microwave and millimeter-wave engineering due to its simplicity and efficiency. The cutoff frequency and corresponding TE10 wavelength are critical parameters in the design of waveguides and microwave circuits.

Calculation Formula

The TE10 mode wavelength can be calculated as follows:

1. Cutoff Frequency:
   \[ f_c = \frac{c}{2a} \]
   where:

   • \( c \) is the speed of light (\( 299,792,458 \, \text{m/s} \))
   • \( a \) is the width of the waveguide in meters

2. TE10 Wavelength:
   \[ \lambda_{TE10} = \frac{c}{\sqrt{f^2 - f_c^2}} \]
   where:

   • \( f \) is the operating frequency in Hz
   • \( f_c \) is the cutoff frequency in Hz

Example Calculation

For a waveguide width \( a = 40.9 \, \text{mm} \) and frequency \( f = 10 \, \text{GHz} \):

1. Convert the waveguide width to meters:
   \[ a = 40.9 \, \text{mm} = 0.0409 \, \text{m} \]

2. Calculate the cutoff frequency:
   \[ f_c = \frac{c}{2a} = \frac{299,792,458}{2 \times 0.0409} \approx 3.665 \, \text{GHz} \]

3. Compute the TE10 wavelength:
   \[ \lambda_{TE10} = \frac{299,792,458}{\sqrt{(10 \times 10^9)^2 - (3.665 \times 10^9)^2}} \approx 36.59 \, \text{mm} \]

Importance and Usage Scenarios

Understanding the TE10 mode wavelength is critical for designing waveguides, antennas, and microwave components such as filters and couplers. The wavelength determines the physical dimensions of components and affects their performance in specific frequency bands.

Common FAQs

1. What is the TE10 mode?

   • The TE10 mode is the dominant mode of propagation in rectangular waveguides, characterized by one half-wavelength variation across the broader dimension.

2. Why is the TE10 mode important?

   • It is the most efficient and commonly used mode in rectangular waveguides, providing the lowest loss and simplest field configuration.

3. Can I use this calculator for frequencies below the cutoff frequency?

   • No, the waveguide cannot support propagation below the cutoff frequency. Ensure that the operating frequency is greater than the cutoff frequency.