## Rectangular waveguide formula for cutoff frequency calculator

The cutoff frequency (also known as the critical frequency) of a rectangular waveguide is the lowest frequency at which the waveguide can support a particular mode of electromagnetic wave propagation. Rectangular waveguides can support several different modes, and each mode has its own cutoff frequency. The fundamental mode, often referred to as the TE10 mode, is the most commonly used and is typically the mode of interest. The generic rectangular waveguide cutoff frequency formula is as follows.

The cutoff frequency for TE10 mode in rectangular waveguide can be calculated using following formula. Keep in mind that this formula assumes that the waveguide is operating in a vacuum or a homogeneous dielectric medium with the same properties as a vacuum. In practical applications, the waveguide might have a dielectric material inside it, which can affect the cutoff frequency and mode propagation.

In this formula, 'a' represents the dimension of the waveguide's narrow side (the width), and the TE10 mode is the mode with the lowest cutoff frequency. Other modes in rectangular waveguides will have different cutoff frequencies, and they can be calculated using more complex mathematical expressions.

### Rectangular waveguide cutoff frequency calculator

The cutoff frequencies for different modes of rectangular waveguides are determined by the waveguide's dimensions and the operating frequency. The following calculator can be used to calculate lowest cutoff Frequency of the rectangular waveguide as per generic formula mention in equation-1 above.

EXAMPLE calculation :

INPUTS: a=0.072, b=0.034, m=1, n=0, Er=8.85E-12, Mu=1.25E-6

OUTPUT: Lowest Cut-off Frequency = 2.08 Hz

### Rectangular waveguide calculator for TE_{10} Mode

Following calculator calculates lowest cutoff frequency of rectangular waveguide as per TE10 mode and equation-2 that is Fc = c/2a , where 'c' is speed of light and 'a' is large dimension of waveguide.

EXAMPLE calculation :

broad dimention (Input ) = 0.072 meter

Cutoff frequency (output) = 2.08 Hz

**Conclusion** : In summary, the rectangular waveguide cutoff frequency calculator and formula are indispensable tools for RF engineers.
They provide critical information for mode selection, frequency planning, interference mitigation, impedance matching, filter design, antenna feed systems
and overall system performance. These tools streamline the design process and help ensure that waveguide-based RF systems meet their performance requirements.