Calculate the motor torque using:
\[
T = \frac{60\,P}{2\pi\,n}
\]
where \(P\) is power in watts and \(n\) is speed in rpm.
* Enter the mechanical power (W) and speed (rpm).
Example: 5000 W
Example: 1500 rpm
Calculate the average DC output voltage for a single-phase fully controlled full-wave rectifier.
Using the formula:
\[
V_{dc} = \frac{2V_m}{\pi}\cos\alpha
\]
where \(V_m\) is the peak AC voltage and \(\alpha\) is the firing angle.
* Enter the peak voltage (V) and firing angle (°).
Example: 170 V
Example: 30°
Calculate Voltage, Current, or Resistance using Ohm’s Law.
Voltage: \( V = I \times R \)
Current: \( I = \frac{V}{R} \)
Resistance: \( R = \frac{V}{I} \)
Example: 2 A
Example: 5 Ω
Calculate the effective Geometric Mean Radius (GMR) of a two-layer ACSR conductor.
Using the formula:
\[
\text{GMR}_{\text{eff}} = \left( \text{GMR}_{\text{steel}}^{n_s} \times R_{\text{alu}}^{n_a} \right)^{\frac{1}{n_s+n_a}}
\]
where:
\( \text{GMR}_{\text{steel}} \) is the steel core GMR,
\( R_{\text{alu}} \) is the effective radius for the aluminum layer,
\( n_s \) is the number of steel core elements, and
\( n_a \) is the number of aluminum strands.
* Enter values in meters for radii and the counts for elements.
Example: 0.005 m
Example: 1
Example: 0.03 m
Example: 26
Calculate the effective aperture of an antenna using:
\[
A_e = \frac{\lambda^2 \, G}{4\pi}
\]
where \(\lambda\) is the wavelength and \(G\) is the antenna gain (linear scale).
* Enter the wavelength (m) and antenna gain (unitless).
Example: 0.3 m (corresponding to 1 GHz)
Example: 10 (linear gain, not in dB)
Estimate the resonant frequency of an air-filled rectangular cavity resonator.
Using the formula:
\[
f_{mnl} = \frac{c}{2\pi}\sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2 + \left(\frac{l}{d}\right)^2}
\]
where \(c \approx 3 \times 10^8\) m/s.
* Enter the cavity dimensions (in meters) and mode numbers (m, n, l).
(For the common TE101 mode, use m=1, n=0, l=1.)
Example: 0.1 m
Example: 0.05 m
Example: 0.2 m
Example: 1
Example: 0
Example: 1
Rectangular cavity resonators are widely used in microwave engineering for filters, oscillators, and various high-frequency components. When the cavity is air-filled, its resonant frequency depends purely on its physical dimensions and the electromagnetic mode of operation. This guide explains how to estimate the resonant frequency of an air-filled rectangular cavity resonator, focusing on a common mode.
An air-filled rectangular cavity resonator is a hollow, metal box with rectangular cross-section that supports electromagnetic standing waves at specific resonant frequencies. The dimensions of the cavity (length, width, and height) determine which frequencies are sustained. These resonators are essential components in many microwave circuits.
In rectangular cavity resonators, various transverse electric (TE) and transverse magnetic (TM) modes can exist. A commonly used mode is the TE₁₀₁ mode, where:
This mode is often chosen for its favorable field distribution and ease of excitation in practical applications.
For a rectangular cavity resonator operating in the TE₁₀₁ mode, the resonant frequency \( f_{101} \) is given by:
Where:
Note that in this simplified formula for the TE₁₀₁ mode, the height \( b \) does not appear because there is no field variation in that dimension.
Evaluate the terms inside the square root and multiply by the prefactor to obtain the resonant frequency in Hertz (Hz).
Given: A rectangular cavity with width \(a = 0.05\,m\) and length \(d = 0.10\,m\).
Calculation:
Compute the terms:
Now, the prefactor:
Thus:
The resonant frequency is approximately 3.35 GHz.
Given: A cavity with \(a = 0.03\,m\) and \(d = 0.06\,m\).
Calculation:
The resonant frequency in this case is approximately 5.59 GHz.
The Air-Filled Rectangular Cavity Resonator Calculator for the TE₁₀₁ mode provides an efficient method to estimate the resonant frequency of a rectangular cavity based on its dimensions. By applying the formula:
where \(c\) is the speed of light, \(a\) is the cavity width, and \(d\) is the cavity length (or depth), engineers and researchers can accurately design resonant structures for a variety of microwave and RF applications. Mastery of these calculations is key to developing efficient, high-performance components in advanced electronics.
Estimate the resonant frequency of an air-filled cylindrical cavity (TE₀₁₁ mode).
Using the formula:
\[
f_{011} = \frac{c}{2\pi}\sqrt{\left(\frac{3.832}{a}\right)^2 + \left(\frac{\pi}{d}\right)^2}
\]
where \(c \approx 3 \times 10^8\) m/s.
* Enter the cavity radius (a) and height (d) in meters.
Example: 0.05 m
Example: 0.1 m
Estimate the resonant frequency of an air-filled cylindrical cavity (TE₀₁₁ mode).
Using the formula:
\[
f_{011} = \frac{c}{2\pi}\sqrt{\left(\frac{3.832}{a}\right)^2 + \left(\frac{\pi}{d}\right)^2}
\]
where \(c \approx 3 \times 10^8\) m/s.
* Enter the cavity radius (a) and height (d) in meters.
Example: 0.05 m
Example: 0.1 m
This guide explains how to estimate the resonant frequency of an air-filled cylindrical cavity operating in the TE₀₁₁ mode. Such resonators are vital in microwave and RF engineering, used for filters, oscillators, and other high-frequency components. By understanding the underlying principles and the role of the cavity dimensions, you can accurately predict the resonant behavior.
A circular cavity resonator is a hollow, cylindrical metal structure that supports electromagnetic resonances at discrete frequencies. When filled with air (or vacuum), its resonant behavior is determined purely by its geometry. These resonators are widely used in microwave engineering for constructing filters, oscillators, and sensors.
In a cylindrical cavity, electromagnetic waves can propagate in various modes. The TE₀₁₁ mode is one where:
This mode is particularly popular due to its favorable field distribution and ease of excitation in many RF applications.
For an air-filled circular cavity resonator operating in the TE₀₁₁ mode, the resonant frequency \( f_{011} \) is given by:
Where:
Evaluate the terms inside the square root and multiply by the prefactor to obtain the resonant frequency in Hertz (Hz).
Given: A cylindrical cavity with radius \( a = 0.05\,m \) and height \( d = 0.10\,m \).
Calculation:
Calculate the radial term:
Calculate the axial term:
Sum under the square root:
Taking the square root:
Prefactor:
Finally, the resonant frequency is:
Thus, the resonant frequency is approximately 3.95 GHz.
Given: A cavity with \( a = 0.03\,m \) and \( d = 0.05\,m \).
Calculation:
Compute the radial term:
Compute the axial term:
Sum under the square root:
Taking the square root:
With the same prefactor:
Thus, the resonant frequency is approximately 6.80 GHz.
The Air-Filled Circular Cavity Resonator Calculator for the TE₀₁₁ mode offers a systematic approach to determine the resonant frequency of a cylindrical cavity based on its physical dimensions. By applying the formula:
where \(c\) is the speed of light, \(a\) is the cavity radius, and \(d\) is the cavity height, engineers and researchers can accurately design and optimize resonant structures for microwave and RF applications. Understanding this calculation process is crucial for the effective implementation of resonators in a variety of high-frequency systems.
Estimate the maximum power a rectangular waveguide can transmit before breakdown.
Using the formula:
\[
P_{br} = \frac{a \, b \, E_{br}^2}{2 \, Z_0}
\]
where \( Z_0 \approx 377\,\Omega \).
* Enter the waveguide width (a), height (b) in meters, and breakdown electric field \( E_{br} \) in V/m.
Example: 0.1 m
Example: 0.05 m
Example: 30,000 V/m (30 kV/m)
Calculate the operating frequency of a reflex klystron using a linear tuning approximation.
Using the formula:
\[
f = f_c + k \,(V_r – V_c)
\]
where:
\( f_c \) is the center frequency (MHz) at the reference voltage \( V_c \) (kV),
\( V_r \) is the actual reflector voltage (kV), and
\( k \) is the tuning sensitivity (MHz/kV).
* Enter all values in the specified units.
Example: 10 MHz
Example: 4 kV
Example: 20 MHz/kV
Example: 4.5 kV
When you visit our website, it may store information through your browser from specific services, usually in the form of cookies. Here you can change your Privacy preferences. It is worth noting that blocking some types of cookies may impact your experience on our website and the services we are able to offer.