Effective Radius of Circular Microstrip Patch Calculator

Formula Used:

\[ a_{eff} = a_c \times \left(1 + \frac{2h_o}{\pi a_c E_r} \times \left(\ln\left(\frac{\pi a_c}{2h_o}\right) + 1.7726\right)\right)^{0.5} \]

Effective Radius of Circular Microstrip Patch (a_eff):

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1. What is the Effective Radius of Circular Microstrip Patch?

The Effective Radius of Circular Microstrip Patch is related to the physical radius of the circular patch but is adjusted to account for the fringing fields affecting the performance of the antenna. It provides a more accurate representation of the antenna's electrical behavior.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ a_{eff} = a_c \times \left(1 + \frac{2h_o}{\pi a_c E_r} \times \left(\ln\left(\frac{\pi a_c}{2h_o}\right) + 1.7726\right)\right)^{0.5} \]

Where:

\( a_{eff} \) — Effective Radius of Circular Microstrip Patch (m)
\( a_c \) — Actual Radius of Circular Microstrip Patch (m)
\( h_o \) — Thickness of Substrate Microstrip (m)
\( E_r \) — Dielectric Constant of Substrate
\( \pi \) — Archimedes' constant (≈3.14159)
\( \ln \) — Natural logarithm function

Explanation: The formula accounts for the fringing fields at the edges of the patch, which effectively increase the electrical size of the patch compared to its physical dimensions.

3. Importance of Effective Radius Calculation

Details: Accurate calculation of the effective radius is crucial for designing circular microstrip patch antennas with the desired resonant frequency and radiation characteristics. It helps in predicting the actual performance of the antenna.

4. Using the Calculator

Tips: Enter the actual radius in meters, substrate thickness in meters, and dielectric constant. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the effective radius different from the physical radius?
A: The effective radius accounts for fringing fields at the edges of the patch, which effectively increase the electrical size of the patch beyond its physical dimensions.

Q2: What is the significance of the dielectric constant in this calculation?
A: The dielectric constant affects how the electromagnetic fields are confined within the substrate, which influences the amount of fringing and thus the effective radius.

Q3: How does substrate thickness affect the effective radius?
A: Thicker substrates generally result in more pronounced fringing fields, leading to a larger difference between physical and effective radius.

Q4: What are typical values for these parameters?
A: Typical values range from: a_c (0.001-0.1 m), h_o (0.0001-0.01 m), E_r (2-12 depending on substrate material).

Q5: How accurate is this formula?
A: This formula provides a good approximation for most practical applications, though more complex models may be needed for very precise designs or unusual substrate materials.