The Microstrip Line Calculator is a valuable tool used to determine the critical parameters of a microstrip line, which is a type of electrical transmission line commonly used in microwave circuits. This calculator helps in designing microstrip lines by providing accurate values for the effective dielectric constant, characteristic impedance, wavelength, and phase velocity. These parameters are essential for ensuring the efficient and reliable performance of microwave circuits.
Key Formulas of Microstrip Line Calculator
Below are the key formulas used in a microstrip line calculator.
Effective Dielectric Constant (epsilon_eff)
The effective dielectric constant (epsilon_eff) accounts for the fringing fields around the strip and the substrate. It is given by:
epsilon_eff = (epsilon_r + 1) / 2 + (epsilon_r – 1) / 2 * (1 + 12 * h / W)^(-0.5)
where:
- epsilon_r = relative dielectric constant of the substrate
- h = height of the substrate
- W = width of the microstrip line
Characteristic Impedance (Z_0)
The characteristic impedance (Z_0) of the microstrip line can be calculated using:
Z_0 = 60 / sqrt(epsilon_eff) * ln(8 * h / W + 0.25 * W / h)
For W/h > 1:
Z_0 = 120 * pi / sqrt(epsilon_eff) * (W / h + 1.393 + 0.667 * ln(W / h + 1.444))
Microstrip Line Wavelength (lambda_g)
The wavelength of the signal on the microstrip line (lambda_g) is given by:
lambda_g = lambda_0 / sqrt(epsilon_eff)
where lambda_0 is the free-space wavelength.
Phase Velocity (v_p)
The phase velocity (v_p) of the signal on the microstrip line is:
v_p = c / sqrt(epsilon_eff)
where c is the speed of light in a vacuum.
Pre-Calculated Values Table
Below is a table with some pre-calculated values for quick reference:
| Relative Dielectric Constant (epsilon_r) | Substrate Height (h) | Microstrip Width (W) | Effective Dielectric Constant (epsilon_eff) | Characteristic Impedance (Z_0) |
|---|---|---|---|---|
| 4.5 | 1.6 mm | 3.0 mm | 3.3 | 50 ohms |
| 2.2 | 1.0 mm | 2.0 mm | 1.9 | 75 ohms |
| 6.0 | 2.0 mm | 4.0 mm | 5.0 | 30 ohms |
Example of Microstrip Line Calculator
Let’s go through an example calculation using the Microstrip Line Calculator:
Input Values:
- Relative Dielectric Constant (epsilon_r): 4.5
- Substrate Height (h): 1.6 mm
- Microstrip Width (W): 3.0 mm
Calculate Effective Dielectric Constant (epsilon_eff): epsilon_eff = (4.5 + 1) / 2 + (4.5 – 1) / 2 * (1 + 12 * 1.6 / 3.0)^(-0.5) epsilon_eff ≈ 3.3
Calculate Characteristic Impedance (Z_0): Z_0 = 60 / sqrt(3.3) * ln(8 * 1.6 / 3.0 + 0.25 * 3.0 / 1.6) Z_0 ≈ 50 ohms
Most Common FAQs
A microstrip line is a type of electrical transmission line use to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate
The characteristic impedance (Z_0) of a microstrip line can be calculate using specific formulas that take into account the width of the strip, the height of the substrate, and the effective dielectric constant.
The effective dielectric constant (epsilon_eff) is important because it accounts for the influence of both the dielectric material and the air surrounding the microstrip line, affecting the propagation of signals.