Average Power Loss In Resonator Calculator

Formula Used:

\[ P = \frac{R_s}{2} \times \int_{0}^{r_r} (H_t)^2 x dx \]

Surface Resistance of Resonator (R_s):

Ohm

Tangential Magnetic Intensity Peak Value (H_t):

A/m

Radius of Resonator (r_r):

Average Power Loss in Resonator (P):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Average Power Loss in Resonator?

Average Power Loss in Resonator represents the energy dissipated as heat in a resonator due to surface resistance. It can be evaluated by integrating the power density over the inner surface of the resonator.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = \frac{R_s}{2} \times \int_{0}^{r_r} (H_t)^2 x dx \]

Where:

\( P \) — Average Power Loss in Resonator (W)
\( R_s \) — Surface Resistance of resonator (Ω)
\( H_t \) — Tangential Magnetic Intensity Peak Value (A/m)
\( r_r \) — Radius of resonator (m)

Explanation: The formula calculates power loss by integrating the squared tangential magnetic intensity over the resonator's radius, multiplied by half the surface resistance.

3. Importance of Power Loss Calculation

Details: Accurate power loss calculation is crucial for resonator design, efficiency optimization, and thermal management in electromagnetic systems.

4. Using the Calculator

Tips: Enter surface resistance in ohms, tangential magnetic intensity in A/m, and radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is surface resistance in a resonator?
A: Surface resistance is the ratio of applied voltage to current flowing from two electrodes, representing the material's resistance to current flow at the surface.

Q2: Why is tangential magnetic intensity important?
A: Tangential magnetic intensity at the surface determines the induced currents and subsequent power dissipation in the resonator.

Q3: How does radius affect power loss?
A: Larger radius increases the integration area, typically resulting in higher total power loss for the same magnetic intensity.

Q4: What are typical values for these parameters?
A: Surface resistance varies by material (typically 0.001-10 Ω), magnetic intensity depends on application (1-1000 A/m), and radius is design-specific (0.01-1 m).

Q5: Can this formula be used for all resonator types?
A: This formula is specifically for cylindrical resonators with uniform properties. Other geometries may require different formulations.