Dielectric Resonator Puck (DRO) Calculator

Microwave Dielectric Resonator Oscillators (DROs)

At microwave and millimeter-wave frequencies (4 GHz to 40 GHz), planar microstrip and lumped LC resonators suffer from severe conductive and radiation losses, limiting their unloaded quality factor to $Q_0 \approx 100 - 300$. A Dielectric Resonator (DR)—a cylindrical ceramic puck fabricated from ultra-low-loss materials such as barium tetratitanate or zirconium tin titanate with high relative permittivity ($\varepsilon_r \approx 30 - 90$)—confines electromagnetic energy almost entirely within its boundaries, delivering exceptional $Q_0$ values of 5,000 to 20,000.

Fundamental $TE_{01\delta}$ Mode Frequency Formulation

The dominant mode used in DROs is the transverse electric $TE_{01\delta}$ mode, where $\delta$ represents the non-integer fractional half-wavelength standing wave along the axial height $H$. Using the established Cohn and Itoh-Rudokas analytical waveguide model:

Where:

• $c = 299.79\ \text{mm}\cdot\text{GHz}$: Speed of light in vacuum.
• $D$: Resonator outer diameter (mm).
• $H$: Resonator height / thickness (mm).
• $D / (2H)$: Puck aspect ratio. To maintain maximum frequency separation from higher-order spurious modes ($HE_{11\delta}$ and $TM_{01\delta}$), the optimal aspect ratio is between $1.0$ and $1.5$.

Mechanical Cavity Tuning & Microstrip Coupling

A dielectric puck is enclosed in a metallic shield to eliminate radiation and prevent EMI. Placing an adjustable metallic tuning screw in the enclosure ceiling directly above the puck perturbs the fringing external magnetic fields: as the screw approaches the puck (decreasing $h_{cov}$), magnetic energy is expelled, causing the resonant frequency to shift upwards by $1\%$ to $4\%$.