Loaded Q
Understanding Loaded Q
The distinction between loaded and unloaded Q is critical for filter and resonator design. Unloaded Q represents the resonator alone; loaded Q includes the effects of the source, load, and coupling networks.
Q Relations
- Unloaded Q (QU): Q of the resonator alone. Limited by internal losses (conductor, dielectric).
- External Q (QE): Q contribution from the external coupling. 1/QE = 1/QE_source + 1/QE_load.
- Loaded Q (QL): 1/QL = 1/QU + 1/QE. Always less than both QU and QE.
Filter Design
In a bandpass filter, the loaded Q of each resonator determines the bandwidth: BW = f0/QL. The coupling between resonators is adjusted to set the desired bandwidth. Tighter coupling (lower external Q) gives wider bandwidth.
1/QL = 1/QU + 1/QE
Bandwidth: BW = f0/QL
Example: f0 = 10 GHz, QU = 5000, QE = 200
1/QL = 1/5000 + 1/200 = 0.0002 + 0.005 = 0.0052
QL = 192
BW = 10 GHz / 192 = 52 MHz
Insertion loss increases with QL/QU ratio
Frequently Asked Questions
What is loaded Q?
Loaded Q is the Q factor of a resonator when connected to external circuits. It is lower than unloaded Q because external circuits add energy dissipation. Loaded Q determines the bandwidth of a resonant circuit: BW = f0/QL.
How does loaded Q affect filter insertion loss?
Filter insertion loss increases as the ratio QL/QU increases. If QL approaches QU, most of the stored energy is dissipated internally rather than delivered to the load. Using high-QU resonators with moderate QL gives the best combination of bandwidth and low insertion loss.
How do you control loaded Q?
Loaded Q is controlled by the coupling between the resonator and external circuits. Stronger coupling (larger aperture, closer probe) increases energy exchange rate, lowering QL and widening bandwidth. Weaker coupling raises QL and narrows bandwidth.