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--- rfmeasurement:ringresonatormethod [2021/10/20 22:49] – created neilhao
+++ rfmeasurement:ringresonatormethod [2023/02/11 17:30] (current) – external edit 127.0.0.1
@@ Line 17: / Line 17: @@
 ===== The Ring Resonator Design =====
+{{ :rfmeasurement:ringresonatormethod_ring_resonator_design.png?nolink&600 |}}
 The substrate thickness is 0.5mm and silver conductor thickness is 5um. HTCC substrate was manufactured by using Al2O3 thus the Er could be expected to be about 9.8.
@@ Line 23: / Line 24: @@
 The ring will resonate at multiples of lambda which corresponding to the circumference of the ring.
-For example, Fo(n) = n*(C0/l) when Er =1.
+When Er = 1, the resonate frequency points can be calculated by following equation:
-C0 = 2.99792458×108m/s
+{{:rfmeasurement:ringresonatormethod_frequency_points_equation_.png?nolink|}}
-l = 3.14*40mm = 0.12566m
 Thus,
@@ Line 36: / Line 36: @@
 |n=6	|Fo(6)=14.32129576 GHz|
+When Er = 9.8, the simulated resonate frequency points:
+{{ :rfmeasurement:ringresonatormethod_simulatedresults.png?nolink&350 |}}
 ===== Measurement =====
+{{ :rfmeasurement:ringresonatormethod_fixture.png?nolink&600 |}}
+Six peaks of S21 were measured within the frequency from 300KHz to 6GHz:
+{{ :rfmeasurement:ringresonatormethod_measuredresults.png?nolink&350 |}}
+Thus for Fn with n=1…6,
+^N  ^Fn             |
+|1  |F1 = 0.9483 GHz|
+|2  |F2 = 1.896 GHz |
+|3  |F3 = 2.844 GHz |
+|4  |F4 = 3.78 GHz  |
+|5  |F5 = 4.728 GHz |
+|6  |F6 = 5.652 GHz |
+The effective dielectric constant is defined as
+{{ :rfmeasurement:ringresonatormethod_effective_dielectric_constant.png?nolink |}}
+And due to (W/H) <1, so that the dielectric constant is defined as
+{{ :rfmeasurement:ringresonatormethod_dielectric_constant.png?nolink |}}
+H is substrate thickness, 0.5mm for this DUT
+W is the width of microstrip line, 0.48mm for this DUT
+Finally, the effective dielectric constant and dielectric constant can be calculated by using above two equations:
+{{ :rfmeasurement:ringresonatormethod_finalresults.png?nolink |}}
+We could conclude that this substrate has stable dielectric constant (Er) over wide frequency range. The average dielectric constant within the frequency from 1GHz to 6GHz is 9.42.
 ===== Reference =====
+[1] Neil Hao. The Considerations of Antenna Design for IOT and Wearable Devices. Retrieved Oct 21, 2021, from https://uniteng.com/index.php/2019/11/20/the-considerations-of-antenna-design-for-iot-and-wearable-devices/
+[2] Measuring the dielectric constant 𝜺𝒓 of Teflon, Polyester, FR4, G10, or FR4 with an RF generator and a good bolometer. Retrieved Oct 21, 2021, from https://www.e-doodles.it/wp-content/uploads/2019/05/Measuring-the-dielectric-constant-%CE%B5_r-of-Teflon-Polyester-FR4-G10-or-FR4-with-an-RF-generator-and-a-good-bolometer.pdf