The waveguide was measured with a VNA in a shielded anechoic chamber. An SMA jack was installed across the ends of the split ring, and connected to a VNA. Multiple frequency sweeps were preformed, spanning 1 MHz to 4 GHz. The VNA was recalibrated each time the frequency range was changed.
The measured resonant frequencies, looking into the Split Ring, are listed below. Resonance is defined as the frequency at which the impedance Z of the DUT is purely real and contains no reactance.
FREQUENCY Z
---------------------------
56.620 1400 + j0
182.770 23.6 + j0 ***
192.820 55 + j0
318 9.7 + j0
651 52 + j0
1119 34 + j0
1334 300 + j0
1867 44 + j0
3934
Frequency in MHz.
The calculated resonant frequencies of all the cylinders are as follows. The circumference of each cylinder was used as 1 wavelength.
## CIRCUMFERENCE WAVELENGTH FREQUENCY
---------------------------------------------------
0 23.938936 23.938936 1252321564.104184
1 38.734012 38.734012 773977291.460816
2 62.672948 62.672948 478344272.643368
3 101.406960 101.406960 295633018.817448
4 164.079908 164.079908 182711253.825920 ***
5 265.486869 265.486869 112921764.991528
Dimensions in cm.
If the circumference of the split ring is considered to be one wavelength, then we have
c / lambda = f
3 * 10^8 / 1.64 m = 182.7 MHz
The calculated resonant frequency of the split ring is 182.711 MHz. One of the actual measured frequencies at which it resonates is 182.7 MHz. These are in agreement. The measured impedance at 182.7 MHz is Z = 23 + j0 ohms.
The split ring also resonates at approximately 56.5 MHz. It has a high impedance at this frequency; it behaves like a parallel LC ciruit at resonance -- like an open circuit. 56.5 MHz is exactly half of what would be the resonant frequency of the next larger ring, if we continued the pattern and built one more ring.
When the widest ring is excited with a wavelength equal to its circumference, it presents a low impedance (23 ohms). It behaves like a Series LC circuit at resonance.
When it is excited with a wavelength equal to 2 * 1.618 * Circumference, it presents a high impedance (1400 ohms) and behaves like a Parallel LC circuit at resonance.
If this relationship holds true in general, then we can hypothesize the resonant frequency of a device constructed with central element of length L.
## LENGTH CIRCUMFERENCE 1 L L / (a^3) 2 L / a L / (a^2) 3 L / (a^2) L / a 4 L / (a^3) L 5 L / (a^4) L * a "6" L / (a^5) L * (a^2) a = (1 + sqrt(5)) / 2 = 1.618... For low impedance, i.e. Series LC circuit at resonance: lambda = L * a frequency = c / lambda frequency = (3 * 10^8) / (L * a) For high impedance, i.e. Parallel LC circuit at resonance: lambda = 2 * L * (a^2) frequency = c / lambda frequency = (3 * 10^8) / (2 * L * (a^2))
A wideband noise source was connected through a -20dB attenuator and a Tee to the DUT and the Spectrum Analyzer. That way, whatever frequencies the DUT absorbs would be visible as a "valley" on the Spectrum Analyzer. The connection was made to the split ring.
The Spectrum Analyzer shows that the split ring absorbs energy at about 55.5 - 56 MHz.We used a VNA to preform S11 measurements. A sweep from 1 - 300MHz shows that the split ring resonates at about 56.5 MHz. (It also resonates at other frequencies). At 56.5 MHz, the split ring behaves like a Parallel LC circuit -- that is, like an open circuit. (high impedance).
The resonant frequency measured with the VNA (56.5 MHz) is in agreement with the absorbtion frequency observed on the spectrum analyzer.
However, the Spectrum Analyzer shows no valley at 182.7 MHz. Why?
Where does this 56.5 MHz come from? It is not a harmonic of 182.7 MHz. It is, however, exactly half the resonant frequency of what would be the next wider ring, if we continued the pattern and built one extra ring.
The images below show readings on the VNA and spectrum analyzer around 56MHz.
Additional data that we have not yet analyzed can be found here:
Lab Notebook Scans, part 1
(PDF)
Lab Notebook Scans, part 2
(PDF)
VNA and Spectrum Analyzer Snapshots
