It's definitely going to be risky to try and measure the Q of the 49 turn solenoid with an s11 measurement using a VNA because my software program lists the magnitude of the reflection coefficient as 0.9987 at 1.45 MHz.
This would be stretching the limits of the VNA to measure with much confidence. It might still show a reasonable result but there would be a fair bit of uncertainty in the measurement.
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If it was resonated using a parallel cap the Rp would be about 75,000 ohms at 1.45 MHz. This is also just about OK to measure at 1.45 MHz with a good VNA with a reflection measurement, but a 75,000 ohms resistance measurement is close to the limits of a good VNA at 1.45 MHz.
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If it was resonated in series, the Rs would be just under 5 ohms at 1.45 MHz and this would be quite easy for a good VNA to measure at 1.45 MHz with very good accuracy. So I would favour this method.
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The other good way to measure the Q would be to configure the series tuned circuit as a shunt acceptor circuit and measure the insertion loss at the resultant null at 1.45 MHz with an s21 measurement. If the Rs was about 4.8 ohms then there would be a null about 15.9 dB deep at 1.45 MHz for example. As long as the VNA ports are corrected to 50 ohms or attenuators are used to improve the VNA port match this method should measure the Q extremely accurately.
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The 3dB bandwidth method is also viable here and it should give similar results for Q because the test frequency of 1.45MHz is going to be about 1/10th of the first self resonance frequency of the inductor. It can be fiddly to make this measurement though. I normally do this using a netbook PC to continually measure the 3dB bandwidth via GPIB. It's also possible to get a real time readout of Q on the VNA screen using this method.
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