Inside the PARADOX
Dear Reader, this post is not about Philosophy :-D
This shows what's inside the transmitter that Mr. Hartley has built into his portable wireless set, named 'PARADOX'. An EL86 tube crystal oscillator, fed by a 12VDC-220VAC inverter, which output is rectified and filtered. The circuit is derived from the well known 'PARASET'.
The plate tank has been simulated with a modern Finite Element program for electromagnetic calculations, to estimate with a reasonable degree of accuracy, the self and the mutual inductances of the Primary and the Secondary coils. Here below two interesting pictures: the Magnetic Induction field intensity (the colour scale is in TESLA unit measure), for an hypothetical 1A DC current in the Primary. And below, the vectorial representation of the Magnetic field.
The simulation is bi-dimensional, exploiting the axyal symmetry of the solenoids
The Primary inductance resulted about 10 uH, the antenna link inductance is 17 uH, and the mutual inductance is about 0.15 uH. The 'coupling coefficient' resulting from these values, is K = 0.125.
By application of the Theory, the above figures tells that the real impedance transformation ratio is around 100 and not 1.5, which last figure can be computed by squaring the real coil turns ratio.
It is then as if the real antenna link has only 2 turns or so. The explanation is evident from the pictures above: the Induction field decays very fast out from the Primary coil, so that the concatenated magnetic flux at Secondary is very low (in fact, the coulpling coefficient 'K', is low).
Considering the EL86 load impedance for its rated output in class C, the antenna load for optimum power transfer should be in the range from 25 to 75 ohm roughly (the formal demonstration will be published ...). The apparent excess of Secondary turns, then, in reality is used to compensate the capacitive reactance typical of short atennas.
We asked to modern calculation programs if the Paraset engineers did ther job well: we confirm this ! :-) But, we think interesting to explain the Reader what's behind the choice of such an impedance transformer, with such number of turns and with such a Primary to Secondary distance. Which our analysis tells it's what one might vary if he wants to adjust the impedance ratio, for what has been explained above. A moving link works as if the Secondary is tapped. The closer the link to the Primary, the higher the optimum antenna impedance needed for maximum power transfer.
The original Paraset antenna coil has also two single turns circuits, placed at the coils support ends. Both are connected to a lamp and serve to indicate the plate tank resonance point, and the antenna link maximum coupling. There is a specific reason why they are placed at the coils outer ends: in this position they 'catch' mostly the magnetic flux developed respectively by the main coil they are close to, and not that of the other opposite coil. So, when the current is maximum in the 'sensed' coil, then the corresponding lamp has its maximum brightness. By use again of Simulation software, it is possible to calculate the coupling entity (coupling coefficients) and demonstrate by use of some electric circuit simulator, the real behavior of the complete system.
Mr. Hartley connected a couple of LEDS instead of traditional lamps, to those sensing coils. We will not blame this ... violation of purity with regards to the original Paraset concept. But he did so because their brightness is better visible in daylight.
You know ... when you are pushed by the hurry and by the risk of being detected, when carrying out traffic in 'Full Spectrum' mode, every saved second might be a matter of life or death ! :-)
Radioman, August 2015
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