An improved attempt at simulating the Miracle Whip attached to a transmitter case. This model behaves similarly to the real Miracle Whip as far as VSWR simulations are concerned. Not only may it provide some useful indication of relative radiation patterns but it may also indicate actual gain with an uncertainty of some +/-3dB when used with parameters and guidelines provided in a related paper "EZNEC Simulation of Miracle Whip Antenna and Extensions" by the same author.

No claim can be made for the accuracy of the model. It has been neither sanctioned by nor validated by Miracle Antennas, the manufacturer of the Miracle Whip. The model is purely the invention of the author who shall not be held liable for any loss or damage that may ensue from anyone's use of the model or from the application of changes to the Miracle Whip antenna that may appear to work in the model. 

Wire #1 is the 57" vertical whip, simplified to a constant 1/4" diameter originating at the left rear corner of the transmitter case. Wire 2 represents the left side of the transmitter case along the X-axis in the direction of the operator, wire 3 - the rear edge of the transmitter case and Wire 4 a diagonal from the left rear corner, the origin, to the right front corner, i.e. the longest dimension. The "case" wires are 2" diameter. For this simulation, the case wires have 2 segments each, leaving 14 available for the whip to fit within the 20 segment limit of EZNEC Demo. EZNEC Pro has a better way of representing a solid - a wire grid.

The model starts with the origin at 30" above ground, i.e., table height. The Wires dialog Wire menu has a handy tool to change height.

Problem making and attaching an autotransformer to the 57" whip. EZNEC has a transformer model but there seems to be no way to connect a primary terminal to a secondary terminal to emulate the autotransformer. It is also unrealistically lossless with no inductance - transformer losses and self-inductance figure significantly in the Miracle Whip's success at matching a very short whip. 

To provide simulation of the transformers loss and inductance, the model has an L-network object inserted between the transformer and antenna acting as a series R-L path with an open circuit shunt path. The R value represents the transformer loss. The L value or its +jX reactance represents the inductive loading the transformer would provide at the base of the whip. Stray inductance and capacitance have been ignored for simplicity but may be of increasing importance at higher frequencies with the model becoming less realistic.

The L-network object cannot be attached to the very end of a wire. It is inserted into the end segment of the vertical; in this case with 14 segments, the insertion point is offset from the end by 3.6% or approximately 2". The length of the vertical was increased from 57" to 59" to compensate; there's nothing we can do about the 2" tail attached to the case but that corresponds reasonably with the construction of the Miracle Whip.

Reactance is added to the L-network to balance the capacitive reactance of the short antenna, most conveniently done with the transformer impedance ratio at 50/50. Given the reactance  of the L-network, a table in the aforementioned paper is used to look up the setting for the output impedance of the transformer that corresponds with the turns ratio at the position the autotransformer would provide the needed reactance. The R value of the L-network is then adjusted to provide a low VSWR.

Having matched the antenna system to the 50 ohm source, losses in the Miracle Whip should have been reasonably accounted for and the far-field plot should indicate gain figures that are a reasonable approximation to real world.

Tom Holden
VE3MEO
3 Feb 2009