Non-Radiating Network Analysis

Physical network vs. Non-radiating network

An antenna normally consists of the radiating element(s) and a feed-network that delivers the power with a desired amplitude and phase distribution to these elements.

Although it is often not required to include the feed-network when simulating the radiation pattern of an antenna array, the feed-network remains to be an important part of the design. For example the input impedance of the antenna will depend on the input impedance of each element and the way they are connected via the feed-network.

In FEKO the feed-network can be included as part of the 3D problem (i.e. full 3D simulation) or it can be simulated as a non-radiating network.

Physical network simulated in FEKO.	Non-radiating network components connected together.

Specification

The non-radiating feed is defined by several multi-port sub-networks (or elements) which can be interconnected in different ways:

• No connection (open-circuit)
• Connected to another network (cascade)
• Connected to geometry (wire and edge ports). The excitation (source) can be at the same segment as to which the network is connected.
• Connected to a network load or network excitation

Each network can be characterised by way of an:

• S-matrix
• Z-matrix
• Y-matrix

The data of each sub-network can also be imported from a Touchstone file. Spline interpolation is used on the Touchstone data in order to obtain values at those frequencies where FEKO simulations are done.

After the simulation the output can be exported to a Touchstone file(*.snp)

Example

A quadrifilar helix antenna (QFA) consists of an end-cap and 4 helical wire elements connected to the end-cap. The helical wire elements are fed with an equal amplitude but with sequential 90 degrees phase increase, as shown in the image below.

QFA Complete geometry, antenna and feed network.	Top: QFA antenna element. Bottom: Feed-network, one input port, 4 output ports, amplitude evenly distributed and the phase shifted by 90 degrees from port (element) to port.

Radiation Pattern

1. Simulate the antenna only (right top image in the table above) and enforce the correct feed at the 4 ports.
2. Same as above but include feed-network using the functionality offered by FEKO to include this.
   
3. Full 3D simulation of the complete structure i.e. antenna and the feed (left image in the table above).
   

The effect of the network should be negligible on the radiation pattern of the antenna and either options 1 and 2 should be sufficient.

Input Impedance

Several options are available to obtain the input impedance of the complete structure.

• Circuit simulator then FEKO simulation
  

1. Simulate the feed only using a fast (2D) circuit simulation e.g. Microwave Office (MWO).
2. Use these results (S-parameters) as inputs to the non-radiating network in the FEKO simulation including the antenna.

• FEKO simulation then Circuit simulator (MWO)
  

1. Obtain the input impedance of all 4 ports of the antenna (i.e. at the base of each helical element) through a full 3D simulation of the antenna (without feed).
2. Use these input impedances, i.e. at the ports, in the circuit simulator to get the input impedance of the complete structure.

• Complete (3D) simulation of the feed and antenna in FEKO
  

1. Although this is an attractive option the run-times are longer than the those when the feed-network is solved using a 2D simulation technique. There might however be cases where it is required to do such a more accurate full wave solution.
   

Results: Feed-network only

The input impedance of the feed-network only (i.e. without the antenna load) is shown below. A comparison between the results as obtained using the the full 3D MoM simulation (FEKO) and the circuit simulator (MWO) shows that there is fair agreement. Some of the factors responsible for a difference in the results are:

1. The coupling between the transmission lines are included in the full 3D (FEKO) simulation.
2. For the FEKO simulation the port termination is the actual (non-perfect) vertical pin whereas MWO assumes a perfect port termination.

Re(Z) of the Feed only.	Im(Z) of the Feed only.

Results: Antenna + Feed-network

The input impedance of the complete structure (i.e. antenna and the feed-network) is shown below. The effect of feed was accounted for in three ways:

• Full 3D (MoM) simulation [blue curve].
  
• Non-radiating network (NW-card) with S-parameters as obtained earlier from a FEKO (3D) simulation of the feed only [green curve].
  

• Non-radiating network (NW-card) with S-parameters as obtained earlier from a circuit simulator (MWO) [red curve].

The agreement between the results is good. Differences can, amongst other factors, be attributed to:

1. Inclusion of coupling between the transmission lines and/or coupling between the feed and the antennas elements, which can only be simulated when the full 3D structure is solved.
2. Differences between the way the port terminations are handled.
   

Re(Z) of the Helix + Feed. Helix+Feed (full MoM), Helix (full MoM) + NW (from FEKO simulation) Helix (full MoM) + NW (from MWO simulation)	Im(Z) of the Helix + Feed. Helix+Feed (full MoM), Helix (full MoM) + NW (from FEKO simulation) Helix (full MoM) + NW (from MWO simulation)