Materials and Methods

The Antenna Array:

Diagrams of the front radiating (patient) side and back (feedlines) side of the applicator can be seen in figures 9-10. The applicator is an array of 27 Dual Concentric Conductor (DCC) microstrip patch antennas printed on very thin (9mil) and flexible printed circuit board material. A microstrip feedline network feeds the middle of all four sides of the powered patch, which is capacitvely coupled to the radiating patch.

The array has overall dimensions of 20.8 by 43.2cm and can treat an area of up to 13 by 43cm. Figure 9 shows the front or groundplane side of the applicator. The floating patch and large groundplane can be clearly seen. Figure 10 shows the backside or feedlines side of the applicator. On the feedline side of the applicator can be seen the powered patch, the microstrip feedline matching network and the miniature on-board co-axial PMMX connector.

Figure 1 Complete diagram of radiating side of applicator showing scale.

Figure 2 Complete diagram of feedlines side of applicator showing scale.

The geometry and electric field distribution of the DCC can be seen in figure 11 below.

Figure 3 Side view of DCC antenna geometry showing near electric field lines.

The electric field from the radiating patch terminates on the groundplane through the gap between patch and groundplane. It has been shown that this geometry produces a near field which is dominated by components that are predominantly parallel to the plane of the radiating patch above and near the gap and normal to the patch over its center. The antennas are specified by the size of the rectangular hole in the groundplane and the width of the gap. In the studied array the aperture size is 3cm with a gap size of 2.5mm.

Network Analyzer:

In the preceding section the methods used to match a load to a microstrip line were presented. What was not discussed is how exactly the load impedance is determined. To determine the input impedance the Swiss army knife of microwave measurement equipment, the vector network analyzer with S parameter test set was used.

The HP 8753C vector network analyzer used for this project is shown below.

Figure 4 Hewlert Packart 8753C vector network analyzer with 85047A S parameter test set.

 

The vector network analyzer processes the transmitted and reflected waves from a network to give readings of input impedance, VSWR, return loss and many other network characteristics. Because it uses a mathematical error correction/calibration technique and preserves both magnitude and phase information from the signal this type of instrument can make very accurate circuit measurements, even at microwave frequencies.

Network Analyzer Calibration Method

A short length of high quality coaxial cable is connected to the analyzer output. At the end of this cable is attached, in sequence, a high quality 50 ohm load, a short circuit plug and a calibrated open

The analyzer has stored, in its memory, mathematical models of these standard loads. The analyzer sends out a signal and reads the reflections from each load. It can then mathematically subtract out all the discontinuities between the analyzer output and the end of the cable. If the cable is of high enough quality, its properties do not change when it is flexed. It can then be attached to the unknown circuit component and the properties of the circuit measured without distortion by the cable.

Time Domain Reflectometry

The 8753C analyzer also has the ability to do a Fourier transform of the frequency data into the time domain, to provide the time domain response of the network. This method is called Time Domain Reflectometry (TDR). The analyzer sends out a broadband step function and performs a fast Fourier transform on the reflections to recover information on the reflections as a function of time after the impulse. Taking into account the speed of light on the transmission line, the circuit information may be displayed as a function of distance down the line. The resolution in time is directly related, through the FFT, to the bandwidth of the frequency range in the step function. The broader the range, the higher the resolution. The highest bandwidth range possible with the 8753C analyzer is from 39 MHz to 5.99 GHz. With this range, the smallest distance between two discontinuities that the analyzer can distinguish is 10 millimeters.

TDR mode is most useful when the analyzer is set to display the real component of the signal. In frequency mode, when the display is set to real only, the real part of the impedance as a function of frequency is plotted on a linear axis. In TDR mode

Figure 5 Standard TDR graph of microwave antenna showing how the impedance varies from the ideal 50 ohms as a function of distance.

(see figure 13) the horizontal axis is distance. The vertical axis is a unitless quantity that represents the strength of the reflection. The vertical scale runs from +1000 milli-units to -1000 milli-units. +1000 is said to be an open, -1000 is said to be a short and 0 on this scale is 50 Ohms. By looking at the plot, it can be seen where reflections are being generated, if the discontinuities are inductive or capacitive in nature and what the impedance is at a point in relation to a perfect open or short. This mode is very useful for checking solder joint connections at the coaxial cable to microstrip transitions. Conditions where the center pin is shorted to the ground plane or not sufficiently well soldered to the microstrip are easily spotted. It can also characterize how clean a connection has been made by displaying the magnitude of the reflection from that point.

Gating

Gating is another useful feature that is used often. The analyzer has the ability to set a gate around a region ( in either frequency space or distance/time) and ignore all other information that is not contained within that measurement window.

Standard Measurement Procedure

The standard procedure for network-analyzer measurements was as follows. The unit was turned on and allowed to warm up for at least five minutes. A short length of coaxial cable was connected to the analyzer input. The analyzer was calibrated out to the end of the test cable. The end of the cable was then attached to the RF connector jack on the PCB array edge. The analyzer was put in TDR mode. The gate was set around the distance region of interest. The analyzer was then switched into frequency mode and measurements were made. It is believed that performing the measurements in this way improved measurement accuracy significantly by reducing the noise and unwanted reflections to a minimum.

All antenna measurements were performed in exactly the same way. Because of the radiation pattern characteristics of the DCC patch antenna, it is sensitive to the lossy muscle medium it is looking into. If the loading changes, so will its edge impedance and therefore its measured characteristics. The antennas tested all looked into the same load, consisting of a distilled water bolus and muscle phantom. In this way, we tried to recreate the load the antenna would see in a clinical situation.

 

Network Analyzer Measurements:

All microwave transmission line matching algorithms start with a known load. In our case the load was not known originally and had to be determined either theoretically or experimentally before a matching network could be designed. The load, in our case, is the edge impedance of the powered patch. An extensive search of the literature for an analytical solution was conducted. I found that there does not exist a theoretical formula for the unique geometry of the DCC antenna. Standard formulas are available for the edge impedance of rectangular microstrip patch over an infinite groundplane. A few commercial microwave analysis programs were also investigated but they would not produce a stable-believable analysis, due to limitations on computer memory for physically large and complex antenna geometry. For these reasons, it was decided to experimentally determine the edge impedance of the radiating patch using the vector network analyzer.

Finding the Edge Impedance

The network analyzer uses reflections from the discontinuity of interest to make its measurements. For this reason every care must be taken to minimize all other reflections. The matching network (see figure 16 ) has many discontinuities; including coax to microstrip transitions, bends, step changes in width and two T-junctions. If we were to try to determine the patch edge impedance by looking into the beginning of the network the results would be contaminated by the spurious reflections. Though, this method is fine for determining the overall properties of the feedline-patch network. To eliminate these reflections a test board was improvised. An older, professionally made antenna array (see figure 15)

Figure 6 Older non-optimized antenna array used to determine the correct edge impedance.

with non-optimized microstrip feedline network was altered to give an as accurate reading of antenna patch edge impedance as possible. To minimize reflections, networks with the fewest bends between the 2nd T-junction and the on-board coaxial connector were used. Then, using a dremel tool, one arm of each T-junction was ground away, as cleanly as possible. This reduced the network to one continuous length of microstrip with six bends and feeding the patch on one side only (see figure 14). For this configuration, the input impedance signal that was cleaner than before but still contaminated by multiple unwanted reflections. To remove these reflections, the analyzer was set to TDR mode and the gate was placed just over the area where the feedline meets the patch. In this way the analyzer mathematically ignores all other reflections except those coming from the gated region. The analyzer was then returned to frequency mode and accurate input impedance measurements of the input impedance of the patch edge were made.

Microwave Network Parameters

The analyzer was calibrated and connected to the antenna array as described above. The array was then attached to the bolus and the bolus was firmly attached to the muscle phantom-making sure no air gaps existed between the array, bolus and load. The TDR mode was used to set the gating. The gate was set so that only reflections starting from the PMMX connector to the patch edge were considered. The analyzer was then returned to frequency mode and the microwave parameters were measured. The measured parameters are: input impedance, VSWR and return loss. Each antenna was characterized separately and this information was entered into an Excel spreadsheet. The spreadsheet calculated the overall averages and deviations of the above parameters by row and column.

 

Feedline Network Design:

With a known input impedance a suitable matching network could be designed. A Mathematica notebook was written to help in the calculations (see appendix 1). An explanation of the general matching techniques used is presented and then the slight variations investigated on different columns in the array will be described. The design for this test array can be seen in figure 9. For the particular geometry of the test array it was found that the edge impedance of the microstrip patch was . The standard matching network used can be seen in figure 15.

Figure 7 Diagram of standard matching network showing the impedances at different points and the microwave compensation techniques used.

 

The calculations were made for a microstrip width that would result in a characteristic impedance of 46 Ohms. The distances a and b were set to be at least three times the width and the right angle bends are microwave mitered. The base width of the 1st T-junction was calculated to give an even 3dB split in power and to minimize reflections The bases of both 1st T-junctions continue on without a change in width to form the arms of the 2nd T-junction. The radius of the curve c was made as broad as possible within the space constraints. It was determined from previous prototypes that when the curve c was made too sharply that it was a source of unwanted radiation and insertion loss. The distance d was constrained to be at least 3W of the broader 23-Ohm line that forms the arms of the 2nd T-junction. In this standard case, there were no specific constraints on the length of line between the patch and the 1st and 2nd T-junction. The base width of the 2nd T-junction was calculated to give an impedance of 11.5 Ohms. The base of the 2nd T-junction is very short . A quarter wave transformer is then used to match the 11.5 Ohm 2nd T-junction input impedance to the 50 ohm microstrip line. The quarter wave transformer has a characteristic impedance of 24 Ohms and a length of 5cm. After the quarter wave transformer the microstrip line runs all the way to the PMMX connector with as few bends as possible and maintaining at least a 3W distance to the nearest microstrip lines to minimize cross coupling between adjacent lines. The length of feedline from the end of the quarter wave transformer to the PMMX connector was constrained. The longest run was designed first then all following feedline runs were constrained to be the same length. The length was fixed because, as was shown in the microwave theory section, with a mismatched load, impedance varies as distance from the load. The shorter runs were lengthened with short serpentine runs called meander lines. With all the feedlines having the same length, then theoretically they will all have the same input impedance.

The preceding standard optimization was done on four of the nine columns. On the remaining five columns additional matching techniques were investigated.

In column one the length between the patch and 2nd T-junction was constrained to be 1/8th of a wavelength (see figure 16).

Figure 8 Diagram of standard matching network plus additional 1/8th wavelength matching section.

This 1/8th section was used to force the feedline/patch interface to be an anti-node in the standing wave pattern. If the interface could be forced to be a node, the voltage would be a maximum and the maximum amount of power would be delivered to the patch.

In column four the distance between the 1st and 2nd T-junctions was constrained to be 1/4 wavelength (see figure 17).

Figure 9 Diagram of standard matching network plus additional 1/4 wavelength matching section.

This additional quarter wave transformer was used to eliminate reflections between the 1st and 2nd T-junctions.

The sixth eighth and ninth columns used both the quarter wave transformer between the T-junctions and the 1/8th section between the 1st T-junction and the patch (see figure 18)

Figure 10 Diagram of standard matching network plus additional 1/8th and wavelength matching section.

These techniques were used concurrently in the hopes that there effects would be additive and produce an aperture with improved matching and superior radiation characteristics.

Electric Field/SAR Scans

The computer-controlled three dimensional electric-field-probe scanning device used to characterize the electric field radiating into homogeneous muscle-tissue equivalent liquid phantom media from the antenna array can be seen in figure 19.

Figure 11 Experimental setup for the mapping of the electric field at depth in muscle equivalent liquid phantom.

The antenna arrays to be tested were first attached to a de-ionized de-gassed water bolus of thickness .5-1.5cm. The bolus/array was then inserted into a large bag, constructed of the same polyurethane material as the water bolus, with Plexiglas backing board to hold the flexible array flat during the electric field scans. The backing board is printed with an orthogonal grid that the bolus/array is aligned with. This assembly is then inserted into the liquid muscle scan tank and leveled to ensure the array is not skewed relative to the scanning apparatus.

The scanning apparatus consists of an electric field probe, a three-axis computer controlled servomotor motion system, an input/output card and a computer running the data acquisition software. The electric field probe used is a Narda model 8010 miniature 3-axis probe. This probe consists of three orthogonal diode dipole sensors housed in the tip of a miniature wand. Three low level DC signals proportional to are transmitted to a low-noise differential summing amplifier via high resistance leads and then to the computer for digitization. The amplifier can be set to amplify all three components of the electric field or one component or any combination of the three required. The squares of all three electric field components were summed so that the total electric field squared could be recorded.

After the board/bolus is inserted, the electric field probe is positioned next. The probe is mounted at a right angle on the end of a long Teflon rod. The probe is positioned over the center of an antenna, making sure that it is orthogonal to the plane of the array. In this way it is certain that all elements are orthogonal to each other and the probe will be correctly centered in the array.

The data acquisition program can now be started and the scanning parameters set. With this system we can scan in planes parallel to the array surface, at any depth in muscle phantom greater than the minimum 3.5mm distance, which represents the distance from the center of the 3 orthogonal dipole sensors to the probe tip. In practice, the antennas are scanned in parallel planes to the antenna surface, 5mm and 10mm away from the surface on a 2.5mm grid. A vertical cross section can also be scanned to record information on how the electric field varies with depth. The scanning program creates data files that contain two dimensional arrays of DC voltages as function of position. Another program is used to convert these values to SAR as a function of position. The commercial data visualization software Surfer is used to plot contour and surface maps of the experimental SAR data.

The above measurements/characterizations were performed on the most recent optimized array and on several older non-optimized arrays. The newer optimized arrays are professionally constructed by the PCB manufacturer Labtech LTD. The older non-optimized arrays were manufactured in-house with a PCB home hobbyist kit. The older arrays are non-optimized in the sense that no consideration was given to microwave matching techniques. The older arrays (see figure 14 for an example) have the same basic feedline shape: one line splits into four via two T-junctions. The width of the feedlines are the same throughout, and this width was constrained by manufacturing concerns, not matching concerns. With the home hobbyist technique used it was found nearly impossible to consistently produce quality lines of width less than .4mm. With the given PCB geometry, a microstrip line of .4mm would have a characteristic impedance of 12 Ohms, a poor match for the 50 Ohm coaxial cable and PMMX connector. At both T-junctions the 12 Ohm feedline sees an input impedance looking into the base of only 6 Ohms. At the patch/feedline interface, the 12 Ohm line sees a load of ~46 Ohms. It was thought that all of these mis-matches must produce an antenna that is far from optimized. The older non-optimized arrays were used as a control and their measured parameters were used to judge the success of the different optimization techniques.

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