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# A Quadrafilar Helical Antenna for Low Elevation GPS Applications

#### A low cost implementation of a quadrafilar helical antenna designed for use in Global Positioning System (GPS) applications

**A Quadrafilar Helical Antenna for Low Elevation GPS Applications**

*This article presents a low cost implementation of a quadrafilar helical antenna for Global Positioning System (GPS) applications. The antenna is designed to produce a right-hand circularly polarized (RHCP), elevated omnidirectional radiation pattern with constant azimuth gain at low elevation angles. This type of antenna is ideal for satellite communications (SATCOM) ground terminals, which operate at low elevation angles with respect to the satellite position. The antenna is designed to operate in a typical SATCOM receive band from 1525 to 1559 MHz and is specifically intended for use in differential GPS (DGPS) network applications.*

**Senglee Foo**

*CAL Corp. Ottawa, Ontario, Canada*

DGPS technologies are being used extensively for various commercial services related to geophysical surveying and mapping, geographic information management, construction and farming. For such applications at remote sites, these services rely on a constant link to a SATCOM satellite to receive the precise DGPS information. Antennas with low elevation radiation patterns allow these receivers to operate at low tracking angles relative to the satellite with a substantial improvement in the signal-to-noise ratio compared to a typical zenith pointing antenna. A RHCP, elevated omnidirectional radiation pattern is achieved by using a quadrafilar helix with a long element length (longer than one wavelength).

**The Antenna Configuration**

The concept of a resonant, fractional-turn, quadrafilar helix (also known as a volute antenna) was first introduced by Kilgus.^{1} It was shown that this antenna can produce a highly directive circularly polarized radiation pattern by feeding a proper complex excitation to the four helices. It was later shown^{2} that a shaped-conical pattern also can be achieved by using helices of an integral number of turns and varying pitches. Since then, several derivatives of the concept have evolved. This article extends this antenna concept to produce an elevated omnidirectional radiation pattern with dielectric-loaded four-arm helices.

A conventional volute antenna consists of two to four helices of short element length (a multiple of a quarter-wavelength). Typically, these designs form one-quarter-, one-half- or full-turn quadrafilar helical antennas. To obtain the elevated beam peak angle in this design, the overall element length of each helix is slightly longer than a conventional volute antenna helix and has an effective length of approximately one-and-a-quarter wavelength. One side of the helices is connected directly to the feeds while the other terminals are left open. One major advantage of this type of antenna is that it allows the setting of the beam pointing angle by selecting an appropriate overall helix length and pitch angles. The actual length and pitch angle of the helices are adjusted to compensate for the loading of the dielectric tubing. **Figure 1** shows the physical configuration of the antenna. The design of the quadrafilar helix is based on the concept of four helices operating in a quadrature phase separation, that is, Df = ± (m – 1)p /4, where m is the helix number. The sign of the phase difference between the helices and the winding direction of the helices are related intimately. One direction of the phase difference produces cardioid-shaped radiation patterns over the front hemisphere; the other direction produces the desired elevated omnidirectional patterns. The sign of the phase difference between helices also depends on the winding direction of the helices. To obtain an elevated omnidirectional pattern, the sign of the phase difference and the direction of the helix winding occur in the opposite direction. For instance, a Df = +90° phase difference between the helices in the clockwise direction produces a RHCP omnidirectional pattern if the helices are wound in a left-hand sense. Similarly, the same RHCP radiation pattern also can be obtained using right-hand-wound helices by implementing the phase difference between the helices in the exact opposite direction (Df = –90°). **Figure 2** shows the design. The four helices are wound on thin cylindrical polyvinylchloride (PVC) dielectric tubing. In this case, the helices are wound in a left-hand sense and the feed network is designed to produce a +90° phase difference in the clockwise direction. The feed network is printed on a thin, low loss, woven-glass polytetraflouroethylene laminate. The feed input of each helix is soldered directly to the circuit side of the microstrip feed network. This microstrip feed network provides a simple means of achieving a low cost balun/combiner. This circuit is designed and optimized using the Series IV microwave CAD program. Amplitude and phase balances of this circuit are critical. If all the helices are impedance matched to the 50 W microstrip line, an amplitude balance of less than ± 0.25 dB and phase balance of less than 10° can be achieved. In practice, this precision can be achieved by tuning each helix element with all other helices in place and terminated to a 50 W load. By doing so, the effect of mutual coupling between the helices is included in the matching process. It usually takes a few iterations to achieve the match condition for all ports.

**Impedance Matching**

Each of the helix elements is matched to its corresponding 50 W microstrip feed line by fine-tuning the helix element length and shaping the first quarter turn of the helix winding during prototyping. The pitch angle of this first quarter turn is designed to act as a direct impedance transformer between the helix winding and the 50 W microstrip transmission line. The shape of this matching section is critical to obtaining a good input SWR. The coordinate of this matching section must be measured and reproduced precisely using a mandrel for volume production. Using this technique, an SWR of less than 1.3 can be achieved over a five percent frequency bandwidth.

**The EM Model and Simulation**

The design was modeled and optimized using moment-method-based electromagnetic (EM) codes. The computer modeling does not include the dielectric loading, which will be corrected by using a measurement method. During the design, two software tools were used for the simulation. One tool is a moment method using composite wire and plate structures (WIPL-4) developed at the University of Belgrade, Yugoslavia. The other tool is a moment method using a thin wire model (NEC-2) developed by Lawrence Livermore Laboratory, CA. **Figure 3** shows the electrical model. The two models are identical except for the modeling of the finite ground plane. In the WIPL model, the ground plane is modeled as a single metal plate; the NEC model approximates the ground plane using a wire mesh model. Both methods are based on the solution of the electric field integral equation method. However, the WIPL code uses high order polynomial basis functions to approximate the current distribution in the wires and plates; the NEC model uses sinusoidal basis functions. A total of 300 and 472 unknowns are present in the WIPL and NEC models, respectively. These two models are run on a 90 MHz 486 DOS platform. The total run time is 51 s for the WIPL-4 simulation and 59 s for the NEC simulation. **Figure 4** shows a comparison of the co-polar radiation patterns (principal plane) generated by the two models. As shown, the results are closely related. The peak gain between the two models is within 0.5 dB. The pattern difference within the main beam is relatively small. The larger pattern difference at low gain angle, in the null area, is a direct result of the differences in the modeling of the ground plane. The wire mesh approximation in the NEC model cannot approximate the surface current distribution on the ground plane as accurately as the WIPL model, especially in the excitation regions. **Figure 5** shows the contour plots of the co-polar and cross-polar radiation patterns of the antenna generated by the NEC model. In this case, the antenna is designed to provide an elevation beam peak approximately 30° from the horizon and produce an omnidirectional pattern with a minimum of 3.4 dBiC gain in the azimuth plane at the elevation beam peak angle. This antenna exhibits a relatively constant gain in the azimuth direction. Typically, the left-hand cross-polar component within the 3 dB beamwidth is below –16 dB, which produces an axial ratio of better than 2.77 dB. These characteristics also allow the antenna to be used for low elevation communications without requiring azimuth tracking.

**Dielectric Loading and Measurement Results**

The effect of dielectric loading on a helical antenna has been investigated extensively.^{3,4} The loading of the dielectric shell alters the phase velocity of the RF current along the helix windings. As a result, it also severely alters the radiation patterns of the antenna. To correct for this effect, the pitch angle and overall helix length are reduced slightly to compensate. **Figure 6** shows the measured radiation patterns of the compensated and uncompensated antennas compared to the NEC result. In this case, the dielectric cylinder has a wall thickness of less than a few millimeters with a dielectric constant of less than 4. In the uncompensated case, the dielectric loading causes the radiation pattern to peak at a lower elevation angle and suffer a significant loss in the peak gain. A reduction in the helix length and pitch angle effectively shortens the electrical path length of the helices and compensates for the phase error. By using measurement results, an appropriate change in the pitch angle and helix length can be determined. Note that the null at the zenith is also partially filled in the compensated case. **Figure 7** shows the measured return loss at the input of a typical quadrafilar antenna. This type of antenna can offer a relatively wide frequency bandwidth. In this case, an SWR of 1.2 is achieved over a 10 percent frequency bandwidth.

**Conclusion**

The design and low cost implementation of a quadrafilar helical antenna have been presented. The design uses four electrically long (greater than one wavelength) helical elements. It has been shown that, with proper phase excitations at the four input ports, an elevated omnidirectional beam pattern with a beam peak at the desired elevation angle can be obtained. The design of a simple microstrip power combiner including the quadrature phase distribution was shown to provide the proper balun/power-combining network. It was also shown that the effect of the dielectric loading is significant and can be compensated by varying the pitch angles and helix length.

**Acknowledgment**

The Series IV microwave CAD program is a product of HPEEsof, Santa Rosa, CA.

**References**

*1. C.C. Kilgus, "Resonant Quadrafilar Helix," IEEE Transactions on Antennas and Propagations, Vol. AP-17, May 1969, pp. 349–451.*

*2. C.C. Kilgus, "Shaped-conical Radiation Pattern Performance of the Backfire Quadrafilar Helix," IEEE Transactions on Antennas and Propagations, Vol. AP-23, May 1975, pp. 392–397.*

*3. S. Foo, P. Wood and P. Cowles, "A Low Cost, Lightweight, Aeronautical SATCOM Antenna," Microwave Journal, Vol. 40, No. 1, January 1997, pp. 166–173.*

*4. D.E. Baker, "Design of a Broadband Impedance-matching Section for Peripherally Fed Helical Antennas," Antenna Applications Symposium Proceedings, University of Illinois, September 1980.*