In an undergraduate electromagnetics syllabus, an introduction to the topic of circular polarization is necessary to promote an understanding of the propagation ...
Understanding and Measuring Circular Polarization Reference : B. Y. Toh, R. Cahill, and V. F. Fusco, “Understanding and measuring circular polarization,” IEEE- Trans. on Education, Vol. 46, No. 3, Aug. 2003.
Outline Introduction Definition And Measurement Techniques Experiments With Circularly Polarized Dipole Antennas
Conclusions
Introduction In an undergraduate electromagnetics syllabus, an introduction to the topic of circular polarization is necessary to promote an understanding of the propagation aspects of modern communications system design. Students new to the antennas and propagation discipline often have difficulty in grasping the concept of CP; therefore, in this paper, the essential aspects of this topic are reinforced by a tutorial description of CP in terms of wave propagation, antenna properties, and measurement techniques.
Definition and Measurement Techniques A. Definitions The polarization of an electromagnetic wave is defined by the shape and orientation of the tip of the E vector as it varies with time. In this paper, this situation is defined in a frame of reference from an observation point at the source looking in the direction of propagation in the axis, as shown in Fig. 1. The sense of a circularly polarized wave is determined by the rotation direction of the vector E as it describes a circle.
Definition And Measurement Techniques A. Definitions A practical antenna usually generates an imperfect circularly polarized field; therefore, the E vector traces out an ellipse, instead of a circle, as shown in Fig. 1(c). The ratio of the major to minor axes defines the AR of the polarized wave.
For perfect CP wave propagation, where only one hand of polarization is generated, the AR will have a value of 1.
Definition And Measurement Techniques A. Definitions In the extreme case where the magnitude of the RHCP and LHCP components are the same, the circle formed by the tip of the E vector degenerates into a line, the polarization becomes linear, and the AR value becomes infinite. If the complex voltage terms in the horizontal and vertical planes (or any two orthogonal cuts) EH and EV are of equal amplitude and in phase quadrature (±90o), these terms may be combined to express either the RHCP or LHCP wave components 1 1 𝐸𝑅𝐻𝐶𝑃 = 𝐸𝐻 + 𝑗𝐸𝑉 ，(1) and 𝐸𝐿𝐻𝐶𝑃 = 𝐸𝐻 − 𝑗𝐸𝑉 ，(2) 2
2
Definition And Measurement Techniques
(a)
(c)
(b)
Fig. 1. (a) Left-hand circular polarization. (b) Right-hand circular polarization. (c) Polarization ellipse.
Definition A\and Measurement Techniques B. Measurement Techniques
Fig. 2. Antenna range setup for determining the gain of an elliptically polarized antenna .
Definition And Measurement Techniques B. Measurement Techniques Equations (1) and (2) may be expanded to give simple expressions that can be inserted into data logging software to provide a direct conversion from dual linear to RHCP and LHCP power at each measurement angle. Let the real and imaginary components of the horizontal and vertical response be expressed as 𝐸𝑉 = 𝐸𝑉𝑟 + 𝑗𝐸𝑉𝑖 ，(4) 𝐸𝐻 = 𝐸𝐻𝑟 + 𝑗𝐸𝐻𝑖 ，(3) 𝐸𝐻𝑟 = 𝐻𝐴 cos(𝐻𝑃 )
𝐸𝑉𝑟 = 𝑉𝐴 cos(𝑉𝑃 )
𝐸𝐻𝑖 = 𝐻𝐴 sin(𝐻𝑃 )
𝐸𝑉𝑖 = 𝑉𝐴 sin(𝑉𝑃 )
Definition And Measurement Techniques Inserting into (1) and (2) gives the field in the two hands of polarization 𝐸𝐿𝐻𝐶𝑃 =
𝐸𝑅𝐻𝐶𝑃 =
1 2 1
𝐻𝐴 cos(𝐻𝑃 ) + 𝑉𝐴 sin(𝑉𝑃 ) + 𝑗 𝐻𝐴 sin(𝐻𝑃 ) − 𝑉𝐴 cos(𝑉𝑃 )
𝐻𝐴 cos(𝐻𝑃 ) − 𝑉𝐴 sin(𝑉𝑃 ) + 𝑗 𝐻𝐴 sin(𝐻𝑃 ) + 𝑉𝐴 cos(𝑉𝑃 )
2 In each hand of polarization, the power can be expressed by 𝑃 𝑑𝐵 = 10 log10
𝐸2 377
Definition and Measurement Techniques The ripples in the radiation pattern plotted in Fig. 3 are a consequence of the beam ellipticity, which occurs when a finite cross-polar component exists. The depth of the nulls defines the AR, which is related to cross-polarization by the expression 𝐴𝑅 = 20 log10
1+𝑒 1−𝑒
where 𝑒 = 10−𝑃𝑑𝐵 /20 and PdB is the cross-polar power.
Definition And Measurement Techniques
Fig. 3. Radiation pattern comparison of an elliptically polarized antenna and a standard gain antenna .
Definition and Measurement Techniques Gain 𝐺0 dBil = 𝐺𝑠𝑡𝑑 − ∆ 𝐺𝐴𝑈𝑇 dBi𝑐 = 𝐺0 + 3 𝐺𝑐 dB = 20 log10 0.5 1 + 10−AR/20
𝐺𝐴𝑈𝑇 dBi𝑐 = 𝐺0 + 𝐺𝑐 + 3 G0：Absolute gain of the AUT Gstd：Gain of standard gain antenna ∆：Difference in the Measured power level GAUT：Gain of AUT Gc：Correction factor
Fig. 3. Radiation pattern comparison of an elliptically polarized antenna and a standard gain antenna .
Experiments With Circularly Polarized Dipole Antennas
Fig. 4. Layout of a prototype 1.7-GHz CP dipole.
Fig. 5. Swept frequency measured return loss and impedance of 1.7-GHz CP dipole
Experiments With Circularly Polarized Dipole Antennas
Fig. 6. CP radiation patterns of 1.7-GHz CP dipole.
Conclusions To promote a better understanding and visualization of the physical principles, a laboratory-based project involving a series of simple experiments has been designed to enable students to observe the essential amplitude and phase criteria associated with this mode of wave propagation. Reference : B. Y. Toh, R. Cahill, and V. F. Fusco, “Understanding and measuring circular polarization,” IEEETrans. On Education, Vol. 46, No. 3, Aug. 2003.
