Chapter 2 Part 2

Co and Cross Polarization Axial Ratio The Smith Chart CHAPTER 2 ANTENNA PARAMETERS

1 Chapter 2 Part 2 Additional Antenna Parameters Polarization

Co-polarization

Cross polarization

Axial Ratio (AR)

Input impedance

VSWR

2 Chapter 2 Part 2 Polarization

• Defined as the direction of the electric field ofan electromagnetic field. • Linear polarization: Vertical vs Horizontal • Circular polarization: left handed circular (LHC) vs right handed circular (RHC) • Elliptical polarization • Elliptical polarization is the most general form: x and y components of the E-field have aphase difference and unequal amplitudes. • Linear polarization = elliptical with x and y components with zero phase difference (any amplitudes) • Circular polarization = elliptical with x and y componentswith 90o phase difference and equal amplitude

3 Chapter 2 Part 2 Types ofPolarization

4 Chapter 2 Part 2 Concept ofPolarization

• First, a horizontally polarized antenna will not communicate with a vertically polarized antenna. • Due to the reciprocity theorem, antennas transmit andreceive in exactly the same manner. • Hence, a vertically polarized antenna transmits and receives vertically polarized fields. • Consequently, if a horizontally polarized antenna is trying to communicate with a vertically polarized antenna, there willbe no reception.

5 Chapter 2 Part 2 Concept of Polarization (cont)

• In general, for two linearly polarized antennas that are rotated from each other by an angle Φ , the power loss due to this polarization mismatch will be described by the Polarization Loss Factor (PLF):

• Hence, if both antennas have the same polarization, the angle between their radiated E-fields is zero and thereis no power loss due to polarization mismatch. If one antenna is vertically polarized and the other is horizontally polarized, the angle is 90 degrees and no power will be transferred.

6 Chapter 2 Part 2 Footnote:

• Circular polarization is a desirable characteristic for many antennas. Two antennas that are both circularly polarized do not suffer signal loss due to polarization mismatch. • Another advantage of circular polarization is that a RHCP wave will reflect off a surface and be LHCP. This is advantageous because an antenna designed to receive RHCP waves will have some immunity to the signal-fading effects of reflected waves interfering with the desired wave. These are some of the reasons GPS signals from satellites are RHCP. • Suppose now that a linearly polarized antenna is trying to receive a circularly polarized wave. Equivalently, suppose a circularly polarized antenna is trying to receive a linearly polarized wave. What is the resulting Polarization Loss Factor? • Recall that circular polarization is really two orthongal linear polarized waves 90 degrees out of phase. Hence, a linearly polarized (LP) antenna will simply pick up the in-phase component of the circularly polarized (CP) wave. As a result, the LP antenna will have a polarization mismatch loss of 0.5 (-3dB), no matter what the angle the LP antenna is rotated to. Therefore:

7 Chapter 2 Part 2 Polarization LossFactor

• It referred to as polarization efficiency, antenna mismatch factor, or antenna receiving factor. All ofthese names refer to the same concept.

8 Chapter 2 Part 2 Applications

• Linear polarization is by far the most widely used formost radio communications applications • Vertical polarization is often used for mobileradio communications. • This is because many vertically polarized antenna designs have an omni-directional radiation pattern and it means that the antennas do not have to be re-orientated as positions as always happens for mobile radio communications as the vehiclemoves. • Circular polarisation for precision reception such asGPS systems

9 Chapter 2 Part 2 Co-polarization Vs Crosspolarization

• Analysis of circular polarization utilizes twoindependent, orthogonal, components: right- and left-hand circular (RHC and LHC).

Co-polarization Cross polarization The desirable component, The undesirable having the intended sense component, with the of rotation (right, or left), opposite polarization, is is called the co- called the cross polarization component. polarization component.

• The mix of co-polarization and cross polarization components determine the quality of Circular Polarization and correlates with the axial ratio(AR). 10 Chapter 2 Part 2 Co-polarization and Cross polarization • Graph below shows the 2D radiation patterns of co- andcross polarized components for 1296 MHz and a 3 m diameterdish

11 Chapter 2 Part 2

• A measure of how purely polarized an antenna is, is the cross polarization level. • It is defined as the difference in decibels between the maximum radiation intensity of the co and crosspolarizations respectively. • Antennas must operate in similar polarizations in orderto ensure optimal performance. • Antennas operating in orthogonal polarizations willnot perform at all due tosignificant polarization losses.

12 Chapter 2 Part 2 Axial Ratio(AR)

• The axial ratio is the ratio of orthogonal components of an E- field. • The axial ratio for an ellipse is ≥3 dB. • The axial ratio for pure linear polarization is infinite, because the orthogonal components of the fieldis zero. • The axial ratio for circular polarization is<3dB. • However for ideal axial ratio for circularly polarized fields is 0 dB.

13 Chapter 2 Part 2 How to measure AR

• The axial ratio tends to degrade away from the main lobe of an antenna, so the axial ratio may be indicated in a data sheet for an antenna as follows: "Axial Ratio: <3 dB for ±30 degrees from main lobe".

• This indicates that the deviation from circular polarization is less than 3 dB over the specified angular range.

14 Chapter 2 Part 2 Input Impedance

• Another parameter describing antennas is their input impedance, i.e. the ratio between the voltage and the current at their terminals. • EM power is delivered to an antenna via a transmission line or a waveguide - devices used to guide EM waves from the transmitter to the antenna. • In this process EM waves can be attenuated or reflected. In order to avoid reflections of EM waves back to thetransmitter, the antenna input impedance should match that of the driving transmission line (usually 50 ohm and 75 ohm).

15 Chapter 2 Part 2 VSWR

• Nevertheless, the antenna’s input impedance varies with frequency, and could not be equal to that of the transmission line at all frequencypoints.

• This indicates that some reflections are unavoidable. The Voltage Standing Wave Ratio (VSWR) is a measure for how much power is reflected.

• A low valued VSWR indicates that the majority of the incident power is delivered to the antenna and reflections are nearly avoided

16 Chapter 2 Part 2 VSWR (cont)

• The VSWR is always a real and positive number for antennas. • The smaller the VSWR is, the better the antenna is matched to the transmission line and the more power is delivered to the antenna. • The minimum VSWR is 1.0. In this case, no power is reflected from the antenna, which isideal. • In general, if the VSWR is under 2 the antenna match is considered very good and little would be gained byimpedance matching.

17 Chapter 2 Part 2

• If the reflection coefficient is given by , then the VSWR is defined by the following formula:

• The reflection coefficient is also known as s11 or return loss. • See the vswr table next to see a numerical mapping between reflected power, s11 and VSWR.

18 Chapter 2 Part 2 VSWR Table

SWR Power Power Return Loss Reflection Reflected (%) Transmitted (%) (dB) Coefficient, τ 1.25 1 99 20 0.11 1.58 5 95 13 0.22 1.92~ 2 10 90 10 0.32 5.80 50 50 3 0.71

% Pr = τ 2 100

% Pt = 1- 𝑥𝑥τ 2 100

RL (dB) = 20 log𝑥𝑥 ІτІ

−1 τ = +1 𝑉𝑉 𝑆𝑆 𝑊𝑊 𝑅𝑅 𝑉𝑉 𝑆𝑆 𝑊𝑊 𝑅𝑅

19 Chapter 2 Part 2 Smith Chart

• Origin 1939: Invented by P.H. Smith. Graphical method for performing transmission line calculations. (Well before pocket calculators or computers) • Today Useful for displaying information: shows reflection coefficient and impedance/admittance simultaneously • Helps engineer gain intuition about using transmissions lines / creating matching circuits.

20 Chapter 2 Part 2 Smith ChartParametric Equations

rLcircles

rL circles are contained inside the unit circle

xL circles

Only parts of the xL circles are contained within the unit circle 21 Chapter 2 Part 2

22 Chapter 2 Part 2 Transmission LineCharacteristic

• Characteristic impedance , 0 • For this Smith Chart tutorial, we will assume 0 is 50 Ω, which is often, but not always the case𝑍𝑍 . Note that the Smith Chart can be used with any value of 0. 𝑍𝑍 • Load impedance , 𝑍𝑍 𝑍𝑍𝐿𝐿 • Reflection coefficient, τ

• VSWR (Voltage Standing Wave Ratio) and is also referred to as Standing Wave Ratio (SWR)

23 Complete Smith Chart Chapter 2 Part 2

Positive xL Circles

rL Circles

Negative xLCircles

24 Reflection coefficient at the load Chapter 2 Part 2

25 Input Impedance Chapter 2 Part 2 Constant SWR circle (standing-wave ratio)

26 Maxima and Minima Chapter 2 Part 2

27 Chapter 2 Part 2

(c) Normalized ZL:

(d)

(a) Find dmax and dmin

(b)

28 Chapter 2 Part 2

Given: SWR= 3 Z0 = 50 Ω first voltage min is 5 cm from load Distance between adjacent minima = 20 cm

Determine: ZL

λ/2 =20

29 Chapter 2 Part 2

30 END OF CHAPTER 2 Next… Tutorial