Wide Band Antennas

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Final Thesis Report 2010, UNSW@ADFA

1

Ultra Wideband (UWB) Antennas

Andrew J. Spear1

University of New South Wales at the Australian Defence Force Academy

The aim of the project was to develop a diagnostic tool for evaluation of Ultra

Wideband (UWB) antenna performance. The evaluation involves determining if the

antenna has minimum phase properties, which allows the use of a passive equalisation

network. This passive equalisation network is designed to linearise the phase response

and hence give a constant group delay which is a desirable property for a UWB antenna.

The diagnostic process evaluates how close an antenna is to minimum phase and how

complex the equalisation network would have to be to give a constant group delay. This

process was illustrated using simulation and measurement of 2 different UWB antenna

designs and gave results for varying degrees of equaliser complexity.

Contents

Ultra Wideband (UWB) Antennas 1Contents 1I. Introduction 2II. The 2-Port Network 2III. Minimum Phase Systems 3IV.

Antenna Transfer Function 4

V. Equalization Network 4VI. Antenna Parameters 4VII. Literature Review 5VIII. Simulation 6A. Circular Monopole 8B. Vivaldi Antenna 10IX. Procedure 13X. Results 14A.

Comparison of Simulation to Measurements 14

B. Characterization of Substrate Permittivity 15C. Measured Data 16XI. Discussion 21XII. Conclusion 25XIII. Recommendations 25XIV. Acknowledgements 25XV. References 26

1OFFCDT, School of Engineering & Information Technology. Electrical Engineering Project ZEIT4299.


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2

I. NomenclatureUWB = Ultra Wideband

FCC = Federal Communications Commission

LHP = Left Half Plane

= Phase [rad]

= Frequency [rad/s]g = Group Delay [ns]

R = Antenna Separation [m]

= Reflection Coefficient

= Propagation Coefficient

= Dielectric Permittivityo = Free Space Permittivity [8.854x10

-12F/m]

o = Free Space Permeability [4x10-7

H/m]

II. IntroductionThe Federal Communications Commission (FCC), the U.S. telecommunications regulator, has allocated

7.5GHz of spectrum for unlicensed use of ultra wideband devices (UWB) in the 3.1GHz to 10.6GHz frequencyband with a maximum transmit power spectral density of -41dBm/MHz [1]. The FCC defines UWB as any

signal that occupies a bandwidth of more than 500MHz or 20% of the centre frequency [26] in the 3.1GHz to

10.6GHz band. Due to the broad bandwidth, UWB technology allows both high-data-rate personal area network(PAN) wireless connectivity and longer-range, low-data-rate applications [2]. Using signals of a large

bandwidth adds an increased level of complexity when it comes to characterizing UWB antennas. Traditional

antennas are designed to operate at either a particular frequency or over a small range of frequencies depending

on their applications because antenna parameters change significantly over frequency. Operating over a large

frequency band has the effect of incorporating these significant changes in antenna parameters hence traditional

antenna theory is only applicable to a certain degree. The most important parameter of UWB antennas whichchanges with frequency is the phase response. It is desired to have a linear phase response which gives a

constant group delay (given in (1)). A constant group delay results in all spectral components of a UWB signal

being received at the same time. Having a non constant group delay results in time dispersion of signals

meaning that different spectral components of a UWB signal arrive at different times which gives distortion inthe signal. This makes the signal processing very complicated to recreate the original signal. For this reason, a

diagnostic tool is developed in order to determine whether a particular UWB antenna can be equalised over theUWB frequency band to achieve a constant group delay given in (1).

( )( )

= -g (1)

Where is the phase response of the antenna and is the frequency in radians per second. This project took

antenna designs from [6] to [16] and analysed and characterized these antennas according to the data that was

published along with these designs. From this point, several designs were selected and simulated using CSTMicrowave Studio and the antennas with the best performance were then constructed and tested. The antenna

designs chosen were the circular monopole antenna proposed by [15] and the Vivaldi antenna proposed by [13].These were then tested in an anechoic chamber using a network analyser to determine the antenna S-parameters

over the UWB frequency range. The diagnostic tool was then developed using MATLAB to take the S-

parameters of the antenna link and determine how close the antennas are to minimum phase. If an antenna is

minimum phase then it can, in principle, be equalised over a wide frequency band using a passive network. Thediagnostic tool then determines what effect equalisation has on the antenna phase response and how the

complexity of the equalisation network effects the equalisation over the UWB frequency band.

III. The 2-Port NetworkThe 2-port network in the case of this project consists of two antennas separated by a free space gap as

shown in Figure 1.


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Figure 1. 2-Port Antenna Network

The 2-port network has four S-parameters; these being S11, S12, S21 and S22. In the case of an antenna link,

S11 describes the reflections at the input of port 1, S12 describes the transmission from port 1 to port 2, S 21describes the transmission from port 2 to port 1 and S22 describes the reflections at the input of port 2. In the

case of an antenna 2-port network, the distance R is not a fixed distance. This is because over the UWB

frequency range, the phase centre of the antennas can move with respect to the antenna structure. The phase

centre of an antenna is the point at which the far field radiation appears to be radiated from. In this project, thephase centre is assumed to be at a single point over the entire UWB frequency range; this point is on the antenna

structure itself. The free space gap has a linear phase response associated with it. In air, the phase response ofthe signal is equal to

( ) jkRe = (2)

Where k is the frequency in radians per second divided by the speed of light. To remove this linear phaseterm, the distance R was set to the separation of the antennas. It was later found that R had to be changed to

account for the movement of the phase centre and another linear phase term was removed to account for signal

propagation through the antenna structure itself.

IV. Minimum Phase SystemsA minimum phase system is defined as a system which has all poles and zeroes of a transfer function in the

j domain in the left half plane (LHP) [4]. [4] also states that any rational system can be separated into a

minimum phase system and an all-pass system

( ) ( ) ( ) jGjGjG apmin= (3)

A minimum phase system can, in principle, be equalised to have a linear phase over unlimited bandwidth

using an equaliser physically realisable from passive components [5]. This is done by creating a passivenetwork consisting of capacitors and inductors to give LHP poles and zeroes to compensate for those (placing a

pole for every zero and a zero for every pole) of the minimum phase system. The minimum phase component

of a system is defined as the negative Hilbert transform of the attenuation of the system [21], given by

( ) ( )[ ] jGHjG lnmin = (4)

Where ln|G(j)| is the attenuation of the system. The minimum phase function can also be represented by

the symbol m. This can also be defined mathematically from [20] as

( )( )[ ] ( )[ ]

d

jGjGjG

=

0

22min '

ln'ln2(5)

Where S21 is the transmission phase response of the system. Once the minimum phase term has been

calculated, the all-pass phase is the transmission phase response minus the minimum phase response. The

magnitude response of the all-pass system is unity by definition and if the system is minimum phase, the all-

Port 1Port 2

R


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pass phase response will be zero.

equalised over a wide frequency ran

The property of minimum pha

transfer function of a single antetransmission characteristic (S21 par

parameter is equal to

where HTX() and HRX() are t

is the separation of the 2 antennas

identical antennas with a single pol

If the antenna were minimum

magnitude of H() and the phase re

are minimum phase, it is unlikely t

when it comes to the design of the e

Any non minimum phase comp

reason, the antenna transfer functioof H() and phase equal to m/2.using a passive network, the best p

the system. Using this transfer fun

minimum phase transfer function athe complexity has a significant

equalisation network, the synthesis

that the order of the transfer functi

higher the order, the more capacito

complexities will be investigated wtransmit antenna and after the recei

Figure

Because a UWB antenna is onl

important than others however most

a trade-off is required to achieve th

important parameters when it cobandwidth. Size is important becau

inal Thesis Report 2010, UNSW@ADFA

4

If the all-pass phase response is non-zero then t

ge to ideally give this all-pass phase response.

V. Antenna Transfer Functionse can then be applied to the antenna 2-port netwo

nna. The antenna transfer function can be determeter) in terms of the components in the system; ac

( ) ( ) ( )o

jkR

RXTXRc

eGGj

221

=

e transfer functions of the transmit and the receive a

and co is the speed of light. Assuming the 2-port n

risation then the antenna transfer function can be giv

( ) ( ) ocRj

o eSj

RcH

212

=

phase then the magnitude response of the antenna

sponse would be equal to m/2. However, as it is unat this will be exactly the transfer function of the ant

qualisation network.

VI. Equalisation Networknents of the system cannot be equalised using a pas

n, for the purposes of equalisation, has a magnitudeAs any non-minimum phase components of the syst

ssible outcome of the equalisation is to be left with t

ction, the equalisation network can be defined as the

d implemented as such. If the equalisation networkffect on the physical equalisation network. For

becomes very difficult with higher order transfer fu

n reflects upon the amount of components used in t

rs and inductors are required. For this reason sever

ithin this project. In practice, the equalisation netwoe antenna as shown in Figure 2.

2. Antenna Network with Equalisation Network

VII. Antenna Parametersy one particular type of antenna, some of the antenn

parameters are still desired to be as close to ideal as

e best performance in the largest amount of paramet

es to ultra wideband antennas are size, radiationse UWB communications has a major application in

e system can only be

rk where G(j) is the

ined by defining theording to [20], the S21

(6)

ntennas respectively, R

twork consists of two

n as

(7)

would be equal to the

likely that the antennas

nna. This is important

sive network. For this

qual to the magnitudem cannot be equalised

he all-pass response of

inverse of the antenna

ere to be synthesized,larger complexities of

nctions due to the fact

he network, that is, the

l equalisation network

rk is placed before the

a parameters are more

ossible. This is where

rs possible. The more

attern and impedanceobile communications


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5

hence it is desired for the size of the antenna to be as small as possible. The radiation pattern of an antenna in

practice can either be omnidirectional or directional with the pattern being selected for the intended use of the

antenna. Impedance bandwidth is important because a UWB antenna operates over a wide range of frequencies.

In practice it is not possible to achieve ideal performance in all of these parameters hence a trade-off is required

in the design process to achieve the best performance in these parameters.

For a UWB antenna, the size is desired to be what is known as electrically small. An electrically small

antenna is defined as an antenna that is about to fit into a sphere that has a radius of one electrical radian givenby /2. Because in UWB applications there is a requirement for the antenna to operate at frequencies between

3.1GHz and 10.6GHz, the relative size of the antenna varies depending on which end of the frequency spectrum

is being used. An electrically small antenna over this entire frequency range cannot simultaneously provide the

required impedance bandwidth or efficiency for typical UWB applications. For this reason, it is common for an

antenna to be electrically small at the lower end of the frequency range and have a moderate electrical size at the

upper end of the frequency range.

A common way of defining the impedance bandwidth of an antenna is the frequency range over which the

system has greater than a 10dB return loss; that is, the magnitude of S 11 is less than -10dB. For a UWB

application, a good impedance match can be defined as an antenna system which has a voltage standing wave

ratio (VSWR) of less than 2 [3]. For a perfectly matching system, the VSWR, given as

+

= 1

1

VSWR(8)

has a reflection coefficient () of zero. This is because it is desired that the transmit antenna radiate all of

the power input to the antenna and that nothing be reflected by the transmit antenna back to the source, hence

is zero. For a good matching system (VSWR


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6

IX. SimulationThe simulation section of the project utilised Computer Simulation Technologys (CST) Microwave Studio

to perform 1-port simulations of single antennas and 2-port simulations of a link between two antennas for the

various antenna structures discussed in section VIII. The parameters simulated were the impedance bandwidth

(obtained from the magnitude of the S11 parameter), the transmission characteristic (obtained from the

magnitude of the S21 parameter), the antenna phase (obtained from the phase of the S21 parameter) and the

radiation pattern. All simulations were conducted between 1GHz and 12GHz with the radiation pattern beingmeasured at 4.5GHz, 6.5GHz and 8.5GHz. The simulation frequency range was selected in order to cover the

entire UWB frequency range with a buffer either side of the frequency band. The bandwidth can easily be

increased however the increased bandwidth leads to extra computation time for information that is not required.

The three radiation pattern frequencies were selected in order to show the trend of the radiation pattern over the

UWB frequency range and it was decided that the three frequencies sufficiently demonstrated this. Simulationswere conducted using the adaptive mesh refinement utility enabled in order to give the most accurate results.

The excitation signal used was a Gaussian pulse and can be seen below in Figure 3 (a).

Figure 3 (b) shows the spectral component of the excitation signal used and it can be seen from this plot that

the Gaussian pulse contains spectral components between the simulation frequency range of 1GHz and 12 GHz.

2-port measurement of a microstrip printed a fibreglass board were taken to characterise the permittivity of

the FR-4 fibreglass board used for making the antenna structures. The 2-port measurements were taken using an

Agilent E5071C network analyser which gave the 2-port measurements in the form of S-parameters. The

permittivity of FR-4 is given as 4.3 at 10GHz according to [23] however the permittivity of FR-4 changessignificantly between different manufacturers. It is intended for the board to be used over the UWB frequency

range however the permittivity is not constant over the frequency range. Practically, it is not important to know

how the permittivity changes over the UWB frequency range however as the simulation uses an assumedpermittivity characteristic for FR-4, it is important to characterise the actual FR-4 board used for the antenna

construction to improve the fidelity of the simulation. Once the 2-port measurements for the microstrip had

been obtained, 1-port measurements for the connectors and adapters used were taken in order to remove theireffect upon the 2-port measurements. Once left with the 2-port parameters of just the microstrip, the S-

parameters were converted to ABCD parameters according to the conversion given in [17]. From there, by

assuming that the microstrip is a lossy transmission line, the propagation coefficient of the microstrip can be

calculated using the conversion given in (9) from [17].

( ) ( )

( )( )

=

lZ

l

lZl

D

C

B

A

coshsinh

sinhcosh

0

0

(9)

(a) (b)

0 1 2 3 4 5 6 7

x 10-19

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Excitation Signal

Time, ns

Magnitude,

V

2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25Spectral Density of Excitation Signal

Frequency, GHz

Magnitude,

V

Figure 3. (a) Time domain plot of the excitation signal used in simulation. (b) The spectral component of the

excitation signal used in simulation.


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7

Where is the propagation coefficient of the transmission line, l is the length of the transmission line and Z0

is the characteristic impedance of the transmission line. From (9) the propagation coefficient can be calculated

and can be split into its real and imaginary parts with the real part () being the attenuation coefficient and the

imaginary part () being the propagation coefficient. The phase velocity can then be calculated using

according to (10).

=pu

(10)

Using the phase velocity, the effective permittivity of the substrate can then be calculated using (11) from

[22].

2

=

p

eu

c

(11)

Where c is the speed of light. The calculated effective permittivity can then be used to calculate the relative

permittivity of the FR-4 board. The relative permittivity is calculated according to (12) from [22].

1

1211

1212

++

+

=

W

d

W

de

r

(12)

The relative permittivity can then be put into CST in the form of = j where the data to be input is

/o and /o. /o is equal to r and /o is given in (13), from [22].

poo uc 2'' =

(13)

Once this data is put into CST, the software package performs a regressive fit in order to produce a model

which represents the input data.


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8

A. Circular MonopoleFigure 4 shows the model of the circular

monopole antenna from [15] used for

simulation in CST with the dimensions

shown below in Figure 5 where Ws = 42mm,

Ls = 50mm, Wp = 20mm, Lf= 20.3mm, Wf=2.6mm and Lg = 20mm. The red rectangle

at the bottom of the antenna structure in

Figure 4 is the waveguide port used to excite

the antenna structure in place of a coaxial

feed used in practice.

Figure 6 shows the plot of the S11 magnitude

which indicates that the circular monopole antenna

has an impedance bandwidth which covers the entireUWB frequency range of 3.1GHz to 10.6GHz. As

discussed in section VII of this report, the impedance

bandwidth is given by the frequency bandwidth over

which the magnitude of S11 is less than -10dB.

Figure 6 shows that the circular monopole antenna

has an S11 magnitude of less than -10dB fromapproximately 2.25GHz upwards.

The next parameter which was simulated was the

radiation pattern at 4.5GHz, 6.5GHz and 8.5GHz.

The results of this simulation can be seen below in

Figure 7.

Lg

Ls

Ws

Lf

Wp

Wf

Figure 4. Circular Monopole Antenna from [15] modelled in

CST

Figure 5. Dimensions of Circular Monopole Antenna from [15].

Figure 6. S11 magnitude of Circular Monopole

antenna

0 2 4 6 8 10 12-40

-35

-30

-25

-20

-15

-10

-5

0|s11| of Circular Monopole Antenna

Frequency, GHz

Magnitude,

dB


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9

It can be seen in Figure 7 that the radiation pattern for the circular monopole antenna at 4.5GHz radiates in

main lobes at the front and back of the structure with a portion being radiated to the sides of the structure. At

6.5GHz, the radiation pattern shifts to having to main lobes off towards the upper left and right of the structure.

At 8.5GHz, the radiation pattern is similar to that at 6.5GHz however the main lobes are oriented more upwards

and have a narrower beamwidth. This means that for one particular orientation, the antennas are not going to be

to be situated within the main lobe over the entire frequency band which causes degradation of the received

signal. This demonstrates that the radiation pattern changes dramatically with frequency and will pose

restrictions on the types of applications for which this antenna can be used.

Following the 1-port simulation of the antenna, a 2-port simulation was conducted using 2 antenna structures

separated by a nominal distance. The nominal distance was set corresponding to the antenna separation used in

the practical testing of the antennas which in the case of the circular monopole antennas was 395mm. The

model used for the 2-port simulation in CST can be seen below in Figure 8.

(a) (b)

(c)

Figure 7. Radiation Patterns of Circular Monopole antenna at (a) 4.5GHz, (b) 6.5GHz, (c) 8.5GHz

Figure 8. 2-port simulation model from CST for a link between 2 circular monopole antennas.


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10

The data extracted from the 2-port simulation included the magnitude of the S21 parameter and also the phase

response of the antenna. The results for both are shown below in Figure 9.

The magnitude plot shown in Figure 9 (a) can be used to determine the minimum phase component of the

antenna which can then be compared to the antenna phase in order to determine whether the antenna can be

equalised using a passive network. The antenna phase shown in Figure 9 (b) was obtained from the S21 phase

data by removing the phase due to the free space gap between the 2 antennas and also any linear phase due to

signal propagation through the structure itself. The resultant data is then divided by 2 to give the phase responsefor one antenna.

B. Vivaldi AntennaFigure 10 shows the model of the Vivaldi antenna

from [13] used for simulation in CST with the

dimensions shown below in Figure 11 where Ws =

74mm, Ls = 107mm, Wff = Wfb = 23mm, Lff = Lfb =

40mm, Wf1 = 1mm and Wf2 = 10mm. Similarly to the

simulation of the circular monopole antenna, the Vivaldi

antenna was also excited using a waveguide port in place

of a coaxial cable.

(a) (b)

0 2 4 6 8 10 12-60

-55

-50

-45

-40

-35

-30|s21| of Circular Monopole Antenna

Frequency, GHz

Magnitude,

dB

0 2 4 6 8 10 12-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5Antenna Phase of Circular Monopole Antenna

Frequency, GHz

Phase,rad

Figure 9. (a) Magnitude of S21 parameter obtained from simulation. (b) Antenna phase fromsimulation.

Wfb

Ls

Ws

LffWff

Wf1

Lfb

Wf2

Figure 10. Vivaldi Antenna from [13] modelled in

CST.

Figure 11. Dimensions of Vivaldi Antenna from [13].


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11

Figure 12 shows the plot of the S11 magnitude which

indicates that the Vivaldi antenna has an impedance

bandwidth which covers the majority of the UWB frequency

range of 3.1GHz to 10.6GHz. Figure 12 shows that the

Vivaldi antenna was not a good match between

approximately 3.2GHz to 3.7GHz. Performance wise, this is

an undesirable characteristic of the antenna however for thepurpose of the analysis to be performed on the antenna in

terms of phase equalization, this poor impedance match

between 3.2GHz and 3.7GHz does not have a significant

impact on the outcome of the analysis.

The next parameter which was simulated was the

radiation pattern at 4.5GHz, 6.5GHz and 8.5GHz. The

results of this simulation can be seen below in Figure 13.

It can be seen in Figure 13 that the radiation pattern for the Vivaldi antenna is far more directional than the

circular monopole antenna with the majority of the energy being radiated in the y direction (towards the top of

the antenna structure). As the frequency was increased, the radiation pattern did not change a significantamount compared to the circular monopole antenna. This shows that the antenna is more stable in terms of its

directivity and the energy delivered over the UWB frequency band is approximately the same for the sameorientation of the antenna.

0 2 4 6 8 10 1-45

-40

-35

-30

-25

-20

-15

-10

-5

0|s11| of Vivaldi Antenna

Frequency, GHz

Magnitude,d

B

Figure 12. S11 magnitude of Vivaldi antenna

Figure 13. Radiation Patterns of Vivaldi antenna at (a) 4.5GHz, (b) 6.5GHz, (c) 8.5GHz

(a) (b)

(c)


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12

Once again, following the 1-port simulation of the antenna, a 2-port simulation was conducted using 2

antenna structures separated by a nominal distance. The nominal distance was set corresponding to the antenna

separation used in the practical testing of the antennas which in the case of the Vivaldi antennas was 290mm.

The model used for the 2-port simulation of the Vivaldi antenna in CST can be seen below in Figure 14.

The data extracted from the 2-port simulation included the magnitude of the S21 parameter and also the phase

response of the antenna. The results for both are shown below in Figure 15.

In the same way as for the circular monopole antenna, the data shown in Figure 15 can be used to determine

the minimum phase component of the antenna and then compared to the antenna phase in order to determine

whether the antenna can be equalised using a passive network. The antenna phase was extracted using the same

process detailed for the circular monopole antenna.

(a) (b)

0 2 4 6 8 10 12-45

-40

-35

-30

-25

-20

-15|s21| of Vivaldi Antenna

Frequency, GHz

Magnitude,

dB

0 2 4 6 8 10 12-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0Antenna Phase of Vivaldi Antenna

Frequency, GHz

Phase,rad

Figure 14. 2-port simulation model from CST for a link between 2 Vivaldi antennas.

Figure 15. Magnitude of S21 parameter obtained from simulation. (b) Antenna phase from simulation.


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X. ProcedureThe practical testing consisted of two parts, the first being a 2-port measurement of a simple microstrip

printed on a fibreglass board with SubMiniature version A (SMA) connectors. The second part consisted of the

1-port and 2-port measurements of the circular monopole antennas and the Vivaldi antennas. All 1-port and 2-

port measurements were taken over the frequency range of 2GHz to 12GHz. This range exceeds the UWB

frequency range which allows greater continuity of data for analysis.

The second part of testing consisted of the 1-port and 2-port testing of the Circular Monopole and Vivaldiantennas. The 1-port testing was conducted using an Agilent E5071C network analyser to measure the S11

parameter of each antenna structure. The S11 parameter magnitude was then able to be compared to the S11

magnitude plot obtained from CST to confirm the accuracy of the simulations. The 2-port testing was

conducted such that each antenna was receiving in the far field. This meant that the antenna separation had to

be at least twice the distance of the calculated far field for a single antenna. The far field is given according to(14) from [25].

22D

R =(14)

Where D is the size of the antenna and is the wavelength of the transmitted/received signal. As the

frequency is varied over a large bandwidth, this leads the wavelength to also vary and hence the far field

distance varies with frequency. For this reason, it was ensured that the antennas would be in the far fieldregardless of the frequency which meant that the far field was calculated at the upper frequency limit (being

12GHz for testing purposes) hence giving the minimum wavelength of signal that will be used. For the circular

monopole antenna, the size of the radiating section of the antenna is 2cm and hence (14) can be used to give a

far field distance of 3.2cm meaning that the antenna separation has to be at least 6.4cm for the antennas to be

operating in the far field. For the Vivaldi antennas, the largest radiating section is approximately 4cm in length.

Once again, using (14) the far field distance can be calculated to be 12.8cm and hence the antenna separationhas to be at least 25.6cm.

The 2-port testing consisted of several iterations of tests conducted to achieve an accurate data set over the

UWB frequency range. The 2-port testing consisted of a Agilent E5071C network analyser with ports 1 and 2

each connected to an antenna and the antennas oriented towards each other separated by a free space distance R.

Figure 16 shows a block diagram of the final experimental setup and depicts the various components that are

incorporated into the measured data. In the final experiment, the data for the circular monopole antennas wastaken with an antenna separation of 395mm and for the Vivaldi antennas, the antennas were separated by

290mm.

Figure 16. Block diagram of experimental setup.

As the desired data from this setup is the magnitude and phase response of a single antenna and the

experimental data contains characteristics associated with each component in Figure 16, the undesired data has

to be removed; this is done both experimentally and mathematically. The 2-port data of each cable was

measured and the results can be seen in Fig. 1 and Fig. 2 in appendix B. The magnitude of the cables (in dB)

was then subtracted from the magnitude of the entire system (in dB) and the phase of the cables (in radians) wassubtracted from the phase of the entire system (in radians) giving the magnitude and phase response of the two

antennas and the free space gap between the antennas. Assuming that free space is a lossless medium, the free

space component can be removed mathematically by measuring the antenna separation R and calculating the

phase according to the free space transmission term e-jkR

where k is the frequency in radians per second divided

by the speed of light. The phase due to this free space gap can then be removed by once again subtracting the

phase of the free space term (in radians). Whilst removing the free space component due to the antenna

separation R, any other linear phase components due to propagation through the structure are accounted for by

adjusting R. Keeping R constant over the entire frequency band assumes a constant phase reference although

the phase centre of the antenna can move over the frequency band. Finally, what is left is the phase contribution

jkRe

R


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14

due to the two antennas and the magnitude response of the two antennas. Because the antennas are of the same

design, it was assumed that both antennas behaved identically and hence to obtain the phase and magnitude of

an individual antenna, the magnitude is given as the square root of the magnitude for both antennas and phase

response could be divided by two. The result of this can be seen in section XI.

XI. ResultsA. Comparison of Simulation to Measurements

Figure 17 shows the comparison of the simulated and measured antenna magnitude and phase responses for

the circular monopole antenna. It can be seen that the plots show similar trends however there are far moresmall scale variations in the phase response of the measured data. The plots also show a significant difference

in the magnitude response of the antenna between the measured and simulated results.

(a) (b)

0 2 4 6 8 10 12-45

-40

-35

-30

-25

-20

-15|S21| for Measured and Simulated Data

Frequency, GHz

Magnitude,

dB

Measured

Simulated

0 2 4 6 8 10 12-10

-5

0

5S21 phase for Measured and Simulated Data

Frequency, GHz

Phase,rad

Measured

Simulated

(a) (b)

0 2 4 6 8 10 12-100

-90

-80

-70

-60

-50

-40

-30|S21| for Measured and Simulated Data

Frequency, GHz

M

agnitude,

dB

Measured

Simulated

0 2 4 6 8 10 12-6

-5

-4

-3

-2

-1

0

1

2S21 phase for Measured and Simulated Data

Frequency, GHz

Phase,rad

Measured

Simulated

Figure 17. (a) - Magnitude of S21 for Circular Monopole antenna, (b) - S21 phase for Circular Monopole antenna

Figure 18. (a) - Magnitude of S21 for Vivaldi antenna, (b) - S21 phase for Vivaldi antenna


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15

Figure 18 shows the comparison of the simulated and measured antenna magnitude and phase responses for

the Vivaldi antenna. Similarly to circular monopole antenna results, the plots show similar trends however the

small scale variations are much more prevalent in the measured data. It can be seen in Figure 18 (b) that there is

a large difference between the measured and simulated phase response. This is due to the lack of phase

reference of the measured data.

B. Characterization of Substrate PermittivityFigure 19 shows the plot of the relative

permittivity of the FR-4 substrate used for the

construction of the microstrip and also used in the

construction of the antennas. The permittivity of FR-

4 is stated to be 4.3 however this plot shows how the

permittivity of the board changes over the UWBfrequency range. The plot shows several

discontinuities in the data and this is believed to be

the points at which the phase of the S21 parameter is

equal to zero or wraps from pi radians to pi radians.

Figure 20 shows the complex permittivity of the FR-4

substrate used in the construction of the antennas. The

complex permittivity can be seen in (13) in section IX of

this report. The complex permittivity of the substrate isused to demonstrate how lossy it is over the frequencyband. Representing the microstrip as a lossy transmission

line, it would be expected to see the complex permittivity

increase with frequency. Figure 20 shows that the

complex permittivity does increase over frequency which

confirms the assumption that the microstrip is a lossy

transmission line.

2 4 6 8 10 123

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5Relative Permittivity vs Frequency

Frequency, GHz

R

elativePermittivity

2 4 6 8 10 120

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Complex Permittivity vs Frequency

Frequency, GHz

Permittivity

Figure 20. Complex Permittivity of FR-4 Substrate

Figure 19. Relative Permittivity of FR-4 Substrate


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16

C. Measured DataFigure 21 shows the S11 magnitude of the antennas measured in experimentation compared to the simulated

S11 magnitude for both antennas. It can be seen from both plots that the data shows similar trends however there

are differences between them. In terms of impedance bandwidth, the antennas show better performance in the

measured data than in simulation.

Figure 22 shows the comparison of the S21 magnitude and S12 magnitude of the antenna link for both

antennas. These figures show the reciprocity of the antennas and given that S21 is very similar to S12 for both

antennas, it is safe to assume that the antennas are reciprocal. A slight difference can be seen between the S21

and S12 of the Vivaldi antennas however this is insignificant in that the difference is at a maximum of

approximately 0.5dB at approximately -44dB leading to a difference of 0.00051 in linear magnitude. This

difference can be attributed to the physical differences between the antennas in either the manufacturing processor the connection of the SMA connector. Both antennas were constructed using a computer automated milling

machine using the same set of design files however no system is perfect and imperfections may have arisenduring this process. Also, to connect the antenna structure to a coaxial cable, an SMA connector was soldered

(a) (b)

2 4 6 8 10 12-110

-100

-90

-80

-70

-60

-50

-40

-30|S21| compared to |S12|

Frequency, GHz

Magnitude,

dB

S21

S12

2 4 6 8 10 12-46

-44

-42

-40

-38

-36

-34

-32

-30

-28

-26|S21| compared to |S12|

Frequency, GHz

Magnitude,

dB

S21

S12

(a) (b)

2 4 6 8 10 12-60

-50

-40

-30

-20

-10

0|s11| Measured and Simulated

Frequency, GHz

Magnitude,

dB

Simulated

Measured

2 4 6 8 10 12-60

-50

-40

-30

-20

-10

0|s11| Measured and Simulated

Frequency, GHz

Magnitude,

dB

Simulated

Measured

Figure 21. Comparison of Simulated and Measured S11 magnitude data for (a) Circular Monopole

antenna, (b) Vivaldi antenna

Figure 22. Comparison of measured S21 magnitude to S12 magnitude for (a) Circular Monopole

antenna, (b) Vivaldi antenna


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17

onto the structure. Although due care was taken when soldering the connectors, imperfections may have arisen

during this process.

To extract the antenna phase, it was necessary to assume reciprocity of the antennas, that is, each antenna

behaves identically. Figure 22 shows that the antenna links has almost exactly the same S21 and S12 parameters

which confirms this assumption of reciprocity between each pair of antennas.

Figure 23 is an example of the smoothing function

used in MATLAB to smooth the group delay data inorder for it to be readable. The function smoothes the

data contained in a matrix using a mean filter over a

size specified by the user. It can be seen that the

smoothing function produces a smooth curve that

accurately represents the original data. The smoothing

function itself was written by [25].

This smoothing function was used because in the

raw group delay data there was a lot variation in the

plot which can be seen as the blue curve in Figure 23.

The reason there is a lot of variation in the group delay

is due to the small inaccuracies of the network analyser

which cause the phase to appear to have a general trend

due to the large amount of data points however closerinspection reveals that there are small scale variations

between the data points. When this data is

differentiated, the small scale variations become

positive and negative numbers which leads to the large

variations which can be seen in Figure 23.

Figure 24 shows the magnitude data of the antenna link with the free space gap separation. A Hilberttransform is performed on this data to obtain the minimum phase function for the antenna.

2 4 6 8 10 12-30

-20

-10

0

10

20

30Measured Group Delay vs Smoothed Group Delay

Frequency, GHz

GroupDelay,ns

Measured

Smoothed

Figure 23. Effect of Smoothing Function on data

Figure 24. (a) - Magnitude plot of two Circular Monopole antennas separated by free space, (b) -

Magnitude plot of two Vivaldi antennas separated by free space

(a) (b)

2 4 6 8 10 12-100

-90

-80

-70

-60

-50

-40

-30|s21| for 2 Antennas Separated by Free Space

Frequency, GHz

Magnitude,

dB

2 4 6 8 10 12-40

-38

-36

-34

-32

-30

-28

-26

-24

-22|s21| fo r 2 Antennas Separated by Free Space

Frequency, GHz

Magnitude,

dB


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18

Figure 25 shows the measured and minimum phase response and group delay of the circular monopole

antenna. The plot of group delay has been smoothed using the previously mentioned smoothing function. It can

be seen in Figure 25 that there is a discontinuity at approximately 9.8GHz. This is due to the S21 magnitude

(seen in Figure 24) pushing against the threshold of the network analyser. At this frequency, the magnitudedrops to a point at which the data is too small to make sense of and hence the phase reference is lost causing this

discontinuity. It can also be seen that the phase does not begin at zero. This is because a proper phase reference

is not obtained due to the fact that the frequency band begins a 2GHz rather than DC. Figure 25 (b) shows

points at which the group delay is negative. This is not physically possible as it would indicate that the signal

sent at that frequency is arriving before it is actually sent. This is believed to be due to the effect of the

smoothing function on the data combined with the small scale inaccuracy in the network analyser. The points at

which the group delay goes negative are at points where the actual (not smoothed) group delay becomes verynoisy due to slight changes in the phase and hence when put through a mean filter, the average becomes an

arbitrary number in the noisy data range.

It can be seen that the minimum phase response/group delay is similar to the measured phase response/group

delay however the results are still slightly different. This dissimilarity is highlighted in Error! Reference

source not found. which shows the all-pass group delay of the circular monopole antenna where the all passgroup delay is the minimum phase group delay subtracted from the antenna group delay. If the antenna were

minimum phase then the all-pass phase would be constant however it is quite clear that this is not the case; the

all-pass group delay of the circular monopole antenna varies a significant amount with frequency making

equalisation of the antenna particularly difficult due to a passive network only being able to equalise the

minimum phase component of the antenna.

(b) (b)

2 4 6 8 10 12-0.5

0

0.5

1

1.5

2

2.5Measured Phase vs Minimum Phase

Frequency, GHz

Phase,rad

Measured

Minimum Phase

2 4 6 8 10 12-3

-2

-1

0

1

2

3

4Measured Group Delay vs Minimum Phase Group Delay

Frequency (GHz)

GroupDelay(ns)

MeasuredMinimum Phase

Figure 25. (a) Measured and Minimum Phase Responses of Circular Monopole antenna, (b) Measured and

Minimum Phase Group Delay of Circular Monopole antenna.

(a) (b)

2 4 6 8 10 12-4

-3

-2

-1

0

1

2Measured Phase vs Minimum Phase

Frequency, GHz

Phase,rad

Measured

Minimum Phase

2 4 6 8 10 12-3

-2

-1

0

1

2

3

4

5

6Measured Group Delay vs Minimum Phase Group Delay

Frequency (GHz)

GroupDelay(ns)

Measured

Minimum Phase

Figure 26. (a) Measured Phase Response and Minimum Phase Response of Circular Monopole antenna,

(b) Measured Group Delay and Minimum Phase Group Delay of Vivaldi antenna.


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19

Figure 26 shows the measured and minimum phase response and group delay of the Vivaldi antenna and the

group delay data has been smoothed using the smoothing function. Figure 26 (a) shows that there is a large

difference between the measured and minimum phase response however Figure 26 (b) shows that the group

delays are rather similar. The difference in phase response is due to the lack of phase reference because thefrequency band did not start at DC. For the purposes of the data analysis, the difference in the measured phase

and minimum phase response is insignificant as the group delays are relatively similar.

Figure 26 shows the comparison of the

measured antenna phase response and group delay

to the calculated minimum phase response and

group delay for the Vivaldi antenna. The plot of

the group delay shows that the minimum phase

group delay is very similar to the measured group

delay up until approximately 6GHz at which point

the two begin to differ. Error! Reference source

not found. also confirms this showing the all-pass

group delay of the Vivaldi antenna remaining

relatively constant up until approximately 6GHz.The all-pass group delay of the Vivaldi antenna

varies significantly less than the circular

monopole antenna hence making the task of

equalization less difficult for the Vivaldi antenna

compared to the circular monopole antenna.

Figure 27 shows the all-pass group delay ofboth antennas calculated by subtracting the

calculated minimum phase from the antenna

phase. It can be seen that the circular monopole

group delay goes negative over certain frequencies.

As mentioned previously, this is not physically

possible and is due to the negative group delay seen in Figure 25 as this data was used for the calculation.

Figure 28 shows the effect of equalisation on the group delay of the both antennas for varying equalisation

network complexities. As per previous group delay plots, the data has been smoothed. The negative group

delay components which can be seen are due to the small scale inaccuracies in the phase response which are

reflected in the group delay and then smoothed which produces the negative value.

The data indicates that for the circular monopole antenna, equalisation had a limited effect. This wasexpected as the antenna had a significant all-pass phase component which is not able to be equalised using a

(a) (b)

2 4 6 8 10 12-6

-4

-2

0

2

4

6Equalised Group Delay vs Measured Group Delay

Frequency (GHz)

GroupDelay(ns)

MeasuredEqualised (N=5)

Equalised (N=10)

Equalised (N=14)

2 4 6 8 10 12-2

-1

0

1

2

3


Frequency (GHz)

GroupDelay(ns)

Measured

Equalised (N=5)

Equalised (N=10)

Equalised (N=14)

Figure 28. Equalised Group Delay vs Original Group Delay for (a) Circular Monopole antenna for

various equalisation network complexities, (b) Vivaldi antenna for various equalisation network

complexities

2 3 4 5 6 7 8 9 10 11 12-6

-4

-2

0

2

4

6

8

3.1GHz 10.6GHz

All-Pass Group Delay

Frequency (GHz)

Group

Delay(ns)

Circular Monopole

Vivaldi

Figure 27. All-Pass Group Delay for both antennas.


20/27


20

passive network. Varying the complexity had an effect on the level of equalisation; the 5th

order equalisation

network had a very limited effect on the antenna phase, the 10th

order equalisation network had a significantly

greater effect on the antenna phase compared to the 5th order equalisation network and the 14th order

equalization network did not have a significantly greater effect than the 10th

order equalisation network. A

similar statement can be made about the effect on equalisation for the Vivaldi antenna; that it did not have a

significant effect on the antenna phase. As expected from the all-pass phase component of the Vivaldi antenna,

equalisation would only have a limited effect and it can be observed that all equalisation networks had the sameeffect on the antenna with very little difference between them. It was noticed from the all-pass phase

component of Vivaldi antenna that equalisation may be effective up to 6GHz, for this reason, equalisation

networks with the same orders of complexity were developed over the frequency band of 3.1GHz to 10.6GHz

and the results can be seen in Figure 29. This plot shows that over the smaller frequency range, the 10th

and 14th

order equalisation networks had a significant effect on the antenna phase with all larger scale variations in group

delay being removed leaving a relatively smooth curve for the antenna phase. This increase in the effectiveness

of the equalisation is firstly due to the fact that the all-pass phase is almost constant over this frequency range

and secondly due to the fact that 10 th and 14th order transfer functions can more accurately represent the

magnitude and phase response of the minimum phase component over a smaller frequency band which in turn

means that the equalisation networks can more accurately equalise the minimum phase component over a

smaller frequency range rather than a larger frequency range. This indicates that if the complexity of an

equalisation network can be increased above 14th

order, then the equalisation network can have a far more

significant effect on flattening the group delay over the entire UWB frequency range. However, having thislarger order equalisation network does increase complexity of the network significantly which has an inherent

difficulty in the synthesis of the equalisation network.

Figure 29. Equalisation over a smaller frequency band

3 3.5 4 4.5 5 5.5 6-0.5

0

0.5

1

1.5


Frequency (GHz)

GroupDelay

(ns)

Measured

Equalised (N=5)

Equalised (N=10)

Equalised (N=14)


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21

XII. DiscussionThe simulation showed the radiation patterns for both the circular monopole antenna and the Vivaldi

antenna, showing that both had rather different radiation patterns. It can be seen that for the circular monopole

antenna the radiation pattern varies significantly with frequency, meaning that for one particular orientation, the

antennas are not going to be to be situated within the main lobe over the entire frequency band which would

explain why the magnitude of the S21 parameter dropped significantly at higher frequencies. For the Vivaldi

antenna, very little variation was seen in the radiation pattern over the frequency range which shows that theVivaldi antenna has far greater stability than the circular monopole antenna. Figure 24 shows that the

magnitude does not change significantly with frequency (except at approximately 9.1GHz) which contributes to

its better performance compared to the circular monopole antenna.

Part B of the results details the characterization of the FR-4 dielectric substrate used for the construction of

the antenna structures. The relative permittivity shown in Error! Reference source not found. can be seen tovary between approximately 3.8 and 4.1 over the UWB frequency range. The discontinuities seen in this plot

can be attributed to the points in the data at which the phase of the S21 parameter passes through zero or wraps

(and hence passes through zero). The data obtained from these measurements was able to be fed back into CST

in order to improve the fidelity of the simulations.

Figure 30. Comparison of Simulation Accuracy for Circular Monopole Antenna

Figure 30 shows a comparison between CSTs model for the FR-4 substrate, the data input into CST for the

FR-4 substrate obtained using the microstrip and the measured data from the antenna structure. There is not a

significant difference between the results showing that CSTs model for the FR-4 substrate is adequate howeverthis process was important to confirm the accuracy of the model. When the relative permittivity data is input

into CST, a regressive fit is performed on the data automatically by CST in order to produce this model. It was

found that the model which produced the best fit was a seventh order model (determined by CST). Whichever

model for FR-4 used would produce very similar results so it is not important which model is chosen howeverthe model based on the physical data was used because as the FR-4 substrate performed similarly in this

situation, this may not be the case for all situations.As the permittivity of the substrate varies significantly over the UWB frequency range, the performance of

UWB antennas may be increased by using a different substrate for the antennas. It could be seen from the

complex permittivity that the FR-4 substrate was lossy and hence using a different substrate such as Teflon may

reduce how lossy the substrate is which would improve the magnitude response of the antennas.

As mentioned in section X, the experiment used to obtain accurate 2-port measurements underwent several

iterations. The first iteration of 2-port testing consisted of connecting the antennas to the network analyser andthe antennas placed on a wooden structure to support the antennas and provide the free space gap for the

antenna link. In this setup, there were no extra cables used other than those connected directly to the network

analyser itself. The network analyser was calibrated such that the results obtained were measured from the end

of each of the cables (hence including the SMA connectors attached to the antenna structure). When the data

was analysed it was noticed that there was a significant amount of back-scatter from objects around the testsetup. For this reason it was decided to conduct further testing inside the anechoic chamber using a Hewlett-Packard 8719A network analyser.

0 2 4 6 8 10 12-40

-35

-30

-25

-20

-15

-10

-5

0Comparison of Simulation Accuracy

Frequency, GHz

Magnitude,

dB

MeasuredActual FR-4

CST FR-4


22/27


22

Having the antenna link in the anechoic chamber required approximately 9m of cable to connect the

antennas to the network analyser. This addition of 9m of cable had two issues associated with it; these being

attenuation in the magnitude of the S21 parameter and an added linear phase component. The first (and most

apparent) issue noticed was the addition of a linear phase component due to the length of cable. As the network

analyser can take a maximum of 1601 data points over the frequency range of interest, the frequency was swept

in steps of 6.25MHz. Another characteristic of the network analyser is that the measured phase is wrapped

around 180o

. At larger antenna separations it was noticed that the phase of the S21 parameter had a positivegradient. This was quickly realised to be impossible and it was discovered that the issue was to do with the

number of data points, phase wrapping and the large linear phase component introduced by the large amount of

cable and the large free space gap between the antennas. This was because the number of data points over this

frequency range lead to the phase wrapping between subsequent measuring of the phase and causing the phase

to appear as if it had a positive gradient. It was found that this issue could be negated by reducing the free space

gap between the antennas however this lead to the discovery of the second issue. It was noticed that as the

measurements reached the upper limit of the frequency band, the magnitude of the S21 parameter would reach a

constant value and appear very noisy around this point. This constant value was noticed to be the threshold in

accuracy of the network analyser and hence would give results that were so small that no sense of their phase

could be made. The reason the data was reaching this threshold was due to the large amount of cable which was

used to connect the antennas to the anechoic chamber. 2-port measurements of the cables themselves were

taken and the results of this can be seen in Fig. 1of appendix B. It can be seen in this plot that at the upper

frequency limit the magnitude of the S21 parameter drops to approximately -30dB. This was the reason that thedata was reaching the threshold of the network analyser. At this point, there were three possible solutions to the

problem.

The first solution was to simply use less cable however as the network analyser being used could not be

moved and the anechoic chamber could certainly not be moved, this was not able to be done. The second

solution was to use the Agilent E5071C network analyser used in the first experiment and use anechoic foam

tiles outside the anechoic chamber to, in essence, create a smaller anechoic chamber closer to the networkanalyser and hence requiring a shorter amount of cable to connect the antennas to the network analyser.

Creating an anechoic chamber outside of the anechoic chamber proved to be a more difficult task than initially

anticipated and the results still showed a significant amount of back-scatter. The third solution was to move the

Agilent E5071C network analyser next to the door of the anechoic chamber which meant that the anechoic

chamber could be utilised using a reduced amount of cable compared to that which was initially used with the

anechoic chamber. The data from this setup was significantly better than anything previously obtained in the

project.The linear phase component of the system due to the free space gap was removed using a nominal distance

R which was assumed to be the physical antenna separation. The data was analysed with the free space

component removed and the distance R was altered to account for any linear phase delay due to propagation

through the antenna structure and also for any movement in the antenna phase centre. It can be seen in section

XI that the group delay goes negative at points and it was suggested that this could be due to the smoothingfunction. This negative group delay could also be due to the removal of too much linear phase from the system.

Increasing the value of R increases the amount of linear phase delay that is removed from the system and

removing more linear phase delay results in a reduction in group delay. If too much linear phase delay is

removed from the system then this could cause the group delay of the antenna to appear negative.

A system that is minimum phase can be equalised over a wide frequency band using a passive network. Thisis because a minimum phase system has all left half plane (LHP) poles and zeroes. The results show that neither

of the antennas are exactly minimum phase but do exhibit minimum phase properties over certain frequency

ranges. The all-pass component of the system (shown in Figure 27) is the component of the system whichcannot be equalised using a passive network; therefore, the best possible outcome of equalisation using a

passive network is this all-pass group delay. To develop the theoretical equaliser, the transfer function of the

minimum phase component of the antenna response must be obtained. This was done using MATLABs inbuiltinvfreqs function which allows a transfer function to be approximated with varying degrees of complexity. The

limiting factor of the function is that MATLAB is only able to compute a transfer function up to 14 th order,

anything higher than this MATLAB is unable to obtain a solution. Once a transfer function is found for the

minimum phase component of the antenna, the equalisation network transfer function is equal to the inverse of

this function as shown in (14).

( )( )

jG

jGeq

min

1= (14)


23/27


23

This is the equivalent of placing a LHP pole for every LHP zero in the minimum phase component and vice

versa for placing LHP zeroes for every LHP pole. Once the transfer function of the equalisation network has

been computed, the phase response is then computed and is added to the antenna phase. This is done because

the equalisation network is placed in cascade with the antenna according to Figure 2. Mathematically, this

appears as (15).

( ) ( ) ( ) ( ) jGjGjGjG apeq min= (15)

Assuming that the equalisation transfer function is the exact inverse of the minimum phase transfer function,

the equalised group delay would be exactly the same as the all-pass group delay. However, as the invfreqs

function is limited to a 14th

order transfer function, an equalisation network transfer function that is exactly the

inverse of the minimum phase transfer function was unable to be obtained.Using the invfreqs function within MATLAB had an intrinsic flaw associated with it; this being the

difficulty for it to recreate a complex phase response with a maximum of 14th

order. The definition of a

minimum phase system is that it has all LHP poles and zeroes however the invfreqs function does not always

allow this. It was noticed that when invfreqs function was used to compute the transfer function of the

minimum phase component of both antennas, the resultant transfer function would have one right half plane(RHP) pole and zero. This is not possible for a minimum phase function or for a passive network therefore

when implementing the transfer function of the equalization network, all RHP poles and zeroes that were

computed by the invfreqs function were neglected from the equalisation network transfer function. This in turn

reduced the effect that the equalisation network had on the antenna phase.

The minimum phase component of the antenna was calculated using MATLABs inbuilt Hilbert transform

function. As stated in section IV, the phase of a minimum phase system is related to the magnitude through theHilbert transform. The mathematical solution for the Hilbert transform is given in (5) in section III and can also

be implemented in MATLAB to give the minimum phase component. MATLABs inbuilt function performs a

Fast Fourier Transform (FFT) on the input magnitude data, this data is then multiplied by the signum function

and the inverse FFT is then performed on it, the resultant data is the Hilbert transform of the original data. This

computation time of this function does not change significantly with an increase in the frequency range of the

data however the mathematical solution, which was implemented in MATLAB using for loops, did sufferfrom a significant increase in the computation time for an increase in the frequency range. (5) shows the limits

of the Hilbert transform going between zero and infinity however the data measured was between 2GHz and

12GHz. The Hilbert transform is sensitive to truncation of the data according to [20] hence continuity in themeasured data was assumed. This assumption lead to the data being extended on the lower side of the measured

frequency band to DC using the first value of the data set by assuming it was constant from DC to 2GHz and

similarly the last in the data set was assumed to be the constant value between 12 GHz and 400GHz.

The sensitivity of the Hilbert transform was confirmed using a simple transfer function and performing the

Hilbert transform on the data. The results of this can be seen in Figure 31 below.

Figure 31. Test of Hilbert Transform Calculations

0 2 4 6 8 10

x 106

-7

-6

-5

-4

-3

-2

-1

0

1Minimum Phase Response

Frequency, rad/s

Phase,rad

MATLAB H Transform

Mathematical H Tranform

Calculated Phase


24/27


24

Figure 31 shows that MATLAB Hilbert transform is rather sensitive to truncation of data at the upper and

lower limits of the data set whereas the mathematical solution for is rather accurate at these limits. However,

truncation of data has the effect of zooming in on a frequency range of interest so in this test example, if the

frequency range of interest was between 2GHz and 4GHz, both functions have the same performance. For this

reason, it was decided to use MATLABs built in Hilbert transform because the frequency range can be easily

changed without an increase in computation time. It was also found that when using the mathematical solution

for the Hilbert transform on the measured data (from experimentation), the solution was very sensitive to thesmall scale variations that were seen in the measured data and hence did not produce accurate results. Although

the mathematical solution appears to be a more accurate representation of the minimum phase component in an

ideal case, it did not perform well in a practical case.

Along with the confirmation of the Hilbert transform method of using a simple transfer function of a

minimum phase system and inspecting the results shown such as that depicted in Figure 31, this minimum phase

method was supported by another fact. [19] states that the minimum phase component represents the small

scale changes in phase and hence when the minimum phase component is subtracted from the antenna phase

component, the result is a smooth curve.

Figure 32. Comparison of Phase Terms for Vivaldi Antenna

Figure 32 shows that the all-pass phase of the Vivaldi antenna is a smooth curve showing that the small scale

changes in phase a represented in the minimum phase component. This supports the method used to calculate

the minimum phase components from the magnitude response of the antenna. Another experiment conducted to

confirm the accuracy of the diagnostic tool was measure the 2-port parameters of a link of horn antennas. This

was performed due to the results published in [20] stating that the double ridged horn antennas were very close

to minimum phase. This experiment suffered from the previously mentioned issue in that the phase responseappeared to have a positive gradient due to the large free space gap between the antennas as well as the 9m of

cable which was used to connect the network analyser to the antennas. In this situation, the antennas were

unable to be moved and hence the free space gap was not able to be shortened in order to remove this problem.

A solution was found by setting an electrical delay on the network analyser which was a crude way of removing

the effect of the cabling on the system. The data was then run through the diagnostic tool however the hornantennas were not shown to be more minimum phase than the UWB antennas used for experimentation. This isdue to the fact that the results published in [21] were for a pair of double ridged horns whereas this experiment

used regular horn antennas.

As mentioned in section XI, the network analysers were observed to have a threshold at which the phase

data became unrecognizable. This point was noticed to be when the magnitude is at approximately -85dB.

Because the network analyser produces the polar coordinates for the S-parameter of a network, the linear

magnitude at -85dB is equal to 5.610-5

. With such a small linear magnitude, it becomes difficult to measuredifferentiations in the phase of adjacent data points leading to a loss of the phase reference.

2 4 6 8 10 12-0.5

0

0.5

1

1.5

2

2.5Phase Terms

Frequency, GHz

Phase,rad

Antenna

Minimum Phase

All-Pass


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XIII. ConclusionIt was found that the diagnostic tool was able to accurately reproduce the minimum phase component of an

antenna phase response using the principle of minimum phase systems. Also, using this minimum phase

component, a theoretical passive equalisation network can be calculated to equalise the minimum phase

component of the antenna phase response. The antenna phase response was able to be split up into the

minimum phase component and the all-pass phase component. However, only the minimum phase component

of the antenna can be equalised using a passive network and hence with an ideal passive equalisation network,the best possible result is that the antenna phase becomes the same as the all-pass phase. The diagnostic tool is

also able to calculate passive equalisation networks of varying complexities in order to show the effect that the

complexity has on the amount of equalisation. It was found that the Vivaldi antenna outperformed the circular

monopole antenna in almost every aspect. The Vivaldi antenna had a more stable radiation pattern however the

circular monopole had a better impedance match over the UWB frequency range. The Vivaldi antenna also hadshowed a greater potential for equalisation over the UWB frequency range and showed a particularly good level

of equalisation between 3.1GHz and 6GHz.

XIV. RecommendationsFor future work, this diagnostic tool can be used to characterize other antenna designs according to their

minimum phase properties and move into the synthesis and fabrication of equalisation networks. As well ascontinuing the work done in this project, other projects could be done in UWB antennas including the

design/optimization of design of UWB antennas or the signal processing and modulation schemes necessary for

UWB communications.

XV. AcknowledgementsI would like thank Dr. Greg Milford from the School of Engineering and Information Technology at the

University of New South Wales at the Australian Defence Force Academy for supervising this project. Dr.

Milford was extremely helpful in all aspects of the project whether it be technical knowledge or knowledge ofthe underlying theoretical concepts and he also passed on many of his exceptional engineering practices and

procedures.


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XVI. References[1] Aiello, R 2003, Ultra-Wideband Wireless Systems, IEEE Microwave Magazine, June 2003

[2] Aiello, R 2006, Ultra Wideband Systems: Technologies and Applications, Elsevier, Burlington, USA

[3] Stutzman,W. L., Thiele, G. A.: Antenna Theory and Design second edition, John Wiley & Sons, Inc.

[4] Oppenheim, A., Schafer, R., 1989. Discrete-Time Signal Processing, Prentice Hall.

[5] McLean, J., Sutton, R., Foltz, H., 2009, Minimum Phase / All-Pass Decomposition LPDA Transfer Functions, IEEE

International Conference on Ultra-Wideband, September 2009, pp. 525 529.

[6] Sibbile, A 2005, Modulation Scheme and Channel Dependence of Ultra-Wideband Antenna Performance, IEEE

Antennas and Wireless Propagation Letters, vol. 4

[7] Yang, Y, et al. The Design of Ultra-wideband Antennas with Performance Close to the Fundamental Limit, Virginia

Tech Antenna Group, Blacksburg, VA, USA

[8] Wong, K.L. High-Performance Ultra-Wideband Planar Antenna Design, Dept. of Electrical Engineering National sun

Yat-Sen University Kaohsiung, Taiwan.

[9] Chen, S.Y., et al. 2006, Unipolar Log-Periodic Slot Antenna Fed by a CPW for UWB Applications, IEEE Antennas and

Wireless Propagation, vol. 5

[10] Xiao-Xiang, HE, 2009, New band-notched UWB antenna, College of Information Science and technology, Nanjing

University of Aeronautics and Astronautics, Nanjing, P.R. China

[11] Zhao, CD, 2004, Analysis on the Properties of a Coupled Planar Dipole UWB Antenna, IEEE Antennas and Wireless

Propagation Letters, vol. 3

[12] Choi, SH, 2003, A new Ultra-Wideband Antenna for UWB Applications, Microwave and Optical Technology Letters,

vol. 40, no. 5, Mar 2004

[13] Mehdipour, A. 2007, Complete Dispersion Analysis of Vivaldi Antenna for Ultra Wideband Applications, Progress in

Electromagnetics Research, pp 85-96.

[14] Hecimovic, N. The Improvements of the Antenna Parameters in Ultra-Wideband Communications, Ericsson Nikola

Tesla, d.d., Croatia.

[15] Liang, J. 2005, Study of Printed Circular Disc Monopole Antenna for UWB Systems, IEEE Transactions on Antennas

and Propagation, vol. 53, no. 11.

[16] Lim, K.-S. 2008, Design and Construction of Microstrip UWB Antenna with Time Domain Analysis, Progress in

Electromagnetics Research, vol.3 pp 153 164.

[17] Pozar, D. Microwave Engineering, Third Edition, John Wiley & Sons, Inc. 2005, pp 187.

[18] Pedro, L.D., et al. 1998, Transmission Line Modelling: A Circuit Theory Approach, Society for Industrial and

Applied Mathematics, Vol. 20 No. 2 June, pp. 347 352.

[19] McLean, J., Sutton, R., Foltz, H., 2009, Minimum Phase / All-Pass Decomposition LPDA Transfer Functions, IEEE

International Conference on Ultra-Wideband, September 2009, pp. 525 529.

[20] Foltz, H., et al. 2007, UWB Antenna transfer Functions Using Minimum Phase FunctionsIEEE.

[21] Bode, H.W. Network Analysis and Feedback Amplifier Design, D. Van Nostrand, Co., Inc., New York, N. Y., 1945.

[22] ZEIT4223 Engineering Electromagnetics Course Notes. Course offered in session 1 of 2010 at the University of New

South Wales at the Australian Defence Force Academy. Course taught by and notes written by Dr. Greg Milford.

[23] Computer Simulation Technology, Germany, http://www.cst.com

[24] Balanis, A, 2005, Antenna Theory: Analysis and Design, John Wiley & Sons, Inc., New Jersey.


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[25] MATLAB function smooth2a. Written by Greg Reeves, CalTech. Obtained from

http://www.mathworks.com/matlabcentral/fileexchange/23287-smooth2a.

[26] LaComb, J, et al. 2009, Ultra Wideband Surface Wave Communication Progress in Electromagnetics Research C,

Vol. 8, pp 95 105.

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