antennasfundamentalv2.pdf

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Antennas for CommunicationsInput Parameters and Fundamental Limits

Prof. Jordi Romeu

UNIVERSITAT POLITECNICA CATALUNYA

Barcelona, Spain

Review of antenna input parameters

2

• Antenna from the input port

Consider a one port antenna. From the input port and assuming a time dependence j te

ZoI1

Block 1. Review antenna input parameters

o

V1V

We can define the antenna input impedance

V

3

1

1

( )in in in rad loss in

VZ R jX R R jX

I

Notice that in general Rin and Xin are a function of frequency

• There are several quantities that are usually employed and are related to the input impedance.

Reflection coefficient

( )

( )in o

i

Z Z

Z Z


( )in oZ Z

Return loss20log( )RL dB

Voltage Standing Wave Ratio (VSWR)

1VSWR

“IEEE standard dictionary of electrical and electronic terms”, IEEE Press, 4th Edition, 1988

According to the standard definition, for a passive element (i.e. an antenna) is a positive quantity.

4

1VSWR

Impedance mismatch factor

21C

Usually expressed as 10 log(C) dB

3

800

1000

R()

X()

• Numerical simulation for a dipole. Length 48 mm, radius 0. 4 mm

INPUT IMPEDANCE


600

-400

-200

0

200

400

600

resonance antiresonance

0 2 4 6 8 10 12-800

-600

frequency (GHz)

5

The input impedance is a succession of interlaced resonances and antiresonances. Around these

frequencies we can model the behavior of the antenna as an equivalent series or parallel resonant circuit.

• Resonances are those frequencies for which Xin=0.

• This condition is equivalent to the physical definition of resonance that is, the stored magnetic energy equals the stored electric energy.


• We make the distinction between equivalent LC series (resonance) and LC parallel (antiresonance) behavior.

• Antennas are usually operated around resonances. Since generators or loads have real impedances, the condition for maximum power transfer (complex conjugate matching) implies that the antenna must have also a real impedance.

• The antenna can be self-resonant, or resonance can be achieved by the addition of external networks.

6

4

-4

-2

0


14

-12

-10

-8

-6

20*l

og(

)

7

Typical specification for an antenna is that return loss must be greater than 10 dB in the operating band.

0 2 4 6 8 10 12-16

-14

frequency (GHz)

Voltage Standing Wave Ratio


8

The 10 dB return loss corresponds to a VSWR of 2.

5

SMITH CHART

Return loss greater than 10 dB


fmin

fmax

9

The plot of the antenna impedance (reflection coefficient) in the Smith Chart always moves clockwiseas the frequency increases. This is also true for any lossless one port network.

Maximum Power Transfer

Zo

Vmatching


V

ZAZA*

network

10

To have maximum power transfer from the transmitter to the antenna there must be complex conjugatematching. This can be achieved with a matching network that must change the generator impedanceto ZA

* on the desired frequency range.

6

Impedance of thematching networkto obtain conjugatematching.


11

Antennaimpedance

To match the antenna over all the frequency range the impedance of the matching network mustturn counterclockwise on the Smith Chart as frequency increases.

BY MEANS OF PASSIVE LOSSLESS NETWORKS IT IS ONLY POSSIBLE TO MATCH THE


BY MEANS OF PASSIVE LOSSLESS NETWORKS IT IS ONLY POSSIBLE TO MATCH THE ANTENNA IN A LIMITED FREQUENCY RANGE. THERE IS A FUNDAMENTAL LIMIT IN THE ATAINABLE BANDWIDTH THAT DEPENDS ON THE CHARACTERISTICS OF THE ANTENNA, AND SPECIFICALLY ITS QUALITY FACTOR Q AND THE DESIRED RETURN LOSSES. THIS IS THE FANO’S BANDWIDTH LIMIT

12

7


CAPACITIVE BEHAVIOR

INDUCTIVE BEHAVIORTHE ANTENNA CAN ALWAYS BE MADE RESONANT BY ADDING AN EXTERNAL CAPACITOR OR INDUCTOR THAT CANCELS THE ANTENNA REACTANCE AT A GIVEN FREQUENCY.THE QUALITY FACTOR Q CAN BE ESTIMATED AT THE TUNING FREQUENCY AS

13

THE QUALITY FACTOR Q CAN BE ESTIMATED AT THE TUNING FREQUENCY AS:

2

2 | ( ) |'( ) '( )

2 rad

XQ R X

R

Yaghjian, A.D.; Best, S.R.; , "Impedance, bandwidth, and Q of antennas," Antennas and Propagation, IEEE Transactions on , vol.53, no.4, pp. 1298- 1324, April 2005doi: 10.1109/TAP.2005.844443

• This is the computed Q for the dipole antenna from the input impedance data.


140

160

20

40

60

80

100

120

Q

14

That is the resulting Q if we would tune the antenna (make it resonant) with an external reactance.Note that:• below the resonance (3 GHz) as the frequency decreases the Q increases.

0 2 4 6 8 10 120

frequency (GHz)

8


• FANO’S Bandwidth limit

1FBW

There is a fundamental limit for the maximum fractional bandwidth that can be achieved with a passive reciprocal lossless network that matches a given impedance. For series or parallel resonant circuit the maximum bandwidth is:

max ln(1/ )FBW

Q

Where: 2 1max

r

f fFBW

f

Q is the quality factor of the antenna.

is the desired reflection coefficient after matching.

Expression that can be written as:

15

max

27 1FBW

Q RL

Where RL is the desired return loss.NOTE: Note that for a desired RL the product FBW Q is a constant.


16COMPACT ANTENNAS

A.R. Lopez, “Wheeler and Fano impedance matching”, IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007”

9

• This is maximum fractional bandwidth for the dipole example for a 10 dB return loss.


70

80

90

27FBW

Q RL

1 1S

FBWQ S

20

30

40

50

60

70

FB

W (

%)

Q S

17

1 1.5 2 2.5 3 3.5 40

10

frequency (GHz)


270.054

10 50FBW

ExampleA resonant antenna with Q=50 at a frequency of 2.45 GHz has according to Fano’s limit and for a return loss of 10 dB a maximum fractional bandwidth of:

10 50

2.45 0.054 132B GHz MHz

And a maximum bandwidth of:

If we require a return loss of 15 dB the maximum bandwidth is 88 MHz

If we consider the more realistic limit a 10 dB Return Loss that corresponds to a S=21 1 0.707

FBW

18

max2

FBWQ Q

gives as a maximum bandwidth 35.3 MHz, which is far from the maximum 132 MHz given by Fano’s limit. Any technique to increase the 35.3 MHz bandwidth to approach the maximum is known as BROADBANDING techniques.

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• Example of a microstrip patch antenna “single tuned mid-band”. As the height of the antenna increases the Q reduces and the bandwidth increases.

• Q·FBW=0.707 (VSWR=2, RL= 10 dB)

19COMPACT ANTENNAS

Microstrip patch antenna Double tuned matchingQ·FBW=1.732 (VSWR=2, RL= 10 dB)

20COMPACT ANTENNAS

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• Fano’s limit is a maximum. Practical realizations will show a smaller fractional bandwidth due to the limitation of the matching networks and the fact that the antenna behavior can be approximated by a resonant circuit in a small frequency range (For example the

CONCLUSIONS

resistance also changes with frequency).• The Q of an antenna is a characteristic feature of the structure.• For a given antenna, and therefore Q, the product Return Loss Bandwidth is essentially

constant. In consequence requiring greater Return Losses will result in smaller Bandwidth.

• A realistic limit for a simple matching network is given by:

1 1S

21

max

1 1SFBW

Q S

where S is the Voltage Standing Wave Ratio

COMPACT ANTENNAS

Prof. Jordi Romeu, Lluís Jofre

UNIVERSITAT POLITECNICA CATALUNYA

Barcelona, Spain

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Fundamental limits of small antennas

23COMPACT ANTENNAS

Modern personal communications require larger bandwidths and smaller size terminals.

The following question arises:

Is there any fundamental relationship between antenna size and its bandwidth?

The answer is yes and it is given by what is known as Chu’s fundamental limit for the

24COMPACT ANTENNAS

Q of electrically small antennas.

13

Block 2. Fundamental limits of small antennas

SOME DEFINITIONS:

An electrically small antenna is defined as an antenna that fulfills the condition that ka<1 where

k is the wavenumber in free space, k=2 and a is the radius of the minimum sphere that encloses the tantenna.

CHU’S FUNDAMENTAL LIMIT

For lossless electrically small antenna with linear polarization

1 1

25

3 3

1 1Q

k a ka

• The antenna Q increases as the size of the antenna reduces

small antenna


26

14

The biggest challenge in designingelectrically small antennas is toapproach Chu’s limit as much aspossible. It turns out that practicalantenna realizations are usually far

nten

nas”

,


from reaching Chu’s limit.

Han

sen,

“Fun

dam

enta

lLi

mita

tions

inAn

Vol.

69,N

o.2,

pp.1

70-1

82,F

eb.1

981

]

27

[Fig

ure

from

:R

.C.

Proc

.oft

heIE

EE,V

o

Goubau’s AntennaGoubau’s Antenna

[Figure from: C.F. Friedman, “Wide-band matching of a small disk-loaded monopole”, IEEE Transactions on Antennas and Propagation,Vol. 33, No. 10, pp. 170-182, Oct. 1985 ]

Chu’s derivation of the Q does not consider the stored energy inside the volume r < a

Thal has revised Chu’s limit considering the stored energy inside the volume and has shown that for

i lik t Ch ’ li it t b i d b


wire-like antennas Chu’s limit must be increased by a factor of 1.5 or 3 depending on the nature of the fundamental spherical mode excited by the antenna (TM or TE).

Best has numerically shown the implementation of these antennas with Q 1.53 and 3.18 times larger than Chu’s limit.

28COMPACT ANTENNAS

Thal, H.L.; " New Radiation Limits for Spherical Wire Antennas," Antennas and Propagation, IEEE Transactions on , vol.54, no.10, pp.2757-2763, Oct. 2006doi: 10.1109/TAP.2006.882184

Best, S.R.; , "A Low Q Electrically Small Magnetic (TE Mode) Dipole," Antennas and Wireless Propagation Letters, IEEE , vol.8, no., pp.572-575, 2009doi: 10.1109/LAWP.2009.2018496

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Convoluted electrically small wire antennas can be self-resonant, but the obtained Q is about one order of magnitude than Chu’s Fundamental limit.


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J.M. Gonzalez, S. Blanch, J. Romeu, “The Hilbert curve as a small self-resonant monopole from a practical point of view”, Microwave and Optical Technology Letters, Vol. 39, No.1 October 5, 2003

Planar antennas have a worse performance than volume antennas due to their inefficient use of the available


inefficient use of the available volume.

The use of dielectric materials in the construction of the antenna increases the stored energy and in consequence the Q.

30COMPACT ANTENNAS

As a rule of thumb a save approximation is to consider that the Q of a planar electrically small antenna will be about one order of magnitude (10 times) larger

than Chu’s fundamental limit.

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• A more appropriate limit has been proposed for wire antennas with sinusoidal current distribution

G.A. Thiele, et. al, “On the lower Bound of the Radiation Q for Electrically Small Antennas”, IEEE Transactions on Antennas and Propagation, Vol. 51, no. 6, June 2003.


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Thiele’s bound it is not actually a limit in the sense that it can be surpassed, but it offers a good estimation of the Q. It has the inconvenient that its computation is cumbersome.

As the antenna dimensions are reduced the Q increases.


3 3

1 1Q

k a ka

The Fractional Bandwidth (FBW) is inversely proportional to the Q.

Therefore reducing the antenna dimensions implies a reduction in bandwidth.

max

1 1SFBW

Q S

32

17

Which are the antenna dimensions when we consider a wireless device?


33


With a simple simulation we can show that in designing antennas for small wireless terminals the whole structure plays a role in the radiation.

Metal plate part of the PCB

34

18

In approaching the design of antenna for a wireless device try to use all the available space.

35COMPACT ANTENNAS

Antenna LossesAs we reduce the electrical size of the antenna its efficiency due to ohmic losses also reduces.

Let’s consider a conductor surface S with all of its dimensions smaller than , so S<<. For simplicity there is a uniform current density in the conductor directed along the z axis Under these assumption the radiation


is a uniform current density in the conductor directed along the z axis. Under these assumption the radiation vector is approximately

ˆ '

'ˆ ' 'jkrr

oVN J r e dv J S z

y

z

The radiated Electric field is

ˆsin( )2

jkr

o

eE j J S

r

And the total radiated power is given by

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x

S

0 ˆJ J z

And the total radiated power is given by

2 2

2 2* 32 2

0

Re sin2rad o o

S SP E H dS J d J

On the other hand, if the conductor has a surface resistance due to losses Rs, the dissipated power is2 2

loss s o oP R J S J S

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2

1 1radd

Pe

P

Antenna efficiency

The antenna efficiency can be computed as:


2

1 1rad

lossrad loss

rad

ePP P

CP S

Where C is certain positive constant that ultimately will depend on the material.Under the hypothesis of small antenna that is, S<<2 it is clear that the efficiency is smaller than 1 and it will decrease as S decreases.

Electrically small antennas are usually inefficient.2

37

2

2'

rad

kae

ka C

We can also write, making the assumption that

2

2

1

S ka


38

This is an example for self-resonant wire antennas. As we reduce the electrical size of the antenna, the Q increases and the efficiency reduces.

Plot of

2

2'

rad

kae

ka C

for C’=0.05

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• OBSERVATION: In the previous figures the Q is defined by considering only the radiation resistance. If the antenna has losses the observed Q from the antenna ports must take also into account the antenna losses.

radiation


losses (heat)

rad r

WQ

Let’s define:

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T r rad radloss

WQ e Q

P

rad rrad

QP

Qrad is what is limited by Chu’s limit, but the observed Q at the input terminals is:

radrad

rad loss

Pe

P P

• One of the effects of the losses is to decrease the Q of the antenna.

• How does it affect to the radiation?

• A simple circuit analysis allows to plot the following figure:


erad=1, Qrad=QT=100lossless antenna

erad=0.1, Qrad=100,QT=10antenna with losses

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Which antenna is better?

21

For the transmission of a carrier or single tone the lossless antenna is clearly better.


If we need to transmit over a certain bandwidth the lossless antenna will filter the transmitted signal resulting in a di t ti Th l l t d t di t t f th

41

distortion. The lossless antenna does not radiate out of the resonance because of the impedance mismatch. The lossy antenna has a flatter frequency response, in consequence the signal is less distorted. The price to be paid is that the we need more available power in the transmitter.

Example

The bluetooth system operates on a frequency band from 2.402 GHz to 2.48 GHz (78 MHz allocated band). A power class 2 device for ordinary range devices (~10m), has a maximum output power of 4 dBm. The received power to ensure a Bit Error Rate (BER) of 0.1 % must be -70 dBm or better. You want to design an antenna for bluetooth that for terminal size restrictions must fit in a 1 cm by 1cm square. Can

id hi t b t th f ibilit f h t ?


6

6

78 100.0319 (3.2%)

2441 10FBW

0.70722TQ

FBW

0.5 2 0.7 ; 12.3 ; 0.357a cm cm ka

you provide any hint about the feasibility of such antenna?

Required Fractional Bandwidth

Minimum antenna Q to meet the FBW requirement(consider a -10 dB return loss)

Ch ’ f d l li i

Radius of the minimum sphere that encloses the antenna

1 1

42

Chu’s fundamental limit 3 3

1 125Q

k a ka

Realistic designs show that practical realizations exceed Chu’s limit by factor of 10. Expected Q for a lossless antenna with this dimensions

250radQ

22

Example (continuation)


0.1 250 25T rad radQ e Q

An electrically small antenna will in fact have losses. If we assume an efficiency of 10 % the resulting Q for the lossy antenna is:

This value of Q is close to the required from the bandwidth point of view.

Will the system work with such a lossy antenna?

2

4 60 10 664L rad T R radP P D D e dBm dBm

r

The received power assuming isotropic antennas at 10 m is:

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The sensitivity of the receiver is -70 dBm, so there is an extra 4 dB margin.

IT SEEMS IT IS A FEASIBLE DESIGN

CONCLUSIONS

For an electrically small antenna there are fundamental limits on the minimum Q that can be achieved.

The Q of the antenna increases as the antenna dimensions decrease.

The larger the Q the smaller the bandwidth.

Try to use all available space in designing antennas for small wireless devices.

Consider the role of losses in your design and system performance.

44COMPACT ANTENNAS

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