University of Colorado at Boulder - 1 -

AbstractIn this project a printed dipole antenna is beingdesigned. Printed dipole antennas are of interest, whenan electronic product, which is implemented on aprinted circuit board (PCB) is in need of a cheap,compact antenna. This antenna has a fairly isotropicpattern, which makes it a good transmitter / receiver forportable devices. This design is based on the US patentheld by Motorola [1]. It was originally designed forportable pager device for operation in the 900 MHzband.For this design the dipole as suggested by the patent wasslightly remodeled and adopted to the 400 MHz band.The antenna was built and measured.

Index TermsPrinted dipole, resonant antenna, compact antenna

I. INTRODUCTION

Printed antennas are very popular because of their ease offabrication. If the antenna is to be implemented on the samePCB as the circuitry, practically no additional costs arise.For a system where an isotropic pattern is required, as forexample in a portable device, a dipole is a good and easyapproach. To get a good performance out of a dipole, onelikes to design it as resonant dipole. This requires the dipoleto be slightly less then half a wavelength long. A goodguess is 0.47 times the wavelength [3]. We can calculate thelength of the resonant dipole with the equation (I-1).

fv

rd ⋅=⋅= 47.047.0 λ (I-1)

Where v is the actual propagation speed on the dipoleradials. This speed depends on the effective dielectricconstant of the environment surrounding the radials. Wecan calculate the speed with the equation (I-2).

eff

cvε

= (I-2)

Where c is the speed of light in vacuum and εeff is theeffective dielectric constant of the surrounding media.The effective dielectric constant for a printed radial on asubstrate depends on the geometry and the dielectricconstant of the substrate. We can calculate the effective

dielectric constant for a narrow trace usingequation (I-3) [4]

−⋅+

⋅+⋅−++=− 2

21

104.01212

12

1hw

whrr

effεεε (I-3)

Where h is the thickness of the substrate, w the width of thetrace and εr the relative dielectric constant of the substrateused.

II. DESIGN

Using the equations introduced in section I we design aresonant printed dipole for 433 MHz. We use a standardFR-4 PCB with an estimated εr of two at 433MHz and athickness of 1.25mm. The trace width for the radials we setto 0.625mm.First we calculate the effective dielectric constant usingequation (I-3):

( )mF

eff 6.15.004.02521

23 22

1

=

⋅+⋅+=

−ε (II-1)

With the effective dielectric constant we can calculate thespeed on the radials with equation (I-2):

smv 8

8

1037.26.1

103 ⋅=⋅= (II-2)

With this speed we can go now into equation (I-1) to get thelength of the resonant printed dipole on our PCB:

cmrd 7.25104331037.247.0 6

8=

⋅⋅⋅= (II-3)

So, if we want a device to operate at 433 MHz and want tohave a resonant dipole, our device shouldn’t be smaller then26cm. That’s not very practical.The idea is now to shorten the physical extent further by“folding” the dipole antenna. With this approach, we canreduce the length of the dipole again by a factor of two(ideally). Then we are at the length of

Printed Dipole AntennaReto Zingg

University of Colorado at Boulder - 2 -

cmrdfd 9.12

27.25

2=== (II-4)

This is more of what we are looking for. If we would use afrequency of 900 MHz this even reduces to 6.2cm (assumedεr of the dielectric is constant over the frequency range).

III. RESULTS / EXAMPLES

A. Simulations

As the length calculated in (II-4) is based on the assumptionthat the physical extent is halved if we bend the radials, wenow simulate a model of the antenna and find the resonantlength for 433MHz.The model that will be used for these simulations is shownin Figure III-1. Figure III-2 and Figure III-3 show the topand bottom layer of the PCB separately. The radials onopposite sides of the PCB are connected at the outer endswith vias. The ground plane is introduced to reproduce theeffect of electric circuitry on the PCB.

ab

Figure III-1 Top view dipole, all layers

Figure III-2 Top view dipole, top layer

Figure III-3 Top view dipole, bottom layer

After several simulations the resonant length (a) for433MHz was found. It is at 205mm for an estimated εr of 2.A separation of 3cm was used between the ground plane

and the antenna radials (b). Figure III-4 shows the S11parameter of this configuration. It clearly shows theresonance with –17dB at 433MHz (marker M1).

Figure III-4 S11, b=30mm

Figure III-5 shows the Smithchart of the sameconfiguration. The upper of the two squares in the loop is at433 MHz. The loop shows that the antenna is resonant atthis frequency. It also shows that the design with the foldedradials seems to be stable (i.e. no additional resonance).

Figure III-5 Smithchart, b=30mm

Figure III-6 shows the input impedance (Z11) of theantenna. Once again the resonance is clearly visible. Wecan read out an input-impedance of 40Ω. This is alreadyquiet close to 50Ω, which would be very convenient.

University of Colorado at Boulder - 3 -

Figure III-6 Z11, b=30mm

How are these characteristics influenced by the designparameters? To find that out some variations of the designhave been simulated. First the distance between the groundplane and the antenna radials (b) has been reduced to 2cm.As the nearby ground plane loads down the antenna weexpect a less strong resonance. In Figure III-7 we see thatthe resonance was shifted towards higher frequencies andthat S11 at resonance increased from –17dB (with 3cmdistance between ground and the radials) to –8.3dB.

Figure III-7 S11, b=20mm

In Figure III-8 can also be seen that the loop got smaller,which indicates a weaker resonance. Finally Figure III-9shows that we have an input-impedance of 27.5Ω atresonance.

Figure III-8 Smithchart, b=20mm

Figure III-9 Z11, b=20mm

Now what happens if the radials are moved away from theground plane? In Figure III-10, Figure III-11 and FigureIII-12 the results of a simulation is presented, where thedistance between the ground plane and the radials (b) is40mm. In Figure III-10 we see that the resonant frequencyhas been moved to a lower frequency and that S11 atresonance decreased from -17dB to -17.7 dB. This is no bigchange for an increase in used space for the antenna of33%. Also the Smithchart (compare Figure III-5 and FigureIII-11) has no large change. The input impedance atresonance even decreased slightly. From this results we cansay, that a distance of the radials from the ground plane (b)of 30mm is enough and a further increase doesn't bring anyadvantage but uses valuable PCB space.

University of Colorado at Boulder - 4 -

Figure III-10 S11, b=40mm

Figure III-11 Smithchart, b=40mm

Figure III-12 Z11, b=40mm

How about other parameters like the ground plane widthrelative to the radial length? Let's extend the ground planeas shown in Figure III-13 and have a look at the simulationresults. The antenna length (a) was kept at the resonantlength of 205mm, the distance between ground plane andthe radials (b) was set to 30mm and the ground plane wasextended on both sides by 30mm, resulting in a total widthof 265mm (c).

ab

c

Figure III-13 All layers, extended ground plane

In Figure III-14, Figure III-15 and Figure III-16 the resultsof the simulation of the antenna with extended ground planeis shown. The resonant frequency was lowered from433Mhz to 424Mhz. This might indicate that the edge ofthe ground plane is also working as a part of the antenna.Most interesting is the decrease of the S11 parameter from-17dB to -23dB at resonance.

Figure III-14 S11, wide ground plane, c=265mm

Also in the Smithchart (Figure III-15) the strongerresonance is obvious (larger loop). The input impedance wecan read out of Figure III-16 is 56Ω.

University of Colorado at Boulder - 5 -

Figure III-15 Smithchart, c=265mm

Figure III-16 Z11, c=265mm

B. Discussion of Simulation Results

If we compare now the different results of the simulationswe come to the conclusion, that the length of the radials (a)determines the resonant frequency (which is obvious fromthe theory). The ground plane near the antenna furtherinfluences the resonance frequency. Here both of the twoinvestigated parameters, width of the ground plane anddistance from the radials, influence the resonant frequency.The further away the ground plane, the lower the resonantfrequency. The wider the ground plane, the lower theresonant frequency. This brings up the question if a part ofthe ground plane works as antenna.Furthermore the ground plane influences the "strength" ofthe resonance and therefore the input impedance. Thefurther away the ground plane, the stronger the resonance.

C. Measurements

To verify the theory and the simulation results, two printeddipole antennas have been built and measured. Figure III-17shows the top and bottom view of antenna . Figure III-18

shows the top and bottom view of antenna . Table III-1shows the dimensions of the antennas.

b

a

Figure III-17 Antenna top and bottom view

b

a

Figure III-18 Antenna top and bottom view

Table III-1 Dimensions of prototype antennas

Antenna Antenna Substrate material FR-4 PCB FR-4 PCBSubstrate thickness 1.25 mm 1.25 mmWidth (a) 180 mm 180 cmGround distance (b) 17 mm 25 mmTuning style Outer end

shorteningInner endshortening

First the input impedance of the two antennas wasmeasured with a network analyzer. This measurement wasperformed inside the laboratory. The antenna was keptaway from metallic objects as far as possible. Of course theground plane on the PCB and also the connecting cable willalways be close to the antenna.

University of Colorado at Boulder - 6 -

The two prototype antennas are same, except for thedistance between the radials and the ground plane (b).Antenna has a distance of b=17mm, antenna adistance of b=25mm. The two antennas have beenmechanically tuned to a resonance at 433MHz. This wasdone by simply shortening the radials until the resonanceoccurred at 433MHz. Antenna was tuned by shorteningthe outer end of the antenna (bends around the PCB),antenna was tuned by shortening the inner end of theantenna (end of radials close to feed).The antennas have an extent of a=180mm. This is close tothe simulated 205mm. The difference can be explained dueto an incorrectly assumed εr=2.In the following figures the S11 plots and Smithcharts ofthe two antennas are presented.Figure III-19 shows the S11 Parameter of antenna . At433MHz we have –8.6dB.

Figure III-19 Measured S11, antenna

Figure III-20 shows the S11 Smithchart of antenna . Alsohere is the loop of resonance clearly visible. The additionaltwo loops indicate resonance of higher order or othermodes. These were not visible in the simulation results, asthey occur above the simulation limit of 500MHz. Themeasured input impedance at 433MHz of antenna is47 + j34 Ω.

Figure III-20 Measured Smithchart, antenna

Figure III-21 shows S11 of antenna . Note the differentvertical resolution compared to Figure III-19. Antenna has an S11 at 433MHz of –12.4dB. This is what weexpected from the simulations.

Figure III-21 Measured S11, antenna

The Smithchart in Figure III-22 shows again the resonanceat 433MHz and an input impedance of 56 + j19 Ω

Figure III-22 Measured Smithchart, antenna

D. Far Field Radiation Pattern

The far field radiation pattern of the antenna with a distancebetween the radials and the ground plane of 30mm wassimulated and is shown in Figure III-23 and Figure III-27.The coordinate system for the simulations andmeasurements is defined by the following: The PCB wherethe antenna is printed on lies in the x-y plane, where theradials are in the direction of the x-axis. The positive ydirection goes from the radials to the ground plane. Thepositive z-axis rises perpendicular from the top plane of theantenna. The graphs have been rotated in such a manner,that the curves can be compared directly (measurement andsimulation uses different angle definitions). Themeasurements show the E-fields in phi direction (as muchas a separation is possible with the used antennas). Astransmitter was antenna used. A constant power level of7.5 Watts at 433 MHz was applied to the antenna. The

University of Colorado at Boulder - 7 -

receiver antenna (antenna ) was rotated in such a manner,that the desired patterns where measured.If we compare the simulated and the measured results of thex-y plane pattern we see clearly, that the actual antennabehaves very much like the simulation. We also see that themain beam is not pointed perpendicular to the radials, butabout 20° to the ‘left’. This could be a further sign that theedge of the ground plane is acting as second dipole radial.As the ground plane is set back by 25mm from the radialthat is connected to ground, this would result in a rotationof the pattern to the ‘left’. The nulls, perpendicular to themain beam, typical for a dipole, are 15dB deep in thesimulation and 10dB to 15dB deep in the measurement.

Figure III-23 Simulated E-field pattern in x-y plane

Figure III-24 Measured phi directed power-pattern inx-y plane

To verify the assumption, that a part of the ground plane isradiating, a reason is to be found. One reason could be, thatthe abrupt change of the ground plane to the transmission

line to feed the dipole causes reflections. To find out moreabout that , a modification was made to the original design.The line feeding the dipole from the ground plane wastapered, as shown in Figure III-25.

Figure III-25 Dipole with tapered ground feed line

The resulting far field in the x-y plane is shown in FigureIII-26. It is clearly visible that the rotation of the patterndisappeared. It seems that really the reflection at thetransition from the ground plane to the feed line caused therotation.

Figure III-26 Simulated E-field pattern in x-y plane withtapered ground feed

If we compare the simulated and the measured results of they-z plane pattern we also see that the actual antennabehaves very much like the simulation. We also see insimulation and measurement, that the dipole radiates about2 dB more towards the ground plane than away from theground plane. The sharp, deep null as it appears in thesimulation could not be measured.

University of Colorado at Boulder - 8 -

Figure III-27 Simulated E-field pattern in y-z plane

Figure III-28 Measured phi directed power-pattern iny-z plane

E. Gain

Even though no standard gain antenna for the usedfrequency of 433 MHz was available, a rough measurementshould show the approximate gain of the antenna. Usingantenna as transmitter and antenna as receiver, we tryto calculate the gain of the system. Using Friis transmissionformula [3]

( )2

2

4 RGGPP rtt

r ⋅⋅⋅⋅⋅=

πλ (III-1)

the total gain of the system can be calculated

( )2

22 4

λπ⋅

⋅⋅⋅=

t

r

PRP

G (III-2)

As gain is not taking mismatch in account, the measuredpower values have to be adjusted to take the mismatch inaccount.

( )pW

sP

P

WsPP

measuredr

r

measuredtt

8.51967.0

101

68.6891.05.71

1043

211

211

==−

=

=⋅=−⋅=− (III-3)

Using the parameters of the measurement and assuming thetwo antennas have the same gain we get

( ) 329

107.4248.068.6

334108.51 −−

⋅=⋅

⋅⋅⋅⋅= πG (III-4)

This is a rather small gain. As we use antenna , which hasonly a distance of 17 mm between the radials and theground plane, we can assume that the gain of antenna with 25 mm distance between the radials and the groundplane is considerably larger. Also was the transmitterantenna not exactly oriented for maximum directivity.

IV. CONCLUSIONS

A resonant dipole antenna for the frequency of 433 MHzhas been designed which uses a space of 18 cm by 2.5 cm atthe edge of a PCB. Measurement and Simulation resultshave been presented. From these results, we can concludethat such an antenna is convenient for a design of a basestation of a portable device such as a hand-held remotecontrol. Further investigation of the effect of the groundplane size would be interesting. Design alterations toincrease radiation efficiency are necessary.

V. REFERENCES

[1] US Patent 5,495,260Motorola Inc., Schaumburg, Ill.

[2] FCC Part 15 regulationshttp://www.fcc.gov/oet/info/rules/part15/part15-mar99.pdf

[3] Antenna Theory and DesignWarren L. StutzmannGarry A. ThieleISBN 0-471-02590-9

[4] High-Speed Digital DesignHoward JohnsonMartin GrahamISBN 0133967241

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