WangandJZLi Department of Information and Electronic Engineering Zhejiang University Hangzhou 3100 7 China LXRan The Electromagnetics Academy at Zhejiang University Zhejiang University Hangzhou 310058 China Abstract This paper presents an eective mod ID: 29160 Download Pdf

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WangandJZLi Department of Information and Electronic Engineering Zhejiang University Hangzhou 3100 7 China LXRan The Electromagnetics Academy at Zhejiang University Zhejiang University Hangzhou 310058 China Abstract This paper presents an eective mod

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ProgressInElectromagneticsResearch,PIER82,433445,2008 ANEQUIVALENTCIRCUITMODELINGMETHOD FORULTRA-WIDEBANDANTENNAS Y.WangandJ.Z.Li Department of Information and Electronic Engineering Zhejiang University Hangzhou 3100 7, China L.X.Ran The Electromagnetics Academy at Zhejiang University Zhejiang University Hangzhou 310058, China Abstract This paper presents an e)ective modeling methodology for Ultra-wideband -UW/0 antennas1 The methodology is based on augmenting an existing narrow-band model with a macro-model while simultaneously perturbing component values of the narrow-band

model1 The narrow-band model is an empirical-based circuit and the macro-model described by rational functions is determined using data 3tting approaches1 The perturbation of component values of the narrow-band model is achieved by adjustments in 45ICE1 This method is demonstrated on the example of a 15 cm dipole antenna and a circular disc monopole antenna for UW/ systems1 4imulation results show that this methodology is e)ective over a wide bandwidth and suitable for modeling most UW/ antennas1 1. INTRODUCTION Worldwide interest in Ultra-wideband -UW/0 61, 7 wireless has increased greatly

with the release in 8eb1 00 by the 8CC of their 3rst authorization for UW/ in several frequency bands -0960 =Hz, 3111016 GHz, and 9 GHz0 6371 Although the large bandwidth enables short-range, high data-rate communication and high resolution positioning 647, it imposes new design challenges in UW/ systems 6 3, 471 One challenge is the co-design of UW/ antennaAcircuit interface1 It is necessary to do co-simulation of the antennas with the

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434 Wang, Li, and Ran UW/ transmitter and receiver1 4ince circuit simulation is traditionally done in a time-domain simulator such as

45ICE, a general equivalent circuit model of UW/ antennas is required1 There are two basic requirements for the equivalent circuit model of UW/ antennas1 8irst, input impedances or admittances of the equivalent circuit model should match up with those of the modeled antenna 6571 In traditional narrowband systems, all the design parameters of antenna are expressed in single values and antennas are modeled as resistors with a standard value1 However, the parameters are frequency-dependent in UW/ systems, so it is not reasonable using traditional model1 4econd, load resistor is an important

parameter to describe radiated waveforms 6671 In a UW/ communication system, the antennas act as major pulse-shaping 3lters1 /andwidth limitations of the antennas show up as a frequency-domain transfer function and as time-domain distortion of the received pulse 6771 The equivalent circuit model should capture the waveform distortion so that one can compensate at the transmitterAreceiver1 Extensive studies have been reported in the literature regarding the determination of the input impedance or admittance function1 These include HamidBs graphical 3tting method 687, CongBs transmis- sion line

method 697, GerritsBs intuitive electrical schematic 6107, Dam- babuBs broadband equivalent circuit consisting of a series resonant cir- cuit and two parallel resonant circuits 6117, EieBs accurate numerical modeling 61 7 and TangBs four-element lumped-parameter equivalent circuit 61371 These models above are physically based and propose sev- eral equivalent circuit topologies from the aspect of input impedance or admittance matching1 A more e)ective model is the degenerated 8oster canonical forms proposed by Wang 61471 The model introduces a load resistor to reproduce the radiated waveform1

The resulting impedances match well up to 5 GHz, almost twice the 3rst resonant frequency1 There are also studies of antenna modeling regarding 3eld distribu- tion and reFection coeGcient1 These include 4ijherBs Genetic Algo- rithm -GA0 optimization method 6157, GustafssonBs resonance model 6167, =arroccoBs approximate space-time-frequency 3eld representation 6177, and 4henBs modal-expansion method 61871 This paper describes an e)ective modeling methodology for UW/ antennas, the circuit re3nement method1 8irst, a narrow-band model as degenerated 8oster canonical form is built1 4econd, the

narrow- band model is augmented with a macro-model described by rational functions, and then the macro-model is converted into the equivalent circuits1 8inally, the macro-model a)ects the poles of initial narrow- band model, so perturbation of component values of the narrow-band model is needed1 The ultimate model matches the admittances of the

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Progress In Electromagnetics Research, PIER 82, 2008 435 modeled antenna over a wide bandwidth, and reproduces the far-zone 3eld using the load resistor rad of the narrow-band model1 This paper is organized as follows1 4ection presents

the concept of circuit re3nement method and the details of the modeling method1 In 4ection 3, several practical examples are presented to verify the proposed modeling method1 2. CIRCUITREFINEMENTMETHOD The initial concept of the circuit re3nement method for UW/ antennas is introduced in 8ig1 11 /y 3tting admittance data of the antenna obtained by simulation, the antenna is modeled by a narrow-band model augmented with a macro-model1 The narrow-band model is an empirical-based circuit and forms the base of the ultimate model1 The macro-model described by rational functions is parallel with the

narrow-band model and is used to increase the accuracy of input admittance matching1 The load resistor rad reproduces the far-zone 3eld1 The ultimate model preserves the physical intuition of equivalent circuits and utilizes the accuracy of macro-model data 3tting1 narrow-band model macro-model rad in Figure1. Concept of circuit re3nement method1 2.1. Narrow-bandModel Generally, UW/ antennas act as band-pass 3lters, so the circuit topology shown in 8ig1 is chosen as the narrow-band model1 The series resonant circuit worHs as a high-pass 3lter, while parallel resonant circuit as a low-pass

3lter1 The whole circuit worHs as a band-pass 3lter and models the UW/ antenna roughly1 rad is an important parameter to reproduce the radiated waveform, furthermore, the transfer function1 The component values of the narrow-band model can be calculated by utilizing the application bandwidths, center frequencies or resonant frequencies of antennas1 The circuit topology has been successfully employed to model the dipole antenna 6871

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436 Wang, Li, and Ran rad rad Figure2. Circuit topology of narrow-band model1 2.2. Macro-model The narrow-band model serves only as an

approximation for the modeling of UW/ antennas1 The antennaBs admittance data obtained from I8DTD is then compared with input admittance of narrow- band model derived in 45ICE, and the di)erences between them are modeled by a macro-model1 It is e)ective to augment the macro-model to guarantee the accuracy of input admittance matching over a wide bandwidth1 /ased on the parallel topology, it is straightforward to calculate the macro-model data1 The admittance function for the macro-model, macro 0, can be obtained from the admittance parameters of the antennas, ant 0, and of the narrow-band

model, narrow 0, as macro 0J ant narrow -10 The admittance function macro 0 can be approximated by rational functions in rational polynomial, pole-zero or pole-residue form, such as macro 0J =1 se - 0 where jw are the complex frequency points1 The unHnown parameters and in - 0 are obtained using data 3tting approaches, such as vector 3tting 6197 or least-squares 3tting1 After all of the parameters of admittance function are calculated, it is feasible to convert it into circuits using the equivalent circuit for rational approximation of transfer functions and the component values of circuits

are derived from calculation 6 071 macro 0 can be considered as parallel addition of some branch circuits shown as 8ig1 31

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Progress In Electromagnetics Research, PIER 82, 2008 437 -1 Ln ... Figure.. Equivalent circuits of macro-model1 2... PerturbationApproac1 After the narrow-band model is augmented with the macro-model, the poles of initial narrow-band model have been a)ected by the augmented macro-model 6 17, so it is important to modify the component values of narrow-band model to compensate this disadvantage1 If the narrow- model is not perturbed, accurate results may

require a high-order macro-model networH which will increase overall simulation time and be contrary to our philosophy1 /y appropriately adjust component values of the narrow-band model in 45ICE, a relatively lower order macro-model for a given quality of 3t can be obtained1 The ultimate model is composed of the perturbed narrow-band model combined with the macro-model1 The narrow-band model is shown as 8ig1 with relevant component values1 The macro-model is converted into equivalent circuits shown as 8ig1 31 The parallel networH of the circuits as 8ig1 and 8ig1 3 composes the ultimate model1

8rom the above, the antennas have been modeled into spice- compatible circuits by circuit re3nement method, so it is easy to do the co-simulation of the UW/ antennas with the UW/ transmitter and receiver in 45ICE1

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438 Wang, Li, and Ran .. EXAMPLERESULTS This section demonstrates the application of the circuit re3nement method on several antennas, including a dipole antenna and a printed circular disc monopole antenna1 ..1. ModelingaDipoleAntenna 8irst a small dipole antenna is used to verify the proposed modeling approach1 The application bandwidth is from 311 to 1016 GHz, and

the center frequency is 6 GHz1 The length of dipole antenna is 15 cm by calculation1 The circuit shown in 8ig1 is used as the narrow-band model1 The initial component values of narrow-band model are calculated and chosen by J1 /LC , where is the resonant frequency1 The optimizations of the component values are made in 45ICE so that the input admittance of a narrow-band model should equal to that of the dipole antenna at the center frequency, the component values of narrow-band model can be obtained as J 011 p8, J 10 nH, 011 p8, J 60 nH, and rad J 68 L1 The resulting admittances from 45ICE and

I8DTD in 8ig1 4 show that the narrow-band model serves only as an approximation to the dipole antenna in input admittance matching from 311 GHz to 1016 GHz1 0 4 6 10 12 -0.01 -0.005 0.005 0.01 0.015 0.02 Frequency (GHz) Input admittance Real( in) Imag( in) Real( crm) Imag( crm) Figure2. Comparison of admittances of the dipole antenna - in 0 and the narrow-band model - narrow 01 Then a parallel macro-model is added to re3ne the narrow-band model1 A two-order circuit networH is needed by calculation and the

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Progress In Electromagnetics Research, PIER 82, 2008 439 circuit

topology as 8ig1 3 with two branches is served as the macro- model1 The component values of the macro-model are calculated by the method proposed in 4ection 1 1 Eext, perturbation is applied to the component values of initial narrow-band model1 /y slightly adjusting the Hnown component values of the narrow-band model in 45ICE to achieve a better 3tting of input admittance, the component values of the narrow-band model after perturbation are obtained1 Table 1 shows the values of the 3ve elements of the narrow-band model before and after perturbation1 8ig1 5 compares the admittance of the dipole

antenna with that of the ultimate model obtained by circuit re3nement method1 The admittance of the ultimate model is virtually indistinguishable with that of the dipole antenna1 Table 1. Component values of the narrow-band model before and after perturbation1 rad Beforeperturbation 0.12pF 10nH 0.12pF 60nH 68 Afterperturbation 0.118pF 10.15nH 0.123pF 62nH 69.1 0 2 4 6 8 10 12 10 12 14 16 x 10 Frequency (GHz) Input admittance Real( in Imag( in) Real( crm) Imag( crm Figure3. Comparison of admittances of the dipole antenna - in 0 and the ultimate model obtained by circuit re3nement method - crm

01

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440 Wang, Li, and Ran 8inally, the radiated waveform across the load resistor rad is veri3ed by simulation1 A 013-ns-wide Gaussian voltage waveform 68ig1 67 is sent into the antenna and the ultimate model1 The voltage waveform rad across the load resistor and the far-zone 3eld at J90 at 1 m away from the antenna are derived in 45ICE and I8DTD, respectively1 8ig1 6 shows that the two normalized waveforms match well after scaling and time shifting, which means the load resistor models the scattered waveform 3eld perfectly1 The ratio of rad to rad at 1 m before normalization

is approximately , so waveform dispersion can be compensated at the transmitterAreceiver1 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1.2 Time (ns) Amplitude ()urce pulse Vrad(V) Erad(V/m) Figure 4. Time-domain waveforms of Gaussian source pulse with a width of 013 ns, normalized rad form 45ICE and rad -in J90 from I8DTD1 ..2. ModelingaPrintedCircularDiscMonopoleAntenna A printed circular disc monopole antenna, shown in 8ig1 7, has been proposed as a typical UW/ antenna 6 71 The circuit shown in 8ig1 is used as the narrow-band model1 The initial component values of narrow-band model are calculated and

chosen by J1 /LC , where is the resonant frequency1 The optimizations of the component values are made in 45ICE so that the input admittance of a narrow- band model should equal to that of the printed circular disc monopole antenna at the center frequency, the component values can be obtained as J 011 p8, J 101 nH, J 011 p8, J 315 nH, and rad J 718 L1 The resulting admittances from 45ICE and I8DTD in

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Progress In Electromagnetics Research, PIER 82, 2008 44 ground plane ground plane in back microstrip feed line Figure5. A printed circular disc monopole antenna1 0 2 4 6 8 10 12

0.1 0.2 0.3 0.4 0.5 0.6 Frequency (GHz) Input admittance Real( in Imag( in) Real( narr)-) Imag( narr)-) Figure6. Comparison of admittances of the monopole antenna - in and the narrow-band model - narrow 01 8ig1 8 show that the narrow-band model only worHs well in a narrow bandwidth1 Then a parallel macro-model is added to re3ne the narrow-band model1 A six-order circuit networH is needed by calculation and the

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442 Wang, Li, and Ran Table 2. Component values of the narrow-band model before and after perturbation1 rad Beforeperturbation 0.12pF 10.2nH 0.1pF 3.5nH 27.8

Afterperturbation 0.118pF 10.18nH 0.11pF 3.6nH 27.7 circuit topology as 8ig1 3 with six branches is served as the macro- model1 The component values of the macro-model are calculated by the method proposed in 4ection 1 1 8inally, perturbation is applied to the parameters of initial narrow- band model during the circuit re3nement process1 /y slightly adjusting the Hnown component values of the narrow-band model in 45ICE to achieve a better 3tting of input admittance, the component values of the narrow-band model after perturbation are obtained1 Table shows the values of the 3ve elements of the

narrow-band model before and after perturbation1 8ig1 9 compares the admittance of the monopole antenna with that of the ultimate model obtained by circuit re3nement method1 The admittance of the ultimate model is virtually indistinguishable with that of the monopole antenna1 8rom the above it is shown that the circuit re3nement method worHs e)ectively over a large bandwidth and is suitable for modeling of UW/ antennas1 0 2 4 6 8 10 12 0.1 0.2 0.3 0.4 0.5 0.6 Frequency (GHz) Input admittance Real( in Imag( in) Real( crm) Imag( crm Figure7. Comparison of admittances of the monopole antenna - in

and the ultimate model obtained by circuit re3nement method - crm 01

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Progress In Electromagnetics Research, PIER 82, 2008 443 2. CONCLUSION An equivalent circuit modeling method has been presented for the broadband circuit models of UW/ antennas that are compatible with time-domain circuit simulators1 The main philosophy is to taHe advantage of the physical information provided by an existing narrow- band model and use data 3tting approach to automatically develop a suitable macro-model which improves the overall performance of the ultimate model1 One of the Hey advantages of

the hybrid narrow-band model with a macro-model compared to complete macro-model is the reduced complexity of the circuits describing the macro-model networH, which generally improves the robustness of the data 3tting process1 5erturbation of component values of the narrow-band model is used to guarantee the accuracy of modeling1 The ultimate model worHs well as far as 1016 GHz, theoretically to more, and taHes into account the waveform dispersion, which is useful for compensation at transmitterAreceiver1 The new methodology should be useful for modeling a wide range of UW/ antennas1

AC8NOWLEDGMENT The worH is sponsored by the Zhejiang Eatural 4cience 8oundation -ZME480 under grants Eo1 N106360 and Eo1 D105 53, the E48C -Eos1 605310 0, 606710030, the ECET-07-0750, and the 5h1D1 5rograms 8oundation of =EC -Eo1 00703351 001 REFERENCES 11 Chen, 81 C1 and W1 C1 Chew, OTime-domain ultra-wideband micr owave imaging radar system,P Journal of Electromagnetic Waves and Applications , Qol1 17, 313331, 0031 1 8an, Z1, C1 I1 Dan, and M1 A1 Rong, O4ource pulse optimizations for UW/ radio systems,P Journal of Electromagnetic Waves and Applications , Qol1 0, 15351550, 0061 31 ODevision

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