Modeling Omnidirectional Small Antennas for UWB Applications

1
Modeling Omnidirectional Small Antennas for UWB
Applications

• Stanley Wang, Ali Niknejad
• and Robert Brodersen
• University of California, Berkeley
• June 22, 2004

2
Introduction of UWB

• According to FCC, UWB devices required to have
• -10dB Fractional BW ? 0.2 or
  -10dB BW ? 500MHz
• EIRP -41.3 dBm/MHz
• Large BW enables short range, high speed
  communications
• Large BW enables high resolution positioning
• Better through-wall capability at low frequency

3
Antennas for lt960MHz UWB Applications

• Free space wavelength at 960MHz 31cm
• Antennas of size 5cm are electrically small
• Pros and cons of small antennas
• Low directivity
• Maximize allowable radiation power
• Waveform omni-directional
• Receiver gets the same waveform regardless of the
  relative position to the transmitter
• High qualify factor (Zin ?)
• Poor impedance matching and efficiency
• Waveform dispersion from input V/I to far-zone
  E-fields (Whats the transfer function?)

4
Modeling Zin of Small Antennas

• Antennas are linear, passive networks
• R and jX are not arbitrary functions, e.g.
  and
• Foster canonical forms

First Foster canonical form
Second Foster canonical form
5
Waveform Dispersion
Large Antenna
Small Antenna

• Waveform directional (or
• direction-dependent dispersion)

• Waveform omni-directional (or
• direction-independent dispersion)

6
Modeling Transfer Functions
1. Small antenna models
2. Waveform omni-directional
Only one resistor in each network ? Presistor
Pradiation
Radiation E-field
Voltage across Rrad
7
Modeling Small Dipole Antenna
Analytical equations for small dipole
When khltlt1,
Waveform omni-directional!
8
Modeling 6cm Dipole Antenna

• Verification of waveform omnidirectionality
• Identical normalized magnitude response in all
  directions
• Identical phase response in all directions
  (linearity not required)

Phase (degree)
Magnitude (dB)
Norm. Magnitude Response from XFDTD
Phase Response from XFDTD
9
Modeling 6cm Dipole (cont.)

• Simplified Foster canonical forms
• Tangs model C1 0.67pF, C2 0.11pF, L2
  7.34nH, Rrad 294.71?
• Hamids model C1 0.68pF, L1 1.24nH, C2
  0.64pF, L2 4.91nH, Rrad 187?

Real(Zin)
Impedance(?)
Frequency(GHz)
Imag(Zin)
Impedance(?)
Frequency(GHz)
10
Modeling 6cm Dipole (cont.)
f-10dB750MHz
Rs 50?
XFDTD
6cm
Vin
Amplitude (V)
SPICE
11
Modeling 6cm Dipole (cont.)
f-10dB 2 GHz
f-10dB 1.72.5 GHz
Rs 50?
Rs 50?
Vin
Vin
Amplitude (V)
Amplitude (V)
Amplitude
Amplitude
12
Modeling Large-Current Radiator
Vin
Rs 1?
Magnetic antenna
Inductor dominant network
13
Generalization to 3-10GHz UWB

• In 3.1-10.6GHz band, small antennas are still
  preferred
• Small antenna modeling methodology can still be
  applied if requirements are met

3cm Circular Planar Dipole
C10.58pF L10.85nH C20.53pF L21.50nH Rrad81?
14
Generalization to 3-10GHz UWB
f-10dB 211 GHz
f-10dB 5.5 GHz
Rs 50?
Rs 50?
Vin
Vin
15
Conclusions

• Small antennas are simple in terms of input
  impedance and radiation pattern
• Simplified Foster canonical forms for small
  antennas not only model the input impedance, but
  also give information about transfer function to
  radiation E-fields
• Modeling methodology applicable to many UWB
  antennas
• Enable fast antenna/circuit co-simulation and
  design

16
Acknowledgement

• Supported by Army Research Office grant 065861
• Robert Fleming and Cherie Kushner at Aether Wire
  Location, Inc
• Industrial members of BWRC
• Ian ODonnel, Mike Chen, Chinh Doan, Ada Poon at
  BWRC