R F 2008 IEEE INTERNATIONAL RF AND MICROWAVE CONFERENCE PROCEEDINGS
December 22-4, 2008, Kuala Lumpur, MALAYSIA
M 08
Representation of Antenna in Two-Port Network S-Parameter Teguh Prakoso, Razali Ngah, and Tharek Abdul Rahman Wireless Communication Centre, Faculty of Electrical Engineering Universiti Teknologi Malaysia 81310 Skudai, Johor Bahru, Malaysia
[email protected],
[email protected],
[email protected]
Abstract – Antenna return loss and gain as function of frequency are not readily accommodated in many communication system software. This paper proposes solution to the problem by representing the antenna in two-port network s-parameter. The representation exploits the analogy between antenna and two port network. Simulation using communication system software shows that the proposed method is validated.
Γ in =
Z − Z0 V1− S S Γ = S11 + 12 21 L = in + 1 − S22 Γ L Z in + Z 0 V1
(4)
S S Γ Z − Z0 V2− = S22 + 12 21 S = out (5) + 1 − S11Γ S Z out + Z 0 V2 In transmitting mode, equivalent isotropically radiated power ( EIRP ) of antenna is analogous with power delivered to load ( PL ) in S2P, power accepted
Γ out =
by the antenna ( PO ) is analogous with power delivered
Keywords: antenna representation, two port netwok, sparameter.
to network ( Pin ) in S2P.
(
EIRP = PO G = 1 − Γ in
1. Introduction
2
) GP
M
(6)
Simulation and measurement of antenna commonly produces parameters such as return loss ( S11 ) and gain at some frequencies. Many communication system simulation softwares (such as Optisystem, VPIphotonics, AWR VSS, Agilent ADS) do not include the frequency dependent parameters of antenna in their model. This situation causes researchers often find difficulties to simulate wireless systems in the software. This paper proposes solution to the problem by representing the antenna in two-port network s-parameter. This method is chosen because system software commonly has filter model represented in two-port network s-parameter (S2P) as function of frequency.
2. Method
Figure 2: A two port network with general source and load impedance
Relationship between antenna parameters is depicted in Figure 1, and the explanation of symbol in tabulated in Table 1 [1]. It is noted here that antenna gain only includes dissipation loss, and does not include mismatched and polarization loss. Our proposed method is based on analogy between antenna and two-port network model (S2P) as described in Figure 2 [2]. Relationship between voltages in the twoport model is [2] (1) V2+ = Γ LV1−
V1− = S11V1+ + S12V2+ = S11V1+ + S12 Γ LV2− − 2
+ 21 1
+ 22 2
+ 21 1
Figure 1: Gain and directivity flowchart
− L 2
V = S V + S V = S V + S 22 Γ V
978-1-4244-2867-0/08/$25.00 ©2008 IEEE
(2) (3)
293
Table 1: Glossary of antenna terms η = radiation PA = power available from efficiency the generator GR = realized gain PM = power to matched transmission line G = gain PO = power accepted by D = directivity the antenna gR = partial realized PR = power radiated by the gain antenna g = partial gain I = radiation intensity d = partial directivity In = partial radiation intensity p = polarization M1 = impedance mismatch efficiency factor 1 M2 = impedance mismatch factor 2
By observing Figure 2 and using its analogy for antenna, we find that there is no reflection in Z L so that Γ L = 0 ; V2− is resulted only from V1+ , therefore
S22 = 0 or Γ L = 0 ; V1− is resulted only from V1+ , therefore S12 = 0 or Γ L = 0 . The consequence is that Γ in = S11 . Antenna gain definition by IEEE [1] is analogous with power gain ( GP ) in S2P [2], and using Γ L = 0 and Γ in = S11 resulting in S21
GP =
(
2
)
(
S21 = G 1 − S22
2
)
(10)
Values of S2P file for antenna is receiving mode is tabulated in Table 3. Table 3: S2P values for antenna in receiving mode
S11
(8)
Value for S2P file is tabulated in Table 2. To guarantee that Γ L = 0 , we have to set load impedance
Z L = Z 0 . The value of S12 and S22 can be arbitrary, but to ensure unilaterality, S12 and S22 should be zero. Phase of S11 may be important, but phase of S21 is not. Table 2: S2P values for antenna in transmitting mode ∠S11 ∠S21 S11 S21
S11
(9)
2
∠S11
∠S11
of the antenna of the antenna
(
S 21 = GP 1 − S11
2
)
∠S21
S21
(
2
)
0
0
S12
∠S12
S 22
∠S22
0
0
S11
∠S11
of the antenna
of the antenna
S 21 = GP 1 − S22
(7)
2
S 21 = GP 1 − S11
2
1 − S22 and therefore resulting
2
1 − S11 and therefore
S21
G = GA =
0
As antennas have the same characteristics in transmitting and receiving mode, it is needed to build bidirectional S2P for antenna. However, S2P of antenna in receiving mode requires that S12 = 0 , causing transmitting antenna gain cannot be included the S2P file. Hence, it is not possible to build bidirectional S2P for antenna.
3. Validation
0
Optisystem v7.0, optical communication system simulation software produced by Optiwave System Inc. is used to validate the proposed method. Power available from generator ( PM ) is 500 mW, with
S12
∠S12
S 22
∠S22
antenna return loss is -10 dB ( S11 = 0.316 ) and gain
arbitrary
arbitrary
arbitrary
arbitrary
is 3 dB, producing EIRP of 29.53 dBm (897.9 mW). Table 4 describes S2P data from antenna return loss and gain. S2P data in 500 MHz is for antenna in transmitting mode only, 490 MHz is for receiving mode only, 510 MHz and 520 MHz is an experiment for bidirectional S2P, and S2P data in 530 MHz is for antenna in receiving mode (but the input is port 2).
In receiving mode, VS in Figure 2 is representing power captured by isotropic antenna ( PS ). There should be no reflection in source ( V1− = 0 ), so Z S must be set to Z 0 . However, Z L (filter, LNA, etc.) may
Table 4: Values of S2P file for simulation using Optisystem v7.0
not be matched to Z 0 , so Γ L is not always zero. Hence, − 1
to guarantee that V = 0 , it is mandatory that
Frequency (MHz) S11 ∠S11 S 21 ∠S 21
S11 = S12 = 0 . Using this result, Γ out = S22 but the value of S22 in S2P file in receiving mode must be taken from value of S11 of the antenna. VS represents power captured by isotropic antenna, and after multiplied by antenna gain ( G ), it produces available power from the antenna ( PO ). The PO is analogous with power available from network ( Pavn ) in S2P [2]. Using Z in = Z 0 = Z S , Pin is equal to power available from the source ( Pavs ). Then antenna gain definition is analogous with power available ( GA ) definition in S2P [2].
490 500 510 520 530
0 0.316 0.316 0.316 0.316
0 0 0 0 0
1.34 1.34 1.34 1.34 0
0 0 0 0 0
Frequency (MHz) S12 ∠S12 S 22 ∠S 22 490 500 510 520 530
294
0 0 1.34 1.34 1.34
0 0 0 0 0
0.316 0 0 0 0
0 0 0 0 0
Figure 3 (Figure 4) shows that the method functions well in transmitting (receiving) mode. Figure 5 shows that bidirectional S2P gives wrong result for receiving mode (input: port 2) although has different frequency (520 MHz) with the transmitting mode (510 MHz). However, if we assign value unidirectional for receiving antenna, ‘bidirectional’ operation of single S2P block is possible but must use different frequency with transmitting mode, as depicted in Figure 6.
Acknowledgment This work is supported by Science Fund (Vot 79022) from Ministry of Science, Technology, and Innovation, Malaysia. The grant is managed by Research Management Center (RMC), Universiti Teknologi Malaysia.
References
4. Conclusion
[1]
Simulation result shows that the proposed method working well and accurate. It is also shown that ones cannot build bidirectional S2P for antenna. Therefore, separate S2P block is needed for transmitting and receiving.
[2]
"IEEE standard definitions of terms for antennas," IEEE Std 145-1993, p. i, 1993. D. M. Pozar, Microwave Engineering, 3 ed. New Jersey: John Wiley & Sons, Inc., 2005.
Figure 3: Validation of antenna in transmitting mode
295
Figure 4: Validation of antenna in receiving mode
Figure 5: An Experiment for Bidirectional S2P
296
Figure 6: Bidirectional S2P block using unidirectional transmitting and receiving S2P at different frequency.
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