HARMONIC PERFORMANCE OF SINGLE AND DUAL DEVICE GUNN OSCILLATOR MICROSTRIP ANTENNAS Christos Kalialakis, Peter Gardner, Peter S. Hall University of Birmingham School of Electronic and Electrical Engineering, Edgbaston, Birmingham, B15 2TT, United Kingdom Email:
[email protected]
INTRODUCTION Integrated active antennas offer compact and multifunctional configurations. Arrays of compact antenna-circuit modules utilising quasi-optical power combining techniques avoid interconnect losses, offering an attractive solution for power generation[1]. Nonlinearities of active devices cause harmonic generation. The compact arrangement does not accommodate the use of filters. Consequently harmonics can become a problem when addressing system specifications. This paper focuses on the harmonic performance of single and dual device Gunn oscillator microstrip antennas. A great number of configurations have been shown in the literature [2]. The engineering process demands CAD (Computer Aided Design) and CAE (Computer Aided Engineering) tools, which are necessary to avoid costly trial and error approaches. The issues that need to be addressed for the successful analysis and design of integrated active antennas are nonlinearities from active devices, broadband operation and parasitic coupling. Here the lumped element FDTD (or extended) method is used. FDTD is a structure and geometry flexible method with the capability of including circuit elements [3]. The wealth of information produced by FDTD simulations can be very useful especially when novel combinations are sought [4].
GUNN DIODE MODELLING One port active elements like Gunn and IMPATT diodes exhibit negative resistance. The most common way of representing them is through equivalent circuits. There are different equivalent circuits even for the same device. A current source F(V) in parallel with a capacitor was used in [5]. More recently, a large signal equivalent circuit was implemented allowing for loss (Fig. 1a) in an attempt to model a single device waveguide oscillator [6] The nonlinear current source is represented as a function of the voltage involving cubic nonlinearities:
F ( V S ) = − G1 ⋅V S + G 2 ⋅V S
3
(1)
In order to produce an FDTD expression, the discrete solution of the circuit of Fig. 1(a) is required. The numerical solution is given by
V Sn + 1 =
where:
A A1 n A2 VS − F ( V Sn ) − 3 ∆z( E Zn + 1 + E Zn ) β β β
(2)
β = 2 RC + ∆t( 1 + RF& )
(3)
A1 = 2 RC − ∆t( 1 − RF& )
(4)
A2 = 2 R∆t
(5)
A3 = ∆t
(6)
The corresponding FDTD solution at the Gunn diode cell reads
E zn+ 1
ε ∆z 1 − A3 − ∆t ∆x ⋅∆y 2 R 1 = E zn + ( ∇ × H )zn + 1 / 2 ε ∆z 1 − A3 ε ∆z 1 − A3 + + ∆t ∆x ⋅∆y 2 R ∆t ∆x ⋅∆y 2 R (7)
( 1 + A1 )V Sn − A2 F ( V Sn ) − ε ∆z 1 − A3 + 2 R S ⋅∆x ⋅∆y( ) ∆t ∆x ⋅∆y 2 R 20
A +
C
15
R
Vs
10
Vz F(V s )=Is
Current(mA)
IL
5 0 -5 -10 -15
+ (a)
-20 -1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Voltage(V)
(b)
Fig. 1. (a) Equivalent circuit used for the Gunn diode with F(Vs) representing a nonlinear dependent current source with series loss R=1Ω , C=0.2pF (b) Nonlinear Current Source Characteristics for an X-band Gunn diode (G1=0.0252 S G2=0.0265 S) Expressions (2) and (7) constitute a two level iterative procedure. At each time step, first calculate
E Zn+ 1 via (7). Then
n+ 1
calculate V S through (2). Our Gunn model was validated by studying a microstrip line Gunn oscillator and compared favourably with an HP-MDS solution[7]. GUNN-OSCILLATOR MICROSTRIP ANTENNAS Configurations In Fig.2a, a module is shown where the Gunn diode is located on the patch. Such an arrangement avoids any interconnection losses, optimises substrate space, provides a compact arrangement suitable for use in a power combining array, and minimises cost. This configuration, first suggested in [9], is to be contrasted with the one analysed in [8] which involves a microstrip line Gunn oscillator feeding a microstrip antenna. The same structure was studied in [10] and [11]. The very high cross polarisation of the single device Gunn has led to research into balanced multiple diode topologies, providing the additional advantage of increased radiated power. An experimental investigation of a dual device configuration (Fig. 2b) was reported in [11]. The antenna, with dimensions 9.8×8.0 mm and with εr=4.1, was integrated with X-band Gunn diodes. In the new work reported here, the Gunn diode large signal equivalent circuit of Fig. 1 was used in an FDTD analysis of these active antenna configurations. The Gunn diodes serve as feeding pins similar to those commonly used in microstrip feeds[12]. The position of the diodes determines the input impedance [13].
Substrate
Substrate
L
L
Gunn Diode
Gunn Diode
W
Gunn Diode
W
xG
xG
xG
(a)
(b)
Fig. 2. Microstrip antenna-Gunn oscillator module (a) single (b) dual Harmonic Performance The calculated output spectra for the single and dual device configurations are shown in Fig. 3. The fundamental oscillation frequency, close to 10GHz, is in agreement with [11]. The third harmonic is also present in both spectra, as expected, since the nonlinear characteristic (1) has first and third order terms. The frequency of oscillation for the dual diode case is slightly lower, as expected due to the extra capacitance from the second Gunn diode. An interesting feature is the presence of a second harmonic in Fig. 3b, which is not present in the spectrum of the single device, Fig. 3a. A possible explanation of this effect is that one diode perturbs the operation of the other in such a degree that the I-V curve of the Gunn contains second order terms. If a slight deviation δV in equilibrium from the I-V characteristic expression (1) due to the presence of the loss resistor R (Fig. 1) is allowed then
F (VS + δV ) = − G1 (VS + δV ) + G2 (VS + δV ) 3
(8)
Expanding (8) and neglecting terms containing δV2, δV3 then
F (VS + δV ) = − G1 (VS + δV ) + G2VS3 + 3G2VS2δV
(9)
0
0
-10
-10
Normalised Spectrum(dB)
Normalised Frequency Spectrum(dB)
Observe that in expression (9), there is now an additional square term, which becomes more significant as the deviation δV becomes stronger. In the dual device module each diode distorts the other and the deviation δV becomes significant unlike the single device module case. Since our results hold for a nonlinear negative resistance, they are equally applicable to dual FET configurations such as that reported in [15].
-20
-30
-40
-50
-20
-30
-40
-50
-60
-60 0
5
10
15
frequency(GHz)
20
25
30
0
5
10
15
20
25
frequency(GHz)
(a) (b) Fig. 3. Calculated spectrum for the oscillator-antenna at the Gunn position (a) Single device (b) Dual device (FDTD details, ∆x=0.24mm,∆y=0.31mm,∆z=0.51mm, ∆t=0.6ps, patch dimensions=41x25 cells)
30
Radiation Patterns The calculated copolar radiation patterns of the single diode module are asymmetric, a feature that has been explained by calculating the field distribution [14]. Another striking feature is the high cross polarisation especially for the Hplane. For angles larger than 45o and less than -45o the crosspolarised radiation becomes more significant than the copolarised radiation, by as much as 10dB. This is in agreement not only with [11] but also with [9]. The high cross polarisation levels imply that a transverse mode is excited in addition to the fundamental mode. In general, the diode presents a field discontinuity and higher order modes are excited in order to accommodate its presence. In the dual diode module the main patterns are more symmetrical. This is attributed to the more symmetrical field distribution. The striking feature is the significant reduction of the H-plane cross polar radiation, suggesting that a balanced feed approach would be the solution for better power combining arrays. The cross polar isolation at boresight is very close to -30 dB. All of these findings are in agreement with the experimental results of [9], [10] and [11]. In terms of radiation patterns the dual device is preferable. CONCLUSIONS A Gunn diode model was adapted from the literature and incorporated into the FDTD code. This was validated successfully by studying a microstrip line Gunn oscillator having very good agreement with the HP-MDS simulator. Compact Gunn oscillator antennas were studied with single and dual device configurations. Radiation patterns were calculated for the first time and compared favourably with published experimental results. The dual device module was proved to give reduced cross polar levels and improved radiation characteristics. However it was shown that additional harmonics are generated. REFERENCES [1] J.W. Mink, “Quasi-optical Power Combining of Solid State Millimeter-Wave Sources”, IEEE Transactions on Microwave Theory and Techniques, vol. 34, pp. 273-279, 1986. [2] R.A. York and Z.B. Popovich (eds), Active And Quasi-Optical Arrays For Solid State Power Combining, John Wiley, 1997. [3] M. Piket-May, A. Taflove and J. Baron, "FDTD Modelling of Digital Signal Propagation in 3D Circuits with Passive and Active Loads", IEEE Transactions on Microwave Theory and Techniques, vol. 42, pp. 1514-1523, 1994. [4] C.Kalialakis, M.J. Cryan, P.S. Hall and P. Gardner,“ FDTD Simulation of an Active Integrated Antenna”, Electronics Letters, vol. 33, pp. 2091-2092, 1997. [5] T.Hirota, M. Nakajima and J.-I. Ikenoue, “A Simple Equivalent Circuit of Microstrip Oscillator Allowing for Nonlinearity”, International Journal of Electronics, vol. 48, pp. 427-434, 1980. [6] B. Toland, B. Housmand and T. Itoh, “Modelling of Non-Linear Active Regions with the FDTD Method”, IEEE Microwave and Guided Wave Letters, vol. 3, no. 9, pp. 333-335, 1993. [7] V.Fusco, P.S. Hall, M.J.Cryan, “Circuit Simulator Based Methods”, Ch.3 in K.C. Gupta and P.S.Hall(eds), Analysis of Integrated Circuit Antenna Modules, John Wiley, 1999. [8] V.A. Thomas, K.M.- Ling, M.E. Jones, B. Toland, J. Lin and T. Itoh, "FDTD Analysis of an Active Antenna", IEEE Microwave and Guided Wave Letters, vol. 4, no.9 , pp. 296-298, 1994. [9] H.J. Thomas, D.L. Fudge and G. Morris, “Gunn Source Integrated with Microstrip Patch”, Military Microwaves Conference Proceedings, pp. 245-249, 1984. [10] K.Chang, K.A. Hummer and J.L. Klein, “Experiments on Injection Locking of Active Antenna Elements for Active Phased Arrays and Spatial Power Combiners”, IEEE Transactions on Microwave Theory and Techniques, vol. 37, pp. 1078-1084, 1989. [11] R.A. York and R.C. Compton, “Dual-device active patch antenna with improved radiation characteristics”, Electronics Letters, vol. 28, no. 11, pp. 1019-1021, 1992. [12] J.A. Navarro, K.A. Hummer and K. Chang, “Active Integrated Antenna Elements”, Microwave Journal, pp.115126, 1991. [13] R.J.Luebbers and H.S. Langdon, “A Simple Feed Model that Reduces Time Steps Needed for FDTD Antenna and Microstrip Calculations”, IEEE Transactions on Antennas and Propagation, vol. 44, pp. 1000-1005, 1996.. [14] C.Kalialakis, FDTD Analysis of Microstrip Antenna-Circuit Modules, Ph.D. Thesis, No. 864, School of Electronic and Electrical Engineering, University of Birmingham, UK, 1999. [15] X.D. Wu and K. Chang, “Dual FET active patch elements for spatial power combiners”, IEEE Transactions on Microwave Theory and Techniques, vol. 43, pp. 26-30, 1995.
