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Theoretical analysis and simulation for avoiding antenna oscillations without distributed resistance
Journal of Applied Geophysics 67 (2009) 374–385
Contents lists available at ScienceDirect
Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / j a p p g e o
Theoretical analysis and simulation for avoiding antenna oscillations without distributed resistance Gonzalo Garcia a,b,⁎, José A. Uribe b, David Ulloa b, Rodrigo Zamora b, Gino Casassa b a b
Dirección de Programas, Investigación y Desarrollo de la Armada de Chile, General del Canto398, Playa Ancha, Valparaíso, Chile Centro de Estudios Científicos, Arturo Prat 514, Valdivia, Chile
a r t i c l e
i n f o
Article history: Received 31 October 2007 Accepted 25 September 2008 Keywords: Impulse radar Transmission line Dipole antenna Electromagnetic equations
a b s t r a c t The so-called Wu and King antenna pattern is widely used in GPR because of its simple design and construction features. The main disadvantage is its limited efficiency due to transmitter energy losses which occur through lumped resistors. Based on the analysis of the electromagnetic field behaviour across the antenna, it is possible to replace the effect of the resistors by either storing the energy of the electric pulses, or damp them by means of one matched resistor, which will theoretically improve the efficiency of the antenna. In this paper we provide a theoretical analysis using a modified transmission line model together with simulation based on delayed potentials among other electromagnetic software, and measurement results using an impulse transmitter with fast MOSFET switches and a matched resistor that support this idea. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Analysis of a simple dipole antenna with no resistors
The task of an impulse radar antenna, as is true for any antenna, is to transfer the energy delivered by the transmitter into the target medium in the most efficient way. Based on electromagnetic theory, this can be done with a simple dipole, which has the limitation that it works best only for narrow band signals. In order to radiate a broad band signal efficiently, it is necessary to modify the dipole antenna. This has been traditionally done by means of a lumped resistive pattern based on a logarithmic model, derived originally by Wu and King (1965). The antenna resistors gradually reduce the energy of the positive and negative electric pulses, as they progress from the centre of the dipole to its ends. The underlying idea is to let the pulses reach the outer part of the dipoles with minimal energy, allowing to radiate only one or one and a half monocycles. If the goal of radiating only one or one and a half monocycle can be achieved by another means, which can minimize energy losses and simplify the antenna design, this will result as well in a large improvement of the efficiency of the radar system. This paper proposes a theoretical approach based on several simulation algorithms and some basic measurements that allow the removal of the resistors without adding extra ringing.
A dipole can be considered as a modified transmission line, which retains the physical behaviour of the antenna. The transmission line equations (Eq. (1)) correspond to the one-dimensional wave equation, meaning that any waveform inserted into the inner terminals (at z =z1) will then propagate through the line toward the outer terminals, with a speed given as a function of the intrinsic parameters of the line:
⁎ Corresponding author. Dirección de Programas, Investigación y Desarrollo de la Armada de Chile, General del Canto398, Playa Ancha, Valparaíso, Chile. Tel.: +56 32 2529683; fax: +56 32 2963438. E-mail address: [email protected] (G. Garcia). 0926-9851/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jappgeo.2008.09.014
∂2 ∂2 X ðz; t Þ = LC 2 X ðz; t Þ; 2 ∂z ∂t
ð1Þ
where X(z,t) = V(z,t) or I(z,t) are the voltage or current waveforms developed in the line, and L and C are the distributed inductance and capacitance parameters, respectively. In this case both intrinsic parameters L and C are normally constant along the line. As shown in Fig. 1, together with the voltage and current travelling waves, an electric field signal – also a magnetic signal, not shown – Ē(z,t) propagates as well, which is indeed the real physical entity together with the electric charges that travels along the antenna at the same speed, which is a function of the intrinsic parameters. This electric field, in this case extending perpendicular to the transmission lines, is the crucial phenomenon when analysing the dipole as a transmission line with open arms. Not considering the natural losses associated to the ohmnic impedance of the line cables, but taking into account the constant distance between these lines, it can be assumed that the shape and energy of the signals remain constant. Thus the electric and magnetic fields generated between the electric charges do not change within the transmission line.
G. Garcia et al. / Journal of Applied Geophysics 67 (2009) 374–385
Fig. 1. Signals in a normal transmission line.
This effect is no longer valid in a dipole, simply because the distance between the charges is continuously changing, demanding continuous delivery of energy to expand the electromagnetic field, energy which is taken from the kinetic energy of the charges. This physical effect can be mathematically expressed through the nonconstant intrinsic parameters of the distributed capacitance C(z) and inductance L(z) (see Eq. (2) and Fig. 2), where E(r,t) is now a function of the spatial vector r ̄ = (x,z). ∂2 ∂2 X ðz; t Þ = LðzÞC ðzÞ 2 X ðz; t Þ ∂z2 ∂t
ð2Þ
Based on the transmission line model, and taking into account that the speed of the electric field lines in a nearly perfect electric conductor is comparable to the speed of light in free space, and assuming that the transmitter has a high conductivity, the following temporal sequence (Fig. 3a, b, c and d) shows how the electric field should propagate around an antenna without lumped resistors. A simulation, based on an electromagnetic software, was run to confirm the expected physical behaviour. A wire dipole located in free space, and excited by a pulsed voltage was tested. Fig. 4 (a, b, c, and d) shows the results, which closely agree with the transmission line model. The outer ends of the dipoles act as an open circuit and the inner ends act as a closed one. According to transmission line theory, both ends react as perfect reflectors, as it can be seen in Figs. 3 and 4. The outer ends reflect the signal without changing the sign, and due to low voltage source impedance the inner ends reflect the signal changing its polarity. This behaviour implies a high level of oscillation, and the decay observed in real antennae is attributable to the ohmnic losses and the energy delivered to propagate the electromagnetic field. For GPR antennae it is common to locate the pulse circuit at the dipole centre, so the distance between the generation and the feeding point is not significant for our analysis. This condition was adopted in our simulations and implemented in our measurements.
accepting no more than one or one and a half monocycles, depending on the environment and the specific application requirements. As Kappen and Mönich (1987) illustrate, charge pulses start losing energy while they are travelling through the arms of the antenna, presenting an evident dispersion effect smeared over the antenna's length, affecting the second half of the first monocycle, resulting in a non-symmetrical cycle. Therefore the electric charges return to the inner ends of the antenna with very low energy, through a recombination process and producing no new reflections. Most of all the lost energy is dissipated into the resistors by means of heat. Thus the Wu and King antennae have a relatively low efficiency. As could be seen from the former section, the electric field lines, as electrostatic theory claims, start attached to the electric charges. While the charge pulses travel outward within the antenna, the electric field spreads outwards through the surrounding space, describing a circular curve pattern in a planar representation or a spherical shape in space. After these charges reflect at the outer ends of the dipoles and start travelling to the inner ends, the electric field lines cannot immediately follow the charges, which now are moving in an opposite direction behind the lines, at an almost similar speed, describing an umbrella-shaped curve. Finally, when both charge pulses with opposite polarity meet at the centre of the antenna, a zero net charge is produced, forcing the extended electric field lines to close onto themselves and detaching from the sources. At this very moment an electromagnetic field is radiated. After the charges meet at the centre of the antenna, they cross the transmitter due to its low impedance, exiting into the other arm of the dipole, which can be understood as a reflection with polarity change. This new charge departure is the beginning of a new monocycle that will follow the first one already generated. The core idea in implementing a dipole antenna with no resistors is that if it is possible, by some means, to capture this electric charge which represents electric energy, thus avoiding the new charge departure from the inner part of the antenna, the extra oscillations will be cancelled. Moreover, if this electric charge could be reused in the following radiation process, the overall efficiency would increase. Figs. 5 (a and b) and 6 show the results of a simulation, based on an electromagnetic software, using two similar 35 meter-long dipoles –
3. The Wu and King antenna Based on the physical behaviour of the dipole with no resistors, we can analyse the electric field of a Wu and King (1965) antenna in a qualitative manner. Any Wu and King antenna or a derived one rely their design on a resistively lumped pattern following a logarithmic curve. The core idea is to diminish the energy of the electric pulses, decreasing thus the electric current density so no further reflections will occur,
375
Fig. 2. Signals in a modified transmission line.
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Fig. 3. Expected field in a dipole antenna with no resistors. a) pulses start to propagate b) pulses reaching the outer ends c) pulses travel backwards. d) pulses cross the transmitter.
without and with Wu and King resistive pattern – located in free space, and excited by a Gaussian voltage pulse of a duration of 200 [nanoseconds]. Fig. 5 shows a comparison between these two similar antennas, concerning the electric current signal in the feeding side and the radiated electric far field, calculated in the perpendicular radial plane at a distance of 55 m. This comparison highlights the effect of the Wu and King pattern effect, which diminishes the ringing while reducing the overall efficiency.
Fig. 6 shows the entire electric field evolution around a Wu and King antenna. It is interesting to compare this sequence with Fig. 4. and appreciate the differences, especially in the last stage (d). 4. Proposed physical solution The idea of a new antenna design is to achieve a similar damping effect as the lumped resistors, but wasting less energy, in order to radiate a wide band signal, that is, a signal composed of one or one and
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Fig. 4. Simulated field in a dipole antenna with no resistors:(from left to right) a) pulses start to propagate b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
a half monocycles. The pulse energy would be taken from the returning charges and stored for later use. It is usual that impulse radar transmitters use capacitors of high capacitance to store energy, which is discharged extremely fast into the antennae, after a trigger signal. Working with fast switches should allow to connect and disconnect the transmitter from the antenna, in order to deliver the electric charge and subsequently storing it, thus avoiding a new reflection. Given the behaviour of a capacitor connected to a transmission line, it should be expected that the returning current pulse will tend to charge the capacitor again in an exponential mode. This simple effect accomplishes the main requirement, that is, it captures the energy from the pulse and stores it back into the capacitor (García et al., 2007). This could be achieved by controlling the switches, not only closing them at a desired instant, but opening them at another specific moment as well. The switch control should be realized by some electronic device taking into account the physical dimensions of the antenna and the electric characteristic of the capacitors, in order to calculate the precise closing and opening times. The switches must be reopened considering the two-way travel time of the charges, which is directly related to the length of the dipole arms, and the effective pulse width of the capacitor discharge. This time could be estimated but ideally should be measured to find its optimal value. The idea is that after the capacitors are discharged, they remain open waiting for the charges to return. After reaching their highest recharge voltage they should be reopened. This proposal strongly relies on the returning pulse shape. For an optimal performance the returning pulse should have an increasing shape or at least a nearly rectangular shape – but never a decreasing shape – in order to have an increasing charging function. In simple words, the pulse amplitude must always be higher than the charge voltage to keep the charges together. If this is not accomplished part of the previously stored charges should start repulsing each other and discharge the capacitor before the pulse is completely received, due to the inability of the remaining part of the pulse to continue charging the capacitor. If this requirement is not fulfilled, the formerly stored charges will produce antenna ringing thus radiating a longer signal than expected.
A new approach is developed here in order to avoid this effect, but seeking the same objective of radiating a symmetric wide band signal. Following the study of the dipole as a modified transmission line, the idea is to search for a replacement of the capacitor the moment the charge pulse returns to the transmitter. This solution seeks an independence from the returning pulse shape. In order to avoid undesired reflections in the transmitter and having in mind the similar behavior with respect to a transmission line, the inner terminal of the antenna should be temporarily terminated with a resistance with the same value of the characteristic impedance, that is the inner voltage to current ratio. This matching will optimize the power transfer, transferring all the energy to this resistor, and avoiding reflections as it occurs in any transmission line. This new solution will not attain the objective of saving energy, but at least will assure a more symmetrical radiated pulse shape with a length similar than the one obtained with a Wu and King pattern, but with a simpler pattern design. The solution only needs to electrically connect a predetermined – matched – resistor R between the inner terminals of the dipole before the returning pulse arrives, by the action of rapid switches Sw which disconnect the electric source V. This action will simply terminate the inner dipole – seen as a transmission line – avoiding any reflections. The solution is sketched in Fig. 7. To prove the effectiveness of this solution, an electromagnetic simulation was run comparing a Wu and King antenna with this new design. Two 35 meter dipoles located in free space were excited by a voltage Gaussian pulse. Due to a technical limitation of the software, the resistor between the inner ends of the dipole was connected during the entire simulation, and the voltage source was replaced by an equivalent current source. This simulation limitation has the disadvantage that it consumes half of the available power at the feeding stage, when the transmitter splits the energy into the dipole and the resistor as well — of similar ohmic value. This should be avoided using an adequate device with fast switches. In order to design the optimal resistance value placed between the inner terminals, the ratio between the voltage and the induced current
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Fig. 5. Signals without and with Wu and King resistive pattern: a) electric current b) electric far field.
signals was calculated, based on the same simulation model. In this particular design a 686 Ω value was found. Figs. 8 and 9 show the results. The first one compares the electric current developed in the inner terminals of both designs together with the electric far field, and the last figure shows the evolution of the entire electric field into the surrounding space of the new solution. Assuming that the disconnection of the resistors at the feeding stage is possible to implement, it is important to emphasize that the use of this resistor will prevent from saving the returning energy for future pulses. It is also important to stress that if this resistor can be replaced by another active device, which can present a resistive behavior and at the same time can capture the energy instead of
burning it, the objective of saving energy will be accomplished as well. Considering the technical limitation of energy saving, the following section will attempt to visualize the phenomenon occurring when a theoretical electronic device is able to capture the incoming charges and prevent extra ringing, but without burning the power into a matched resistor. For this purpose a straightforward simulation algorithm is performed, based on the calculations of the Maxwell equations in their integral form. The starting point for any simulation is to formulate the electromagnetic equations. Knowing the environmental parameters and the sources, it is possible to calculate the electromagnetic fields in the
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Fig. 6. Simulated field in a dipole antenna with Wu and King pattern resistors: (from left to right) a) pulses start to propagate b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
space–time continuum. In order to avoid numerical errors, it is preferable to use integral equations rather than differential ones. With this in mind, the following equations (Eq. (3)), the socalled delayed electromagnetic potentials, as an exact derivation from the differential form of the electromagnetic equation set (Cardama et al., 2002), are formulated in an integral form:
Φð⇀ r; t Þ = ∫v′
j⇀ r −⇀ r ′j ρ ⇀ r ′; t − s
dv′ 4πɛ j ⇀ r−⇀ r′j j⇀ r −⇀ r ′j ⇀ μJ ⇀ r ′; t − s ⇀⇀ Að r ; t Þ = ∫v′ dv′ 4π j ⇀ r −⇀ r′j
ð3Þ
Where ϕ(r ̄ ,t) and Ā(r ̄ ,t) are the electric scalar and magnetic vector delayed potentials, evaluated at the space–time point (r ̄ ,t). The electric ̄ ′̄ ,t′) and the charge density ρ(r ′̄ ,t′) are the sources current density J (r within the antenna at the space–time point (r ′̄ ,t′) (see Fig. 10 where a new spatial dimension was added). For the sources, t′ =t − |r −r′| /c is the retarded time and r′ the retarded position. The following remarks can be made concerning the equations of the potentials (Eq. (3)). The potentials depend linearly with respect to the sources, simplifying the algorithm. The permittivity and permeability of the surrounding medium, ε(r ̄) and μ(r ̄), respectively, allows the algorithm to simulate any kind of environment, like two half spaces. Lastly, it is possible to discretise the integrals, performing the
calculation for point-like sources as a summation of effects, but in that case it must be taken into account that this manipulation will transform the equations into the so-called Liénard–Wiechert potentials (García, 2005), which describe the complete, relativistically correct, time-varying electromagnetic field for a point-charge. The speed at which the potentials travel through space will be a function of the permittivity and permeability of the medium, s(ε,μ). Starting from the delayed potentials, it is possible to obtain in a direct way the electromagnetic fields Ē(r ̄ ,t) and B̄(r ̄ ,t) (electric and magnetic field, respectively) at any point in the space–time surrounding the antenna. For this the following expressions (Eq. (4)) are used: ⇀ ∂ A ð⇀ r ; tÞ r ; t Þ = − ∇ϕðr; t Þ − E ð⇀ ∂t ⇀ Bð⇀ r ; t Þ = ∇ × A ð⇀ r ; tÞ
ð4Þ
The following Fig. 11 (a, b, c and d) is the result of a simulation which allows to check the effects presented above. The fields will be shown in a three dimensional sketch, using the third coordinate (vertical) as the amplitude of the field (with an exponential modification), in a specific two-dimensional point (horizontal). A 6 [m] long dipole, without lumped or matched resistors, was chosen. The charge pulse has a nearly Gaussian shape, with a spatial width of 90 [cm], meaning that the exciting signal has already dropped to zero when each pulse reaches the antenna ends. This is not the normal condition, and has only been used for drawing purposes.
Fig. 7. Electric circuit sketch of the solution.
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Fig. 8. Signals with the new antenna pattern and with the Wu and King pattern: a) electric current b) electric far field.
Usually the pulse width is directly related to the length of the antenna (Chen, 2006). Each division of the grid is 15 [cm] and 60 [ns]. In order to capture the pulse energy, a theoretical electronic device was considered for accumulating the electrical charges as these reach the inner ends of the antenna. Observing Fig. 11d, it is evident that the extra ringing due to the absence of resistors is avoided by using an electronic device able to store the energy of the pulses. An unexpected half cycle was detected (García et al., 2007). This effect also appears as an extra semi cycle in Figs. 8 and 9. The similarity between Figs. 9 and 11 is indeed evident, supporting the thesis that, either with a matched resistor or with a not
yet existing special electronic device, the outcome of the lumped resistors can be achieved, in an efficient and easier way. As a geophysical application, based on Eq. (3) it is possible to simulate an antenna located between two half spaces by setting the correct permittivity and permeability parameters. Fig. 12 shows the situation when the radar is located over an ice body, meaning that one half space (the lower one) is ice and the other (the upper one) is air. Because the permittivity of ice is about three times larger than that of air, the propagation of the radar signal in ice is nearly half the speed in air, producing a flatter radiation pattern. The unexpected new radiation waveform previously mentioned is clearly detectable. Fig. 13 shows a new semi cycle which appears after
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Fig. 9. Simulated field in a dipole antenna with the new pattern: (from left to right) a) pulses start to travel b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
the monocycle. This mean that the signal radiated has a time width one and half times larger than the expected one (see Fig. 8). 5. Measurements In order to seek experimental evidence to confirm both the theoretical and the quantitative conjectures, an experiment was designed. A special radar transmitter was constructed with the ability of operating with extremely fast MOSFET switches. Fig. 14 shows a sketch of the impulse transmitter, based on the rapid discharge of two capacitors. A matched resistor was used in order to prevent extra ringing. A thin wire dipole of 45 m long was used, fed by the impulse transmitter. A Fluke 196B oscilloscope was used as receiver, located 25 m apart from its centre and perpendicular to the antenna axis, connected to a small antenna 3 m long, oriented parallel to the transmitting antenna. The idea is that this small antenna acting as a “probe” together with the oscilloscope, records the axial component of the electromagnetic field.
Fig. 10. Geometry involved in the delayed potentials.
Fig. 14 shows a simple sketch of one pulser of the impulse transmitter. This pulser operates with another pulser in anti-phase – positive and negative – configuration, connecting each pulser to a dipole arm, therefore doubling the amount of energy delivered to the dipole. The circuit sketch works as follows. In each pulser, the switches are implemented by four MOSFETS (STP4N150), which allow the two capacitor banks to discharge in a series connection into the antenna arms. The normal operation is as follows: - The four MOSFETS are normally in a non conduction state. - A positive low voltage pulse is applied into their gate-source terminals turning them on. This is achieved theoretically in no more than 65 ns. - The positive low voltage pulse width (which goes from 50 ns to more than 1 μs) controls the time the MOSFETS are closed and at the same time controls the discharge time of the capacitors banks. - After the positive low voltage pulse finishes a negative low voltage pulse starts forcing the opening of the MOSFETS, which is achieved in no more than 90 ns. The capacitors C1 and C2 are charged through resistors R1 and, R2 and R3, respectively. Each capacitor is charged up to the high voltage source level and after the trigger – POS and NEG CONTROL – acts on the MOSFET, they are discharged into one arm of the dipole. The configuration of two anti-phase pulsers allows a balanced energising, but conceptually it could be implemented by only one pulser. After the positive low voltage pulse, a negative one is applied in order to force the MOSFET closing. In particular the STP4N150 MOSFET has less than 7 Ω between drain and source during the switch-on stage, being typically 5 Ω, and an output capacitance of 120 pF. No substantial interference is produced by the MOSFET switches due to their non ideal behaviour. Fig. 15 shows the received waveform after performing an experiment, which agrees closely with the expected waveform as shown in Fig. 8. While the waveforms are similar, especially the non ringing nature, with the same number of semi-cycles and the quick subsequent dampening to zero level, the time scale are different, being severely affected by the contrasting environments, one in free space and the other over a non conducting surface corresponding to a paved parking ground at the Navy air base of Punta Arenas, Chile. The
382 G. Garcia et al. / Journal of Applied Geophysics 67 (2009) 374–385 Fig. 11. Electric field around an antenna with no lumped resistors, using a charge-capturing device: a) charges moving outward b) charges reaching the outer ends of the dipole c) charges returning to the inner ends d) charges stored in the transmitter.
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383
Fig. 12. Electric field around an antenna without resistors located between two half spaces.
red fraction in Fig. 15 corresponds to part of the discharge time. Approximately at 400 ns the returning charges start arriving to the transmitter and tend to recharge the capacitors. At 500 ns the switches are opened, and the remaining pulse, which has not yet charged the capacitors, feeds the matched resistor. 6. Concluding remarks A new method to avoid antenna ringing without the use of Wu and King lumped resistors has been analysed. The goal of the new technique is to either store the energy of the electric pulses, which are otherwise
responsible for the extra oscillations, or damp them through one resistor matched to the electric characteristics of the dipole. Both methods achieve a short and more symmetrical transmitted waveform. The modified transmission line model for a dipole antenna demonstrated to be a useful tool for visualizing qualitatively the wave propagation around the antenna. The delayed potentials allowed computing the electromagnetic fields, with practical advantages over the traditional Maxwell equations, achieving good coincidences with the traditional electromagnetic algorithms. Future experimental testing is necessary in order to improve and test further this new technique.
Fig. 13. Unexpected radiations.
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Fig. 14. Circuit sketch of the impulse transmitter.
Fig. 15. Received waveform after performing an experiment with the impulse transmitter and dipole antenna mentioned in the text.
G. Garcia et al. / Journal of Applied Geophysics 67 (2009) 374–385
Acknowledgements This study is part of the SIRAHT (Airborne Radar System for Temperate Ice) project, funded jointly by Armada de Chile and Centro de Estudios Científicos (CECS), and partly sponsored by the Ministry of Defence of Chile. The Centro de Estudios Científicos (CECS) is funded by the Chilean Government through the Millennium Science Initiative and the Centers of Excellence Base Financing Program of CONICYT. CECS is also supported by a group of private companies which at present includes Antofagasta Minerals, Arauco, Empresas CMPC, Indura, Naviera Ultragas and Telefónica del Sur. References Cardama, A., Jofre, L., Ruiz, J., Romeo, J., Blanch, S., Ferrando, M., 2002. Antenas 2° Ed. UPC Editions, Barcelona, España.
385
Chen, C., 2006. GPR antenna design. 11th International Conference on Ground Penetrating Radar Short Course. OHIO, USA. García, B., 2005. Electrodinámica. Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, España. García, G., Casassa, G., Ulloa, D., Zamora, R., 2007. Analysis of a non electrical resistive GPR antenna. 4th International Workshop on Advanced Ground Penetrating Radar, Naples, Italy. Kappen, F., Mönich, C., 1987. Single pulse radiation from a resistive coated dipole antenna. Proc. IEE Fifth Int. Conf. on Antennas and Propagation, ICAP' 87, pp. 90–93. Publ. 274, York, UK. Wu, T., King, R., 1965. The cylindrical antenna with non-reflecting resistive loading. IEEE Trans. Antennas and Propagation 13, 396-373.
Contents lists available at ScienceDirect
Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / j a p p g e o
Theoretical analysis and simulation for avoiding antenna oscillations without distributed resistance Gonzalo Garcia a,b,⁎, José A. Uribe b, David Ulloa b, Rodrigo Zamora b, Gino Casassa b a b
Dirección de Programas, Investigación y Desarrollo de la Armada de Chile, General del Canto398, Playa Ancha, Valparaíso, Chile Centro de Estudios Científicos, Arturo Prat 514, Valdivia, Chile
a r t i c l e
i n f o
Article history: Received 31 October 2007 Accepted 25 September 2008 Keywords: Impulse radar Transmission line Dipole antenna Electromagnetic equations
a b s t r a c t The so-called Wu and King antenna pattern is widely used in GPR because of its simple design and construction features. The main disadvantage is its limited efficiency due to transmitter energy losses which occur through lumped resistors. Based on the analysis of the electromagnetic field behaviour across the antenna, it is possible to replace the effect of the resistors by either storing the energy of the electric pulses, or damp them by means of one matched resistor, which will theoretically improve the efficiency of the antenna. In this paper we provide a theoretical analysis using a modified transmission line model together with simulation based on delayed potentials among other electromagnetic software, and measurement results using an impulse transmitter with fast MOSFET switches and a matched resistor that support this idea. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Analysis of a simple dipole antenna with no resistors
The task of an impulse radar antenna, as is true for any antenna, is to transfer the energy delivered by the transmitter into the target medium in the most efficient way. Based on electromagnetic theory, this can be done with a simple dipole, which has the limitation that it works best only for narrow band signals. In order to radiate a broad band signal efficiently, it is necessary to modify the dipole antenna. This has been traditionally done by means of a lumped resistive pattern based on a logarithmic model, derived originally by Wu and King (1965). The antenna resistors gradually reduce the energy of the positive and negative electric pulses, as they progress from the centre of the dipole to its ends. The underlying idea is to let the pulses reach the outer part of the dipoles with minimal energy, allowing to radiate only one or one and a half monocycles. If the goal of radiating only one or one and a half monocycle can be achieved by another means, which can minimize energy losses and simplify the antenna design, this will result as well in a large improvement of the efficiency of the radar system. This paper proposes a theoretical approach based on several simulation algorithms and some basic measurements that allow the removal of the resistors without adding extra ringing.
A dipole can be considered as a modified transmission line, which retains the physical behaviour of the antenna. The transmission line equations (Eq. (1)) correspond to the one-dimensional wave equation, meaning that any waveform inserted into the inner terminals (at z =z1) will then propagate through the line toward the outer terminals, with a speed given as a function of the intrinsic parameters of the line:
⁎ Corresponding author. Dirección de Programas, Investigación y Desarrollo de la Armada de Chile, General del Canto398, Playa Ancha, Valparaíso, Chile. Tel.: +56 32 2529683; fax: +56 32 2963438. E-mail address: [email protected] (G. Garcia). 0926-9851/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jappgeo.2008.09.014
∂2 ∂2 X ðz; t Þ = LC 2 X ðz; t Þ; 2 ∂z ∂t
ð1Þ
where X(z,t) = V(z,t) or I(z,t) are the voltage or current waveforms developed in the line, and L and C are the distributed inductance and capacitance parameters, respectively. In this case both intrinsic parameters L and C are normally constant along the line. As shown in Fig. 1, together with the voltage and current travelling waves, an electric field signal – also a magnetic signal, not shown – Ē(z,t) propagates as well, which is indeed the real physical entity together with the electric charges that travels along the antenna at the same speed, which is a function of the intrinsic parameters. This electric field, in this case extending perpendicular to the transmission lines, is the crucial phenomenon when analysing the dipole as a transmission line with open arms. Not considering the natural losses associated to the ohmnic impedance of the line cables, but taking into account the constant distance between these lines, it can be assumed that the shape and energy of the signals remain constant. Thus the electric and magnetic fields generated between the electric charges do not change within the transmission line.
G. Garcia et al. / Journal of Applied Geophysics 67 (2009) 374–385
Fig. 1. Signals in a normal transmission line.
This effect is no longer valid in a dipole, simply because the distance between the charges is continuously changing, demanding continuous delivery of energy to expand the electromagnetic field, energy which is taken from the kinetic energy of the charges. This physical effect can be mathematically expressed through the nonconstant intrinsic parameters of the distributed capacitance C(z) and inductance L(z) (see Eq. (2) and Fig. 2), where E(r,t) is now a function of the spatial vector r ̄ = (x,z). ∂2 ∂2 X ðz; t Þ = LðzÞC ðzÞ 2 X ðz; t Þ ∂z2 ∂t
ð2Þ
Based on the transmission line model, and taking into account that the speed of the electric field lines in a nearly perfect electric conductor is comparable to the speed of light in free space, and assuming that the transmitter has a high conductivity, the following temporal sequence (Fig. 3a, b, c and d) shows how the electric field should propagate around an antenna without lumped resistors. A simulation, based on an electromagnetic software, was run to confirm the expected physical behaviour. A wire dipole located in free space, and excited by a pulsed voltage was tested. Fig. 4 (a, b, c, and d) shows the results, which closely agree with the transmission line model. The outer ends of the dipoles act as an open circuit and the inner ends act as a closed one. According to transmission line theory, both ends react as perfect reflectors, as it can be seen in Figs. 3 and 4. The outer ends reflect the signal without changing the sign, and due to low voltage source impedance the inner ends reflect the signal changing its polarity. This behaviour implies a high level of oscillation, and the decay observed in real antennae is attributable to the ohmnic losses and the energy delivered to propagate the electromagnetic field. For GPR antennae it is common to locate the pulse circuit at the dipole centre, so the distance between the generation and the feeding point is not significant for our analysis. This condition was adopted in our simulations and implemented in our measurements.
accepting no more than one or one and a half monocycles, depending on the environment and the specific application requirements. As Kappen and Mönich (1987) illustrate, charge pulses start losing energy while they are travelling through the arms of the antenna, presenting an evident dispersion effect smeared over the antenna's length, affecting the second half of the first monocycle, resulting in a non-symmetrical cycle. Therefore the electric charges return to the inner ends of the antenna with very low energy, through a recombination process and producing no new reflections. Most of all the lost energy is dissipated into the resistors by means of heat. Thus the Wu and King antennae have a relatively low efficiency. As could be seen from the former section, the electric field lines, as electrostatic theory claims, start attached to the electric charges. While the charge pulses travel outward within the antenna, the electric field spreads outwards through the surrounding space, describing a circular curve pattern in a planar representation or a spherical shape in space. After these charges reflect at the outer ends of the dipoles and start travelling to the inner ends, the electric field lines cannot immediately follow the charges, which now are moving in an opposite direction behind the lines, at an almost similar speed, describing an umbrella-shaped curve. Finally, when both charge pulses with opposite polarity meet at the centre of the antenna, a zero net charge is produced, forcing the extended electric field lines to close onto themselves and detaching from the sources. At this very moment an electromagnetic field is radiated. After the charges meet at the centre of the antenna, they cross the transmitter due to its low impedance, exiting into the other arm of the dipole, which can be understood as a reflection with polarity change. This new charge departure is the beginning of a new monocycle that will follow the first one already generated. The core idea in implementing a dipole antenna with no resistors is that if it is possible, by some means, to capture this electric charge which represents electric energy, thus avoiding the new charge departure from the inner part of the antenna, the extra oscillations will be cancelled. Moreover, if this electric charge could be reused in the following radiation process, the overall efficiency would increase. Figs. 5 (a and b) and 6 show the results of a simulation, based on an electromagnetic software, using two similar 35 meter-long dipoles –
3. The Wu and King antenna Based on the physical behaviour of the dipole with no resistors, we can analyse the electric field of a Wu and King (1965) antenna in a qualitative manner. Any Wu and King antenna or a derived one rely their design on a resistively lumped pattern following a logarithmic curve. The core idea is to diminish the energy of the electric pulses, decreasing thus the electric current density so no further reflections will occur,
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Fig. 2. Signals in a modified transmission line.
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Fig. 3. Expected field in a dipole antenna with no resistors. a) pulses start to propagate b) pulses reaching the outer ends c) pulses travel backwards. d) pulses cross the transmitter.
without and with Wu and King resistive pattern – located in free space, and excited by a Gaussian voltage pulse of a duration of 200 [nanoseconds]. Fig. 5 shows a comparison between these two similar antennas, concerning the electric current signal in the feeding side and the radiated electric far field, calculated in the perpendicular radial plane at a distance of 55 m. This comparison highlights the effect of the Wu and King pattern effect, which diminishes the ringing while reducing the overall efficiency.
Fig. 6 shows the entire electric field evolution around a Wu and King antenna. It is interesting to compare this sequence with Fig. 4. and appreciate the differences, especially in the last stage (d). 4. Proposed physical solution The idea of a new antenna design is to achieve a similar damping effect as the lumped resistors, but wasting less energy, in order to radiate a wide band signal, that is, a signal composed of one or one and
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Fig. 4. Simulated field in a dipole antenna with no resistors:(from left to right) a) pulses start to propagate b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
a half monocycles. The pulse energy would be taken from the returning charges and stored for later use. It is usual that impulse radar transmitters use capacitors of high capacitance to store energy, which is discharged extremely fast into the antennae, after a trigger signal. Working with fast switches should allow to connect and disconnect the transmitter from the antenna, in order to deliver the electric charge and subsequently storing it, thus avoiding a new reflection. Given the behaviour of a capacitor connected to a transmission line, it should be expected that the returning current pulse will tend to charge the capacitor again in an exponential mode. This simple effect accomplishes the main requirement, that is, it captures the energy from the pulse and stores it back into the capacitor (García et al., 2007). This could be achieved by controlling the switches, not only closing them at a desired instant, but opening them at another specific moment as well. The switch control should be realized by some electronic device taking into account the physical dimensions of the antenna and the electric characteristic of the capacitors, in order to calculate the precise closing and opening times. The switches must be reopened considering the two-way travel time of the charges, which is directly related to the length of the dipole arms, and the effective pulse width of the capacitor discharge. This time could be estimated but ideally should be measured to find its optimal value. The idea is that after the capacitors are discharged, they remain open waiting for the charges to return. After reaching their highest recharge voltage they should be reopened. This proposal strongly relies on the returning pulse shape. For an optimal performance the returning pulse should have an increasing shape or at least a nearly rectangular shape – but never a decreasing shape – in order to have an increasing charging function. In simple words, the pulse amplitude must always be higher than the charge voltage to keep the charges together. If this is not accomplished part of the previously stored charges should start repulsing each other and discharge the capacitor before the pulse is completely received, due to the inability of the remaining part of the pulse to continue charging the capacitor. If this requirement is not fulfilled, the formerly stored charges will produce antenna ringing thus radiating a longer signal than expected.
A new approach is developed here in order to avoid this effect, but seeking the same objective of radiating a symmetric wide band signal. Following the study of the dipole as a modified transmission line, the idea is to search for a replacement of the capacitor the moment the charge pulse returns to the transmitter. This solution seeks an independence from the returning pulse shape. In order to avoid undesired reflections in the transmitter and having in mind the similar behavior with respect to a transmission line, the inner terminal of the antenna should be temporarily terminated with a resistance with the same value of the characteristic impedance, that is the inner voltage to current ratio. This matching will optimize the power transfer, transferring all the energy to this resistor, and avoiding reflections as it occurs in any transmission line. This new solution will not attain the objective of saving energy, but at least will assure a more symmetrical radiated pulse shape with a length similar than the one obtained with a Wu and King pattern, but with a simpler pattern design. The solution only needs to electrically connect a predetermined – matched – resistor R between the inner terminals of the dipole before the returning pulse arrives, by the action of rapid switches Sw which disconnect the electric source V. This action will simply terminate the inner dipole – seen as a transmission line – avoiding any reflections. The solution is sketched in Fig. 7. To prove the effectiveness of this solution, an electromagnetic simulation was run comparing a Wu and King antenna with this new design. Two 35 meter dipoles located in free space were excited by a voltage Gaussian pulse. Due to a technical limitation of the software, the resistor between the inner ends of the dipole was connected during the entire simulation, and the voltage source was replaced by an equivalent current source. This simulation limitation has the disadvantage that it consumes half of the available power at the feeding stage, when the transmitter splits the energy into the dipole and the resistor as well — of similar ohmic value. This should be avoided using an adequate device with fast switches. In order to design the optimal resistance value placed between the inner terminals, the ratio between the voltage and the induced current
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Fig. 5. Signals without and with Wu and King resistive pattern: a) electric current b) electric far field.
signals was calculated, based on the same simulation model. In this particular design a 686 Ω value was found. Figs. 8 and 9 show the results. The first one compares the electric current developed in the inner terminals of both designs together with the electric far field, and the last figure shows the evolution of the entire electric field into the surrounding space of the new solution. Assuming that the disconnection of the resistors at the feeding stage is possible to implement, it is important to emphasize that the use of this resistor will prevent from saving the returning energy for future pulses. It is also important to stress that if this resistor can be replaced by another active device, which can present a resistive behavior and at the same time can capture the energy instead of
burning it, the objective of saving energy will be accomplished as well. Considering the technical limitation of energy saving, the following section will attempt to visualize the phenomenon occurring when a theoretical electronic device is able to capture the incoming charges and prevent extra ringing, but without burning the power into a matched resistor. For this purpose a straightforward simulation algorithm is performed, based on the calculations of the Maxwell equations in their integral form. The starting point for any simulation is to formulate the electromagnetic equations. Knowing the environmental parameters and the sources, it is possible to calculate the electromagnetic fields in the
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Fig. 6. Simulated field in a dipole antenna with Wu and King pattern resistors: (from left to right) a) pulses start to propagate b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
space–time continuum. In order to avoid numerical errors, it is preferable to use integral equations rather than differential ones. With this in mind, the following equations (Eq. (3)), the socalled delayed electromagnetic potentials, as an exact derivation from the differential form of the electromagnetic equation set (Cardama et al., 2002), are formulated in an integral form:
Φð⇀ r; t Þ = ∫v′
j⇀ r −⇀ r ′j ρ ⇀ r ′; t − s
dv′ 4πɛ j ⇀ r−⇀ r′j j⇀ r −⇀ r ′j ⇀ μJ ⇀ r ′; t − s ⇀⇀ Að r ; t Þ = ∫v′ dv′ 4π j ⇀ r −⇀ r′j
ð3Þ
Where ϕ(r ̄ ,t) and Ā(r ̄ ,t) are the electric scalar and magnetic vector delayed potentials, evaluated at the space–time point (r ̄ ,t). The electric ̄ ′̄ ,t′) and the charge density ρ(r ′̄ ,t′) are the sources current density J (r within the antenna at the space–time point (r ′̄ ,t′) (see Fig. 10 where a new spatial dimension was added). For the sources, t′ =t − |r −r′| /c is the retarded time and r′ the retarded position. The following remarks can be made concerning the equations of the potentials (Eq. (3)). The potentials depend linearly with respect to the sources, simplifying the algorithm. The permittivity and permeability of the surrounding medium, ε(r ̄) and μ(r ̄), respectively, allows the algorithm to simulate any kind of environment, like two half spaces. Lastly, it is possible to discretise the integrals, performing the
calculation for point-like sources as a summation of effects, but in that case it must be taken into account that this manipulation will transform the equations into the so-called Liénard–Wiechert potentials (García, 2005), which describe the complete, relativistically correct, time-varying electromagnetic field for a point-charge. The speed at which the potentials travel through space will be a function of the permittivity and permeability of the medium, s(ε,μ). Starting from the delayed potentials, it is possible to obtain in a direct way the electromagnetic fields Ē(r ̄ ,t) and B̄(r ̄ ,t) (electric and magnetic field, respectively) at any point in the space–time surrounding the antenna. For this the following expressions (Eq. (4)) are used: ⇀ ∂ A ð⇀ r ; tÞ r ; t Þ = − ∇ϕðr; t Þ − E ð⇀ ∂t ⇀ Bð⇀ r ; t Þ = ∇ × A ð⇀ r ; tÞ
ð4Þ
The following Fig. 11 (a, b, c and d) is the result of a simulation which allows to check the effects presented above. The fields will be shown in a three dimensional sketch, using the third coordinate (vertical) as the amplitude of the field (with an exponential modification), in a specific two-dimensional point (horizontal). A 6 [m] long dipole, without lumped or matched resistors, was chosen. The charge pulse has a nearly Gaussian shape, with a spatial width of 90 [cm], meaning that the exciting signal has already dropped to zero when each pulse reaches the antenna ends. This is not the normal condition, and has only been used for drawing purposes.
Fig. 7. Electric circuit sketch of the solution.
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Fig. 8. Signals with the new antenna pattern and with the Wu and King pattern: a) electric current b) electric far field.
Usually the pulse width is directly related to the length of the antenna (Chen, 2006). Each division of the grid is 15 [cm] and 60 [ns]. In order to capture the pulse energy, a theoretical electronic device was considered for accumulating the electrical charges as these reach the inner ends of the antenna. Observing Fig. 11d, it is evident that the extra ringing due to the absence of resistors is avoided by using an electronic device able to store the energy of the pulses. An unexpected half cycle was detected (García et al., 2007). This effect also appears as an extra semi cycle in Figs. 8 and 9. The similarity between Figs. 9 and 11 is indeed evident, supporting the thesis that, either with a matched resistor or with a not
yet existing special electronic device, the outcome of the lumped resistors can be achieved, in an efficient and easier way. As a geophysical application, based on Eq. (3) it is possible to simulate an antenna located between two half spaces by setting the correct permittivity and permeability parameters. Fig. 12 shows the situation when the radar is located over an ice body, meaning that one half space (the lower one) is ice and the other (the upper one) is air. Because the permittivity of ice is about three times larger than that of air, the propagation of the radar signal in ice is nearly half the speed in air, producing a flatter radiation pattern. The unexpected new radiation waveform previously mentioned is clearly detectable. Fig. 13 shows a new semi cycle which appears after
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Fig. 9. Simulated field in a dipole antenna with the new pattern: (from left to right) a) pulses start to travel b) pulses reach the outer ends c) pulses travel backwards d) pulses cross the transmitter.
the monocycle. This mean that the signal radiated has a time width one and half times larger than the expected one (see Fig. 8). 5. Measurements In order to seek experimental evidence to confirm both the theoretical and the quantitative conjectures, an experiment was designed. A special radar transmitter was constructed with the ability of operating with extremely fast MOSFET switches. Fig. 14 shows a sketch of the impulse transmitter, based on the rapid discharge of two capacitors. A matched resistor was used in order to prevent extra ringing. A thin wire dipole of 45 m long was used, fed by the impulse transmitter. A Fluke 196B oscilloscope was used as receiver, located 25 m apart from its centre and perpendicular to the antenna axis, connected to a small antenna 3 m long, oriented parallel to the transmitting antenna. The idea is that this small antenna acting as a “probe” together with the oscilloscope, records the axial component of the electromagnetic field.
Fig. 10. Geometry involved in the delayed potentials.
Fig. 14 shows a simple sketch of one pulser of the impulse transmitter. This pulser operates with another pulser in anti-phase – positive and negative – configuration, connecting each pulser to a dipole arm, therefore doubling the amount of energy delivered to the dipole. The circuit sketch works as follows. In each pulser, the switches are implemented by four MOSFETS (STP4N150), which allow the two capacitor banks to discharge in a series connection into the antenna arms. The normal operation is as follows: - The four MOSFETS are normally in a non conduction state. - A positive low voltage pulse is applied into their gate-source terminals turning them on. This is achieved theoretically in no more than 65 ns. - The positive low voltage pulse width (which goes from 50 ns to more than 1 μs) controls the time the MOSFETS are closed and at the same time controls the discharge time of the capacitors banks. - After the positive low voltage pulse finishes a negative low voltage pulse starts forcing the opening of the MOSFETS, which is achieved in no more than 90 ns. The capacitors C1 and C2 are charged through resistors R1 and, R2 and R3, respectively. Each capacitor is charged up to the high voltage source level and after the trigger – POS and NEG CONTROL – acts on the MOSFET, they are discharged into one arm of the dipole. The configuration of two anti-phase pulsers allows a balanced energising, but conceptually it could be implemented by only one pulser. After the positive low voltage pulse, a negative one is applied in order to force the MOSFET closing. In particular the STP4N150 MOSFET has less than 7 Ω between drain and source during the switch-on stage, being typically 5 Ω, and an output capacitance of 120 pF. No substantial interference is produced by the MOSFET switches due to their non ideal behaviour. Fig. 15 shows the received waveform after performing an experiment, which agrees closely with the expected waveform as shown in Fig. 8. While the waveforms are similar, especially the non ringing nature, with the same number of semi-cycles and the quick subsequent dampening to zero level, the time scale are different, being severely affected by the contrasting environments, one in free space and the other over a non conducting surface corresponding to a paved parking ground at the Navy air base of Punta Arenas, Chile. The
382 G. Garcia et al. / Journal of Applied Geophysics 67 (2009) 374–385 Fig. 11. Electric field around an antenna with no lumped resistors, using a charge-capturing device: a) charges moving outward b) charges reaching the outer ends of the dipole c) charges returning to the inner ends d) charges stored in the transmitter.
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Fig. 12. Electric field around an antenna without resistors located between two half spaces.
red fraction in Fig. 15 corresponds to part of the discharge time. Approximately at 400 ns the returning charges start arriving to the transmitter and tend to recharge the capacitors. At 500 ns the switches are opened, and the remaining pulse, which has not yet charged the capacitors, feeds the matched resistor. 6. Concluding remarks A new method to avoid antenna ringing without the use of Wu and King lumped resistors has been analysed. The goal of the new technique is to either store the energy of the electric pulses, which are otherwise
responsible for the extra oscillations, or damp them through one resistor matched to the electric characteristics of the dipole. Both methods achieve a short and more symmetrical transmitted waveform. The modified transmission line model for a dipole antenna demonstrated to be a useful tool for visualizing qualitatively the wave propagation around the antenna. The delayed potentials allowed computing the electromagnetic fields, with practical advantages over the traditional Maxwell equations, achieving good coincidences with the traditional electromagnetic algorithms. Future experimental testing is necessary in order to improve and test further this new technique.
Fig. 13. Unexpected radiations.
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Fig. 14. Circuit sketch of the impulse transmitter.
Fig. 15. Received waveform after performing an experiment with the impulse transmitter and dipole antenna mentioned in the text.
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Acknowledgements This study is part of the SIRAHT (Airborne Radar System for Temperate Ice) project, funded jointly by Armada de Chile and Centro de Estudios Científicos (CECS), and partly sponsored by the Ministry of Defence of Chile. The Centro de Estudios Científicos (CECS) is funded by the Chilean Government through the Millennium Science Initiative and the Centers of Excellence Base Financing Program of CONICYT. CECS is also supported by a group of private companies which at present includes Antofagasta Minerals, Arauco, Empresas CMPC, Indura, Naviera Ultragas and Telefónica del Sur. References Cardama, A., Jofre, L., Ruiz, J., Romeo, J., Blanch, S., Ferrando, M., 2002. Antenas 2° Ed. UPC Editions, Barcelona, España.
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Chen, C., 2006. GPR antenna design. 11th International Conference on Ground Penetrating Radar Short Course. OHIO, USA. García, B., 2005. Electrodinámica. Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, España. García, G., Casassa, G., Ulloa, D., Zamora, R., 2007. Analysis of a non electrical resistive GPR antenna. 4th International Workshop on Advanced Ground Penetrating Radar, Naples, Italy. Kappen, F., Mönich, C., 1987. Single pulse radiation from a resistive coated dipole antenna. Proc. IEE Fifth Int. Conf. on Antennas and Propagation, ICAP' 87, pp. 90–93. Publ. 274, York, UK. Wu, T., King, R., 1965. The cylindrical antenna with non-reflecting resistive loading. IEEE Trans. Antennas and Propagation 13, 396-373.