In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.

The effects of high power electromagnetic (HPEM) sources on
electric and electronic systems have been the subject of many studies during
the last decades. Usually, the corresponding physical models focus on the
formulation and solution of electromagnetic boundary value problems. Most of
these models employ linear constitutive equations such that the usual methods
of classical electrodynamics can be used for their solution

Measurement setup to experimentally observe transient responses to HPEM field excitation: a metallic resonator is placed in an open waveguide which is excited by a transient electromagnetic field. The time domain response of a loop antenna within the resonator is measured via an outside feed by means of a digital oscilloscope.

Full-wave model representing the electromagnetic field coupling via
a horizontal slot into the resonator if placed into a wave guide. As
excitation a plane wave with its time dependency being determined by a
measured double-exponential pulse is applied. A quadratic loop antenna of
dimensions

It is the aim of this paper to supplement the obtained results by SPICE
circuit models and simulation. For this purpose, appropriate equivalent
circuit models are required. Such models can be derived based on classical
techniques such as the singularity expansion method

The paper is organized as follows: in the next Sect. 2 an equivalent circuit
model of the considered loop antenna in free space is derived. In Sect. 3 the
equivalent circuit model of the same loop antenna placed inside a resonator
is obtained with the help of a numerical full-wave model, as indicated in
Fig.

Thevenin equivalent of an antenna in receiving mode, according to

Quantities used for the full-wave modeling of the open circuit voltage in case of the antenna being in receiving mode.

In this section an explicit equivalent circuit model of the considered

The numerical computation of the input impedance is a standard procedure and,
in the present case, has been done using the Method of Moments (MoM),
utilizing two different solvers

Computed magnitude of the input impedance using two different
MoM-solvers

Computed phase of the input impedance using two different
MoM-solvers

With these values, the following circuit representation is obtained:
according to Fig.

Equivalent circuit of the loop antenna in free space.

Computed equivalent circuit element values of the loop antenna in free space.

Modeling of the nonlinearly loaded loop antenna in free space. The loop antenna becomes an electric dipole antenna if it is terminated by a nonlinear load opposite to the feed.

If the loop antenna is supplemented by a nonlinear load which is located
opposite to the feed then the linear part needs to be considered as an
electric dipole antenna, as illustrated in Fig.

Computed magnitude of the input admittance of the electric dipole
antenna using two different MoM-solvers

Similar to the previous case, at low frequencies one can determine the
capacitor

Computed phase of the input admittance of the electric dipole
antenna using two different MoM-solvers

Equivalent circuit of the nonlinearly loaded loop antenna in free
space. The representation of the diode follows the model of a realistic diode
which is implemented in the full-wave software that will be used in Sect. 4
for time domain computations

In this section modifications to the equivalent circuits are made that are
required if the loop antenna is placed inside a resonator. In this case the
existence of resonator modes will lead to additional resonances. Using the
full-wave solvers based on the MoM

Computed equivalent circuit element values of the electric dipole antenna in free space.

Computed equivalent circuit element values of the loop antenna inside the resonator.

Computed equivalent circuit element values of the electric dipole antenna inside the resonator.

Computed magnitude of the input impedance of the loop antenna placed
inside the resonator using two different MoM-solvers

Equivalent circuit of the loop antenna inside the resonator.

Computed magnitude of the input impedance of the dipole antenna
placed inside the resonator using two different MoM-solvers

Equivalent circuit of the nonlinearly loaded loop antenna inside the resonator.

Comparison of the computed voltage across the Schottky diode of the nonlinearly loaded loop antenna in free space. A nonlinear effect expressed by the rectification of the diode's voltage is captured well by both methods used.

Comparison of the computed voltage across the Schottky diode of the nonlinearly loaded loop antenna placed inside the resonator. The quantitative differences between both methods are larger if compared to the situation in free space.

It finally is investigated whether full-wave simulations

In this way the case of the nonlinearly loaded loop antenna in free space is
considered first. In Fig.

In this paper equivalent SPICE models of a nonlinearly loaded loop antenna in free space and inside a metallic resonator have been derived. It was shown that in comparison to full-wave models the equivalent circuit models ensure adequate simulation results and quick computation of the nonlinear effects in the system response induced by transient HPEM-fields.

The data presented in this article are available from the authors upon request.

The authors declare that they have no conflict of interest.

The authors would like to thank the Electromagnetic Effects and HPEM team at the Bundeswehr Research Institute for Protective Technologies and NBC Protection, Munster, Germany, for their hospitality and reliable support in the EMC laboratory. The research work was funded by the same institute with contract number E/E590/EZ018/CF162.

Edited by: Lars Ole Fichte Reviewed by: two anonymous referees