## 2 Radiated Coupling and Active Noise Cancellation  
In an electronic warfare environment, the externally intended attack reaches a major friendly facility through the atmosphere. A High-altitude Electromagnetic Pulse (HEMP) or jammer attacks occur at relatively long distances (hundreds of kilometers), and the victims are attacked using plane waves. This attack has a wide frequency characteristic, the strongest of which is at the resonant frequency, which is most affected by the size of the structure of the protective installation. Figure 1 shows the various coupling paths in the electronic warfare environment. This attack affects friendly protection facilities, mainly metal resonators, and the size of the protection facilities determines the resonant frequency. In general, the resonance frequency of an ideal resonator without an aperture is expressed by Equation (1). \[f_{r}^{mnp}=\frac{1}{2\pi\sqrt{\mu\varepsilon}}\sqrt{\left(\frac{m\pi}{a} \right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{p\pi}{c}\right)^{2}} \tag{1}\]  
where \(\mu\) is the permeability, \(\varepsilon\) is the permittivity, \(a\) is the width of the resonator, \(b\) is the length, and \(c\) is the height. \(m\) is a mode number for the resonator transverse axis, \(n\) is a mode number for the longitudinal axis, and \(p\) is a mode number for the height axis. This mode number is the Transverse Electric (TE) mode where \(m\) and \(n\) are integers starting from zero, and \(p\) is an integer starting from one. In the Transverse Magnetic (TM) mode, \(m\) and \(n\) are integers starting at one, and \(p\) is an integer starting at zero. When apertures exist for this resonator for various reasons, the quality factor \(Q\) is determined by the aperture size, which causes a slight shift in the resonant frequency. In the absence of an aperture, one of the most critical parameters of the resonator, \(Q\), is defined as  
\[Q\equiv\omega\frac{W_{t}}{P_{d}}=\omega\frac{W_{e}+W_{m}}{P_{d}} \tag{2}\]  
where \(\omega\) is the angular frequency, \(W_{t}\) is the stored energy inside the cavity, \(P_{d}\) is the dissipated power, \(W_{e}\) is energy due to the electric field, and \(W_{m}\) is energy due to the magnetic field. Total dissipated power is found by adding power dissipated in each of the six walls of the cavity. The dissipated power on the top wall is similar to the bottom, and power on the right wall is like the left. Meanwhile, dissipated power on the back is the same as that on the front. Thus, the total dissipated power can be written by  
\[P_{d}=\frac{R_{s}}{2}\left\{2\iint_{bottom}\mathbf{J}_{b}\cdot\mathbf{J}_{b}^{ \ast}ds+2\iint_{left}\mathbf{J}_{l}\cdot\mathbf{J}_{l}^{\ast}ds+2\iint_{front} \mathbf{J}_{f}\cdot\mathbf{J}_{f}^{\ast}ds\right\}. \tag{3}\]  
where \(R_{s}\) is the surface resistance and \(\mathbf{J}_{b}\), \(\mathbf{J}_{l}\), and \(\mathbf{J}_{f}\) are the current density of bottom, left, and front wall, respectively. If there is an aperture in the resonator, the resulting loss occurs, and the overall \(Q\) value is determined through four mechanisms [15]. The first is caused by the current flowing through the inner  
Figure 1: Radiated coupling path in the electronic warfare environment. wall of the resonator. The internal absorber generates the second. The third is caused by antenna loss, and the last is caused by aperture loss. The total \(Q\) through these four mechanisms is determined by  
\[\frac{1}{Q}=\frac{1}{Q_{surf}}+\frac{1}{Q_{TCS}}+\frac{1}{Q_{ant}}+\frac{1}{Q_{ACS}} \tag{4}\]  
where \(Q_{surf}\) is the \(Q\) value determined by the wall surface, \(Q_{TCS}\) is the abbreviation for the Transmission Cross Section (TCS), and is determined while transmitting internally. \(Q_{ant}\) is the \(Q\) value determined by the antenna loss, and \(Q_{ACS}\) is determined by the abbreviation for the Aperture Cross Section (ACS). As you can see from the above Equation, the smallest \(Q\) value has the most significant effect on the total \(Q\) value.