## 1 Introduction
### Deduction for Space 2
However, the result of \(i_{R1}\ =\ 2\left(1-\frac{D}{x}\right)\cdot i_{F1}\) in Equation (4) is valid only when the spatial position between T and N is symmetrical with the spatial position between N and F and the self-impedance of T is equal to the self-impedance of F. The aforementioned deduced values of \(k_{1}{{}^{\prime}},k_{2}{{}^{\prime}}\)... \(k_{20}{{}^{\prime}},Z_{1}{{}^{\prime}}\) and \(Z_{2}{{}^{\prime}}\) are inaccurate and they can only be regarded as initial results. According to the transformer radio transformer of AT in Space 2, the voltage drop between T and N, i.e., \(u\) in Figure 4 should be equal to the voltage drop between N and F, i.e., \(u^{\prime}\) in Figure 4.  
\[u=u^{\prime} \tag{16}\]  
For the \(\left\{ \begin{array}{c}u\ =\ Z_{1}^{\prime}\cdot i_{T1}\cdot x\\ u^{\prime}\ =\ Z_{1}\cdot i_{T2}\cdot(D-x)+\frac{Z_{2}\cdot i_{T2}\cdot(D-x)}{2}+ \frac{Z_{2}\cdot i_{T1}\cdot x}{2}\end{array} \right.\) in Figure 4, the values of \(Z_{1}\) and \(Z_{2}\) have been obtained after introducing the \(i_{R2}\) = \(2i_{F1}\) of Equation (4) into the inductance matrix of Space 1; the values of \(Z_{1}{{}^{\prime}}\) and \(Z_{2}{{}^{\prime}}\) have been obtained after introducing the \(i_{R1}\ =\ 2\left(\frac{D}{x}-1\right)\cdot i_{F1}\) of Equation (4) into the inductance matrix of Space 2. According to Equation (4) and the circuit of the AT system, the relation of \(i_{T1}\), \(i_{T2}\), \(i_{F1}\) satisfies  
\[\left\{ \begin{array}{c}i_{T1}\ =\ \left(\frac{2D}{x}-1\right)\cdot i_{F1}\\ i_{T2}\ =\ i_{F1}\end{array} \right. \tag{17}\]  
Figure 4: Segment loop circuit network separated by load. By introducing Equation (17) into \(\left\{ \begin{array}{l}u\ =\ Z_{1}^{\prime}\cdot i_{T1}\cdot x\\ u^{\prime}\ =\ Z_{1}\cdot i_{T2}\cdot(D-x)+\frac{Z_{2}\cdot i_{T3}\cdot(D-x)}{2}+\frac{Z_{ 2}^{\prime}\cdot i_{T1}\cdot x}{2}\end{array} \right.\), determining \(x=x_{0}\) (according to the location of load) and setting \(i_{F1}\) as an arbitrary constant of \(c\), it can be found that  
\[\left\{ \begin{array}{l}u\ =\ (2D-x_{0})\cdot c\cdot Z_{1}^{\prime}\\ u^{\prime}\ =\ c\cdot Z_{1}\cdot(D-x_{0})+\frac{Z_{2}\cdot c\cdot(D-x_{0})}{2}+\frac{Z_{ 2}^{\prime}\cdot(2D-x_{0})\cdot c}{2}\end{array} \right. \tag{18}\]  
In Equation (18), \(u\) and \(u^{\prime}\) are always unequal for the reason that the granted results of \(i_{R1}\ =\ 2\Big{(}1-\frac{D}{x}\Big{)}\cdot i_{F1}\) are valid only as an approximation. In order to obtain exact results, an iterative calculation method aimed at satisfying the constraint condition of Equation (16) is proposed, as demonstrated in Figure 5.  
In the beginning, the \(i_{R1}/i_{F1}\) is adjusted to deduce new values of \(k_{1}{}^{\prime},k_{2}{}^{\prime}\...\ k_{20}{}^{\prime},Z_{1}{}^{\prime}\) and \(Z_{2}{}^{\prime}\). On this basis, new \(u\) and \(u^{\prime}\) are obtained after introducing new \(i_{T1}/i_{T2}\) and new values of \(Z_{1}{}^{\prime}\) and \(Z_{2}{}^{\prime}\) into \(\left\{ \begin{array}{l}u\ =\ Z_{1}^{\prime}\cdot i_{T1}\cdot x_{0}\\ u^{\prime}\ =\ Z_{1}\cdot i_{T2}\cdot(D-x_{0})+\frac{Z_{2}\cdot i_{T2}\cdot(D-x_{0})}{2} +\frac{Z_{2}^{\prime}\cdot i_{T1}\cdot x_{0}}{2}\end{array} \right..\) If \(u=u^{\prime}\) is still not satisfied, \(i_{R1}/i_{F1}\) continues to be adjusted and corresponding calculation is repeated again. Only when \(u\) nearly approximates to \(u^{\prime}\) are the deduced values of \(k_{1}{}^{\prime}\), \(k_{2}{}^{\prime}\...\ k_{20}{}^{\prime}\), \(Z_{1}{}^{\prime}\) and \(Z_{2}{}^{\prime}\) considered as final and accurate results for Space 2. When the final and accurate values of \(Z_{1}{}^{\prime}\) and \(Z_{2}{}^{\prime}\) are determined, the impedance of circuit 1 in Figure 4 (marked as \(Z_{a}\)) and the impedance of circuit 2 in Figure 4 (marked as \(Z_{b}\)) are, respectively, calculated by Equations (19) and (20).