Fig. 5.3 Top-down process of quantitative EMC evaluation and design

(6) conduct joint commissioning test of EMC of subsystems/equipment, and optimize the integrated solution of the whole aircraft based on the test results; (7) perform the EMC test of the whole aircraft, and optimize its EMC. These seven steps provide a technical approach for EMC design from conceptual to detailed and then to physical design of the whole aircraft.

5.2 Solution Method for EMC Condition

Electromagnetic compatibility condition (EMC(s)) reflects the overall EMC status of aircraft after the equipment integration. EMC(s) is a metric of the contribution from EMC probability of the susceptive equipment, probability of fuel safety, and probability of personnel safety to the EMC of the whole aircraft system. It also reflects the importance of a different susceptive equipment, fuel, and personnel to the whole aircraft’s system. In the process of aircraft development, two models can be used to solve the system EMC(s): isolated model and serial and isolated mixed model [14].

ports, multiple cable ports, equivalent case shielding ports (including aperture coupling), and equivalent grounding port. For susceptive equipment, its EMC consists of multiple cable ports, equivalent shielding ports (including apertures, slots), and equivalent grounding ports. The safety of fuel system consists of the safety of multiple fuel susceptive points, and the personnel safety consists of the safety of multiple workstations. In the same equipment, these ports are mostly connected in series, which means that as long as one susceptive port is insecure, the probability of EMC of the equipment is 0. On the other hand, only if all the ports are safe, the EMC probability of the equipment will be equal to 1. Only a few backup ports with identical functions have a parallel relationship. The EMC probability of the series model is

where C jk (s) is the probability of safety of the k-th port of the j-th receiving equipment (or other susceptive equipment, fuel subsystem, or personnel subsystem) in the series model.

In addition, the probability of interference of the parallel model is defined as

where I jk (s) is the probability of interference at the k-th port of the j-th receiving equipment (or other susceptive equipment, fuel subsystem, or personnel subsystem) in the series model.

In engineering practice, the EMC probabilistic model of receiving equipment (or other susceptive equipment, fuel subsystems, or personnel subsystems) is usually a pure serial structure of susceptive ports. Some equipment may have backup ports, and the EMC probability becomes a series and parallel mixed structure. In the mixed model, the quantity of serial susceptive ports is much more than the number of parallel susceptive ports, and the parallel form is simpler. The EMC of the mixed model of the entire equipment can be derived from the physical meaning of (5.4)–(5.6).

2. Series-isolated mixed model

Many aircraft have integrated high-power emission equipment, which may interfere with the fuel system and control equipment of the aero engine. Therefore, it is necessary to consider the aircraft safety problems caused by EMC. In the seriesisolated mixed model for EMC prediction, the EMC condition of the whole aircraft is predicted by the probability of EMC condition of the engine control system, the

fuel system, and the equipment and personnel in a series manner, while the safety of receiving equipment, other susceptive equipment, and personnel is still isolated from each other. The EMC condition of the series-isolated mixed model of the whole aircraft in application is

EMC(s) CE (s) · CO (s) · CSW (s)

CE (s) · CO (s) · [W1C1(s) + W2C2(s) + W3C3(s) + · · · + Wn Cn (s)]

where CE (s) is the EMC probability of the engine; CO (s) is the probability of safety of the fuel system (determined by the probability of EMC of multiple fuel susceptive points in series); CSW (s) is the probability of safety of the receiving equipment, other susceptive equipment, and personnel (EMC probability). The value of CSW (s) is determined using an isolated model (receiving equipment, susceptive equipment other than the engine, operator subsystem which are defined as R1, R2, R3, . . . , Rn , respectively); W j , w j , and C j (s) are solved in the same way as before.

The safety of the aircraft engine and the fuel system must be guaranteed first, because poor safety of the engine and fuel is the major problems in EMC design. Therefore, the safety of the aircraft is emphasized in the series-isolated mixed model. Comparing the two prediction models for EMC condition, we think the latter one is more practical.

3. Determination of the probability of interference of subsystems

The probability of interference in the subsystem is related to the following factors: the full-power emission probability Pi(max) of the transmitting equipment, the probability of interference frequency between the susceptive equipment and the transmitting equipment Pi(jf ), the overlapping probability of the working time between the sus-

ceptive equipment and the transmitting equipment Pi(jt), etc.

The probability of a susceptible port can be determined using the following method. Firstly, the worst-case analysis method of EMC (assuming the full-power emission of the transmitting equipment and the most susceptive receiving of the receiving equipment) can be used to analyze whether the susceptive port is interfered. If it is, then the probability of being interfered by the transmitting equipment at the i-th susceptive port is

If the susceptive port is secure, the probability of the port being affected by the i-th transmitting equipment is

In Eqs. (5.8)–(5.11), Ii jk (s) is the value of the probability of interference at the k-th port of the j-th receiving equipment (or other susceptive equipment, fuel subsystem, or personnel subsystem) under the effect of the i-th transmitting equipment. Ci jk (s) is the safety probability of the k-th port of the j-th receiving equipment (or other susceptive equipment, fuel subsystem, or human subsystem) under the effect of the i-th transmitting equipment. ζk is the interference factor of the susceptive port derived from the worst-case EMC analysis method. If it is interfered, then ζk 1; if it is safe, then ζk 0; Pi(max) is probability of the maximum emission during the operation of the i-th transmitting equipment; Pi(jf ) is the combined probability of interference frequencies between the i-th transmitting equipment and the j-th susceptive equipment; Pi(jt) is the overlapping probability of working time between the i-th transmitting equipment and the j-th susceptive equipment.

Since the interference is not only generated in band, the interference frequency combination probability refers to the probability that the transmitting equipment and the susceptive equipment both operate in a frequency band that can generate interference (the frequencies of the two do not necessarily overlap or cover each other). The probability can be expressed as

usage of the N j -th frequency of susceptive equipment in the selected frequency band (Ni 1, 2, . . . , NR ); K Ni N j indicates whether the Ni -th frequency of the transmitting equipment in the selected frequency band and the N j -th frequency of the susceptive equipment constitute an interference relationship (N j -th equals 1 if yes; equals 0 if no).

Overlapping probability of working time between transmitting equipment and susceptive equipment [20]: In general, assuming that susceptive equipment can be switched on at any time t0 and work during t0 + tR , and the transmitting equipment can be switched on and off at any time. When the transmitting equipment is switched on and the time intervals are uniformly distributed, the overlapping probability of working time between the transmitting equipment and the susceptive equipment can be expressed as

k 1

The probability of interference and the probability of EMC of the subsystem using parallel model are

I j (s) I j1(s) · I j2(s) · I j3(s) · I jn (s)

k 1

The above engineering approximations can be applied to the actual EMC analysis of aircraft, but it does not have a wide range of applicability. For systems of larger size, more complex structure, and with more electronic equipment, this method cannot be directly adopted; e.g., this method cannot be used directly for electromagnetic environment performance analysis in battlefield areas.

Theoretically, by substituting the solution of (5.17)–(5.19) into (5.1) we can accurately estimate the EMC condition (EMC(s)) of the whole aircraft system. This method is called EMC accurate evaluation. However, in engineering calculations, many values in the formula are difficult to estimate accurately. Therefore, in order to quickly evaluate EMC(s) of the whole aircraft, some parameters can be further simplified and the worst-case evaluation method of EMC is adopted; i.e., when the susceptibility of the susceptive port is evaluated, the power of the transmitting equipment is considered to be the maximum radiated power and the receiving equipment is considered to operate in the most sensitive state. On this basis, safety margin of the coupled port can be analyzed using the energy criterion. When the safety margin is greater than zero, the port is considered to be safe. When the safety margin is less than zero, the port is considered to be interfered. Therefore, the probability of interference and the probability characteristics of EMC are unnecessary to be considered anymore. Then, Eqs. (5.17)–(5.19) are simplified as

Equations (5.20)–(5.22) indicate that in a series model, as long as one port is interfered, the entire subsystem is considered to be insecure. Similarly, in a parallel model, as long as one port is secure, the entire subsystem is considered to be safe. This kind of EMC analysis is called rough evaluation of EMC, and it is does not accept any degradation of equipment performance in EMC design. Using this method, EMC(s) can be directly evaluated based on the interference correlation matrix. The specific steps are as follows:

(1)List transmitting equipment, other radiating equipment, receiving equipment, other susceptive equipment, fuel safety subsystems, and operator safety subsystems in the aircraft system.

(2)Number the radiation source ports or susceptive ports for each equipment or subsystem, and build the EMC probability prediction model for each subsystem.

(3)Build the interference correlation matrix of the whole aircraft equipment, the fuel interference correlation matrix, and the personnel interference correlation matrix.

(4)Calculate the power of the interference through various coupling paths to different susceptive ports, fuel susceptive points, and operator workstation positions. Calculate the safety margin matrix by comparing the result with the tolerable radiation power and the susceptive ports, fuel susceptive points, and operator’s position in the workstation.

According to the analysis above, the interference power matrix coupled with the susceptive port is

JE [ J1 · · · Jj · · · JN2 ]

where the power coupled with the receiving antenna port refers to the output power of the receiving antenna (the coupling power of the antenna port in Eq. (5.62) is the input power of the receiver).

Similarly, the radiation power matrix coupled with the fuel susceptive point and the radiation power matrix coupled with the operating station of the cabin operator can be obtained.

The radiation power matrices that the susceptive ports, fuel susceptive points, and operator workstation positions can withstand respectively are

The elements of the matrix in (5.24) are obtained by calculating or testing. The elements of the matrix in (5.25) and (5.26) are set according to the corresponding standards.

The safety margin matrix for the susceptive ports is

Similarly, the safety margin matrix of the fuel susceptive point and the operator table can be obtained separately as

(5)Convert the safety margin matrix into a matrix of interference coefficients, extract the matrix elements, calculate Cj(s) of each subsystem, and substitute (5.1) to calculate the EMC(s) of the whole aircraft.

If Jj − JjS > 0, let Jj − JjS 1, which indicates that the probability of the port being interfered is 1; i.e., the port is insecure. If Jj − JjS ≤ 0, let Jj − JjS 0, which indicates the probability of the port being interfered is 0; i.e., the port is safe. Then, we can generate the interference coefficient matrix as ζIE ζ1, ζ2, . . . , ζN2 . It can be seen from Eq. (5.20) that ζIE is the probability matrix of the susceptive port and the matrix can be written as

ζSE [1, 1, · · · 1]1×N2 − [ζ1, ζ2, · · · , ζN2 ] [1 − ζ1, 1 − ζ2, · · · , 1 − ζN2 ]

We can then extract the probability of interference and the EMC probability of all susceptive ports of a certain subsystem from the matrix. Based on the basic model of Eqs. (5.4)–(5.6), we can calculate the EMC probability Cj(s) of receiving equipment and other susceptive equipment.

If JO j − JOS j > 0, let JO j − JOS j 1, which indicates that the probability of inference at the fuel susceptive point is 1; i.e., the sensitive point is interfered. If JO j − JOS j ≤ 0, let JO j − JOS j 0, which indicates the probability of interference at the susceptive point of the fuel is 0; i.e., the sensitive point is safe. The matrix of probability of interference for fuel susceptive points is ζIO [ζO1 , ζO2 , · · · , ζOK ]. The EMC probability of fuel susceptive point is calculated to be ζSO [1 − ζO1 , 1 − ζO2 , · · · , 1 − ζOK ]. Then, we can extract the EMC probability of each element from the matrix and calculate the Cj(s) of fuel subsystem according to Eq. (5.4). Similarly, the EMC probability of the operator’s subsystem can be calculated.

Finally, we can substitute Cj(s) of each system into Eq. (5.1) and obtain the EMC condition (EMC(s)) of the whole aircraft system.