## 3 HESD Structure Design for ERT
### The Second Layer SS2: Between L1-L4 and Electrodes
#### 3.3.1 The First Stage (SS2-1): One-to-One Connection of Electrode and Line  
Four I/O lines, L1-L4, come from main control parts and connect to distributed structures. They are, as a group, called the bus. The distributed structure is responsible for controlling the connection status between lines and electrodes through Series D switches. Figure 5 give the topology structure for the distributed parts of the TESD and the HESD. TESD needs four switches for one electrode (Figure 5a), while HESD only needs one switch for one electrode (Figure 5b). One distributed structure includes multiple electrodes, and four electrodes form a group. As shown in Figure 5b, electrodes E1-E4 are connected successively to L1-L4 through switches D1-D4, and E5-E8 are connected successively to L1-L4 through switches D5-D8. The rest can be done in the same setting. Implementing the first test in the ERT first layer (E1-E4 as testing electrodes connected to AMNB) requires set up connections, as shown in Figure 5c. Close switch K1 to connect L1 and A, close K6 to connect L2 and M, close K11 to connect L3 and N, and close K4 to connect L4 and B. At the same time, close D1-D4 connects E1-E4 with L1-L4. In this way, through L1-L4, E1-E4 are linked together with AMNB ports. In this test, the whole concatenated relations are E1-D1-L1-K1-A, E2-D2-L2-K6-M, E3-D3-L3-K11-N, and E4-D4-K16-B. The subsequent tests will be conducted in similar fashion. For example, the next test is the second test in the ERT first layer, and the connections are E2-D2-L2-K5-A, E3-D3-L3-K10-M, E4-D4-L4-K15-N, E5-D1-L1-K4-B, etc. The circuit design scheme is acquired easily based on the structure in Figure 5c. The circuit for HESD in each distributed structure or cell is shown in Figure 6 (four electrodes in  
Figure 5: Topology of the distributed structure: TESD design (**a**) [24]; the first layer and the first stage of design of the second layer in HESD (**b**); Switch control map for E1-A, E2-M, E3-N, and E4-B (**c**). a cell) as an example, and the structure for eight electrodes in a cell is likely. Conventionally, the most common plan is eight electrodes in one cell. Therefore, the distributed cell (structure) must contain an integer times four electrodes, which could be 4, 8, or 12 electrodes in a cell. In Figure 6, the switch RELAY1 controls the 1 IN to connect to 1 OUT/E1. Connect to 1 OUT means E1 need not connect to L1 and L1 will be left to subsequent cells, whereas connect to E1 means E1 connects to L1. In accordance with this process, the structure described above can finish the first layer test. However, whether it is able to complete any layer's test needs to be studied. HESD has the same SS1. Therefore, one switch is added for one additional electrode in SS2. This means that one electrode could likely only be connected to one predetermined line, e.g., E1 only to L1, E2 only to L2, etc. (Figure 5c). This condition is denoted as a connection condition determined by the designed topology structure. It is noteworthy that the system tests claim that four testing electrodes must be one-to-one connected to four lines (L1-L4). Any two or more testing electrodes cannot be linked to the same line. This condition is denoted as the test condition. Obviously, the connection condition is acceptable or correct when it meets the test condition. To indicate if the two conditions are matched to each other, electrodes and their relevant lines are shown in Table 1 for the foremost four tests in layer 1-layer 8 (the condition of other layers can be deduced from Table 1). In Table 1, in odd layers each electrode pairs with one line, e.g., the testing electrodes are connected to four different lines--L1, L4, L3, and L2 in the first test of the third layer. They fulfill the request. But in even layers, this is not the case. In the first and the third test of the second layer, four electrodes are paired with L1, L3, L1, and L3, respectively. Apparently, four testing electrodes in the even layers match to two lines (blue color) or one line (red color), but not four lines.