*4.3. Filter of E<sup>1</sup> and E<sup>2</sup>*

∆*t* is an invariant constant; τ<sup>1</sup> and τ<sup>2</sup> vary with GC, so *E*<sup>1</sup> and *E*<sup>2</sup> are also variations. Counter *k* is increased once every measurement period *TC*, as shown in Figure 5. To make *k*th measurements *E*<sup>1</sup> and *E*<sup>2</sup> close to the actual value, the average value of *M*<sup>1</sup> and *M*<sup>2</sup> phases are taken according to Equation (6). *E*1(*k*) and *E*2(*k*) can be rewritten as

$$\begin{cases} E\_1(k) = \left(\frac{v\_{11,1}(k) - v\_{11,2}(k)}{v\_{11,2}(k) - v\_{11,3}(k)} + \frac{v\_{12,1}(k) - v\_{12,2}(k)}{v\_{12,2}(k) - v\_{12,3}(k)}\right)/2\\ E\_2(k) = \left(\frac{v\_{21,1}(k) - v\_{21,2}(k)}{v\_{21,2}(k) - v\_{21,3}(k)} + \frac{v\_{22,1}(k) - v\_{22,2}(k)}{v\_{22,2}(k) - v\_{22,3}(k)}\right)/2 \end{cases} \tag{14}$$
 
$$R\_{\mathcal{I}} \text{ change}$$
 
$$\mathbf{1}\_{\mathcal{I}} = \begin{bmatrix} \ddots & \ddots\\ \ddots & \ddots \end{bmatrix}\_{\mathcal{I}} \end{bmatrix}\_{\mathcal{I}}$$

**Figure 5.** Waveform of the bridge voltage.

The estimated value of the *k*th *E*<sup>1</sup> and *E*<sup>2</sup> is set as *E*ˆ <sup>1</sup>(*k*) and *E*ˆ <sup>2</sup>(*k*), respectively, which can be obtained by the following first-order filter, where A is a filter coefficient that satisfies 0 < A < 1.

$$\begin{cases} \triangle\_1(k) = \text{A}\triangle\_1(k-1) + (1-\text{A})E\_1(k) \\ \triangle\_2(k) = \text{A}\triangle\_2(k-1) + (1-\text{A})E\_2(k) \end{cases} \tag{15}$$
