2 Two-point Insulation Resistance Measurements

If the isolation leakage errors happen at both positive terminal and negative terminal of a high-voltage battery, the circuit diagram is as shown in Figure 2-1. Here, R_ISOP represents the parasitic insulation resistance between high-voltage battery positive terminal and chassis ground, while R_ISON represents the parasitic insulation resistance between high-voltage battery negative terminal and chassis ground. In accordance with TIDA-01513 specification, S₁ and S₂ are control switches for positive terminal and negative terminal respectively. Rps (Replace R_ps1+R_ps2 for simplicity) and R_ns (Replace R_ns1+R_ns2 for simplicity) are series resistors in positive terminal and negative terminal respectively. R_s1 and R_s2 are sampling resistors across op-amp. ISO_POS and ISO_NEG are measured by analog-digital converter for signal processing. Additionally, the battery voltage needs to be measured in order to accomplish the entire insulation resistance measurement. In TIDA-01513, AMC1301-Q1 device is used to perform this measurement and provide an isolated signal for analog-digital converter.

When only S₁ is closed, there are two leakage current paths for the high-voltage battery. One leakage current flows from the positive terminal of high-voltage battery (junction a) to chassis ground, and depends on the positive terminal voltage (referred to chassis ground) and R_ISOP. The other leakage current, which goes through high-voltage battery, flows from the negative terminal of high-voltage battery (junction b) to chassis ground, and depends on the negative terminal voltage (referred to chassis ground) and R_ISON.

According to Kirchhoff’s Current Law, the sum of currents entering and leaving the same junction is always zero. Equations are found at junction a and junction c respectively.

Here V_a is the voltage at junction a, which is the high-battery positive terminal voltage referred to chassis ground. V_ref is the reference voltage applied to op-amp non-inverting input (+). R_ps is the sum of R_ps1 and R_ps2, that is R_ps = R_ps1 + R_ps2. HV_BATT1 is the battery voltage measured by ADC when only S₁ is closed. ISO_POS is the top op-amp output voltage during the same scenario. HV_BATT1 and ISO_POS should be sampled by ADC synchronously for calculation accuracy.

Let α = V_a for simplicity, and α can be obtained from Equation 2. The voltage at junction a, which is α, is determined by ISO_POS which is measured by ADC.

When only S₂ is closed, there are also two leakage current paths for the high-voltage battery. One leakage current, which goes through high-voltage battery, flows from the positive terminal of high-voltage battery (junction a) to chassis ground, and depends on the positive terminal voltage (referred to chassis ground) and R_ISOP. The other leakage current flows from the negative terminal of high-voltage battery (junction b) to chassis ground, and depends on the negative terminal voltage (referred to chassis ground) and R_ISON.

Similarly, the equations of junction b and junction d can be obtained according to Kirchhoff's Current Law respectively.

Here V_b is the voltage at junction b, which is the high-battery negative terminal voltage referred to chassis ground. V_ref is the reference voltage applied to op-amp non-inverting input (+). R_ns is the sum of R_ns1 and R_ns2, that is, R_ns=R_ns1+R_ns2. HV_BATT2 is the battery voltage measured by ADC when only S₂ is closed. ISO_NEG is the bottom op-amp output voltage during the same scenario. HV_BATT2 and ISO_NEG should be sampled by ADC synchronously for calculation accuracy.

Similarly, let β = V_b for simplicity, then β can be derived from Equation 5. The voltage at junction b, which is β, can be determined by ISO_NEG which is also measured by ADC.

Different equations are seen during these two switching scenarios, which can be combined to calculate desired R_ISOP and R_ISON. Equation 1 and Equation 4 are combined to form an equation group while replacing V_a and V_b α with and β respectively.

Let R_ps equals to R_ns in the design, that is, R_ps = R_ns, then R_ISOP and R_ISON are found from above equation group.

Generally, the value of α is positive and the value of β is negative as they are referred to chassis ground. In consequence, the ADC measured ISO_POS is smaller than V_ref and ISO_NEG is larger than V_ref. The absolute values of both α and β are much larger than zero under typical conditions as long as no terminal is shorted to chassis ground.

Equation 8 is the explicit formula, that can be integrated in the software to get the desired insulation resistance R_ISOP and R_ISON.