TIDUEU6B September   2020  – December 2021

1.   Description
2.   Resources
3.   Features
4.   Applications
5.   5
6. 1System Description
7. 2System Overview
1. 2.1 Block Diagram
2. 2.2 Highlighted Products
3. 2.3 Design Considerations
1. 2.3.1 Existing architecture
2. 2.3.2 Proposed Design
1. 2.3.2.1 Stability Analysis of the Proposed Design
2. 2.3.2.2 RG = RF Settings and Respective Impedance Ranges
3. 2.3.2.3 Impedance Measurement Procedure
8. 3Hardware, Software, Testing Requirements, and Test Results
1. 3.1 Required Hardware and Software
2. 3.2 Testing and Results
9. 4Design Files
10. 5Software Files
11. 6Related Documentation
12. 7Revision History

#### 2.3.2.1 Stability Analysis of the Proposed Design

When the unknown impedance to be measured is capacitive i.e. CX, it forms the circuit shown in Figure 2-3. The transfer function of VF is given in Equation 4.

Equation 4.
Figure 2-7 Capacitive Measurement with Series Resistance

In comparison with Equation 2, Equation 4 shows that due to presence of RG, there is a pole-zero combination in the feedback path. The zero and pole frequencies in 1/β are given by,

Equation 5.
Equation 6.

The pole and zero frequencies hold the relation ωP = 2*ωZ because RG is equal to RF in every RG - RF setting.

Figure 2-8 Bode Plot of Capacitive Measurement with Series Resistance

This provides the advantage of an inherent pole to cancel the zero. Figure 2-8 shows that the rate of closure of Aolβ is 20 dB/dec for almost all the CX. The exception for this fact is when fCL lies between fZ and fP. The RG - RF settings are selected such that this situation is avoided. This allows for a key factor of this design where ωP = 2*ωZ is independent of the value of CX. The measurement can be done in two ways as explained below,