Introduction

LCR meters and impedance analyzers are used to measure unknown values of passive components like resistors, capacitors, inductors, or a combination of these elements. These lab equipment are similar, except that an impedance analyzer allows measurements at different test frequencies. The auto-balancing (ABB) method, compared to the other architectures, offers good measurement accuracy over a wide range of values of impedance, and is discussed in this technical report.

Auto-Balancing Method

Figure 1-1 shows a representative schematic of an analog front-end using the ABB method. Z_DUT is the unknown impedance (device under test or DUT) and R_F is a known feedback resistance in this circuit. A known voltage V_IN is forced at input to the signal chain. For a voltage V_DUT across Z_DUT and a current I_DUT flowing through it,

Amplifier A1 is used as an inverting amplifier, whose output voltage is given as,

From (1) and (3), the unknown impedance Z_DUT is given by,

Design Challenges

A few things need careful consideration when designing an LCR meter analog front-end circuit using the ABB method:

1. A single value of R_F will not suffice for measuring a wide range of values of Z_DUT. To increase the measurement range and sensitivity of the LCR meter multiple feedback resistors (R_F1,2,3) are switched into the circuit through series switches (SW_F1,2,3), shown in Figure 1-2.
2. A large value of R_F forms a zero in the noise-gain transfer function causing 40 dB/decade rate-of-closure and potential instability. Use of a capacitor C_F in parallel with the large R_F, shown in Figure 1-1, introduces a pole to cancel this zero and restores phase margin, but it is difficult to find a single value of C_F for stability with all values of capacitive Z_DUT. This problem is solved using series resistors R_G1,2,3 with Z_DUT, as Figure 1-2 shows. Use of R_G introduces a pole in noise-gain, cancelling the zero and restoring phase for a stable circuit. Multiple values of R_G (equal to corresponding R_F1,2,3) with corresponding series switches (SW_G1,2,3) need to be used. The same R_F and R_G pairs (marked with the same color in Figure 1-2) are switched in every time for the required measurement range to ensure stable operation.
3. For high accuracy measurements with large value DUTs, V_DUT and I_DUT should be buffered with high-Z input amplifiers (A2 and A3 here, CMOS or FET-input amplifiers with ≈pA range bias currents).

Amplifier A3 can be eliminated for a simplified analog front-end design; however, to maintain measurement accuracy, amplifier A1 should have a large enough open-loop gain (AOL), and hence a gain-bandwidth product at the highest measurement frequency of interest. With a large AOL at the test frequency, a virtual ground is maintained at A1’s inverting input.

Eliminating A3 allows for single-point ground-referenced measurements with need for smaller number of amplifier channels and single-ended ADCs. A general rule-of-thumb is to ensure that A1 has >60-dB AOL at the highest frequency of interest for high accuracy measurements. For higher test frequencies, two-point measurements for V_DUT and I_DUT are needed to calculate Z_DUT with high-accuracy, which requires more amplifiers (A3 in Figure 1-2) and differential input ADCs.

Conclusion

The TIDA-060029 reference design describes this LCR meter analog front-end and the associated challenges in detail. An analog front-end with impedance measurements accurate to 0.1% is implemented in this reference design. Impedance values in the range 1 Ω to 10 MΩ can be measured at frequencies from 100 Hz to 100 kHz. Table 1-1 lists Texas Instruments amplifiers suitable for use in an LCR meter design: