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Issue #214 May 2008
Where Analog And Digital Collide
An Easy-To-Use LCR Meter
Third Place Microchip 2007 Design Contest
by Miguel Rusch
Start | LCR Meter | Back to Basics | The Big Picture | Creating a Wave | Analog Stages | Signal Conditioning | User Interface | Firmware | Take a Measurement | System Performance | Further Development | What's Next? | Sources & PDF
BACK TO BASICS
Existing commercial LCR meters use a number of methods to establish the real and complex components of AC impedance. Although measuring the total impedance (Z) is relatively trivial, phase information is more difficult to obtain accurately. My design makes simultaneous measurements of the voltage and current and applies simple trigonometric equations to recreate and compare the waveforms.
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| Figure 1 — This is the basic circuit for making AC impedance measurements. The voltages across and current through the device under test (DUT) are measured simultaneously. |
Figure 1 is a simplified depiction of how the measurements are made. A sinusoidal waveform of a known frequency is buffered by an op-amp and then applied to the device under test (DUT) via a source resistance. Current flowing through the DUT is directed to the inverting input of a second op-amp. The output voltage of the op-amp ensures that the current flowing through the feedback resistor is equal to that flowing through the DUT. That action induces a voltage across the feedback resistor that is proportional to the current flow through the DUT.
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| Figure 2 — Analysis of recorded data starts with determining the zero-crossing point. Initially, a linear regression is made as a “guess” point. An iterative error function is then run in the neighborhood of the guess point to find the point of minimum error. |
The current and voltage waveforms are sampled simultaneously. After correcting any DC offset, the zero-crossing point is determined. The crossing point is first estimated by using a linear regression between points on either side of the crossing (see Figure 2). The maximum error of the method is set by the ratio of the test frequency to the sample frequency. An area on either side of the initial guess is iteratively evaluated by applying the formula:
The formula calculates the error between theoretical and measured values of points a0 and a1. The width of the search area is determined by the error due to the initial guess. The step size applied to the previous equation determines the improved error. The point representing the minimum error is the zero-crossing point. Using this zero-crossing point, the waveform amplitude can be calculated based on the value of any measured point and its position in time relative to the crossing. In practice, several points are evaluated and the results are averaged. Because measurements are made simultaneously, the relative phase between waveforms is easily evaluated.
There is an important caveat regarding the use of the described method: it is totally reliant on the data being a pure sinusoid. Therefore, the applied test waveform must be a high-quality sinusoidal source and the acquired data must not include any other frequency components. Both issues are addressed with digital methods. First, the waveform is accurately constructed using direct digital synthesis (DDS) technology. Second, the acquired data is band-limited using digital signal processing (DSP) filters.
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