[Analysis of College Students' Electronic Competition Topic] —— 2023 National Competition Topic C "Capacitance and Inductance Measurement Device"

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[Analysis of College Students' Electronic Competition Topic] —— 2023 National Competition Topic C "Capacitance and Inductance Measurement Device" [Copy link]

 

1. Mission

Based on TI's MCU, a measuring device for inductance and its quality factor Q, capacitance and its loss tangent D is designed and manufactured. After the component under test is connected and started with one button, the measurement is automatically completed within the specified time. The measuring device should provide a signal output interface dedicated to monitoring the test frequency, which is used to monitor the test frequency of the device in real time, as shown in the figure.

II. Requirements

1. Basic requirements

Complete the measurement of capacitance and its loss tangent D.

(1) Capacitance measurement range: 1nF ~ 100nF, the absolute value of the measurement relative error is no more than 5%.

(2) Capacitance D value measurement range: 0.005~1, the absolute value of the measurement relative error is not greater than 5%.

(3) Customize a fixed measurement frequency within the range of 1kHz to 100kHz.

(4) The measurement time shall not exceed 1 second.

2. Play part

Complete the measurement of inductance and its quality factor Q.

(1) Inductance measurement range: 10μH ~ 100μH, the absolute value of the measurement relative error is not greater than 5%.

(2) Inductor Q value measurement range: 1~200, the absolute value of the measurement relative error is no more than 5%.

(3) The device can measure in two frequency ranges, not higher than 2 MHz and not lower than 20 MHz. The measurement frequency can be determined by the user.

(4) The measurement time shall not exceed 5 seconds.

(5) Others.

3. Description

(1) All processors of this measurement and display device must use TI's MCU (specific model is not limited), otherwise it will be considered as a violation and will not be tested.

(2) Participating teams need to bring their own commercial measuring instruments, referred to as self-prepared measuring instruments, to calibrate their self-made measuring devices. During the evaluation, the measurement value of the self-prepared measuring instrument is used as the standard value to calculate the measurement error.

(3) It is recommended that the test frequency of the homemade measuring device be consistent with that of the self-provided measuring instrument.

(4) Equivalent impedance elements can be constructed by connecting resistors in parallel or series to calibrate the parameters of homemade measuring devices.

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Topic analysis and solution design

For this question, you can refer to the commercial LCR tester. The LCR tester is also called the LCR digital bridge, which can measure the inductance, capacitance, resistance, and loss of inductance and capacitance (Q value, D value, etc.) of inductors, capacitors or resistors. Its basic structure is as follows:

Its basic working principle is: add a sinusoidal excitation signal to the device under test (DUT), and then measure the voltage across the DUT and the current flowing through the DUT to obtain the properties and parameters of the DUT.

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The working process is explained below using capacitance measurement as an example.

For an ideal capacitor, the current flowing through the capacitor will lead the voltage across its two ends by 90°. However, the actual capacitor has losses, which can be equivalent to an ideal capacitor Cp _and an ideal resistor Rp _in parallel. Therefore, the angle at which the current flowing through the actual capacitor leads the voltage across its two ends will be less than 90°. This reduced angle is the loss angle.

As shown in the figure, assuming that the voltage across the DUT is

, the current flowing through the DUT is . The projection of this current on the imaginary axis is the current flowing through the ideal parallel capacitor, and the projection on the real axis is the current flowing through the loss resistor.

So the capacitive reactance of the ideal capacitor in parallel is

, the capacitance of the capacitor to be tested under the condition of known test frequency is , and the resistance of the loss resistor is .

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The above operations can be completed inside the MCU, the specific process is as follows:

1. Use the timing function of MCU to generate excitation signals regularly.

A specified excitation signal cycle has n points, and each point is output by the DAC according to the sine function value. The output signal is filtered out by a low-pass filter to remove quantization noise and quantization error to obtain a stable sinusoidal excitation signal (if there is no DAC, a square wave can be output directly, but a higher-order low-pass filter is required).

2. At each timing moment, sample the voltage signal across the DUT and the current signal flowing through the DUT, and sample n points in total to complete a signal cycle.

Since the subsequent operations are related to the phase difference between the two signals, it is important to note that the two signal samples should be strictly synchronized, and a sample-and-hold circuit should be used for ADC sampling when necessary. In addition, the subsequent operations are performed according to signed numbers, so the sampled values (usually unsigned numbers) must also be converted to signed numbers.

3. Multiply a pair of voltage signals and current signals sampled at each moment, and then accumulate the products of n points in the entire excitation signal cycle to obtain

.

In the same way, the voltage signal is multiplied and accumulated to obtain V ² .

By multiplying the current signal at each moment with the voltage signal at n/4 points and adding them together, we get

.

4. Calculate the capacitance value and loss tangent according to the formula given above.

The measurement process of resistance and inductance is similar to that of capacitance and will not be described in detail.

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The voltage detection amplifier and current amplification detection circuits are discussed below.

Considering that the measured signal may have a large dynamic range, in order to ensure sufficient measurement accuracy, both amplifiers must have variable gain capabilities. Since stable and accurate gain values are required in measuring instruments, such amplifiers are usually composed of high-precision resistors and precision op amps.

The figure below is a schematic diagram of the voltage detection amplifier circuit in the LCR tester. This is a typical three-op-amp instrumentation amplifier with a voltage gain of

.

What is worth noting in the figure is the connection method of the analog switch used to change the amplifier gain. Since the analog switch has an uncertain internal resistance, the analog switch cannot be connected in series with the feedback resistor in the circuit. In the connection method shown in the figure, since the input impedance of the op amp is extremely high, the current flowing through the analog switch is approximately 0, and the influence of its internal resistance is eliminated.

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The figure below is a schematic diagram of the current detection amplifier circuit in the LCR tester. This is a transimpedance circuit. The output voltage of this circuit is the product of the detection current and the feedback resistance. Changing the feedback resistance can change its gain. Due to the virtual short circuit characteristics of the op amp, the potential of the current test end is approximately 0, that is, the current detection sampling resistance is 0, which will not affect the detection voltage of the DUT.

It is also worth noting the connection method of the analog switch. In this connection method, two groups of analog switches are linked, the lower analog switch changes the feedback resistance, and the upper analog switch takes out the sampled voltage. Due to the virtual open circuit characteristics of the op amp, the upper analog switch internal resistance has no effect on the measurement. Although the lower analog switch internal resistance is connected in series with the feedback resistance, it will not affect the sampled voltage of the upper op amp.

The op amps in the above two amplifier circuits are usually powered by two positive and negative power supplies, but the microcontroller is usually powered by a single power supply, so the level shifting problem must also be considered. Here is a reminder, no more expansion.

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Finally, let’s discuss the contact resistance of DUT.

When the DUT is connected to the LCR tester, the contact resistance between the instrument's fixture and the DUT may affect the test results. In order to eliminate the influence of contact resistance, the four-terminal method should be used when measuring small resistances.

The figure above is a schematic diagram of the four-terminal connection method. The two hollow contacts are current contact terminals, and the two solid contacts are voltage contact terminals. Obviously, due to the high input resistance of the voltage amplifier, the contact resistance of the voltage contact terminal will not affect the voltage measurement result, and the additional voltage drop caused by the contact resistance of the current contact terminal will not be detected by the voltage detection amplifier.

The test fixtures in actual LCR testers all adopt this structure.

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[Analysis of College Students' Electronic Competition Topic] —— 2023 National Competition Topic C "Capacitance and Inductance Measurement Device"

What a detailed analysis!

laker2008

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小-白

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AfterCom

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ew123

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sanskrit

Very clear and concise, very good!

遥望夜空

I admire the film. The explanation is professional and detailed. I have learned a lot. It provides us with ideas for preparing for the 2024 provincial competition. Thank you again for sharing. Thank you.

newtonxihuan

Mr. Chen, I have a question, why is the gain of the high-pass filter not 1 in the passband? I designed it to be 1.

, the chip used is ne5532

newtonxihuan

gmchen

newtonxihuan posted on 2024-7-17 19:57 Teacher Chen, I have a question, why is the gain of the high-pass filter not 1 in the passband? I designed it to be 1, and the chip I used is ne5532

Can you give specific frequency response characteristics or frequency response curves?

newtonxihuan

gmchen posted on 2024-7-18 09:54 Can you give the specific frequency response characteristics or frequency response curve?

Do you want to simulate or actually test? There is no baud meter for actual testing, so you can only use an oscilloscope to test.