[Analysis of College Students' Electronic Competition Topic] - 2023 National Competition Topic B "Coaxial Cable Length and Terminal Load Detection Device"

gmchen

[Analysis of College Students' Electronic Competition Topic] - 2023 National Competition Topic B "Coaxial Cable Length and Terminal Load Detection Device" [Copy link]

 

I didn't see any discussion about Question B of this competition in the forum. I only saw one question, but no one answered it yet.

In fact, among the questions in this year's competition, question B is the one with the least workload. The problem is that you must have a good understanding of transmission line theory to solve this question. So this question is one of those "you either know it or you don't know it", similar to the result of a binary digital signal.

Below is the original question and the author’s analysis.

topic

1. Mission

Design and make a coaxial cable length and terminal load detection device (hereinafter referred to as the "device"), as shown in the figure below. The beginning of the cable to be tested is connected to the device through a cable connector, and the cable terminal can be open circuit or connected to a resistance or capacitance load. Set two buttons "length detection" and "load detection" to select and start the corresponding function. The load resistance value range is: 10Ω~30Ω, and the capacitance value range is: 100pF~300pF. The device is powered by a single power supply of no more than 6V.

gmchen

II. Requirements

1. Basic requirements

(1) The device can display the working status, cable length, load type, and load parameters. The display format is shown in the table below.

Working status	Displays "Detecting" or "Results on Hold"
cable length	Display "XXXX cm"
Load Type	Display one of "Open Circuit", "Resistance" and "Capacitance"
Load parameters	Display the value and unit of resistance or capacitance

(2) When the cable length is 1000cm≤L≤2000cm and the terminal is open, press the "length detection" button to start the detection. The device can detect and display the cable length L. The absolute value of the relative error is no more than 5%, and the detection time is no more than 5s.

(3) After completing the cable length test under the terminal open circuit condition, keep L unchanged, connect a load such as resistance or capacitance to the terminal, press the "Load Detection" button to start the test, and the device can correctly determine and display the load type. The detection time for one test does not exceed 5 seconds.

2. Play part

(1) Improve the accuracy of cable length detection: When the cable length is 1000cm≤L≤2000cm and the terminal is open, the absolute value of the relative error of the cable length detection shall not exceed 1%, and the detection time shall not exceed 5s.

(2) After completing the length detection under the terminal open circuit condition, keep L unchanged, connect a load such as resistance or capacitance to the terminal, and press the "Load Detection" button to start the detection. The device detects and displays the resistance and capacitance values of the load based on the correct judgment of the load type. The absolute value of the relative error is no more than 10%, and the detection time does not exceed 5s.

(3) Reduce the blind area of cable length detection: When the terminal is open, reduce the detectable cable length to L ≤ 100 cm, provided that the absolute value of the relative error of cable length detection is no more than 1% and the detection time does not exceed 5 seconds.

(4) Others.

3. Description

(1) The device should include a signal source and a measurement processing circuit. According to the measurement method, a suitable excitation signal is used to measure the incident and reflected signals at the beginning of the cable and process them to calculate the parameters required for detection.

(2) The coaxial cable to be tested shall be prepared by the participating team and brought to the site when participating in the test. The total length of the cable shall be measured in advance. The length of at least one cable shall not be less than 2000cm. The type of plug connected to the beginning of the cable shall be determined by the team, and the end can be conveniently connected to the load between the core wire and the shielding layer. The cable shall be allowed to be coiled. During the test, other changes to the cable state are not allowed except for shortening the cable to the specified length and connecting the specified load.

(3) During the evaluation process, except for pressing the "length detection" or "load detection" button to start the corresponding function, no other adjustments or operations are allowed on the device.

(4) The absolute value of the relative error in the question is measured by using an LCR meter to measure the actual values of resistance and capacitance.

(5) Performance (3) Full marks are awarded for the minimum detectable length L≤100cm, and no marks are awarded for L≥1000cm. During the test, the participating team shall specify the test length, measure near this length and verify the accuracy. If the absolute value of the relative error of the cable length measurement is no more than 1% and the detection time does not exceed 5s, it is considered to meet the requirements and the length is deemed valid.

(6) Distance measuring sensors and cameras may not be used in the work.

gmchen

Topic analysis and solution design

This topic deals with the theory and practice of transmission lines in high-frequency circuits.

According to transmission line theory, when the wavelength of an electrical signal is comparable to the length of the wire that transmits the signal, due to the reflection of electromagnetic waves in the wire, the voltage and current at different distances in the wire will be related to the load connected to the wire terminal (open circuit and short circuit can also be considered as a load) and the frequency of the input electrical signal.

Assume the length of the transmission line is l, the characteristic impedance of the transmission line is z ₀ , and the terminal load impedance of the transmission line is z _L , then the input impedance seen at the beginning of the transmission line is

In the above formula, β is the phase coefficient of the electromagnetic wave in the transmission line, β=ω/v _p =2π/λ, where ω, λ, and v _p are the angular frequency, wavelength, and propagation speed (phase velocity) of the signal in the transmission line, respectively. Therefore, βl= 2πl/λ represents the spatial distance in the transmission line relative to the signal period, that is, the spatial phase.

gmchen

_{It can be seen that as long as the characteristic impedance z 0} of the transmission line , the transmission speed v _p of the electromagnetic wave in the transmission line, and the signal frequency ω are known , the relationship between the transmission line length, terminal impedance, and input impedance can be obtained according to the above formula. One of the most useful special cases is: when the transmission line length is equal to 1/4 of the signal wavelength, that is, βl = π/2, the impedance at the beginning of the transmission line is

Therefore, when the length of the transmission line is equal to 1/4 of the signal wavelength, if the terminal is open (z _{L =∞), the impedance z in} =0 seen at the beginning of the transmission line , that is, the signal seems to be short-circuited. If the terminal impedance is not 0, for example, a capacitor is connected, the impedance seen at the beginning will be an inductor, and the product of its inductive reactance and the capacitive reactance is equal to the square of the characteristic impedance of the transmission line (the characteristic impedance of common coaxial cables is 50Ω and 75Ω).

gmchen

Based on the above relationship, the design solution structure of this problem can be obtained as shown in the figure below.

The testing process is as follows:

1. According to the requirements of the question, first detect the length of the coaxial cable with the terminal open.

After starting the test, control the high-frequency signal source to gradually increase the test frequency (sweep frequency) from a low frequency, synchronously read the voltage u2 at the beginning of the cable, and record the test frequency ftest when the first u2 minimum value appears ₍ due to the non-ideal characteristics of the cable and the test device, the impedance at the input end of the cable cannot reach 0, as long as the minimum value is observed). At this time, the length of the cable is one-quarter of the wavelength of the frequency, and the cable length can be calculated according to the following formula:

_{The v p} of common commercially available coaxial cables is 0.66c, or 2×10 ⁸ m/s. The cables to be used may also be tested in advance to obtain more accurate values.

2. According to the requirements of the question, test the terminal load while keeping the cable length unchanged.

After starting the test, set the test frequency to f _test and read the amplitude and phase difference of the two voltages u1 and u2. Under the condition of known resistance R, the impedance of the cable input end can be calculated.

The load impedance is thus obtained

Note that in these two calculation formulas, the voltages u1, u2 and the impedances z _in , z _L may all be complex numbers.

Finally, based on the load impedance and test frequency, the resistance or capacitance value of the load can be obtained.

gmchen

Some specific production details are discussed below.

1. The phase velocity of common coaxial cables is 2×10 ⁸ m/s. The question requires that the cable length to be tested is 20m~1m. According to the cable length being equal to one quarter wavelength of the test signal, the corresponding test frequency is 2.5MHz~50MHz. The output signal frequency of the signal source in the test device should be greater than this range and should be a pure sine wave. A high-frequency signal source composed of a DDS chip should be the most suitable.

2. There are two types of coaxial cables on the market: 50Ω and 75Ω. However, the high-frequency instruments commonly used in laboratories are all 50Ω, and common connectors are also 50Ω, so the selected cable should be 50Ω.

3. In order to reduce the impact of impedance discontinuity, the cable connector and the resistor in series at the output of the signal source should all be 50Ω. The two voltage sampling buffer amplifiers should use integrated amplifiers with high input resistance and very small input capacitance. And these devices should be as close to the cable connector as possible.

The above is all about Question B. Isn’t the workload very small?

okhxyyo

Great! Thank you for sharing~ Very cool~~

吾妻思萌

This requires a deep understanding of the transmission impedance S parameter

吾妻思萌

Teacher Chen, you really put it well. I like it.

lansebuluo

Through the explanation of the big brother, I have a basic understanding of the impact of transmission line impedance on signals, which has benefited me a lot.

milliu

gmchen posted on 2023-8-7 13:21 Let's discuss some specific production details. 1. The phase velocity of common coaxial cable is 2×108m/s. The question requires the cable length to be tested to be 20m ...

Oh, I'm stuck on impedance. I haven't learned transmission line theory, and I'm still trying to find distributed parameters... I'm enlightened.

传媒学子

Yes, this kind of question is easier to answer if you know the answer, but because there are fewer groups to choose from, it is a disadvantage in the award.

传媒学子

Azuma Simeng posted on 2023-8-7 16:55 This requires a deep understanding of the transmission impedance s parameter

Simulation software is very powerful

lugl4313820

It’s really exciting. The basic knowledge must be solid!

gl82

Can high school students participate in the eSports competition?

ritinde

DDS chips were used in several questions of this year's competition.

misplace5508

Thank you for sharing, this is the original idea. I didn’t think deeply enough about it during the e-sports competition.

AfterCom

I bow down to you. Your explanation is professional and detailed. I have learned a lot. Thank you again for sharing. Thank you.

wangky

Many modules cannot reach 50MHZ. Do you have any high-speed modules to recommend?

gmchen

wangky posted on 2024-7-10 20:14 Many modules cannot reach 50MHZ. Do you have any high-speed modules to recommend?

Don’t know what module you want?

If it is an amplifier, then many MMICs will do, such as the HMC580, which is about 20dB and has a frequency upper limit of 1GHz. High-speed op amps will also work, such as the THS3201, with GBW = 1.8GHz.