CN113028971A - Method for determining diameter of signal wire conductor according to preset frequency - Google Patents

Method for determining diameter of signal wire conductor according to preset frequency Download PDF

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CN113028971A
CN113028971A CN202110279092.1A CN202110279092A CN113028971A CN 113028971 A CN113028971 A CN 113028971A CN 202110279092 A CN202110279092 A CN 202110279092A CN 113028971 A CN113028971 A CN 113028971A
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conductor
wire
frequency
diameter
radius
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盛经宇
董先达
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Shunshi Shenzhen Technology Co ltd
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Shunshi Shenzhen Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/12—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring diameters

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Abstract

A method for determining the diameter of a signal wire conductor according to a preset frequency belongs to the technical field of signal wires and aims to solve the problems that the diameter of the signal wire conductor is single and fixed and the proper diameter cannot be selected according to the preset frequency in the prior art. The method comprises the following steps: determining the value range of the radius r of the signal line conductor according to a formula (I) and a formula (II): r is less than or equal to 2 delta (one),
Figure DDA0002977774890000011
Figure DDA0002977774890000012
wherein: delta is the skin depth of the skin effect when the lead transmits electrons; pi is a constant; mu.s0Is a constant; σ is the conductivity of the conductor of the lead; f is the frequency of the transmission signal; the diameter d of the conductor is obtained as 2r according to the radius r of the signal wire conductor.

Description

Method for determining diameter of signal wire conductor according to preset frequency
Technical Field
The invention belongs to the technical field of signal wires, and particularly relates to a method for determining the diameter of a signal wire conductor according to a preset frequency.
Background
As a signal transmission wire, the wire has high special requirements on the electrification characteristics of a metal wire, because the frequency of various current signals is wide, for example, an audio signal usually covers 10 Hz-100 kHz, and if the transmission of the signals is to be kept efficient in each frequency band, the conduction characteristics of the signals in each frequency band of the wire are designed in a targeted manner.
For a long time, the common signal wire is mostly made of stranded copper core wires, and is formed by a shielding net and an insulating layer, the wire diameter is single, and the frequency characteristics of different signals are not considered. The prior art has the defects of fixed transmission structure, single cable structure design and incapability of adjusting the cable structure according to the use occasion to achieve the best use effect on the conduction of current signals. The prior art does not carry out the diameter calculation design of the sinle silk of this frequency of exclusive to required signal frequency, but adopts the line base conductor of fixed conventional line footpath design, can let various frequencies pass through for being main, rather than designing the sinle silk diameter to exclusive frequency demand, and the full frequency channel signal conduction of this kind of fixed conventional line footpath is the conductible, nevertheless still has great difference with the high efficiency between switching on.
Disclosure of Invention
The invention aims to provide a method for determining the conductor diameter of a signal wire according to a set frequency, which solves the problems that the conductor diameter of the signal wire is single and fixed and the proper conductor diameter cannot be selected according to the preset frequency in the prior art; the transmission of the signal of the predetermined frequency is enhanced.
To achieve the above object, a method of the present invention for determining a diameter of a conductor of a signal line according to a predetermined frequency comprises:
determining the radius r of the signal line conductor according to the formula (I) and the formula (II)WThe value range of (A):
r W2 delta ≤ (one)
Figure BDA0002977774870000011
Wherein: delta is the skin depth of the skin effect when the lead transmits electrons;
pi is a constant;
μ0is a constant;
σ is the conductivity of the conductor of the wire;
f is the frequency of the transmission signal;
according to the radius r of the signal line conductorWThe diameter d of the obtained conductor is 2rW。
The specific confirmation process of formula (one) is as follows:
the low-frequency impedance r of the conductor can be known according to the formula (III)lfComprises the following steps:
Figure BDA0002977774870000021
wherein: r isDCIs a direct current resistance;
pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
the high-frequency impedance r of the conductor can be known according to the formula (IV)hfComprises the following steps:
Figure BDA0002977774870000022
wherein: pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
rDCis a direct current resistance;
μ0is a constant;
f is the frequency of the transmission signal;
combining the formula (three) and the formula (four), determining the radius r of the wire conductorWWhen the diameter is less than or equal to 2 delta, the skin effect influence is minimum, and the radius r of the wire conductor is determinedWHas a value range of rW≤2δ。
The invention has the beneficial effects that: a method of the present invention determines a diameter of a signal wire conductor based on a known frequency. Provided is a method for calculating and designing an optimum radius of a wire for conducting a signal at a certain frequency, by which a signal cable for use in various situations can be manufactured. From the electrodynamic principle of conductors, considering the influence of the skin effect on the alternating current conductance characteristic, calculating the proper conductor wire diameter according to different skin depths under different frequencies, and designing a proper signal cable structure according to the proper conductor wire diameter. The frequency band is designed to be enhanced according to the frequency band required by work in signal conduction of communication or data and the like. The method is not a fixed design scheme, is a design method and a calculation method, and has high design flexibility in specific application.
Drawings
FIG. 1 is a schematic diagram of skin effect;
FIG. 2 is a graph of impedance versus relative radius change of a wire;
FIG. 3 is a schematic view of a customized wire construction after utilizing the conductors identified in the present invention;
FIG. 4 illustrates the range of frequency bands for various instruments;
FIG. 5 is a table showing frequency ranges of standard musical scales and common musical instruments;
fig. 6 is a table of the frequency ranges of the human voices of various musical instruments.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
One method of determining the diameter of a signal wire conductor from a given frequency is:
determining the radius r of the signal line conductor according to the formula (I) and the formula (II)WThe value range of (A):
r W2 delta ≤ (one)
Figure BDA0002977774870000031
Wherein: delta is the skin depth of the skin effect when the lead transmits electrons;
pi is a constant;
μ0is a constant;
σ is the conductivity of the conductor of the wire;
f is the frequency of the transmission signal;
according to the radius r of the signal line conductorWThe diameter d of the obtained conductor is 2rW。
The specific confirmation process of formula (one) is as follows:
the low-frequency impedance r of the conductor can be known according to the formula (III)lfComprises the following steps:
Figure BDA0002977774870000041
wherein: r isDCIs a direct current resistance;
pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
the high-frequency impedance r of the conductor can be known according to the formula (IV)hfComprises the following steps:
Figure BDA0002977774870000042
wherein: pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
rDCis a direct current resistance;
μ0is a constant;
f is the frequency of the transmission signal;
and (3) obtaining a variation curve of the impedance and the relative radius of the lead by combining the formula (three) and the formula (four), referring to fig. 2, wherein the ordinate is the impedance, and the abscissa is the ratio of the radius of the lead to the skin depth. The curve reflects the variation of the alternating current impedance with the relative radius of the wire. When the relative radius of the wire is greater than 2, the alternating current impedance rises, the value of which is proportional to the square root of the frequency, and when the relative radius is less than 2, the alternating current impedance returns to the direct current impedance. That is, when the ratio of the radius of the wire to the skin depth is within 2 times, the skin effect has minimal effect on current conduction.
See equation (IV), see when rWWhen 2 δ is equal to rDC＝rhfI.e. the high frequency impedance is equal to the dc impedance. The skin effect disappears. Can also refer to the curve when rWWhen the resistance is less than or equal to 2 delta, the curve is a straight line part, namely the resistance of the lead is kept as the direct current resistance. Through curveDetermining wire conductor radius rWHas a value range of rW≤2δ。
In the present embodiment, the audio frequency is transmitted, and a copper wire is selected as an example for explanation;
referring to fig. 1, which is a schematic diagram of the "skin effect", in an ac circuit, as the frequency increases, the current distribution on the cross section of a conducting wire is more and more concentrated on the surface of the conducting wire, resulting in a decrease in effective cross-sectional area and an increase in equivalent resistance. The "skin effect" is significant with increasing frequency, and is quantitatively described by the "skin depth δ". "skin depth" is determined by the following formula:
Figure BDA0002977774870000051
table 1 gives the "skin depth" of the copper conductor at different frequencies: the conductor type is not limited, and the method is applicable to pure silver, pure gold, aluminum and the like; the electrical conductivity of copper is 5.8 × 10 ═ o7S/m。
TABLE 1 "skin depth" of copper conductors at different frequencies "
f δ f δ
50Hz 9.3mm 1MHz 2.6mils
1kHZ 2.09mm 10MHz 0.82mils
10kHZ 0.66mm 100MHz 0.26mils
100kHZ 0.21mm 1GHz 0.0823mils
According to the analysis of the formula (three) and the formula (four), when the radius r of the wire is less than 2 times of the skin depth, the high-frequency conduction characteristic of the conductor is the same as that of direct current, and the influence of the skin effect on the frequency band can be ignored.
Taking a sound wire as an example, the transmission signal range of the sound wire is between 10Hz and 100kHz, in this embodiment, three different wire diameters are adopted to transmit three high, medium and low frequency bands respectively, a wire with a thinner wire diameter is used in the high frequency band to reduce the influence of skin effect, and a thicker wire can be used for energy fullness in the low frequency band. The design can improve the effective conduction area of the wire rod, and the material proportion is more reasonable. Table 2 shows the ratio of the specific wire diameter to the frequency, r, for copper wire as an exampleWWhen the transmission efficiency is 2 δ, the transmission efficiency is the best, that is, table 2 shows the ratio of the line diameter to the frequency when the line diameter is as large as possible and the optimal transmission efficiency is the best. :
TABLE 2 comparison table of wire diameter and frequency of copper wire
Figure BDA0002977774870000052
Figure BDA0002977774870000061
After the diameter of the wire for enhancing the fixed frequency is determined by the determination method of the invention, the structure of the wire can be further formulated, see fig. 3, which is a frequency division conduction balanced signal wire with two groups of same design, one group on the left is seen alone, the wire has 3 wires with different thicknesses, the thick is a low-frequency conduction wire core, the thin is a high-frequency conduction wire core, and the middle is a medium-frequency conduction wire core.
The invention can be further understood that the method is used for determining the diameter of the wire rod and determining the structure of the wire rod, and further performing music integral sound adjustment on the wire rod part, for example, when a lot of low frequencies are needed in an occasion, the wire core suitable for low-frequency conduction can be designed mainly, so that the low-frequency conduction is increased, the hearing of the music is changed, the low-frequency conduction part can be weakened and the design of a plurality of frequency band wire diameters suitable for high-frequency conduction is added aiming at the design that a sound set has more favorite high frequencies, so that the integral music hearing can lead the high-frequency sound to be more beautiful and sweet, and a plurality of independent wires can be used for being woven into a group for use.
The calculation and design scheme of the frequency division conduction is used for tuning an audio signal line, so that the audio signal line has specific sound characteristics, different customer requirements are met, and the design of the audio signal line for private customized tuning is achieved. Because everyone understands sound differently, someone likes high frequency beautiful sound very penetrating, someone likes low frequency powerful have mobility, someone likes the emotional expression of intermediate frequency, so utilize this kind of method, can make into the audio signal line of different sound characteristics with the wire of same model, use this kind of audio signal line, just can increase the frequency channel that the customer wanted, reduce the frequency channel that the customer disliked, make the music more charming.
It should be noted that, in this conduction scheme, instead of the high-frequency channel and the low-frequency channel, the high frequency channel and the low-frequency channel are more and have a small amount of low frequency, and the low frequency channel and the low-frequency channel are more and simultaneously have a small amount of high frequency, but in another fixed low-frequency channel, the high-frequency conduction quantity of the wire is increased, so that the hearing sensation is more and higher.
Referring to fig. 4-6, the most advantageous of the patent is to make a dedicated wire for conducting the frequency band according to the frequency response range of various musical instruments for the range of the musical frequency band of various musical instruments and human voices. In addition, people who like music have different requirements for various forms of music, so that the special frequency division conducting wire can be customized according to the type of music which the people like to listen to and the frequency response range of the included musical instruments.
The determination method of the invention is not only used for the audio signal line, but the embodiment takes the audio signal line as an example for explanation, and the invention is more suitable for the equipment cable signal line with fixed signal frequency, and belongs to the industrial signal line.
The auditory sense of human ears is 20Hz to 20kHz by taking an audio signal as an example, although the specifications of the existing audio signal conductors are different, the audio signal conductors are designed to be conducted in a single channel with a fixed wire diameter, and even if a wire base is designed to be multiple channels, the wire diameters of the channels are the same. Therefore, for example, a common wire diameter of 0.5mm can conduct all bands, but it is found in the patent that a wire diameter of 0.4mm is more suitable for conducting a signal of 100kHz, and the effect is more excellent. The application of this patent can be simply understood as: everyone understands music differently, the pertinence of customer requirements is different, for example, a signal conductor (200Hz-2kHz) suitable for listening to a violin frequency band needs to be customized by one customer, an oxygen-free copper signal wire conducting in a double-wire core of 4.0mm and 2.5mm can be designed and manufactured according to the invention, and therefore, the copper signal wire is more suitable for music conduction of the violin playing frequency band. Similarly, the invention can also be used for increasing the aim-oriented reinforcement of other frequency bands, and only the wire cores with the diameters of the corresponding frequency bands are required to be continuously increased. For a frequency signal with a floating range, such as an audio signal, if the frequency signal is conducted at a fixed frequency in the industry and the signal type of the fixed frequency is more required, for example, when a set of devices simultaneously requires signals of 30kHz, 50kHz and 100kHz, a conventional multi-core conductor with the same diameter (for example, 1.0mm × 3 cores of oxygen-free copper) can be designed as follows: 1.5mm, 1.2mm, 0.8mm, combined wire base to achieve best signal transmission.

Claims (2)

1. A method for determining the diameter of a signal wire conductor according to a predetermined frequency is characterized by comprising the following steps:
determining the radius r of the signal line conductor according to the formula (I) and the formula (II)WThe value range of (A):
rW2 delta ≤ (one)
Figure FDA0002977774860000011
Wherein: delta is the skin depth of the skin effect when the lead transmits alternating current;
pi is a constant;
μ0is a constant;
σ is the conductivity of the conductor of the wire;
f is the frequency of the transmission signal;
according to the radius r of the signal line conductorWThe diameter d of the obtained conductor is 2rW。
2. The method of claim 1, wherein the specific validation process of formula (one) is:
the low-frequency impedance r of the conductor can be known according to the formula (III)lfComprises the following steps:
Figure FDA0002977774860000012
wherein: r isDCIs a direct current resistance;
pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
from equation (four), the high frequency impedance rhf of the conductor is:
Figure FDA0002977774860000013
wherein: pi is a constant;
σ is the conductivity of the conductor of the wire;
rWis the conductor radius;
rDCis a direct current resistance;
μ0is a constant;
f is the frequency of the transmission signal;
combining the formula (three) and the formula (four), determining the radius r of the wire conductorWWhen the diameter is less than or equal to 2 delta, the skin effect influence is minimum, and the radius r of the wire conductor is determinedWHas a value range of rW≤2δ。
CN202110279092.1A 2021-03-16 2021-03-16 Method for determining diameter of signal wire conductor according to preset frequency Pending CN113028971A (en)

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU2786400A (en) * 1999-06-09 2001-01-02 Keith Louis Eichmann A specific cable ratio for high fidelity audio cables
CN2641773Y (en) * 2003-06-25 2004-09-15 永琨有限公司 All frequency adaptive structure improved audio signal wire
CN2650300Y (en) * 2003-10-17 2004-10-20 永琨有限公司 Audio-video signal wire
EP1566817A1 (en) * 2004-02-18 2005-08-24 Rich Electric Wire & Cable Co., Ltd. Improved structure of audio signal cable
CN101202134A (en) * 2007-11-25 2008-06-18 刘文广 High-fidelity acoustics wire rod
CN101398369A (en) * 2007-09-30 2009-04-01 通用电气公司 Device and method for monitoring surface corrosion

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
AU2786400A (en) * 1999-06-09 2001-01-02 Keith Louis Eichmann A specific cable ratio for high fidelity audio cables
CN2641773Y (en) * 2003-06-25 2004-09-15 永琨有限公司 All frequency adaptive structure improved audio signal wire
CN2650300Y (en) * 2003-10-17 2004-10-20 永琨有限公司 Audio-video signal wire
EP1566817A1 (en) * 2004-02-18 2005-08-24 Rich Electric Wire & Cable Co., Ltd. Improved structure of audio signal cable
CN101398369A (en) * 2007-09-30 2009-04-01 通用电气公司 Device and method for monitoring surface corrosion
CN101202134A (en) * 2007-11-25 2008-06-18 刘文广 High-fidelity acoustics wire rod

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
WATT，A.D.: "《甚低频无线电工程》", 31 January 1973 *
戴欣 等: "单轨行车新型供电方式及相关技术分析", 重庆大学学报 *
黄孝键: "基于多物理场的高速永磁同步电机多目标优化研究", 中国优秀硕士学位论文全文数据库工程科技Ⅱ辑 *

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