Cov Txheej Txheem Tshawb Fawb Mesh hauv Circuits
Kev tshuaj xyuas hluav taws xob hauv lub voj voog yog ib qho ntawm cov txuj ci tseem ceeb uas yuav tsum muaj hauv kev tsim hluav taws xob, mechatronics, thiab electronics. Ntawm ntau txoj kev siv los txiav txim siab tam sim no thiab voltage hauv lub voj voog, kev tshuaj xyuas mesh yog ib qho nrov tshaj plaws, tshwj xeeb tshaj yog rau cov voj voog planar uas muaj cov khoom tiv taus thiab cov khoom siv hluav taws xob. Txoj kev no pab peb sau cov kab zauv hauv lub voj voog siv Kirchhoff's Voltage Law (KVL), kom tus nqi tam sim no hauv txhua lub voj voog tuaj yeem tau txais hauv txoj kev teeb tsa thiab ua haujlwm tau zoo.
Nkag Siab Txog Mesh Thiab Loop
Ua ntej nkag mus rau hauv cov kauj ruam xam zauv, nws yog ib qho tseem ceeb kom nkag siab cov lus tseem ceeb:
- Ib lub voj voog yog ib txoj kev kaw hauv ib lub voj voog, pib ntawm ib qho chaw, hla dhau ntau yam khoom, thiab rov qab mus rau qhov chaw pib.
- Ib lub mesh yog ib lub voj tshwj xeeb uas tsis muaj lwm lub voj sab hauv. Hauv lwm lo lus, lub mesh yog "lub voj me tshaj plaws" hauv ib lub voj voog planar.
Kev tshuaj xyuas Mesh ua haujlwm los ntawm kev txiav txim siab cov mesh currents ntawm txhua lub mesh thiab tom qab ntawd siv KVL rau txhua lub mesh. Los ntawm cov qauv tshwm sim, peb tuaj yeem daws rau cov mesh currents thiab tom qab ntawd tau txais cov ceg currents thiab lwm yam khoom voltages raws li qhov xav tau.
Thaum Twg Siv Mesh Analysis?
Cov txheej txheem tshuaj xyuas mesh yog qhov tsim nyog rau kev siv thaum:
1. Lub voj voog yog planar (tuaj yeem kos tau yam tsis muaj xov hlau hla ib leeg).
2. Tus naj npawb ntawm cov meshes yog me me piv rau tus naj npawb ntawm cov nodes, yog li nws muaj txiaj ntsig ntau dua li kev tshuaj xyuas nodal.
3. Lub voj voog muaj ntau qhov chaw hluav taws xob, vim KVL ib txwm muaj cov chaw hluav taws xob ncaj qha.
Ntawm qhov tod tes, yog tias lub voj voog muaj ntau qhov chaw tam sim no lossis yooj yim dua los txheeb xyuas los ntawm sab node, kev txheeb xyuas nodal tuaj yeem yog lwm txoj hauv kev yooj yim dua.
Txoj Cai Tseem Ceeb: Kirchhoff's Voltage Law (KVL)
KVL hais tias qhov sib npaug ntawm cov kev ntxhov siab hauv txoj kev kaw yog xoom. Kev suav lej:
\[
\sum V = 0
\]
Hauv kev tshuaj xyuas mesh, KVL siv rau txhua lub mesh. Lub zog hluav taws xob hla lub resistor feem ntau yog sau siv Ohm's Law:
\[
V = I²D R
\]
Txawm li cas los xij, vim tias tam sim no hauv lub resistor tuaj yeem yog qhov sib txawv ntawm ob lub mesh currents (yog tias lub resistor nyob hauv ib ceg sib koom), ib daim ntawv zoo li qhov no yuav tshwm sim:
\[
V_R = (I_1 – I_2)R
\]
qhov twg \(I_1\) thiab \(I_2\) yog cov mesh currents sib koom cov resistors.
Cov Kauj Ruam Tshawb Fawb Txog Mesh
Cov hauv qab no yog cov txheej txheem tshuaj xyuas mesh dav dav uas tuaj yeem siv rau ntau yam circuits:
1. Txheeb xyuas lub Mesh hauv Circuit
Kos lub voj voog kom meej, tom qab ntawd txhais cov meshes. Xyuas kom tseeb tias txhua lub mesh yog lub voj voog me tshaj plaws uas tsis muaj lwm lub voj voog nyob hauv.
2. Txheeb xyuas qhov kev taw qhia ntawm Mesh Current
Muab cov mesh currents rau txhua lub mesh, feem ntau yog txhua yam clockwise rau qhov sib xws. Xav tias \(I_1, I_2, I_3\), thiab lwm yam.
Qhov kev taw qhia no tuaj yeem xaiv tau ywj pheej. Yog tias qhov tam sim no tshwm sim yog qhov tsis zoo, nws txhais tau tias qhov kev taw qhia tiag tiag yog qhov txawv ntawm qhov kev xav thawj zaug.
3. Sau tus qauv KVL rau txhua lub mesh.
Tshawb nrhiav cov ntsiab lus ntawm lub mesh thiab sau qhov ntau ntawm kev ntxhov siab nce thiab nqis kom txog thaum nws rov qab mus rau qhov chaw pib.
- Rau ib lub resistor uas tsuas nqa ib lub mesh tam sim no: \(V = I_k R\)
- Rau cov resistors sib koom ob lub meshes: \(V = (I_k - I_m)R\), nyob ntawm seb qhov tam sim no coj li cas piv rau lub voj voog uas raug tshuaj xyuas.
- Rau cov qhov hluav taws xob: sau ua +V lossis -V raws li polarity piv rau txoj kev.
4. Npaj cov kab zauv hauv daim ntawv Linear System
Tom qab tau txais tag nrho cov KVL equations, koj yuav tau txais ib qho system ntawm linear equations hauv daim ntawv:
\[
a_{11}I_1 + a_{12}I_2 + \dots = b_1
\]
Lub kaw lus no tuaj yeem daws tau los ntawm kev tshem tawm Gaussian, kev hloov pauv, kev txiav txim siab (Cramer), lossis siv software xws li MATLAB, Python (NumPy), lossis lub tshuab xam zauv scientific.
5. Xam Qhov Tam Sim No Ntawm Ceg Thiab Qhov Hluav Taws Xob Ntawm Cov Khoom
Qhov tam sim no ntawm ib qho khoom tshwj xeeb tuaj yeem sib npaug rau qhov tam sim no ntawm lub mesh, lossis qhov sib txawv ntawm ob lub mesh tam sim no yog tias cov khoom nyob hauv ib ceg ua ke. Tom qab ntawd qhov hluav taws xob ntawm cov khoom raug suav los ntawm kev siv Ohm's Law.
Piv Txwv Lub Tswv Yim (Tsis Muaj Duab)
Xav tias muaj ob lub meshes uas sib koom ib lub resistor \(R_3\). Lub mesh sab laug muaj resistor \(R_1\) thiab lub qhov hluav taws xob \(V_s\), lub mesh sab xis muaj resistor \(R_2\). Resistor \(R_3\) nyob hauv nruab nrab thiab sib koom.
Txheeb xyuas cov mesh currents \(I_1\) (sab laug) thiab \(I_2\) (sab xis), ob qho tib si clockwise.
KVL tus qauv:
Mesh 1:
\[
-V_s + I_1R_1 + (I_1 – I_2)R_3 = 0
\]
Mesh 2:
\[
Kuv_2R_2 + (I_2 – Kuv_1)R_3 = 0
\]
Los ntawm ob qho kev sib npaug no, koj tuaj yeem daws tau rau \(I_1\) thiab \(I_2\). Tam sim no hauv nruab nrab resistor \(R_3\) yog \((I_1 - I_2)\) (nyob ntawm qhov txhais ntawm kev taw qhia).
Qhov piv txwv no qhia txog lub ntsiab lus ntawm kev tsom xam mesh: thaum muaj cov khoom sib koom, lawv cov tam sim no muaj feem cuam tshuam nrog qhov sib txawv ntawm cov tam sim no mesh.
Supermesh: Cov Ntaub Ntawv ntawm Qhov Muaj Nyob ntawm Qhov Chaw Tam Sim No
Qee zaum ib lub voj voog muaj qhov chaw tam sim no ntawm ob lub meshes sib ze. Hauv qhov xwm txheej no, nws nyuaj rau sau KVL ib txwm vim tias qhov hluav taws xob hla qhov chaw tam sim no feem ntau tsis paub. Txhawm rau kov yeej qhov teeb meem no, lub tswv yim ntawm supermesh yog siv.
Supermesh yog dab tsi?
Ib qho supermesh yog kev sib xyaw ua ke ntawm ob lub meshes uas sib koom ib qho chaw tam sim no ntawm tib ceg. Cov kauj ruam yog:
1. Muab ob lub meshes ua ke rau hauv ib lub voj loj (supermesh).
2. Sau ib daim KVL nyob ib ncig ntawm lub supermesh, hla dhau txhua yam tshwj tsis yog qhov chaw tam sim no (vim nws qhov voltage tsis paub).
3. Ntxiv cov kab zauv ntxiv los ntawm qhov chaw tam sim no, piv txwv li:
\[
Kuv_1 – Kuv_2 = Kuv_s
\]
raws li qhov kev taw qhia ntawm qhov chaw tam sim no.
Yog li, tus naj npawb ntawm cov qauv tseem txaus los daws txhua qhov mesh currents.
Cov Zoo thiab Cov Kev Txwv ntawm Kev Tshawb Fawb Mesh
Keunggulan
- Kev siv tshuab thiab yooj yim rau kev siv rau cov voj voog planar.
- Haum rau cov circuits nrog ntau qhov chaw voltage.
- Tus naj npawb ntawm cov qauv feem ntau yog sib npaug rau tus naj npawb ntawm cov meshes, feem ntau tsawg dua li lwm txoj kev.
Cov kev txwv
- Tsis zoo tagnrho rau cov circuits uas tsis yog planar.
- Yog tias muaj ntau qhov chaw tam sim no, supermesh tuaj yeem ua rau cov kauj ruam nyuaj me ntsis.
- Rau cov network loj uas muaj ntau lub meshes, lub kaw lus ntawm cov kab zauv tuaj yeem ntev.
Cov Lus Qhia Siv Tau Thaum Siv Mesh Analysis
1. Ua raws li qhov kev taw qhia tam sim no: xaiv txhua yam raws li moos kom yooj yim dua rau kev cim.
2. Ua tib zoo saib xyuas tus resistor: nws qhov tam sim no yog qhov sib txawv ntawm ob lub mesh currents, tsis yog ib qho xwb.
3. Sau KVL kom zoo: xaiv qhov chaw pib thiab kev tshawb nrhiav kom meej.
4. Tshawb xyuas cov chav thiab cov cim: qhov yuam kev feem ntau tshwm sim los ntawm kev cim tsis raug ntawm qhov chaw polarity lossis lub cim ntawm qhov sib txawv tam sim no.
5. Xyuas kom tseeb tias cov txiaj ntsig: tom qab tau txais tam sim no, rov xyuas dua nrog KCL ntawm ib qho node tshwj xeeb lossis xam lub zog kom ntseeg tau tias muaj kev sib xws.
Kev kaw
Kev tshuaj xyuas mesh yog ib txoj hauv kev tseem ceeb rau kev tshuaj xyuas cov hluav taws xob circuits, tshwj xeeb tshaj yog planar circuits uas muaj resistors thiab voltage sources. Los ntawm kev txhais cov mesh currents thiab siv KVL, peb tuaj yeem tsim ib lub system ntawm cov equations uas lej sawv cev rau tus cwj pwm ntawm lub circuit. Cov tswv yim xws li cov resistors thiab supermeshes tso cai rau txoj kev no kom tseem ua haujlwm txawm tias lub circuit muaj cov ceg sib xyaw lossis cov chaw tam sim no. Kev paub txog kev tshuaj xyuas mesh tsis yog tsuas yog pab daws cov teeb meem kev kawm xwb tab sis kuj muab lub hauv paus ruaj khov rau kev nkag siab txog kev tsim circuit thiab kev daws teeb meem hauv kev xyaum engineering tiag tiag.
Yog tias koj xav tau, kuv tuaj yeem ntxiv ib qho piv txwv lej tiav (nrog rau R thiab V tus nqi, txog rau qhov tam sim no thiab voltage rau txhua yam khoom) kom ua rau tsab xov xwm siv tau ntau dua.
