Dabaru na Binciken Mita a cikin Da'irori
Binciken mita yana ɗaya daga cikin mahimman hanyoyin da ake amfani da su a fannin injiniyan lantarki da lantarki don fahimtar halayen da'ira idan aka ba su shigarwar sigina mai canzawa lokaci. Ba kamar nazarin lokaci-lokaci ba, wanda ke bincika ƙarfin lantarki da halin yanzu a matsayin aikin lokaci, nazarin mita-yankin yana nazarin yadda da'ira ke amsawa ga takamaiman abubuwan da ke cikin mita. Wannan dabarar tana da matuƙar amfani a cikin ƙirar amplifiers na sauti, matattara, tsarin sadarwa, sarrafa sigina, da da'irorin sarrafawa. Ta hanyar fahimtar amsawar mita, mai ƙira zai iya hasashen ribar da'ira, raguwa, karkacewa, kwanciyar hankali, da halayen zaɓi.
Ka'idoji na Asali: Sigina da Bakan Mita
Ana iya bayyana sigina na gaske da yawa a matsayin haɗuwa da raƙuman sine da yawa. Wannan ƙa'ida an san ta ta hanyar jerin Fourier da Fourier transforms, waɗanda ke nuna cewa siginar lokaci-lokaci za a iya raba ta cikin sassan sine ɗinta a cikin mitoci na asali da kuma jituwa. A gefe guda kuma, ana iya yin nazarin siginar da ba ta lokaci-lokaci ta amfani da canjin Fourier mai ci gaba don samun mitoci na mitar su.
A cikin mahallin da'irori, ana yin nazarin mitar ta hanyar bincika martanin da'irar ga siginar sinusoidal guda ɗaya a mitoci daban-daban. Sakamakon shine alaƙa tsakanin mitar da girman fitarwa da canjin lokaci. Idan shigarwar ta kasance \( V_{in}(t)=V_m \sin(\omega t) \), to za a iya rubuta fitowar da'irar layi kamar haka:
\[
V_{out}(t) = |H(j\omega)| V_m \sin(\omega t + \angle H(j\omega))
\]
inda \(H(j\omega)\) shine aikin canja wurin da ke ɗauke da bayanai game da riba da mataki a mita \(\omega\).
Rikici Mai Hadari: Mabuɗin Nazarin AC
Dabaru na nazarin mitar wutar lantarki don da'irori na AC sun dogara sosai akan manufar impedance mai rikitarwa. Resistor, capacitors, da inductors suna da alaƙa daban-daban tsakanin ƙarfin lantarki da halin yanzu da mita. A cikin yankin mitar wutar lantarki, ana wakiltar waɗannan abubuwan kamar haka:
– Resistor: \( Z_R = R \)
– Inductor: \( Z_L = j\omega L \)
– Capacitor: \( Z_C = \frac{1}{j\omega C} \)
Ta amfani da impedance, ana iya amfani da dokar Ohm, dokokin Kirchhoff, da dabarun nazarin da'ira (mesh/nodal) kai tsaye, amma a cikin tsari mai rikitarwa na lamba. Daga wannan, za mu iya gina aikin canja wuri da kuma ƙididdige ƙarfin fitarwa, halin yanzu, da mataki.
Aikin Canja wurin da Amsar Mita
Aikin canja wuri \(H(s)\) shine rabon fitarwa zuwa shigarwa a cikin yankin Laplace:
\[
H(s) = \frac{V_{out}(s)}{V_{in}(s)}
\]
Don nazarin mita, muna maye gurbin \(s\) da \(j\omega\) ta yadda:
\[
H(j\omega) = H(s)\babban|_{s=j\omega}
\]
Ƙimar \( |H(j\omega)| \) tana nuna yawan girman da aka ƙara ko aka rage, yayin da \( \angle H(j\omega) \) ke nuna canjin lokaci.
Amsar mita yawanci ana iya gani ta hanyar amfani da manyan jadawali guda biyu:
1. Girma da mita
2. Mataki vs mita
Sau da yawa ana shirya su duka a cikin siffar Bode.
Tsarin Bode: Kayan aiki Mai Amfani Don Kimanta Da'ira
Tsarin Bode hanya ce ta yau da kullun don tsara martanin mita akan sikelin logarithmic. Yawanci ana bayyana girman a cikin decibels (dB):
\[
|H|_{dB} = 20 \log_{10} |H(j\omega)|
\]
Amfanin ma'aunin logarithmic shine cewa ana iya nuna kewayon mita mai faɗi a sarari, kuma ana iya ganin canje-canje a cikin gangara cikin sauƙi.
A tsarin tsari na farko, gangaren yana canzawa a kusa da mitar yankewa (\( f_c \)). Misali, a cikin matatar RC mai ƙarancin wucewa:
\[
H(j\omega)=\frac{1}{1+j\omega RC}
\]
Ana ƙayyade mizanin yankewa ta hanyar:
\[
\omega_c=\frac{1}{RC}, \quad f_c=\frac{1}{2\pi RC}
\]
A ƙasan \(f_c\), siginar tana wucewa ba tare da raguwa ba. A sama \(f_c\), martanin yana raguwa da kusan \(-20\) dB a kowace shekaru goma.
Ga da'irori masu tsari na biyu, gangaren na iya kaiwa dB a kowace shekara goma kuma yanayin resonance na iya bayyana, ya danganta da ƙimar damping.
Matattara: Babban Amfani da Nazarin Mita
Matattara da'ira ce da aka tsara don wucewa ko ƙin wasu takamaiman mitoci. Nau'ikan matattara da aka saba amfani da su sun haɗa da:
1. Matatar mai ƙarancin wucewa (LPF): tana wuce ƙananan mitoci, tana riƙe manyan mitoci.
2. Matatar mai wucewa mai yawa (HPF): tana wucewa mai yawa, tana riƙe da ƙananan mitoci.
3. Matatar wucewa ta Band-pass (BPF): tana wucewa ta wani takamaiman kewayon mita.
4. Matatar tsayawa/tsayawa: tana ƙin wani takamaiman kewayon mita.
Binciken mita yana taimakawa wajen tantance muhimman sigogi kamar mitar yankewa, bandwidth, quality factor \(Q\), da matakin ragewa. A cikin matatar band-pass ta RLC, misali:
\[
f_0=\frac{1}{2\pi\sqrt{LC}}
\]
Abubuwan Inganci:
\[
Q=\frac{\omega_0 L}{R}
\]
Mafi girman \(Q\), haka ma ƙaramar ma'aunin mitar ke wucewa, kuma zaɓin zai yi kaifi.
Dabaru na Bincike: Nodal, Rataye, da Matsayin Gabatarwa
Ana amfani da dabarun lissafi da dama wajen nazarin mita:
– Nazarin Nodal: yana amfani da ƙarfin lantarki na nodal da kuma hadaddun impedances don gina daidaito. Yana da matuƙar tasiri ga da'irori masu rassa da yawa.
– Binciken raga: ya dace da da'irori masu siffar planar tare da madaukai masu haske.
– Matsayin da ya fi girma: idan akwai maɓuɓɓuka da yawa na mitoci daban-daban, ana nazarin kowace tushe daban-daban kuma ana haɗa sakamakon tare. Duk da haka, wannan ya shafi da'irorin layi ne kawai.
– Ka'idar Thevenin/Norton: tana sauƙaƙa da'irori masu rikitarwa zuwa waɗanda suka yi daidai don lissafin amsawar mita ya fi sauƙi.
Da waɗannan kayan aikin, za mu iya samo aikin canja wurin ko kuma mu ƙididdige martani kai tsaye a wani mita da aka bayar.
Ra'ayi da Kwanciyar Hankali a Da'irori Masu Yawa
A cikin da'irori masu ɗauke da inductor da capacitors, resonance muhimmin abu ne. Resonance yana faruwa ne lokacin da amsawar inductive da capacitive suka soke juna:
\[
\omega L = \frac{1}{\omega C}
\]
Don haka ƙarfin da'irar zai iya zama mafi ƙaranci (a cikin jerin RLC) ko mafi girma (a cikin layi ɗaya RLC). Ana amfani da resonance a cikin masu gyara rediyo, masu juyawa, da masu zaɓar tashar mita.
A cikin da'irori masu ƙara amsawa da tsarin sarrafawa, ana amfani da nazarin mita don tantance kwanciyar hankali. Ra'ayoyi kamar margin phase da gain margin suna taimakawa wajen tabbatar da cewa da'irar ba ta yin motsi ko samar da martani mara kyau ba.
Kayan Aikin Aunawa da Kwaikwayo don Nazarin Mita
A aikace, ana yin nazarin mita ta amfani da:
- Mai samar da aiki don share mitar shigarwa.
- Oscilloscope don duba girman da canjin lokaci.
- Mai nazarin hanyar sadarwa don ƙarin ma'aunin amsawar mita daidai.
– Manhajar kwaikwayo kamar SPICE (LTspice, Multisim, Proteus) tana ba da nazarin sharewa na AC. Tare da kwaikwayon, za mu iya nuna zane-zanen Bode kai tsaye, nemo wuraren yankewa, da kuma duba tasirin juriyar sassan.
Kwaikwayo ba madadin ma'auni na gaske ba ne, amma yana da tasiri sosai don tabbatar da ƙira da wuri.
Kammalawa
Dabaru na nazarin mita a cikin da'irori hanya ce mai mahimmanci ta fahimtar yadda da'irori ke amsawa ga sigina a mitoci daban-daban. Ta hanyar amfani da hadaddun impedances, ayyukan canja wuri, da kuma zane-zanen Bode, za mu iya hasashen halayen riba, mataki, da tacewa da kuma rawar jiki. Wannan bincike yana taimaka wa masu zane su tsara tsarin da ke da zaɓi, kwanciyar hankali, kuma ya dace da aikace-aikace tun daga sauti zuwa sadarwa. Haɗin lissafin ka'idoji, kwaikwayo, da ma'auni masu amfani yana sa nazarin mita ya zama muhimmin ƙwarewa ga duk wanda ke aiki a injiniyan lantarki da lantarki.
