Ngā Tikanga Tātari Auautanga i roto i ngā Porowhita
Ko te tātari auau tētahi o ngā huarahi tino nui i roto i te hangarau hiko me te hangarau hiko hei mārama ki te whanonga o te ara iahiko ina tukuna he tohu whakauru rerekē-wā. Kāore i rite ki te tātari rohe-wā, e tirotiro ana i te ngaohiko me te iahiko hei mahi a te wā, ka ako te tātari rohe-auau i te urupare a te ara iahiko ki ngā wāhanga auau motuhake. He tino whai hua tēnei tikanga i roto i te hoahoa o ngā whakakaha oro, ngā tātari, ngā pūnaha whakawhitiwhiti kōrero, te tukatuka tohu, me ngā ara iahiko whakahaere. Mā te mārama ki te urupare auau, ka taea e te kaihoahoa te matapae i te pikinga, te whakaiti, te whakapōturi, te pumau, me ngā āhuatanga whiriwhiri o te ara iahiko.
Ngā Ariā Taketake: Ngā Tohu me te Auahatanga Auautanga
He maha ngā tohu tūturu ka taea te whakaatu hei huinga o ngā ngaru sine maha. E mōhiotia ana tēnei mātāpono mā roto i ngā raupapa Fourier me ngā panonitanga Fourier, e kī ana ka taea te wehewehe i tētahi tohu ā-wā ki ōna wāhanga sine i tōna auau taketake me ngā harmonics. Ko ngā tohu kore-ā-wā, i tētahi atu taha, ka taea te tātari mā te whakamahi i ngā panonitanga Fourier tonu hei whiwhi i tā rātou whānuitanga auau.
I roto i te horopaki o ngā ara iahiko, ka mahia te tātari auau mā te tirotiro i te urupare a te ara iahiko ki tētahi tohu sinusoidal kotahi i ngā auau rerekē. Ko te hua he whanaungatanga i waenga i te auau me te kaha putanga me te nekehanga ā-wāhanga. Mena ko te tāuru ko \( V_{in}(t)=V_m \sin(\omega t) \), ka taea te tuhi i te putanga o tētahi ara iahiko rārangi penei:
\[
V_{puta}(t) = |H(j\omega)| V_m \sin(\omega t + \angle H(j\omega))
\]
ko \(H(j\omega)\) te mahi whakawhiti kei roto ko ngā mōhiohio whakanui me te wāhanga i te auau \(\omega\).
Āraitanga Matatini: Te Kī ki te Tātaritanga AC
Ko ngā tikanga tātari auau mō ngā ara iahiko AC e whakawhirinaki nui ana ki te ariā o te aukati matatini. He rerekē ngā whanaungatanga ngaohiko-auau o ngā ātete, ngā pūnga, me ngā inductors ki te auau. I roto i te rohe auau, ka whakaatuhia ēnei huānga penei:
– Ātete: \( Z_R = R \)
– Pūwhakakorikori: \( Z_L = j\omega L \)
– Pūngao: \( Z_C = \frac{1}{j\omega C} \)
Mā te whakamahi i te aukati, ka taea te whakamahi tika i te ture a Ohm, ngā ture a Kirchhoff, me ngā tikanga tātari ara iahiko (mata/pūnga), engari i roto i te āhua tau matatini. Mai i tēnei, ka taea e tātou te hanga i te mahi whakawhiti me te tatau i te ngaohiko putanga, te iahiko, me te wāhanga.
Mahi Whakawhiti me te Urupare Auautanga
Ko te mahi whakawhiti \(H(s)\) ko te ōwehenga o te putanga ki te tāuru i roto i te rohe Laplace:
\[
H(s) = \frac{V_{out}(s)}{V_{in}(s)}
\]
Mō te tātari auau, ka whakakapia e mātou a \(s\) ki a \(j\omega\) kia:
\[
H(j\omega) = H(s)\big|_{s=j\omega}
\]
Ko te uara \( |H(j\omega)| \) e tohu ana i te nui o te whakanui, te whakaiti rānei i te kaha, ko te \( \angle H(j\omega) \) ia e tohu ana i te nekehanga ā-wāhanga.
Ko te urupare auau ka whakaatuhia mā te whakamahi i ngā kauwhata matua e rua:
1. Te rahi me te auau
2. Āhuatanga me te auau
He maha ngā wā ka whakaritea ngā mea e rua hei kauwhata Bode.
Te Kaupapa Bode: He Utauta Whai Hua mō te Aromatawai Porowhita
Ko te kauwhata Bode he huarahi paerewa hei kauwhata i te urupare auau i runga i te tauine logarithmic. Ko te rahi e whakaatuhia ana i roto i ngā decibels (dB):
\[
|H|_{dB} = 20 \log_{10} |H(j\omega)|
\]
Ko te painga o te tauine taupū ko te whakaatu mārama i te whānuitanga o te auau, ā, he ngāwari te kite i ngā panonitanga o te pari.
I roto i te pūnaha tuatahi-raupapa, ka huri te pari huri noa i te auau tapahi (\( f_c \)). Hei tauira, i roto i te tātari RC iti-haere:
\[
H(j\omega)=\frac{1}{1+j\omega RC}
\]
Ka whakatauhia te auau tapahi e:
\[
\omega_c=\frac{1}{RC}, \quad f_c=\frac{1}{2\pi RC}
\]
I raro iho i te \(f_c\), ka rere te tohu me te kore e ngoikore. I runga ake i te \(f_c\), ka heke te urupare mā te \(-20\) dB i ia tekau tau.
Mō ngā ara iahiko tuarua, ka taea e te pari te eke ki te \(-40\) dB i ia tekau tau, ā, ka puta pea ngā āhuatanga orooro, i runga i te uara whakaiti.
Ngā Tātari: Te Whakamahinga Matua o te Tātari Auautanga
He ara iahiko te tātari i hangaia hei tuku, hei whakakore rānei i tētahi whānuitanga auau motuhake. Ko ngā momo tātari noa ko:
1. Tātari pā-iti (LPF): ka tukuna ngā auau iti, ka pupuri i ngā auau teitei.
2. Tātari whakawhiti-teitei (HPF): ka tukuna ngā auau teitei, ka pupuri i ngā auau iti.
3. Tātari whakawhiti-roopu (BPF): ka whiti i tētahi awhe auau.
4. Tātari aukati-roopu/tātari notch: ka whakakore i tētahi awhe auau.
Mā te tātari auau ka āwhina i te whakatau i ngā tawhā nui pēnei i te auau tapahi, te whānui o te hononga, te tauwehenga kounga \(Q\), me te taumata whakaiti. Hei tauira, i roto i te tātari whakawhiti-roopu RLC:
\[
f_0=\frac{1}{2\pi\sqrt{LC}}
\]
Ngā āhuatanga kounga:
\[
Q=\frac{\omega_0 L}{R}
\]
Ka teitei ake te \(Q\), ka whaiti ake te rerenga auau, ā, ka koi ake hoki te whiriwhiri.
Ngā Tikanga Tātari: Pūnga, Mata, me te Taupokitanga
He maha ngā tikanga tatau e whakamahia ana i roto i te tātari auau:
– Tātaritanga pona: ka whakamahia ngā ngaohiko pona me ngā āraitanga matatini hei hanga whārite. He tino whai hua mō ngā ara iahiko he maha ngā peka.
– Tātaritanga mata: he pai mō ngā ara iahiko papatahi me ngā koropiko mārama.
– Te Whakatairanga: mēnā he maha ngā pūtake o ngā auau rerekē, ka tātarihia motuhaketia ia pūtake, ā, ka tāpirihia ngā hua. Heoi, ka pā anake tēnei ki ngā ara iahiko rārangi.
– Te ariā Thevenin/Norton: ka whakangawari i ngā ara iahiko uaua ki ngā ara iahiko ōrite kia māmā ake ai ngā tataunga urupare auau.
Mā te whakamahi i ēnei taputapu, ka taea e tātou te whakaputa i te mahi whakawhiti, te tatau tika rānei i te urupare i tētahi auau kua hoatu.
Te Āhuatanga me te Pūmautanga i roto i ngā Porowhita Auautanga
I roto i ngā ara iahiko kei roto ngā inductors me ngā capacitors, he āhuatanga nui te resonance. Ka puta te resonance ina whakakorea ngā tauhohenga inductors me te capacitive:
\[
\omega L = \frac{1}{\omega C}
\]
Nō reira, ka taea te iti rawa o te aukati ara iahiko (i roto i te raupapa RLC) te mōrahi rānei (i roto i te whakarara RLC). Ka whakamahia te haruru i roto i ngā kaiwhakatika reo irirangi, ngā oscillator, me ngā tīpakonga hongere auau.
I roto i ngā ara iahiko whakakaha urupare me ngā pūnaha whakahaere, ka whakamahia hoki te tātari auau hei aromatawai i te pumau. Mā ngā ariā pēnei i te tawhē ā-wāhanga me te tawhē whakanui ka āwhina kia kore te ara iahiko e wiri, e whakaputa rānei i ngā urupare kāore e hiahiatia.
Ngā Utauta Ine me te Whakatauira mō te Tātari Auautanga
I roto i te mahi, ka whakahaerehia te tātari auau mā te whakamahi i:
– Pūwhakaputa mahi hei horoi i te auau tāuru.
– He oscilloscope hei tiro i te nekehanga o te kaha me te nekehanga ā-wāhanga.
– He tātari whatunga mō ngā inenga urupare auau tika ake.
– Mā ngā pūmanawa whakatauira pērā i a SPICE (LTspice, Multisim, Proteus) ka taea te whakarato i te tātaritanga AC sweep. Mā te whakatauira, ka taea e tātou te whakaatu tika i ngā kauwhata Bode, te kimi i ngā pūwāhi tapahi, me te tirotiro i ngā pānga o ngā manawanui wāhanga.
Ehara te whakatauira i te whakakapi mō ngā inenga tūturu, engari he tino whai hua mō te whakamana wawe i te hoahoa.
Whakamutunga
Ko ngā tikanga tātari auau i roto i ngā ara iahiko he huarahi taketake ki te mārama ki te urupare a ngā ara iahiko ki ngā tohu i ngā auau rerekē. Mā te whakamahi i ngā ārai uaua, ngā mahi whakawhiti, me ngā kauwhata Bode, ka taea e tātou te matapae i te whanonga pikinga, ā-wāhanga, tātari me te haruru. Ka āwhina tēnei tātari i ngā kaihoahoa ki te hoahoa i ngā pūnaha he whiriwhiri, he pumau, he pai hoki mō ngā tono mai i te oro ki ngā whakawhitiwhiti kōrero. Mā te whakakotahitanga o ngā tātaitanga ariā, ngā whakatauira, me ngā inenga mahi ka waiho te tātari auau hei pūkenga nui mō te hunga e mahi ana i roto i te hangarau hiko me te hangarau hiko.
