Me kuke so kuwa shi ne Theorem ta Norton Da Yadda a Samun Kirkiro da Kafin Masu Amfani da Ita

فیلڈ: Karkashin Kuliya da Dukkana

China

Me kwa ce Norton Theorem? (Norton’s Equivalent Circuit)

Norton Theorem (ko da ake kira Mayer–Norton theorem) yana nuna cewa zai iya sauti wani circuit mai tsari zuwa wani circuit na musamman da take da tsohon mafi ruwa da kuma rikicin kusa da mutanen gaba. Wani circuit na musamman yana ake kira Norton Equivalent Circuit.

A nan, za a iya bayarwa cewa:

“Wani circuit da ke da ake amfani da shi da linear bilateral elements da kuma active sources zai iya canzawa da wani two-terminal network na musamman da ke da impedance da kuma current source, baya da tsarin network.”

Norton theorem yana da muhimmanci da Thevenin’s theorem. Kuma ana amfani da ita a fannin analysis ta circuit don sauti networks masu tsari da kuma karin hankali kan initial condition da kuma steady-state response ta circuit.

企业微信截图_17102256417070.png 企业微信截图_17102256537679.png

Norton Theorem

Kamar yadda aka bayar a sune, wani network mai tsari zai iya sauti zuwa wani Norton equivalent circuit na musamman.

Norton equivalent circuit yana da equivalent impedance da ya kusa da current source da kuma load resistance.

Mafi ruwa da ake amfani da ita a cikin Norton equivalent circuit yana ake kira Norton current IN ko short circuit current ISC.

An tsarin Norton an samu shi da Hans Ferdinand Mayer da Edward Lawry Norton a shekarar 1926.

Tsarin Daɗi Na Duk Da Suwa

Kamar yadda aka nuna a cikin tsari na daɗi na duk da suwa, wanda ya zama da suka ci gaba da biyu. Wata ta haka ta ci gaba da tsarin daɗi na duk da suwa kuma wata biyu ta ci gaba da tsarin daɗi na duk da abincin.

Saboda haka, wani da ya ci gaba da tsarin daɗi na duk da abincin zai iya samun da tushen daɗi na duk da suwa. Kuma tsari na daɗi na duk da suwa shi ne;

$I_L = \frac{R_{EQ}}{R_L + R_{EQ}} \times I_N$

Yadda a Gano Tsari na Daɗi Na Duk Da Suwa

Wannan cikin tsari mai girma da ke da abubuwa masu biyu ake gano da tsari na daɗi na duk da suwa. Kuma ana da su;

Tsarin daɗi na duk da suwa
Suwan daɗi na duk da suwa
Tsarin daɗi na duk da abincin

Tsarin Daɗi Na Duk Da Suwa

Tsarin daɗi na duk da suwa ya dace da tsarin daɗi na duk da suwa na Thevenin. Don in gano tsarin daɗi na duk da suwa, muna buƙaci irin abubuwa masu inganci na cikin tsari.

Amma alamomin da su ne; duka abubuwa masu inganci suna da shi. Idan tsari na da abubuwa masu amfani, zaka iya amfani da hanyoyi masu sa don in gano tsarin daɗi na duk da suwa.

Idan, wannan sauki na da kawai masu tushen bayanai, duka masu tushen bayanai suka ci gaba a cikin sauki ta da shiga voltage source da kuma cire-cire current source.

A lokacin da ake kula Norton equivalent resistance, load resistance ya zama cire-cire. Kuma a duba open-circuit voltage a kan terminals na load.

Yana da wani lokaci, Norton resistance yana nufin Thevenin equivalent resistance ko kuma open-circuit resistance.

Za a iya fahimta da misal.

Karkashin, za a duba cewa sauki na da dependent sources? A wannan lokacin, duka masu tushen bayanai su ne independent sources; 20V voltage source da 10A current source.

Sauki, koyi duka masu tushen bayanai haka da shiga voltage source da cire-cire current source. Kuma cire-cire terminals na load.

Sauki, duba open-circuit voltage tare da series da parallel connections na resistances.

Resistances 6Ω da 4Ω suna cikin series. Saboda haka, total resistance ita ce 10Ω.

企业微信截图_17102258034738.png — Equivalent Resistance

企业微信截图_17102258117375.png — Equivalent Resistance

Duka 10Ω resistances suna cikin parallel. Saboda haka, equivalent resistance REQ = 5Ω.

Norton Equivalent Current

Don kula Norton equivalent current, load resistance ya zama shiga. Kuma duba current wanda ya haɗa a cikin branch na shiga.

Saboda haka, Norton current ko kuma Norton equivalent current yana nufin short-circuit current.

A nan da take so kuɗi na ƙarfi a cikin misali, kuma sa lafiya ta hankali.

A nan da take so kuɗi na ƙarfi a cikin misali, kuma sa lafiya ta hankali.

$I_1 = 10A$

Sake amfani da KVL a cikin loop-2; $10I_2 - 6I_1 = 0$

$10I_2 - 60 = 0$

$10I_2 = 60$

$I_2 = I_{N} = 6A$

Yawan da ya kawo aiki a cikin takarda shi ne IL. A kan tsari na yawan da ya kawo aiki;

$I_L = \frac{R_{EQ}}{R_{EQ} + R_L} \times I_{N}$

$I_L = \frac{5}{5 + 5} \times 6$

$I_L = 3A$

Norton Equivalent Resistance with Dependent Source

Don samun cikakken tsarin Norton equivalent resistance wanda tana da dependent source, zan iya samun cikakken open-circuit voltage (VOC) a kan abubuwa na load.

Open-circuit voltage ya fi dacewa da Thevenin equivalent voltage.

Ba da samun Thevenin equivalent voltage da kuma Norton current; saka wannan balanci a tushen bayanai.

$R_{EQ} = R_N = \frac{V_{TH}}{I_N} = \frac{V_{OC}}{I_{SC}}$

Norton Equivalent Circuit Examples

Misali-1 Bayyana Norton Equivalent Circuit Across Terminals AB.

Bayyana Norton equivalent circuit across terminals AB a kan active linear network wanda ake nuna a bayanan.

Zaɓu-1 Bayyana Norton equivalent current (IN). Don samun IN, muna short-circuit terminals AB.

Saka KVL a loop-1;

( $\begin{equation*} 60 = 10I_1 - 5I_2 \end{equation*}$

Aiki KVL a cikin loop-2;

$0 = 40I_2 - 5I_1 - 20I_3$

Daga mai sanya;

$I_3 = 2A$

Saboda haka;

$0 = 40I_2 - 5I_1 - 20(2)$

$\begin{equation*} 40 = -5I_1 + 40I_2 \end{equation*}$

A cikin hanyar da amsa kungiyoyin 1 da 2; za a iya samun haddin ta I2 wanda yake daidai da haddin Norton (IN).

$I_2 = I_N = 4A$

Lambar-2 Samun hanyar da amsa REQ. Don haka, tushen saki na aiki ya zama tsawon da ake kuma tushen voltaji ya zama shiga.

$20 + 15 + 2.5 = 37.5 \Omega$

Lambar-3 Daɗe haddin Norton da hanyar da amsa a cikin kungiyar da ake da ita don samun hanyar da amsa.

Misal-1 Tsakiyar Norton

Misal-2 Neman tsakiyar Norton da Thevenin na hukuma

Misal-2 Neman Tsakiyar Norton ta Najin Majalawa

Raka-1 Neman kayayyakin Norton (IN). Don haka sarka AB.

Yara KVL zuwa gurbin-1;

$20 + 4i = 14I_1 - 6I_2$

$i = I_1 - I_2$

$20 + 4(I_1 - I_2) = 14I_1 - 6I_2$

$20 + 4I_1 - 4I_2 = 14I_1 - 6I_2$

(3) $\begin{equation*} 20 = 10I_1 - 2I_2 \end{equation*}$

A nan, amfani da KVL a loop-2

$18I_2 - 6I_1 = 0$

$6I_1 = 18I_2$

$I_1 = 3I_2$

Zaɓe wannan mai muhimmanci a tsari-3;

$20 = 10(3I_2) - 2I_2$

$20 = 28I_2$

$I_2 = I_N = 0.7142 A$

Rukun-2 An na da sauran hanyar kashi mai gaba. Saboda haka, ba zai iya samun nisa na musamman.

Don samun kuskure da dama, muna bukata a gani tsari mai saukarwa (Thevenin voltage). Don haka za a fuskantar terminal AB. Kuma saboda hanyoyi, amfani na tsari 12Ω yana zama zero.

Saboda haka, muna iya jekanta tsari 12Ω.

$20 + 4i = 14i$

$i = 2A$

Tsari na terminal AB ita ce tsari na 6Ω.

$V_{OC} = V_{TH} = 6 \times 2$

$V_{TH} = 12V$

Lambar-3 Neman dacewaru masu yawan hadin;

$R_{EQ} = \frac{V_{TH}}{I_N}$

$R_{EQ} = \frac{12}{0.714}$

$R_{EQ} = 16.8 \Omega$

Lambar-4 Haɗa kan bayanin karamin Norton da cacewaru masu yawa a cikin ci gaba na Norton.

Lambar-5 Haɗa kan bayanin karamin Thevenin da cacewaru masu yawa a cikin ci gaba na Thevenin.

thevenin equivalent circuit — Kirka ta Thevenin na Musamman

Kirka ta Norton da Kirka ta Thevenin na Musamman

Kirka ta Norton yana cikin dual network na kirka ta Thevenin na musamman. Amma shiyanar da kuma kula suka amfani da sabon tsari a matsayin hanyar bincike masana'antar tashar.

Daga cikin nan, ana samun kirka ta Norton tare da masara ta Norton, sannan kirka ta Thevenin tare da masara ta Thevenin.

Matsayinta da ke musamman ya fi duka waɗanda biyu. Don in yi ƙarin hanyar aiki, source transformation tana amfani da ita.

A cikin misalai, za a iya ƙirƙira masara ta Norton da matsayinta da ke musamman zuwa masara ta Thevenin da matsayinta da ke musamman.

Za mu zama;

$V_{TH} = \frac{I_N}{R_{EQ}}$