Ngā Tauira Pātai mō te Kōrero mō ngā Ngaru Reo Irirangi
Ko ngā ngaru reo irirangi he momo irahiko hikohiko e mahi ana i roto i ngā whakawhitiwhiti kōrero ahokore. Me ngā auau mai i ētahi kilohertz (kHz) ki ētahi gigahertz (GHz), e whakamahia ana ngā ngaru reo irirangi i roto i te whānuitanga o ngā tono—mai i ngā pāhotanga reo irirangi me te pouaka whakaata ki ngā pūnaha whakawhitiwhiti kōrero pūkoro. I roto i tēnei tuhinga, ka matapakihia e mātou ngā tauira o ngā ngaru reo irirangi me ō rātou whakamārama hei āwhina i a tātou ki te mārama ki ngā mātāpono me ngā tono o ēnei ngaru i roto i te oranga o ia rā.
Tauira Pātai 1: Auautanga me te Roangaru
Pātai:
Ka tukuna ngā ngaru reo irirangi e tētahi teihana reo irirangi i te auau o te 100 MHz. Tātaihia te roanga ngaru. (Ko te tere o te mārama he 3 x 10^8 m/s.)
Kōrero:
E pā ana te auau (f) me te roanga ngaru (λ) o ngā ngaru hikohiko ki te tere o te mārama (c) mā te whārite:
\[ c = f \times \lambda \]
Dimana:
– \( c \) = te tere o te mārama (3 x 10^8 m/s)
– \( f \) = auau (100 MHz, 100 x 10^6 Hz rānei)
– \( \lambda \) = te roangaru (kia kitea)
Mai i te whārite i runga ake nei, ka taea te tatau i te roanga ngaru mā te:
\[ \lambda = \frac{c}{f} \]
Nā reira:
\[ \lambda = \frac{3 \times 10^8}{100 \times 10^6} = 3 \ \text{mita} \]
Nō reira, ko te roanga ngaru o te auautanga o te 100 MHz he 3 mita.
Tauira Pātai 2: Te Mana Tuku me te Kaha
Pātai:
Ka tukuna e te tuku reo irirangi 50-wati ngā ngaru reo irirangi i runga i te āhua kotahi (he ōrite ki ngā taha katoa). Tātaihia te kaha o ngā ngaru reo irirangi i te tawhiti o te 10 mita mai i te tuku.
Kōrero:
Ka taea te tatau i te kaha (I) o tētahi ngaru e tukuna ana i te taha kotahi mā te:
\[ I = \frac{P}{A} \]
Dimana:
– \( P \) = mana tuku (50 watts)
– \( A \) = horahanga mata o te porowhita (4πr^2)
I te tawhiti (r) = 10 mita, ko te horahanga o te mata o te pōro ko:
\[ A = 4\pi (10)^2 = 400\pi \]
Nā reira:
\[ I = \frac{50}{400\pi} = \frac{1}{8\pi} \ \text{watt/m}^2 \]
Nō reira, ko te kaha o ngā ngaru reo irirangi i te tawhiti o te 10 mita mai i te tuku ko \( \frac{1}{8\pi} \) watt/m².
Tauira Pātai 3: Te Whānuitanga o te Aratuku me te Kaha o te Hongere
Pātai:
Ko te whānui o te hongere whakawhitiwhiti kōrero he 20 MHz. Mēnā kei te whakamahi koe i te whakarerekētanga QPSK (Quadrature Phase Shift Keying), he aha te kaha mōrahi o te hongere?
Kōrero:
E whā ngā wāhanga rerekē o te whakarerekētanga QPSK, nō reira ka taea e ia te tuku i te 2 moka mō ia tohu i roto i te wā kotahi.
Ko te maha o ngā tohu ia hekona ka taea e te whānui o te 20 MHz te whakahaere ko:
\[ \text{Tohu} = 20 \times 10^6 \ \text{tohu/hēkona} \]
Nā te mea e rua ngā moka e tukuna ana e QPSK mō ia tohu, ko te kaha, te maha rānei o ngā moka mō ia hekona (tere moka) ko:
\[ \text{Te tere tere} = 20 \times 10^6 \times 2 = 40 \ \text{Mbps} \]
Nō reira, ko te kaha mōrahi o te hongere he 40 Mbps.
Tauira Pātai 4: Te Whakararuraru me te Whakararuraru
Pātai:
Kei te pāngia tētahi tuku reo irirangi i te auau o te 101.1 MHz e te pokanoa mai i tētahi atu tuku reo irirangi i te auau o te 101.3 MHz. Tātaihia te auau patupatu ka puta.
Kōrero:
Ko te auau o te patu \( f_{patunga} \) ka puta mai i te rerekētanga i waenga i ngā auau tata e rua, ā, ka taea te tatau mā te:
\[ f_{patunga} = |f_1 – f_2| \]
Dimana:
– \( f_1 \) = 101.1 MHz
– \( f_2 \) = 101.3 MHz
Nā reira:
\[ f_{patunga} = |101.1 – 101.3| = | -0.2 | = 0.2 \ \text{MHz} \]
Nō reira, ko te auau patu hua ko 0.2 MHz.
Tauira Pātai 5: Te Pānga Doppler i roto i ngā Ngaru Reo Irirangi
Pātai:
Ka whakapāho te teihana reo irirangi i te auau o te 95 MHz. Ka whakatata atu te waka rererangi ki te teihana reo irirangi i te tere o te 340 m/s. Tātaihia te auau ka riro i te waka rererangi mēnā he ōrite te tere o ngā ngaru reo irirangi ki te tere o te mārama (3 x 10^8 m/s).
Kōrero:
Ka taea te whakaatu i te pānga Doppler mō ngā ngaru reo irirangi penei:
\[ f_{whakaae} = f_{0} \left(\frac{c + v}{c}\right) \]
Dimana:
– \( f_0 \) = auau taketake (95 MHz)
– \( v \) = tere rererangi (340 m/s)
– \( c \) = tere o te ngaru (3 x 10^8 m/s)
Nā reira:
\[ f_{whakaae} = 95 \times 10^6 \left(\frac{3 \times 10^8 + 340}{3 \times 10^8}\right) \]
\[ f_{whakaae} = 95 \times 10^6 \left(\frac{3 \times 10^8 + 3.4 \times 10^2}{3 \times 10^8}\right) \]
\[ f_{whakaae} \tata 95 \times 10^6 \left(1 + \frac{3.4 \times 10^2}{3 \times 10^8}\right) \]
\[ f_{whakaae} \tata ki te 95 \times 10^6 \left(1 + 1.1333 \times 10^{-6}\right) \]
\[ f_{whakaae} \tata ki te 95 \whakaahua 10^6 \whakaahua 1.0000011333 \]
\[ f_{whakaae} \tata ki te 95.000107 \ \kuputuhi{MHz} \]
Nō reira, ko te auau e tae mai ana ki te waka rererangi e whakatata mai ana he tata ki te 95.000107 MHz.
Te Katinga
He mea nui te mārama ki ngā mātāpono taketake me ngā tauira rorohiko o ngā ngaru reo irirangi i roto i ngā momo mara hangarau me te pūtaiao. Kei roto i ngā raruraru i runga ake nei ētahi tauira o te whakamahinga o te ahupūngao o ngā ngaru reo irirangi i roto i ngā horopaki mahi maha. Ko te ara ki te māramatanga hohonu ake ko te mahi tonu me te tūhura i ngā tono o te ao tūturu o ngā ngaru reo irirangi i roto i te hangarau whakawhitiwhiti kōrero e whakamahia ana e tātou i ia rā.
