Waveform

Question

Waveform

Anu Bhardwaj · Accepted Answer

Step 1:- Impedance Ratio : The impedance ratio in a transformer is the square of the turn ratio. For a transformer with a winding ratio 𝑒 e : 𝑍 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑒 2 𝑍 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 Z p r ima ry ​ = e 2 Z seco n d a ry ​ Voltage Ratio : The voltage ratio in a transformer is equal to the turn ratio. For a step-down transformer (primary to secondary): 𝑉 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑒 𝑉 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 V p r ima ry ​ = e V seco n d a ry ​ Current Ratio : The current ratio is the inverse of the turns ratio: 𝐼 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 1 𝑒 𝐼 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 I p r ima ry ​ = e 1 ​ I seco n d a ry ​ Explanation:- We need to understand the relationship between the primary and secondary sides of a YD (Wye-Delta) connected step-down transformer. Given the winding ratio "e" (usually denoted as 𝑁 𝑝 𝑁 𝑠 N s ​ N p ​ ​ where 𝑁 𝑝 N p ​ is the number of turns on the primary winding and 𝑁 𝑠 N s ​ is the number of turns on the secondary winding), we can determine the ratios for impedance, voltage, and current. Step 2:- For a YD transformer: The line voltage on the primary (Y) side is related to the phase voltage by a factor of √3. The line current on the secondary (Δ) side is related to the phase current by a factor of 1/√3. Therefore: Voltage : For a step-down transformer with a winding ratio "e" and considering the YD configuration, the voltage ratio is: 𝑉 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑒 𝑉 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 ⋅ 3 V p r ima ry ​ = e V seco n d a ry ​ ⋅ 3 ​ 𝑉 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑒 ⋅ 3 ⋅ 𝑉 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 V p r ima ry ​ = e ⋅ 3 ​ ⋅ V seco n d a ry ​ ⇒ 𝑉 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 𝑎 3 ⋅ 𝑉 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 ⇒ V p r ima ry ​ = a 3 ​ ⋅ V seco n d a ry ​ Current : For the current: 𝐼 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 1 𝑒 𝐼 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 ⋅ 1 3 I p r ima ry ​ = e 1 ​ I seco n d a ry ​ ⋅ 3 ​ 1 ​ 𝐼 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 1 𝑎 ⋅ 1 3 ⋅ 𝐼 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 I p r ima ry ​ = a 1 ​ ⋅ 3 ​ 1 ​ ⋅ I seco n d a ry ​ ⇒ 𝐼 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 1 𝑎 𝐼 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 ⇒ I p r ima ry ​ = a 1 ​ I seco n d a ry ​ (since 1/√3 cancels out in YD configuration) Impedance : The impedance transformation ratio is 𝑒 2 e 2 , but due to the YD connection factor of 3 (because of the Δ configuration in secondary), 𝑍 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 3 𝑒 2 𝑍 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 Z p r ima ry ​ = 3 e 2 Z seco n d a ry ​ ⇒ 𝑍 𝑝 𝑟 𝑖 𝑚 𝑎 𝑟 𝑦 = 3 𝑎 2 𝑍 𝑠 𝑒 𝑐 𝑜 𝑛 𝑑 𝑎 𝑟 𝑦 ⇒ Z p r ima ry ​ = 3 a 2 Z seco n d a ry ​ Explanation:- However, considering the YD (Wye-Delta) connection, the voltage and current ratios need to incorporate the √3 factors due to the phase difference between the Y and Δ configurations. Final Answer:- 3 𝑎 2 3 a 2 for impedance. 𝑎 3 a 3 ​ for voltage. 1 𝑎 a 1 ​ for current. These correspond to the provided ratios and consider the YD configuration.

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Electrical engineering

Electrical engineering

Anu Bhardwaj

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