class: center, middle # EE-361 # TRANSFORMERS ## Ozan Keysan [keysan.me](http://keysan.me) Office: C-113
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Tel: 210 7586 --- # Ideal Transformer
--- # Ideal Transformer
### \\(e_1 = N_1 \frac{d\Phi}{dt} \;\;\; e_2 = N_2 \frac{d\Phi}{dt} \\) -- ## \\(\frac{V_1}{V_2} = \frac{e_1}{e_2} = \frac{N_1}{N_2}\\) --- ## Higher the number of turns -- ## Higher the induced voltage. # \\(\frac{V_1}{V_2} = \frac{N_1}{N_2}\\) --- # What about current? -- ## No Losses (Ideal Transformer) ## \\(P_1 = P_2 \\) -- ## \\(V_1 I_1 = V_2I_2 \\) -- ## \\(\dfrac{V_1}{V_2} = \dfrac{I_2}{I_1}\\) --- # Current is Inversely Proportional to Turns Ratio -- ## \\(\dfrac{N_1}{N_2} = \dfrac{I_2}{I_1}\\) -- ### Also valid from the magnetic circuit: ### MMF on both sides are equal --- # Transformer Ratio # \\(a = \frac{N_1}{N_2}\\)
--- # Transformer Schematic
### Beware of Dots --- # Transformer with Load
--- ## Transformations between primary and secondary: ## From Secondary to Primary Winding ## Referred to Primary <-- Actual Value ## \\(V_2' = a V_2 \quad \longleftarrow \\) \\(V_2\\) -- ## \\(I_2' = I_2/a \quad \longleftarrow \\) \\(I_2\\) -- ## \\(Z_2' = a^2 Z_2 \quad \longleftarrow \\) \\(Z_2\\) --- ## Transformations between primary and secondary: ## From Primary to Secondary Winding ## Actual Value --> Refeered to Secondary ## \\(V_1 \quad \longrightarrow\\) \\(V_1' = V_1 / a\\) -- ## \\(I_1 \quad \longrightarrow\\) \\(I_1' = a I_1 \\) -- ## \\(Z_1 \quad \longrightarrow\\) \\(Z_1' = Z_1 / a^2\\) --- # Properties of an Ideal Transformer -- - ### The resistance of the coil is zero -- - ### Infinitely permeable core -- - ### No leakage flux. -- - ### No eddy current or hysteresis loss. -- - ### Inter-winding capacitance effects are neglected. --- ## Unfortunately ideal transformers do not exist ![](http://media.giphy.com/media/LfbLBInuSRynK/giphy.gif) --- # Real Transformers --
--- # Real Transformers ### From small transformers in your chargers to:
--- # Real Transformers ### to very big transformers:
[Astor 320 MVA transformer](https://astoras.com.tr/guc-transformatorleri/guc-transformatorleri/#) --- # Different Applications ## A transformer without the iron core
--- # Different Applications ## A transformer without the iron core
--- # Different Applications ## Wireless Electric Car Charging
--- ## Wireless Phone Chargers ### Same Logic Behind: Mutual Inductance
### For curious students: [Link-1](https://www.theseus.fi/bitstream/handle/10024/122796/Wireless%20Inductive%20Charging%20for%20Low%20Power%20Devices.pdf?sequence=1), [Link-2](https://www.st.com/content/dam/technology-tour-2017/session-3_track-7_wireless-charging.pdf), [Link-3](https://www.allaboutcircuits.com/technical-articles/introduction-to-wireless-power-transfer-wpt/) --- # Transformers, same logic behind -- ## Mutual Inductance: \\( V_{2} = M \dfrac{dI_1}{dt} \\)
> --- # Transformers - ## Magnetically coupled circuit - ## Usually has a highly permeable core (Why?) - ## Losses in the coil and core --- ## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)