![4
Analysis of inductor effect during 𝑇𝑂𝐹𝐹 period:
𝐼𝐿 = 𝑇 𝑂𝑁
𝑇 𝑉 𝐿 𝑂𝐹𝐹
𝐿
𝑑𝑡
=
1
L 𝑇 𝑂𝑁
𝑇
𝑉𝐿 𝑂𝐹𝐹 𝑑𝑡
=
𝑉 𝐿
𝐿
𝑇 − 𝑇𝑂𝑁
= −
𝑉 𝐿
𝐿
𝜶𝑇 − 𝑇
𝐼𝐿 =
𝑉𝑠−𝑉 𝐿−𝑉 𝑂
𝐿
[𝜶 − 1]. 𝑇
𝑉𝐿 𝑂𝐹𝐹 − 𝑉𝐿 − 𝑉𝐷 = 0
Here, 𝑉𝐷 = Voltage across diode
= −
(𝑉0+𝑉 𝐷)
𝐿
𝜶 − 1 𝑇
𝐼𝐿 𝑂𝐹𝐹 =
−𝑉0−𝑉 𝐷
𝐿
𝜶 − 1 𝑇 → Equation 2
Solving, Equation 1 = Equation 2
𝐼𝐿 𝑂𝑁 = 𝐼𝐿 𝑂𝐹𝐹
𝑉 𝑆−𝑉 𝑄−𝑉 𝑂
𝐿
𝜶𝑇 =
−𝑉0−𝑉 𝐷
𝐿
𝜶 − 1 𝑇](https://image.slidesharecdn.com/buckconverter-161005062057/85/Buck-converter-4-320.jpg)
More Related Content
Buck converter
- 1.
- 2. As a Chopper •Buck converter is also known as First quadrant or Type-A chopper. • It is step down converter and produces a lower average output voltage than the dc input voltage. For the Resistive load: 𝑉𝑎𝑣𝑔 = 1 𝑇 0 𝑇 𝑂𝑁 𝑉0 𝑑𝑡 = 𝑉𝑠 𝑇 0 𝑇 𝑂𝑁 𝑑𝑡 = 𝑇 𝑂𝑁 𝑇 𝑉𝑠 = 𝜶𝑉𝑠 2 Buck converter with RLE load
- 3. 3 𝑉𝑟𝑚𝑠 = 1 𝑇 0 𝑇𝑂𝑁 𝑉𝑜 2 𝑑𝑡 = ( 𝑇 𝑂𝑁 𝑇 )1/2 𝑉𝑆 = 𝜶.𝑉𝑆 𝐼 𝑎𝑣𝑔 = 𝑉𝑎𝑣𝑔 𝑉𝑟𝑚𝑠 𝐼 𝑎𝑣𝑔 = 𝜶 Analysis of inductor effect during 𝑇𝑂𝑁 period: 𝐼𝐿 = 0 𝑇 𝑂𝑁 𝑉 𝐿 𝑂𝑁 𝐿 𝑑𝑡 = 1 L 0 𝑇 𝑂𝑁 𝑉𝐿 𝑂𝑁 𝑑𝑡 = 𝑉 𝐿 𝐿 𝑇𝑂𝑁 𝐼𝐿 = 𝑉 𝐿 𝐿 .𝜶𝑇 𝑉𝑠 = 𝑉𝑄 + 𝑉𝐿 + 𝑉𝑂 Here, 𝑉𝑄 = Voltage across switch 𝐼𝐿 𝑂𝑁 = 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂 𝐿 𝜶𝑇 → Equation 1
- 4. 4 Analysis of inductoreffect during 𝑇𝑂𝐹𝐹 period: 𝐼𝐿 = 𝑇 𝑂𝑁 𝑇 𝑉 𝐿 𝑂𝐹𝐹 𝐿 𝑑𝑡 = 1 L 𝑇 𝑂𝑁 𝑇 𝑉𝐿 𝑂𝐹𝐹 𝑑𝑡 = 𝑉 𝐿 𝐿 𝑇 − 𝑇𝑂𝑁 = − 𝑉 𝐿 𝐿 𝜶𝑇 − 𝑇 𝐼𝐿 = 𝑉𝑠−𝑉 𝐿−𝑉 𝑂 𝐿 [𝜶 − 1]. 𝑇 𝑉𝐿 𝑂𝐹𝐹 − 𝑉𝐿 − 𝑉𝐷 = 0 Here, 𝑉𝐷 = Voltage across diode = − (𝑉0+𝑉 𝐷) 𝐿 𝜶 − 1 𝑇 𝐼𝐿 𝑂𝐹𝐹 = −𝑉0−𝑉 𝐷 𝐿 𝜶 − 1 𝑇 → Equation 2 Solving, Equation 1 = Equation 2 𝐼𝐿 𝑂𝑁 = 𝐼𝐿 𝑂𝐹𝐹 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂 𝐿 𝜶𝑇 = −𝑉0−𝑉 𝐷 𝐿 𝜶 − 1 𝑇
- 5. 5 𝑉𝑆 − 𝑉𝑄− 𝑉𝑂 . 𝜶 = −𝑉𝑂 − 𝑉𝐷(𝜶 − 1) 𝜶 = 𝑉 𝑂+𝑉 𝐷 𝑉 𝑆−𝑉 𝑄+𝑉 𝐷 𝜶 − 1 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂 −𝑉 𝑂−𝑉 𝐷 = 𝜶−1 𝜶 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂 −𝑉 𝑂−𝑉 𝐷 = 1 − 1 𝜶 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂 −𝑉 𝑂−𝑉 𝐷 - 1 = − 1 𝜶 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂−(−𝑉 𝑂−𝑉 𝐷) −𝑉 𝑂−𝑉 𝐷 = − 1 𝜶 𝑉 𝑆−𝑉 𝑄−𝑉 𝑂+𝑉 𝑂+𝑉 𝐷 −𝑉 𝑂−𝑉 𝐷 = − 1 𝜶 𝑉 𝑆−𝑉 𝑄−𝑉 𝐷 −𝑉 𝑂−𝑉 𝐷 - 1 = − 1 𝜶 𝜶 = −(−𝑉 𝑂−𝑉 𝐷) 𝑉 𝑆−𝑉 𝑄+𝑉 𝐷 𝜶 = 𝑉 𝑂+𝑉 𝐷 𝑉 𝑆−𝑉 𝑄+𝑉 𝐷 Here, 𝑉𝐷 = 𝑉𝑄 = 0 or negligible 𝜶 = 𝑉 𝑂 𝑉𝑠 𝑉𝑂 = 𝜶. 𝑉𝑆
- 6. QUIZ QUESTIONS 1) Whatare the applications of buck converter? 2) Compare the analysis of inductor effect during Ton and Toff period? 3) In what way it differs from boost converter? 4) In stepdown chopper 𝑉𝑂is always less than 𝑉𝑆?(True/False) 5) A step-down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio D. If 𝑉𝑂 is the magnitude of dc output voltage and if 𝑉𝑆 is the magnitude of dc input voltage , the ratio (𝑉𝑂/𝑉𝑆) is given by (a) D (b) 1-D (c) (1/1-D) (d) (D/1-D) 6) A chopper has 𝑉𝑆 as the source voltage, R as the load resistance and 𝜶 is the duty cycle. For this chopper , rms value of output voltage is (a) 𝜶. 𝑉𝑆 (b) 𝜶. 𝑉𝑆 (c) 𝑉𝑆/ 𝜶 (d) 1 − 𝜶. 𝑉𝑆 6