dc to dc 1.pdf

Chapter 5 DC Choppers  The Fully-Controlled Switches (review) Fully controlled switches include : GTO, BJT, MOSFET, MCT, IGBT, IGCT, … The most common presently are the MOSFET and IGBTs The control function has two parameters Tsw and d ON OFF...

Chapter 5 DC Choppers  The Fully-Controlled Switches (review) Fully controlled switches include : GTO, BJT, MOSFET, MCT, IGBT, IGCT, … The most common presently are the MOSFET and IGBTs The control function has two parameters Tsw and d ON OFF d 𝑇𝑜𝑛 vGS/vGE 𝑑≡ 𝑇𝑠𝑤 dTsw (1-d)Tsw Tsw  Quadrant of operation According to the polarity of the output voltage and current, the converter quadrant is identified. First Quadrant: when 𝑣𝑜 and 𝑖𝑜 are positive. Second Quadrant: when 𝑣𝑜 is positive and 𝑖𝑜 is negative. Third Quadrant: when 𝑣𝑜 and 𝑖𝑜 are negative. Fourth Quadrant when 𝑣𝑜 is negative and 𝑖𝑜 is positive. According to this definition: The diode rectifier is a first quadrant converter The three-phase controlled rectifier is ….. The AC controller is …  Step-down choppers The average output voltage, Vo,dc, depends linearly on the duty ratios of chopper switches and, generally, can be adjusted in the –Vi to +Vi range. The magnitude control ratio, M, can be defined as 𝑉𝑜,𝑑𝑐 𝑀= 𝑉𝑖  The output current: exact expression The differential equation of the load is 𝑑𝑖𝑜 𝐿 + 𝑅𝑖𝑜 + 𝐸 = 𝑣𝑜 𝑑𝑡 Which has a solution of the general form: 𝑅 𝑣𝑜 −𝐸 𝐸−𝑣𝑜 − 𝐿 (𝑡−𝑡𝑜 ) 𝑖𝑜 𝑡 = + + 𝑖𝑜 (𝑡𝑜 ) 𝑒 𝑅 𝑅 First Quadrant Chopper A periodic binary switching variable, x1, can be assigned to the fully controlled switch S1, and the output voltage of the chopper can be expressed as: 𝑣𝑜 = 𝑥1 𝑉𝑖 x1 Tsw d1Tsw vo Vi Output voltage and M range x1 𝑡𝑜𝑛 𝑉𝑖 + 𝑡𝑂𝐹𝐹 ∗ 0 𝑡𝑜𝑛 𝑉𝑖 𝑉𝑜,𝑑𝑐 = = = 𝑑1 𝑉𝑖 𝑡𝑂𝑁 + 𝑡𝑂𝐹𝐹 𝑇𝑠𝑤 Tsw d1Tsw vo where d1 is the duty ratio of switch S1. For 1st Quad. Chopper: Vi 𝑀 = 𝑑1 The output current is always positive, the range of the M: 𝐸 ≤𝑀≤1 𝑉𝑖 which implies that d1,min=E/Vi The output current : approximate analysis Tsw 𝑀𝑉𝑖 − 𝐸 d1Tsw 𝐼𝑖,𝑑𝑐 = vo 𝑅 Vi ∆𝐼𝑜 :The current ripple (peak-to-peak) DIo Approximating this current to linear implies that the inductor current is approximated to constant: Io,dc 𝑣𝐿 ≈ 𝑉𝑖 − 𝑀𝑉𝑖 when x1=1 𝑣𝐿 ≈ −𝑀𝑉𝑖 when x1=0 gives 𝑀(1−𝑀)𝑇𝑠𝑤 𝑉𝑖 ∆𝐼𝑜 = 𝐿 Example 1 A step-down chopper fed from a 200-V source operates a dc motor whose armature EMF is 70 V and armature resistance is 0.5 Ω. With the magnitude control ratio of 0.4, (A) Find the average output voltage and current of the chopper and determine the quadrant of operation. (B) The chopper operates with a switching frequency of 1 kHz and the armature inductance of the motor is 20 mH. i- Find the AC component of the armature current and ripple factor of the current, and ii- the ripple factor of the output voltage