DC Choppers and Converters

DC Choppers

• Fully controlled switches include: GTO, BJT, MOSFET, MCT, IGBT, IGCT, and others
• The most common ones are MOSFET and IGBTs

Control Function

• The control function has two parameters: Tsw (switching period) and d (duty ratio)
• d = Ton / Tsw, where Ton is the on-time of the switch

Quadrant of Operation

• Converter quadrant is identified by the polarity of output voltage and current
• Four quadrants:
  • First Quadrant: vo and io are positive
  • Second Quadrant: vo is positive and io is negative
  • Third Quadrant: vo and io are negative
  • Fourth Quadrant: vo is negative and io is positive

Step-Down Choppers

• The average output voltage, Vo,dc, depends linearly on the duty ratio of the chopper switches
• The magnitude control ratio, M, is defined as Vo,dc / Vi
• Vo,dc can be adjusted in the range of -Vi to +Vi

Output Current

• The differential equation of the load is: L(di/dt) + Ri + E = vo
• The output current has a general solution of the form: io(t) = (vo - E) / R + (E - vo) / R * e^(-R(t-to) / L)

First Quadrant Chopper

• The output voltage can be expressed as: vo = x1 * Vi
• The duty ratio, d1, is defined as: d1 = Ton / Tsw

Output Voltage and M Range

• The average output voltage, Vo,dc, is: Vo,dc = d1 * Vi
• The range of M is: E / Vi <= M <= 1, which implies d1,min = E / Vi

Output Current Approximation

• The output current can be approximated as: Io,dc = M * Vi / R
• The current ripple, ΔIo, is: ΔIo = M(1 - M) * Tsw * Vi / L

Example Problem

• A step-down chopper with a magnitude control ratio of 0.4 operates a dc motor with an armature EMF of 70 V and armature resistance of 0.5 Ω
• The average output voltage and current can be calculated using the formulas above
• The AC component of the armature current and ripple factor of the current can be calculated using the approximate analysis formulas