Chopper classification; step-down chopper RL load

Classification of choppers

1. By output voltage level:
   • Step-down chopper (buck): Vo = k·Vs < Vs
   • Step-up chopper (boost): Vo = Vs/(1 − k) > Vs
   • Step-up/down chopper (buck-boost)
2. By quadrant of operation (direction of Vo and Io):
   • Class A: first quadrant (+V, +I)
   • Class B: second quadrant (+V, −I), regenerative
   • Class C: two-quadrant, I and II (current reversible)
   • Class D: two-quadrant, I and IV (voltage reversible)
   • Class E: four-quadrant
3. By commutation: voltage-commutated, current-commutated, load-commutated, impulse-commutated.

Step-down chopper with RL load

       CH
 +Vs --/ --+--------+
           |        R
           FD       L
           |        E (0 if pure RL)
 −   ------+--------+

Mode 1 – CH ON (0 < t < Ton): Load is connected to Vs; FD reverse biased. Current rises exponentially from I1 to I2:

Vs = R·i + L·di/dt + E
i = I1·e^(−t/τ) + ((Vs − E)/R)(1 − e^(−t/τ)),  τ = L/R

Mode 2 – CH OFF (0 < t < Toff): Inductor energy keeps current flowing through FD; vo = 0. Current decays from I2 to I1:

0 = R·i + L·di/dt + E
i = I2·e^(−t/τ) − (E/R)(1 − e^(−t/τ))

Waveforms (continuous current):

vo Vs |‾‾‾‾|____|‾‾‾‾|____
      0   Ton   T
io I2 |   /\     /\
   I1 |__/  \___/  \___
      (rises: CH)(falls: FD)

Output relations:

Vo = (1/T)∫₀^(Ton) Vs dt = k·Vs
Io = (k·Vs − E)/R
ΔI = I2 − I1, maximum at k = 0.5:
ΔImax = (Vs/R)·tanh(R/(4fL)) ≈ Vs/(4fL)

Higher chopping frequency or larger L gives smoother current. Used for DC motor speed control.