Bidirectional current and 4Q converters

Q: What is the key feature of a 2-quadrant DC converter?

A: 

• Combines buck (step-down) and boost (step-up) functionality 

• Allows bidirectional power flow 

• Enables both motoring (Q1) and regenerative braking (Q4) 

Q: Describe current paths during buck vs. boost modes:

A: 

• Buck mode (S1 ON): Current through S1 (Iₐ>0) or D1 (Iₐ<0) 

• Boost mode (S2 ON): Current through S2 (Iₐ<0) or D2 (Iₐ>0) 

• Inductor maintains current continuity 

Q: How are duty cycles related in a 2Q converter?

A: [ D_{S2} = 1 - D_{S1} ] Where: 

• ( D_{S1} ): Buck switch duty cycle 

• ( D_{S2} ): Boost switch duty cycle 

Q: What voltage range can a 2Q converter produce?

A: [ 0 < V_a < V_d ] (same as 1Q buck converter, but with bidirectional current) 

Q: When does regenerative braking occur in Q4?

A: When ( V_a < E_a ) causing: 

• Negative armature current (Iₐ<0) 

• Positive speed (ω>0) 

• Negative torque (T<0) 

Q: Why can't 2Q converters achieve full 4-quadrant operation?

A: 

• Cannot reverse voltage polarity 

• Limited to unidirectional speed control 

• Requires H-bridge for ±Vₐ capability 

Q: How does an H-bridge enable 4-quadrant operation?

A: 

• Two complementary 2Q converters 

• Output voltage: ( V_a = (2D-1)V_d ) 

• Range: (-V_d ≤ V_a ≤ V_d) 

Q: Which switches operate together in an H-bridge?

A: 

• ( S_1 ) & ( S_4 ): ON together (same duty cycle D) 

• ( S_2 ) & ( S_3 ): Complementary to S1/S4 (1-D) 

Q: How is voltage polarity changed in a 4Q drive?

A: 

• ( D > 0.5 ): Positive ( V_a ) 

• ( D < 0.5 ): Negative ( V_a ) 

• ( D = 0.5 ): Zero ( V_a ) 

Q: What quadrants are possible with 4Q drives?

A: 

• Q1: +V, +I (forward motoring) 

• Q2: +V, -I (forward braking) 

• Q3: -V, -I (reverse motoring) 

• Q4: -V, +I (reverse braking) 

Q: For Vd=100V, what D gives Va=-60V in a 4Q drive?

A: [ -60 = (2D-1)×100 ] [ D = 0.2 ] (20% duty cycle for S1/S4) 

Q: How does power flow differ in motoring vs. generating?

A: 

• Motoring: Power source → machine (VₐIₐ>0) 

• Generating: Machine → source (VₐIₐ<0) 

• H-bridge enables both directions