Question E7D02:
How does a switchmode voltage regulator work?  

Choices:  
A: By alternating the output between positive and negative voltages  
B: By varying the duty cycle of pulses input to a filter  
C: By varying the conductivity of a pass element  
D: By switching between two Zener diode reference voltages    

Correct Answer is  B: By varying the duty cycle of pulses input to a filter  

To regulate a DC output efficiently, a switchmode regulator (SMPS) rapidly turns a switch on and off and filters the result.

Why B is correct (By varying the duty cycle of pulses input to a filter):
- The regulator creates a high-frequency pulse train whose duty cycle $D$ (fraction of time “on”) is adjusted by feedback from the output.
- An LC filter averages these pulses to a nearly DC output.
- In ideal basic topologies:
  - Buck (step-down): $$V_{\text{out}} \approx D \, V_{\text{in}}$$
  - Boost (step-up): $$V_{\text{out}} \approx \frac{V_{\text{in}}}{1 - D}$$
  - Inverting buck-boost: $$V_{\text{out}} \approx -\frac{D}{1 - D} \, V_{\text{in}}$$
- Because the switch is either fully on (low $V \times I$ loss) or fully off (near zero current), efficiency is high.

Why the other choices are incorrect:
- A: Alternating between positive and negative voltages describes an inverter/H-bridge or AC generation, not DC regulation via duty-cycle control.
- C: Varying the conductivity of a pass element is a linear (series) regulator method; it wastes power as heat and is not “switchmode.”
- D: Switching between two Zener reference voltages would give only two discrete references and does not provide continuous regulation; Zeners are used as references, not as the primary regulating mechanism in SMPS.

Useful formulas and rules of thumb:
- For a buck converter (ideal):
  - Output relation: $$V_{\text{out}} \approx D \, V_{\text{in}}$$
  - Inductor ripple current: $$\Delta I_L \approx \frac{(V_{\text{in}} - V_{\text{out}})\, D}{L \, f_s}$$
  - Output ripple voltage (ESR neglected): $$\Delta V_{\text{out}} \approx \frac{\Delta I_L}{8 \, C \, f_s}$$
- Typical switching frequencies: tens of kHz to several MHz.
- Practical efficiency often 80–95% depending on design and load.