Question E7D10:
Why is a switching type power supply less expensive and lighter than an equivalent linear power supply?  

Choices:  
A: The inverter design does not require an output filter circuit  
B: The control circuitry uses less current, therefore smaller heat sinks are required  
C: The high frequency inverter design uses much smaller transformers and filter components for an equivalent power output  
D: It recovers power from the unused portion of the AC cycle, thus using fewer components    

Correct Answer is  C: The high frequency inverter design uses much smaller transformers and filter components for an equivalent power output  

Correct answer: C — The high frequency inverter design uses much smaller transformers and filter components for an equivalent power output.

Why C is correct:
- A switching supply first rectifies the AC and then switches it at a high frequency (tens to hundreds of kHz). Transformer and filter component size scale inversely with frequency, so operating at high frequency dramatically reduces the size and weight of magnetics and capacitors for the same power.
- Result: lighter, smaller, and typically cheaper components than the 50/60 Hz transformer and large low-frequency filter caps needed in a linear supply.

Why the other choices are incorrect:
- A: “Does not require an output filter” — False. SMPS absolutely require output LC filters to remove high-frequency switching ripple; they can be more complex than linear supply filters.
- B: “Control circuitry uses less current, so smaller heat sinks” — Misleading. Any heat-sink reduction comes mainly from higher overall efficiency of switching conversion, not because the control circuitry uses less current (the control current is small in either case).
- D: “Recovers power from the unused portion of the AC cycle” — Nonsense in this context. There isn’t an “unused portion” being recovered; while power factor correction may improve mains utilization, it’s not the reason SMPS are lighter/cheaper.

Useful formulas and rules of thumb:
- Transformer size vs. frequency:
  $$V \approx 4.44\,f\,N\,A\,B_{\max} \Rightarrow N A \propto \frac{1}{f}$$
  For a given voltage and flux density, higher $f$ allows much smaller core area $A$ and fewer turns $N$.
- Output capacitor ripple:
  $$\Delta V \approx \frac{I_{\text{load}}}{f_{\text{ripple}}\,C}$$
  Linear supplies have $f_{\text{ripple}} \approx 120\ \text{Hz}$ (full-wave), requiring large $C$. SMPS use $f_{\text{ripple}}$ at the switching frequency (tens–hundreds of kHz), so much smaller $C$ can achieve the same ripple.
- Typical efficiencies: linear 50–65% (or worse under dropout), SMPS 80–95%+, contributing to smaller heat sinks—but the key exam point is the smaller magnetics and filters from high-frequency operation.