# Why Small, Cold and Quiet DC-DC Conversion is Impossible

## TL;DR

This paper demonstrates that due to fundamental thermodynamic and electromagnetic principles, it is impossible for DC-DC converters to simultaneously minimize size, heat, and noise, highlighting inherent trade-offs in their design.

## Contribution

It introduces a holistic figure of merit called non-ideality, based on thermodynamics and harmonic distortion, to evaluate DC-DC converter performance and explains the fundamental trade-offs involved.

## Key findings

- Trade-offs between size, heat, and noise are fundamental and unavoidable.
- Switching inherently generates harmonics that cause these trade-offs.
- Boost conversion requires energy storage, even in ideal conditions.

## Abstract

Using the first law of thermodynamics and the Parseval-Plancheral theorem, it is shown that every DC-DC converter must trade-off size, heat and conducted electromagnetic noise. It is therefore fundamentally impossible to simultaneously reduce all three of these characteristics to their respective theoretical minimum values. A figure of merit is introduced which holistically captures the performance of an arbitrary DC-DC converter, this is called the converter's non-ideality and it has a target value of zero. It is derived using the first law of thermodynamics and is shown to be dependent on the efficiency and the root-mean-squared total harmonic distortion of the output voltage. Interestingly, it is also shown that: boost conversion is impossible without energy storage; ideal rectifiers convert all of the input power spectral density into DC (and introduces more noise in the process); the input current of any DC-DC converter scales with the gain of the device squared. Using an arbitrary DC-DC converter, the culprit of this inherent trade-off is shown to be the act of switching itself. Switching creates harmonics which need to be filtered or transformed into heat in order to get a pure DC voltage at the output of the converter. Even with ideal sub-systems, whether or not resonant conversion is employed, the result stands. The conclusion is that spreading of the switching noise is a primary goal in attempting to reach the impossible.

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Source: https://tomesphere.com/paper/1706.07787