Bandwidth Expansion in <i>N</i>-Fold Frequency Multiplier: Is It <i>N</i> or √<i>N</i>?

Frequency up-conversion is an essential step in wireless communication systems. Meanwhile, frequency multipliers are increasingly becoming an integral part of communication chains operating at millimeter-wave (mmWave) and sub-terahertz (sub-THz) frequencies. They offer a viable alternative to traditional mixers, which are highly constrained by their instability and high phase noise at such high frequencies. Despite the frequency multipliers' advantages and the fact that they are commonly recommended by hardware designers, there is a lack of comprehensive theoretical guidelines detailing their impact on digital communications. One key aspect is their tendency to induce bandwidth expansion, a phenomenon not observed with mixers. When an N-fold frequency multiplier is used, a common practice among hardware designers is to allocate a bandwidth scaled by a multiple of N, which is deemed large enough to keep signals integrity. We provide an analytical framework to quantify the exact scaling factor of the bandwidth expansion. Contrary to common belief, we show that the bandwidth expansion scales as root N , using three counterexamples, namely Gaussian, Sinc, and raised cosine pulses. These findings can help conserve radio resources and further decrease the noise effect.