The disclosed embodiments relate to the design of a linear equalizer that supports low-power, high-speed data transfers. In some embodiments, this linear equalizer contains a passive network that provides selective frequency peaking in a frequency range associated with a falling edge of a frequency response of the channel. It also includes a level shifter coupled between the channel and the passive network, wherein the level shifter is an active component that provides amplification and/or level-shifting. Moreover, the linear equalizer is designed so that power from the level shifter facilitates the selective frequency peaking of the passive network.