We present a technique for enhancing the bandwidth of gigahertz broad-band circuitry by using optimized on-chip spiral inductors as shunt-peaking elements. The series resistance of the on-chip inductor is incorporated as part of the load resistance to permit a large inductance to be realized with minimum area and capacitance. Simple, accurate inductance expressions are used in a lumped circuit inductor model to allow the passive and active components in the circuit to be simultaneously optimized. A quick and efficient global optimization method, based on geometric programming, is discussed. The bandwidth extension technique is applied in the implementation of a 2.125-Gbaud preamplifier that employs a common-gate input stage followed by a cascoded common-source stage. On-chip shunt peaking is introduced at the dominant pole to improve the overall system performance, including a 40% increase in the transimpedance. This implementation achieves a 1.6-k transimpedance and a 0.6-A input-referred current noise, while operating with a photodiode capacitance of 0.6 pF. A fully differential topology ensures good substrate and supply noise immunity. The amplifier, implemented in a triple-metal, single-poly, 14-GHz , 0.5-m CMOS process, dissipates 225 mW, of which 110 mW is consumed by the 50-output driver stage. The optimized on-chip inductors consume only 15% of the total area of 0.6 mm 2 .