We present several new simple and accurate expressions for the DC inductance of square, hexagonal, octagonal, and circular spiral inductors. We evaluate the accuracy of our expressions, as well as several previously published inductance expressions, in two ways: by comparison with three-dimensional field solver predictions and by comparison with our own measurements, and also previously published measurements. Our simple expression matches the field solver inductance values typically within around 3%, about an order of magnitude better than the previously published expressions, which have typical errors around 20% (or more). Comparison with measured values gives similar results: our expressions (and, indeed, the field solver results) match within around 5%, compared to errors of around 20% for the previously published expressions. (We believe most of the additional errors in the comparison to published measured values is due to the variety of experimental conditions under which the inductance was measured.) Our simple expressions are accurate enough for design and optimization of inductors or of circuits incorporating inductors. Indeed, since inductor tolerance is typically on the order of several percent, "more accurate" expressions are not really needed in practice.

We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (op-amps

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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 .