In wireless communication systems, the nonlinear effect and inefficiency of power amplifier (PA) have posed practical challenges for system designs to achieve high spectral efficiency (SE) and energy efficiency (EE). In this paper, we analyze the impact of PA on the SE-EE tradeoff of orthogonal frequency division multiplex (OFDM) systems. An ideal PA that is always linear and incurs no additional power consumption can be shown to yield a decreasing convex function in the SE-EE tradeoff. In contrast, we show that a practical PA has an SE-EE tradeoff that has a turning point and decreases sharply after its maximum EE point. In other words, the Pareto-optimal tradeoff boundary of the SE-EE curve is very narrow. A wide range of SE-EE tradeoff, however, is desired for future wireless communications that have dynamic demand depending on the traffic loads, channel conditions, and system applications, e.g., high-SE-with-low-EE for rate-limited systems and high-EE-with-low-SE for energy-limited systems. For the SE-EE tradeoff improvement, we propose a PA switching (PAS) technique. In a PAS transmitter, one or more PAs are switched on intermittently to maximize the EE and deliver an overall required SE. As a consequence, a high EE over a wide range SE can be achieved, which is verified by numerical evaluations: with 15% SE reduction for low SE demand, the PAS between a low power PA and a high power PA can improve EE by 323%, while a single high power PA transmitter improves EE by only 68%.