The dependence of the communication capacity of multiple-input multiple-output (MIMO) wireless systems on the average received signal-to-noise ratio (SNR), assuming the channel is unknown at the transmitter and perfectly known at the receiver, is studied through full wave electromagnetic tools. Although it is commonly accepted that the capacity of a MIMO system increases linearly at high SNRs when plotted versus the SNR expressed in dB, the fact that the number of effective degrees of freedom (DOF) of the system increases with SNR in many practical environments calls this conclusion into question for reasonably high SNRs. Based on a full wave electromagnetic investigation, we are able to analytically predict and then confirm a significant region on the MIMO capacity curve where the capacity grows quadratically when plotted versus the SNR in dB. This gives analytical insight into a portion of the capacity curve that may previously be (incorrectly) attributed to the concavity of the logarithm function rather than the increase in electromagnetic degrees of freedom. The quadratic, rather than linear, growth of capacity suggests that it may be worthwhile to invest more transmit power to achieve higher performance gains. However, to fully take advantage of this second order benefit, the numbers of antennas at the transmitter and the receiver must be close to or slightly larger than the wavevector-aperture-product (WAP) of the corresponding EM system.