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The total capacity per chip constrained to a given chip pulse waveform of asynchronous code division multiple access (CDMA) channels with random spreading and subject to frequency-flat fading is investigated in the large system limit. The analysis in terms of signal to interference and noise ratio (SINR) is extended to CDMA systems with linear minimum mean square error (MMSE) detectors. The system behaviour is completely described by a positive function n(f) that can be interpreted as the spectrum of the multiuser efficiency. Both total capacity per chip and SINR of linear MMSE detectors can be expressed in terms of the spectrum of the multiuser efficiency. A simple relation between the total capacities per chip of asynchronous CDMA systems with modulation based on sine pulse waveforms and of synchronous CDMA systems is derived.