As discussed above in types, a swept-tuned spectrum analyzer down-converts a portion of the input signal spectrum to the center frequency of a band-pass filter by sweeping the voltage-controlled oscillator through a range of frequencies, enabling the consideration of the full frequency range of the instrument.
The bandwidth of the band-pass filter dictates the resolution bandwidth, which is related to the minimum bandwidth detectable by the instrument.  As demonstrated by the animation to the right, the smaller the bandwidth, the more spectral resolution. However, there is a trade-off between how quickly the display can update the full frequency span under consideration and the frequency resolution, which is relevant for distinguishing frequency components that are close together.  For a swept-tuned architecture, this relation for sweep time is useful:
Where ST is sweep time in seconds, k is proportionality constant, Span is the frequency range under consideration in hertz, and RBW is the resolution bandwidth in Hertz.
Sweeping too fast, however, causes a drop in displayed amplitude and a shift in the displayed frequency.
Also, the animation contains both up- and down-converted spectra, which is due to a frequency mixer producing both sum and difference frequencies. The local oscillator feedthrough is due to the imperfect isolation from the IF signal path in the mixer.
For very weak signals, a pre-amplifier is used, although harmonic and intermodulation distortion may lead to the creation of new frequency components that were not present in the original signal.