Frequency-domain measurements
Lowering the resolution bandwidth of a spectrum analyzer by a factor of ten lowers its noise floor by 10 dB and makes the sweep a hundred times slower.
01The superheterodyne spectrum analyzer
The oscilloscope shows the signal in time; the spectrum analyzer, its power as a function of frequency. The classic analyzer is a self-tuning superheterodyne receiver: a local oscillator sweeps a range of frequencies, a mixer translates each input component to a fixed intermediate frequency, and there a narrow filter, the resolution bandwidth (RBW) filter, lets through only what falls within it. A detector measures the power, and the screen plots it as a function of the local oscillator frequency.
Three controls govern the measurement: the span of frequencies swept, the RBW and the video bandwidth (VBW), a filter after the detector that smooths the trace. The presentation of spectra as an analysis tool was covered in spectra, in Signals and Systems.
02RBW: resolution, noise and time
The RBW decides three things at once. Two signals are seen as separate only if their spacing is of the order of the RBW or greater. The noise entering the detector is proportional to the bandwidth, so the displayed noise floor drops 10 dB for each decade of RBW. And the filter needs time to respond, so the sweep cannot be faster than:
When the two signals have very different levels, the resolution also depends on the filter’s selectivity: the skirt of the strong signal’s response can hide the weak one even if it is farther away than the RBW.
Two close tones, the first at 0 dBm, seen with a Gaussian resolution filter, over a span of 200 kHz. The analyzer has a noise level of −150 dBm/Hz. The tones are considered resolved if between them the trace drops at least 3 dB relative to the weaker one.
03FFT and real-time analyzers
At low frequencies, and in modern analyzers also at the intermediate frequency, the spectrum is calculated by digitizing the signal and applying an FFT. With narrow RBWs it is much faster than sweeping, because it processes all the frequencies at once. Real-time analyzers compute overlapping FFTs with no dead time and can display signals that appear for microseconds, such as a Bluetooth frequency hop, which a sweep would miss. The same instruments measure phase noise, channel power, adjacent-channel leakage ratio and digital modulation quality.
04In the laboratory
Combine two generators with a 5 kHz difference and lower the RBW until they are separated. Repeat with one of them 40 dB lower.
With the input terminated in 50 Ω, measure the noise floor with several RBWs and verify the slope of 10 dB per decade.
Measure the harmonics of a generator with different input attenuations: if the level of the harmonic changes when the attenuation is changed, the analyzer is generating it.
05Common mistakes
- Using a large RBW to see a weak signal. The noise floor hides it.
- Sweeping faster than the filter allows. Amplitudes come out low and frequencies shifted; instruments warn with an uncalibrated alarm.
- Overloading the input mixer. Distortion products appear that are not in the signal.
- Confusing channel power with peak level. For modulated signals, it is measured by integrating over the bandwidth.
06Self-assessment
By how much does the noise floor drop when going from 100 kHz to 1 kHz of RBW?
20 dB.
How long does a 1 MHz sweep take with a 1 kHz RBW and k = 2.5?
\( 2.5 \cdot 10^6/10^6 = 2.5 \) s.
What noise level does a −150 dBm/Hz analyzer show with a 10 kHz RBW?
−110 dBm.
Why does a real-time analyzer see signals that a sweep misses?
Because it processes all the frequencies continuously, with no dead time; the sweep looks at each frequency only for an instant.
07Further reading
- Keysight Technologies. Spectrum Analysis Basics. Application Note 150, Keysight. The classic reference on the superheterodyne analyzer, the RBW and the sweep time.
- Christoph Rauscher, Volker Janssen and Roland Minihold. Fundamentals of Spectrum Analysis. Rohde & Schwarz, 2001. A complete book on swept and FFT analyzers, with their sources of error.
- Clyde F. Coombs Jr. (ed.). Electronic Instrument Handbook. 3rd ed., McGraw-Hill, 1999. Spectrum and signal analyzers within the whole of instrumentation.