8. Spectrum Analyzers // Electronic Measurements and Instrumentation // bhaswanth

8.1 What it is and why

The oscilloscope shows the time domain. The spectrum analyzer shows the frequency domain: amplitude (and sometimes phase) plotted against frequency. Whereas the scope answers "what does this signal look like in time?", the spectrum analyzer answers "what frequencies are present?".

Microscope analogy. A scope is like a high-speed camera: you watch the signal evolve. A spectrum analyzer is like a microscope or a prism: it spreads the signal out by frequency, so you can see structure that is invisible in time. A signal that looks like noise on the scope might reveal a sharp spike at 1.234 MHz on the spectrum analyzer.

8.2 Swept-tuned (superheterodyne) architecture

The classic RF spectrum analyzer is a tunable superhet receiver:

plaintext

                                                            
  Input ─►[Mixer]──►[IF Filter]──►[Detector]──►[Display]   
              ▲                                       ▲    
              │                                       │    
         [Sweep                                  [X-axis = 
          local oscillator]──────────────────────  freq]

A local oscillator sweeps across a range; mixing it with the input shifts each frequency in turn into the IF filter's passband. The IF filter has a fixed center frequency and a user-selectable bandwidth, the resolution bandwidth (RBW). Whatever passes through the IF gets envelope-detected and plotted.

The trade-offs:

Smaller RBW gives better frequency resolution (you can separate two close tones) but requires longer sweep time (the IF must settle within the sweep window). The sweep time is approximately $\text{span}/\text{RBW}^2 \cdot k$ (with $k$ a constant of order 1-10 depending on filter shape).
Larger RBW averages over more spectrum but is fast and gives lower noise floor.
Wider video bandwidth (VBW) smooths the displayed trace less; smaller VBW averages out noise.

A typical Keysight or Rohde & Schwarz spectrum analyzer covers DC to 26 GHz or beyond, with RBW from 1 Hz to 10 MHz, and dynamic range of 100 dB or more.

8.3 FFT-based spectrum analyzer

Modern instruments (and any oscilloscope with FFT) digitize the input and run an FFT. The frequency resolution is $\Delta f = 1/T$ where $T$ is the capture window. The maximum frequency is $f_s/2$ (Nyquist), where $f_s$ is the sample rate.

FFT-based analyzers excel at low frequency (audio, vibration, baseband). Their bandwidth is limited by the ADC. They are also faster than swept-tuned at moderate spans because they capture the whole spectrum at once. Limitations: dynamic range is set by the ADC's effective number of bits (ENOB), and at very high RF, the ADC and front-end are not yet fast enough for the full spectrum at once.

8.4 Real-time spectrum analyzer

A real-time spectrum analyzer (RTSA) does FFTs continuously with no gaps, usually with a "persistence" display that shows how often each frequency-amplitude point is hit. Used for catching transients, intermittent signals, frequency-hopping radios. Tektronix RSA series and Rohde & Schwarz FSVR are typical RTSAs. Important for any radio test where you need to confirm "no leakage anywhere, anytime".

For hardware-security work on RF systems (and RF side channels), an RTSA reveals signal that a swept analyzer would miss because the swept analyzer was looking somewhere else when the signal occurred.

8.5 Span, RBW, sweep time relationship

For swept-tuned analyzers, the sweep time grows with span and shrinks with RBW^2. A common rule: $T_{sweep} \geq k \cdot \frac{\text{span}}{\text{RBW}^2}$ where $k$ is around 2-4 for typical filter shapes. If you violate this, the trace amplitude is suppressed (the IF didn't have time to settle): the displayed peaks are lower than reality. Modern instruments warn you.