Every signal is a sum of sines. The analyzer shows which.
Ten minutes of reading. Move the sliders, then the lines on the spectrum analyzer will make sense.
Two views of one signal
An oscilloscope shows the voltage against time. You see the shape: rise times, distortion, the envelope.
A spectrum analyzer shows power against frequency. You see which frequencies are present and how strong each one is.
The analyzer reads power in dBm (decibels above 1 mW in 50 Ω). 0 dBm is 1 mW; every 10 dB is a factor of 10 in power.
A signal far below another one is invisible on the scope but clear on the analyzer: a line 40 dB down is only 1% of the voltage, yet on a 10 dB per division screen it sits four divisions lower and is easy to read. That is why radio work is done in the frequency view.
Fourier series: periodic signals are lines
Fourier transform: from lines to a spectrum
The Fourier series works for periodic signals. The Fourier transform extends it to any signal: X(f) = ∫ x(t) e−j2πft dt. A periodic signal gives sharp lines; a signal that changes (speech, data) spreads its power over a band of frequencies.
Two properties matter in this lab. Linearity: the spectrum of a sum is the sum of the spectra, so every line can be read on its own. Modulation: multiplying by cos 2πfct moves the whole spectrum up to ±fc. That is exactly what an AM modulator does, and why AM shows a carrier with a sideband on each side.
How a spectrum analyzer works
Frequency (centre)
- Sets the frequency in the middle of the screen. Type it in the Spectrum tab, use the preset, or turn CENTER FREQ (steps of span / 10).
- Peak → CF moves the centre to the strongest line inside the span.
Span
- The width of the screen in frequency. Ten divisions: a 10 MHz span is 1 MHz per division.
- At zero span a real analyzer shows the signal against time. This bench keeps spans from 10 kHz to 100 MHz.
Reference level and RBW
- The reference level is the top line of the screen; each division below it is 10 dB.
- The RBW is the width of the IF filter. Automatic RBW follows the span; a manual value is marked # in the header.
Resolution bandwidth: seeing two lines as two
Every line on the screen is drawn with the shape of the IF filter, so it is as wide as the RBW. Two lines closer together than about one RBW merge into one hump. A narrower RBW separates them and also lowers the noise floor (10 dB for every factor of 10), so weak lines appear. The price is a slower sweep on a real instrument.
Drag the sliders: start with tones 16 kHz apart and an RBW of 30 kHz, then narrow the RBW until there are two peaks.
The spectrum of tone AM
On the bench
The analyzer input is 50 Ω and its lead has a black ground clip like the generator leads: always clip it on a GND socket. Keep the strongest line below the reference level; the manual uses −10 dBm for both exercises.
What you should see
| Exercise | Settings | Lines (marker values) |
|---|---|---|
| 1: square wave, 10 MHz, 100 mV p-p | centre 10 MHz, span 10 MHz (1 MHz/div), ref −10 dBm | 10 MHz at about −13.9 dBm |
| 1: wider span | span 50 or 100 MHz | 30 MHz about −23.5 dBm, 50 MHz about −27.9 dBm, 70 MHz about −30.8 dBm; even harmonics about 50 dB down |
| 2: tone AM, 1 MHz and 20 kHz | centre 1 MHz, span 2 MHz (200 kHz/div), ref −10 dBm, auto RBW | carrier 1 MHz at about −30 dBm, sidebands very close to it |
| 2: span 100 kHz | auto RBW 333 Hz | 980 kHz and 1.02 MHz at about −42 dBm (12 dB below the carrier, m ≈ 0.5) |
Levels are those of the simulator model (ideal 50 Ω source and load). A real generator and cable give slightly different numbers, but the spacing of the lines and the differences in dB between them are the same.
Check yourself
Q1Why is the Fourier series used?
To write a periodic signal as a sum of sines and cosines at multiples of its fundamental frequency. Each term is one line on the analyzer, so the series tells us which frequencies a signal contains and how strong each is.
Q2What is the difference between the Fourier series and the Fourier transform?
The series applies to periodic signals and gives discrete lines at k f0. The transform applies to any signal (periodic or not) and gives a continuous spectrum X(f); for a periodic signal it reduces to lines.
Q3Name the main controls of the spectrum analyzer.
Frequency (centre or start and stop), span, reference level (amplitude), resolution bandwidth, and markers (with peak search).
Q4What does the frequency control do?
It selects the range the local oscillator sweeps through, normally by setting the centre frequency of the display; the span then sets the width around it.
Q5Define resolution bandwidth.
The bandwidth of the IF filter. It sets how close two frequency components can be and still appear as two separate lines; a narrower RBW also lowers the noise floor.
Q6What is the main difference between an oscilloscope and a spectrum analyzer?
The oscilloscope shows amplitude against time; the spectrum analyzer shows power against frequency, on a log (dB) scale that shows very weak components next to strong ones.
Q7A 10 MHz square wave: where are the first three lines and how far down?
10, 30 and 50 MHz. The 30 MHz line is 9.5 dB and the 50 MHz line 14 dB below the 10 MHz line. There are no even harmonics in an ideal square wave.