#### Measurements with a spectrum analyzer

Figure 1: Three-dimensional representation of the viewing directions for the time domain and the frequency domain,
left: the two-dimensional representation using an oscilloscope;
right: the representation as a frequency spectrum.

Figure 1: Three-dimensional representation of the viewing directions for the time domain and the frequency domain,
left: the two-dimensional representation using an oscilloscope;
right: the representation as a frequency spectrum.

#### Measurements with a spectrum analyzer

A spectrum analyzer is a measuring instrument that is constructed very similarly to an oscilloscope. Both measuring instruments are used to display and measure special complex signal shapes. Both instruments display the amplitude of the measured signal in the ordinate. Differences exist in the display on the abscissa. On an oscilloscope this is the time axis, on a spectrum analyzer, this is the frequency axis. The oscilloscope, therefore, measures in the time-domain, while the spectrum analyzer measures in the frequency-domain.

If an ideal sine wave voltage is to be displayed, the oscilloscope displays this sine wave over the entire screen width. In the case of a spectrum analyzer, a narrow vertical line is displayed for this sinusoidal oscillation. Even the smallest changes to the ideal sine waveform, for example, due to low-frequency modulation, would not be visible on an oscilloscope. On the spectrum analyzer, however, several vertical lines with a length-dependent on the amplitude of the respective signal component would then be displayed.

Figure 1 shows a mixture of three sine frequencies. Approximately this mixture of signals would be produced if an FMCW radar were to detect three targets at different distances. On an oscilloscope, these three frequencies would possibly be visible if they did not have too large frequency differences. But measuring the frequency, i.e. measuring the distance, would not be possible with an oscilloscope. Only on the spectrum analyzer can all three frequencies be measured. With an FMCW radar, the spectrum analyzer can be used directly as a distance measuring instrument.

Figure 2: Display of the signal of the transmitter of a pulse radar on a spectrum analyzer

Figure 2: Display of the signal of the transmitter of a pulse radar on a spectrum analyzer

##### Measurement of a spectrum

With a pulse radar, the time sequences are best displayed on an oscilloscope. Here, for example, a spectrum analyzer has the task of evaluating the quality of the probing signal generated by the transmitter. Figure 2 shows the spectrum of a magnetron transmitter. In a magnetron transmitter, for example, the transmission power can be controlled by increasing the magnetrons anode current. However, more power generated does not mean better maximum ranges at the same time. A power measurement is always broadband. This means that those parts of the power that are outside the bandwidth of the other radar modules (e.g. antenna, diplexer) are also measured. The spectrum analyzer can now be used to estimate whether the additional power due to an increase in magnetrona anode current is at all in the range of the desired frequencies. Otherwise, it is pointless to increase the current further, because the only effect would be a shortening of the magnetron’s lifetime.

The spectrum analyzer can also be used to detect temporal correlations of the pulse repetition frequency because the pattern of the frequency lines and their gaps is also meaningful. However: an oscilloscope can do this much more clearly.

Figure 3: R&S®FPC 1500 Spectrum analyzer
(Courtesy of Rohde & Schwarz)

##### Technical specification

Analog measuring instruments use an electrically tunable band filter to separate the frequencies in time and display their amplitudes like an oscilloscope. In practice, this is even a fixed frequency in the band filter and the signal to be measured is mixed with a local oscillator frequency that changes linearly over time (the so-called sweep frequency), as in a superheterodyne receiver. High-quality digital spectrum analyzers also use this principle for reasons of accuracy and resolution. For example, the device shown in Figure 3 can display frequencies up to a maximum of 3 GHz with a resolution of only one Hertz.

With cheaper digital spectrum analyzers, the hardware sometimes differs only slightly from that of an oscilloscope. The difference is essentially only in the software: time-domain signals are converted to the frequency domain using the Fourier transform. This means that modern oscilloscopes are also able to work as spectrum analyzers by using other or additional software. However, their results (in resolution) are then somewhat less accurate because the bandwidths required for this purpose are often not achieved by simple oscilloscopes. Furthermore, the Fast Fourier Transformation also requires time and becomes less accurate for signals that change rapidly over time.