RF technology is increasingly being harnessed to send data from a device under test (DUT) to a receiver. For Internet of Things (IoT) applications, the most common way is to use standards like Bluetooth, Wi-Fi or Zigbee. Data from a test system is modulated to an RF carrier via complex modulation schemes, a process that results in very fast and dynamic signal transfer.

## Analyser Techniques

The complete RF input signal is shifted to an intermediate frequency via a swept local oscillator using a superposition technique. This means that a signal trace from a spectrum analyser (SA) will sweep between start and stop frequencies according to the adjusted centre frequency and span (which determines the frequency range for which an amplitude is plotted).

Spectrum analysers have auto-coupled sweep time that automatically chooses the fastest allowable sweep time based on several parameters, including RBW (resolution bandwidth, which determines the instrumentâ€™s ability to resolve signals of equal amplitude), VBW (video bandwidth, a factor that affects the displayed trace quality of a spectrum analyser) and span. The technology is used for fast overview of a wide spectrum with good amplitude accuracy, and for insertion loss or loltage standing wave ratio (VSWR) measurements. Additionally, a common SA is a very useful tool to perform RF measurements with a large dynamic range and good performance.

For measurement of low-level signals, itâ€™s important to have good dynamic range. Some standards have reference sensitivity below -120dBm, lower than the noise level. Therefore, a test device needs a noise level as low as possible. This is important, because in an SA, blind time occurs when signal information is lost; see Figure 1.

## Bluetooth Example

Random and very fast signals canâ€™t be easily detected. However, a fast-changing frequency-hopping signal like Bluetooth can be measured with an SA, with one trace set to maximum hold, and a second to clear write.

It is not possible to capture all signal components with one sweep; several sweeps are necessary, and they are only visible with the maximum hold function; see Figure 2. However, not all frequency components are visible, thereâ€™s no time information available, and itâ€™s not possible to determine if it is a frequency-hopping spread-spectrum signal.

Frequency, span and RBW have a direct influence on the sweep time in common spectrum analysers. If a better frequency resolution is required, then RBW needs to decrease, which results in slower sweep time and more difficult and time-consuming capture of fast signals.

Real-time spectrum analysis uses Fast Fourier Transform (FFT) technology and works without a sweep and with a different calculation format. In a normal FFT form, the calculation time is longer than the FFT process, which results in loss of information because of the gap between FFT acquisitions; see Figure 3. This type FFT analysis canâ€™t be used for measuring pulsed signals, because parts of the pulse may fall into the gap between FFT acquisitions, resulting in a different frequency for each pass.

In real-time acquisition, the calculation is performed in parallel to the FFT process, and is very fast â€“ faster than the FFT acquisition. Display data changes constantly and fast, resulting in time acquisition of different FFT blocks being gap-free; see Figure 4. Also, the speed wonâ€™t change with different RBW adjustments.

## Gap-Free FFT Example in A Real-Time Operation

A fixed number of samples (1024) is used for one FFT time acquisition. Each FFT calculation uses a window function â€“ windowing is important to define a discrete number of time points for the calculation.

The size of the window can be varied, and is not fixed in the time domain. Varying the window size will affect the real-time resolution bandwidth; or, putting it another way, with changing RBW, the size of the window will also change.

The slew rate and number of window points influence the leakage (operations create new frequency components referred to as spectral leakage), frequency and amplitude accuracy. The downside of using a filter is that some signal information will be lost due to amplitude suppression at the beginning and end of the filter; see Figure 5.

The position of a time signal like a pulse needs to be in the centre of an FFT window to be correctly transformed into a frequency range. If a pulse falls between two FFT events, its amplitude is suppressed by the filter side loops and is no longer correct; see Figure 6.

Some instruments, such as Rigolâ€™s RSA5000 series, use overlapping FFT events to avoid losing signal information. This has the effect of covering a greater spectrum over a given period and the time resolution is better. Smaller events can also be measured (Figure 7), and any signal suppression due to windowing is eliminated.

Itâ€™s obvious that the overlapping process of FFT events directly influences the shortest of pulse widths, which can be measured with a real-time spectrum analyser. The overlapping of FFT frames is not possible during calculation, but the overlap time of FFT frames can be calculated with the following formula: T_{overlap }= T_{acq} – T_{calc}

For example, for a sample rate of 51.2MSps, the overlap is 13.18Âµs, or 65.86%, which results in overlap of 674 sample points.

## Probability of Intercept

Probability of intercept (POI) specifies the shortest pulse duration that can be measured with 100% amplitude accuracy. Furthermore, POI defines the minimum pulse-width where each pulse will be captured; see Figure 8. Such short pulse events canâ€™t be measured continuously with a common SA, and typically require an RT-SA.

POI depends on the FFT rate, used RBW and adjusted span. The principle of POI is described with a span of 40MHz (= 51.2MS/s) and RBW of 3.21MHz (Kaiser window) in Figure 9.

Due to the calculation time, a second FFT acquisition starts after 6.82Âµs. The window size depends on RBW in real-time mode, thus:

The start of the first FFT acquisition and the end of the second FFT acquisition define the POI time.

POI can also be calculated with:

Having POI and the speed determined, it is now possible to measure a Bluetooth signal with the RT-SA mode; using maximum hold is no longer necessary.

## Density Analysis

Density analysis shows the same results as normal trace analysis, but, with it, a signalâ€™s repetition rate can be also analysed.

In normal and density modes it is possible to activate a spectrogram measurement, which is a waterfall measurement frequency over time, measuring the duration of pulses, like Bluetooth signals, for example. With a waterfall spectrogram, signal on/off scenarios can easily be analysed. Density analysis combined with a spectrogram is equivalent to a 4D measurement: power over frequency over repetition rate and power over time; see Figure 10 for a Bluetooth example.

In Power vs time (PvT), it is possible to display a signalâ€™s time domain within adjusted real-time bandwidth. The acquisition time can be changed in this measurement. The PvT analysis is displayed for real-time bandwidth used, and not RBW like with an SA with zero-span configuration. Signal bursts of modulated signals and pulses can be displayed to measure their duty cycle and amplitude, or to display pulse trains over a certain period. PvT can be used in combination with normal trace analysis (frequency spectrum) and a spectrogram; see Figure 11.

Comparing the measurement results for a Bluetooth signal in Figures 10 and 11 with that of an SA in Figure 2, a test engineer now has much more information available. Within the adjusted real-time bandwidth, all frequency components can be measured, and time information can be displayed in parallel with spectrum measurement.

In a spectrogram, itâ€™s clearly visible that the signal is a frequency-hopping spread spectrum one, and the length of data blocks can be easily analysed. PvT no longer depends on RBW like with an SA, and the frequency and time domains can be displayed at the same time.