Application of spectrum analyzer vector signal analysis

With the development and application of modern spectrum analyzer digital intermediate frequency processing technology, it is more and more widely used in various fields such as communication, aerospace, measurement and military industry. It not only makes digital signal demodulation possible, but also provides a better method for demodulating analog modulated signals. At the same time, the frequency and phase stabilization time of the transmitter and frequency synthesis source can also be accurately analyzed.

Vector representation of signals

Understanding the vector representation of signals and the concept of IQ signals is the basis for the understanding and application of modern spectrum analysis and signal analysis. As a graphical tool, a vector is a rotating arrow in a rectangular coordinate system. The length of the arrow represents the peak amplitude of the signal. The counterclockwise rotation direction is the positive direction. The angle between the arrow and the positive half axis of the horizontal axis is the phase. The signal period corresponds to the time it takes for the arrow to rotate once. The number of times the signal completes a rotation per second corresponds to the signal frequency.

The length of the projection of the signal vector on the vertical axis is equal to the peak amplitude of the signal multiplied by the sine of the phase, so if the signal is a sine wave, the projection corresponds to the instantaneous amplitude of the signal (see Figure 1).

Figure 1 The correspondence between the sine wave and the vector signal expressed in the time domain

Figure 2 Schematic diagram of the intermediate frequency signal processing of the spectrum analyzer

Using vectors to represent signals can fully describe the amplitude, frequency and phase of the signal. Therefore, in signal analysis, we often perform vector decomposition on the signal, that is, decomposing the signal into two components with the same frequency and peak amplitude but a phase difference of 90. Usually, we use a sine signal (Asinwt) and a cosine signal (Acoswt) to describe these two components, where the cosine component is called the in-phase component, i.e., the I component; and the sine component is called the orthogonal component, i.e., the Q component.

Digital IF Processing Technology of Spectrum Analyzer

The RF signal input to the spectrum analyzer is mixed and converted into an intermediate frequency signal IF, and then passes through a bandpass filter (IF filter) to enter the A/D converter. In the digital processing part, the IQ signal down-converted to baseband is low-pass filtered and undersampled, and stored in the memory for further processing. The stored data represents the voltage value of the IQ signal.

In the spectrum analyzer setting process, the analog intermediate frequency filter bandwidth is IFBW, and the low-pass filter bandwidth of the digital processing part is the demodulation bandwidth. Undersampling divides the sampling rate of the IQ signal by 2 to the power of n. When the demodulation bandwidth is narrow, a too high sampling rate is meaningless.

Signal demodulation method

The processing methods that can be used for the IQ signal in the memory are: amplitude analysis, frequency analysis, phase analysis and FFT spectrum analysis. In the vector analysis process of the spectrum analyzer, the spectrum analyzer is set to zero SPAN, that is, the analysis is performed at a fixed input frequency within the intermediate frequency bandwidth.

1. Analysis and processing
(1)
Am is the amplitude of the input signal. According to each sample value of the IQ signal, the amplitude value at the corresponding sampling moment can be calculated. The display unit can be a linear voltage value (V), a logarithmic voltage (dBmV) or a power value (dBm). All Am values ​​within the measurement time constitute the IQ amplitude array Am-DC.
(2)
Φm is the phase of the input signal. According to each sample value of the IQ signal, the relative phase value at the corresponding sampling moment can be calculated. All Φm values ​​within the measurement time constitute the IQ amplitude array Φm-DC.
(3)
Fm is the frequency of the input signal. The frequency value is obtained by taking the derivative of the phase difference between adjacent points with respect to time. All Fm values ​​within the measurement time constitute the IQ amplitude array Fm-DC.
(4)
Spec is the frequency spectrum within the intermediate frequency bandwidth of the input signal.

2. Demodulation method

As mentioned above, corresponding to the carrier signal, the amplitude, phase and frequency curves varying with time and the real-time spectrum can be obtained.

AM Demodulation

The AM-DC array is analyzed, which corresponds to the RF power-time curve TRF.

Perform FFT calculation on this array to obtain the AF spectrum, whose fundamental frequency is the modulation frequency fmod. Based on the AF spectrum, the modulation harmonic distortion and signal-to-noise ratio can be calculated.

Perform narrowband low-pass filtering on the array to obtain the carrier amplitude array Vc, calculate the difference array of AM-DC and Vc, and its ratio to Vc, AMdeep array, represents the modulation depth, which is detected: positive peak (+pk): the maximum value in the array; negative peak (+pk): the minimum value in the array; peak-to-peak value/2 (1/2pk-pk): half of the difference between the maximum and minimum values ​​in the array; root mean square value (rms): the root mean square value of the values ​​in the array.

Figure 3 AM demodulation principle

Figure 4 FM demodulation principle

Figure 5 ΦM demodulation principle

FM Demodulation

Analyze the FM-DC array, which corresponds to the frequency curve TFM.

Perform FFT calculation on this array to obtain the AF spectrum, whose fundamental frequency is the modulation frequency fmod. Based on the AF spectrum, the modulation harmonic distortion and signal-to-noise ratio can be calculated;

This array is detected, similar to AM demodulation, to obtain peak and RMS values.

ΦM Demodulation

The ΦM-DC array is analyzed, which corresponds to the frequency curve ΦFM.

Perform FFT calculation on this array to obtain the AF spectrum, whose fundamental frequency is the modulation frequency fmod. Based on the AF spectrum, the modulation harmonic distortion and signal-to-noise ratio can be calculated.

This array is detected, similar to AM demodulation, to obtain peak and RMS values.

Demodulation Example

Figure 6 shows the application of Rohde & Schwarz spectrum analyzer option FS-K7 in analyzing FM signals. It uses the above demodulation principle and can demodulate FM, AM, PM and real-time spectrum in real time.

Figure 6 FM demodulation analysis

Figure 7 Real-time spectrum analysis

Real-time spectrum analysis

Real-time spectrum analysis is different from traditional spectrum analyzer analysis technology. It performs FFT analysis on the intermediate frequency signal based on the traditional superheterodyne spectrum analyzer (see formula 4). Due to its real-time and fast characteristics, it is increasingly used in the analysis of modern communications and radar signals, especially in the monitoring of frequency hopping signals.

Real-time spectrum analysis also includes AF spectrum monitoring, which analyzes the demodulated spectrum of AM or RF power, and helps analyze the symbol rate of unknown signals. For non-constant amplitude continuous digital modulation signals (such as PSK and QAM signals), the first peak point greater than 0Hz on the AF spectrum usually corresponds to the symbol rate of the signal, making vector analysis of unknown signals possible.

Radar signal test analysis

Since the vector analysis function of the spectrum analyzer can analyze the frequency, power, phase and real-time spectrum of the signal in real time, in the research and development and testing of modern radars, spectrum analyzers with vector analysis functions have become an essential tool for radar transmitters and their devices.

The principle of radar signal analysis is consistent with the "signal demodulation method", which analyzes the characteristic curves of amplitude, frequency and phase in the time domain. For common radar signals, such as linear frequency modulation, Barker code, etc., their pulse characteristics can be analyzed, including rising and falling edge analysis, frequency characteristics, phase characteristics and vector diagrams.

Figure 8 Linear frequency modulation signal analysis

Figure 9 Transient characteristics test

Radar signal testing is divided into power and spectrum testing and intra-pulse modulation testing. Figure 8 shows a linear frequency modulation intra-pulse modulation test, which observes the frequency variation within the pulse, including linearity and frequency modulation bandwidth, using the vector analysis function of the spectrum analyzer. In the frequency domain test of the spectrum analyzer's basic spectrum analysis function, the signal spectrum and test power can be observed. The spectrum analyzer's time domain test or vector analysis of AM demodulation can test pulse waveforms, rising and falling edges, and other information.

Transmitter and frequency synthesis source settling time measurement

For transmitters and frequency synthesizers, their amplitude, frequency and phase transient characteristics are important test indicators. Generally speaking, the frequency stabilization time refers to the period of time from the transmitter output level reaching a certain value (usually stable output power -30dB) to monitoring the FM demodulation spectrum until the frequency stabilizes within the design limit.

The analysis principle is consistent with the previous "Signal Demodulation Method", which analyzes the characteristic curves of amplitude, frequency and phase in the time domain, uses the AM curve to define the start time, observes the FM and PM curves, and obtains the test results .

In modern spectrum analysis technology, vector analysis technology is an extremely important part, with broad development and application prospects. At the same time, it is also an indispensable means in demodulation analysis, suitable for demodulation of various analog and digital modulated signals, including some special modulated signals such as VOR/ILS used in aviation systems. In the fields of communication signal demodulation analysis (analog and digital), radar signal analysis, and frequency synthesis transient analysis, the application of vector signal analysis is constantly developing and innovating.