Radio Frequency (RF) and Microwave Spectral Analysis

The display of electromagnetic radiation as a function of wavelength is termed to as electromagnetic spectrum. Based upon the wavelengths, the spectrum is divided into various frequency bands as illustrated in the figure below:

With the rapid advancement of wireless technology and satellite sensor technology, there is need for more and more accurate field measurements to complement overhead data in providing higher spectral resolution over progressively broader wavelengths. In performing spectral analysis, the following factors are considered:

• Power in band
• Occupied bandwidth
• Adjacent channel power
• Resolution bandwidth
• Harmonic distortion
• Noise specification

Power in Band

It is the measurement of total power within any specified range or band. The power in band is calculated by the following equation:

Where X, is the input power spectrum from a specified band, f_l is the low bound of the frequency and f_h is the high bound of the frequency band. The low and high bounds of this band can be determined from the center frequency.

Occupied Bandwidth

It is the measurement of frequency band or bandwidth that contains a specified percentage of the total power of the signal. Occupied bandwidth is the inverse of power in band. For example, if the specified percentage is 99, then the occupied bandwidth is the bandwidth that contains 99% of the total power of the signal i.e. the frequency range in between vertical lines as illustrated below:

Adjacent Channel Power

It measures the way a particular channel and its two adjacent channels distribute power. The measurement is performed by calculating the total power in the surrounding upper and lower channels.

Resolution Bandwidth

This is determined by the smallest frequency that can be resolved. In Fourier-transform-based spectrum analysers, the resolution bandwidth is inversely proportional to the number of samples acquired or the length of the window function. By taking more samples in the time domain or making the acquisition time longer, while keeping the sampling rate the same, the resolution bandwidth will be lowered, meaning higher frequency resolution.

You can also read: Basics of Radio Frequency (RF) and Wireless Communication Systems

Harmonic Distortion

This is a measure of the amount of power that is contained in the harmonics of a fundamental signal. Harmonic distortion is inherent to devices and systems which possess nonlinear characteristics -the more nonlinear the device, the greater its harmonic distortion.

When a signal of a particular frequency f₁ passes through a nonlinear system, the output of the system consists of f₁ and its harmonics f₂ and f₃.

Harmonic distortion is usually expressed as either power or percentage ratio, where harmonic power distortion is P_HD which is obtained from:

P_HD = P_fund – P_harm (dB)

Where, P_HD is the power of harmonic distortion in dBc i.e. relative to the carrier frequency, P_fund is the fundamental signal power in dB or dBm, and P_harm is the power of the harmonic of interest in dB or dBm.

To represent the distortion in the form of percentage ratio, it is converted into voltage, and calculated as follows:

Where, V_harm and V_fund are the harmonic voltage and fundamental voltage respectively.

In some applications, harmonic distortion is measured as a total percentage harmonic distortion (THD). This measurement requires the power summation of all the harmonics in the spectrum band as defined by the below equation:

Phase Noise

There are various sources of noise in RF and Microwave systems. When the carrier signal contains noise due to phase and frequency modulation of the signal then the noise is called Phase noise. The spectrum of phase noise is normally close to the carrier spectrum, and is measured in decibels relative to the carrier frequency (dBc). Noise floor is a specified noise level below which signals cannot be detected under a specified measurement conditions.