What is the frequency domain and why is it so important for RF design, analysis and test?

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What is the frequency domain and why is it so important for RF design, analysis and test? [Copy link]

Why use frequency domain?

On the one hand, when we first came into contact with learning circuits and signals, we were dealing with voltages and currents that were static relative to time. For example, we could use a multimeter to measure directly, but for time-varying signals, we needed to use an oscilloscope to observe the waveform of the signal at different times. In the RF band, this time-varying signal changes extremely quickly, and it is obviously difficult to observe the signal with an oscilloscope. At this time, its frequency components are static values one by one, and its spectrum is observed with a frequency analyzer.

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Fourier Transform

As we have said in " Learning Fourier Transform ", any periodic continuous signal can be expressed as a combination of a set of appropriate sinusoidal curves sin(x). And this combination is the Fourier series. We can express this appropriate sinusoidal curve as its frequency domain state.

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The periodic signal in the time domain and the corresponding frequency domain signal are completely equivalent in describing a radio frequency signal. This set of frequency components after Fourier transformation can accurately describe the radio frequency signal.

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In RF design, Fourier transform can process extremely complex signal changes and convert them into frequency domain components with more information than the original time domain waveform.

The details involved in computing the Fourier transform or discrete Fourier transform (DFT) are not trivial; however, this is not something we need to worry about now. Frequency domain techniques can be understood and used even if you have little knowledge of the underlying mathematical procedures.

The Fourier transform produces an expression that reveals the frequency content of a signal, while the DFT produces the corresponding numerical data. However, in the context of real engineering, graphical representations are often much more convenient. Eventually, these frequency domain plots become as normal and intuitive as oscilloscope traces.

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Spectrum

The spectrum diagram after transformation into frequency domain signal is what we usually call spectrum. The ideal spectrum diagram of a 1MHz sine wave signal is as follows:

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The vertical arrow indicates that there is a certain amount of "energy" at 1 MHz. The line portion of the arrow is very thin because this idealized signal has absolutely no other frequency components - all the energy is concentrated at 1 MHz. This energy is the amplitude of the sinusoidal signal.

If we combine this perfect 1 MHz sinusoid with a perfect 2 MHz sinusoid using a summing circuit, the spectrum will look like this:

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This frequency domain plot provides very clear data about the frequency characteristics of our new signal. If we are primarily interested in the non-instantaneous frequency-dependent behavior of the circuit, the spectrum will provide the information we need. In contrast, the time domain waveform is not simple and appears to be more difficult to handle. The figure below shows a sine wave signal with a frequency of f and a frequency of 2f superimposed. It must be difficult to tell which is which.

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However, the actual spectrum is rarely a very thin arrow, but is usually a signal with a certain bandwidth as shown in the figure below.

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Why does the difference occur? First, the resolution of the measurement system is finite, and this limitation inherently compromises any "ideal" qualities that might have existed in the original signal. But even if we had an infinitely precise measurement device, the spectrum would differ from the mathematical version due to noise.

The only type of signal that can produce the "pure" spectral components shown in the previous section is a perfect sine wave - that is, no noise and no variations in period or amplitude. Any deviation from the characteristics of a perfect sinusoid introduces additional frequency components.

An intuitive example is phase noise: it is unrealistic to expect a real-world oscillator to always produce exactly the same frequency; there will inevitably be (hopefully small) variations in the actual duration of a cycle, which is called phase noise. If you collect data covering a thousand cycles, and then perform a spectral analysis, you are effectively averaging the frequency content of those thousand cycles. The result will be the spectral shape shown above; the width of the waveform corresponds to the average deviation from the nominal frequency.

Spectrum Measurement

Domain diagrams provide a very convenient way to discuss and analyze RF systems. Modulation schemes, interference, harmonic distortion - even a basic spectrum drawn on scratch paper can really help clarify a situation.

However, when it comes to successfully designing RF systems, we often need something more sophisticated. More specifically, we need something that can give us the actual spectral characteristics of a signal. This is important for characterizing the functionality of an existing system, but often the more pressing need is diagnosis and resolution – i.e., why is this device not working and how can we fix it.

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Digital oscilloscopes offer an "FFT" (Fast Fourier Transform) function, which is one way to get spectral measurements. However, the tool of choice for real-world frequency analysis is called a spectrum analyzer. This is a piece of test equipment specifically designed to accept a high-frequency input signal and display a frequency domain representation of that signal. Getting some hands-on experience with a spectrum analyzer is an important initial step in becoming familiar with the practical aspects of RF engineering.

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