An overview of time and frequency domains and demonstration of the Spectrogram.

Hi again and welcome to our 85th Test and Measurement Video. Today we’ll talk about domains in the Tektronix MDO3000 oscilloscope.

By way of background, in mathematics a function is frequently graphed in Cartesian coordinates. Two axes intersect at right angles at the origin which is placed at the center of the graph. By convention, the vertical line is known as the Y-axis and the horizontal line is known as the X-axis. Any value can be represented by a point on the graph, determined by two numbers, one located on the X-axis and the other located on the Y-axis.

All solutions to an equation, f(X) = Y, relating these two numbers, can be represented by a line passing through the points. The domain of a function is the complete set of values of the independent variable. The range of a function is the complete set of values of the dependent variable.

We can say, then, that the range depends upon the domain.

In the time domain, for example, an oscilloscope displays dependent amplitude values plotted against the Y-axis for independent time values plotted against the X-axis. You start with the domain values and then use the function to develop the range values.

In the time domain, an oscilloscope displays amplitude in volts as it varies with time in seconds or fractions of a second.

In other domains, the X- and Y-axes may be defined differently and accordingly totally different displays are shown on the oscilloscope screen.

In the frequency domain, the frequency of a signal in hertz becomes the domain, plotted on the X-axis. Amplitude is still plotted on the Y-axis, but now it is power, expressed in decibels, rather than volts as in the time domain.

Time is the default oscilloscope domain, and it is what you see when you power up the oscilloscope with a signal applied to an analog channel input. There are two ways you can access a frequency domain signal. One is to apply a signal to the RF input through an RF adapter. As soon as you press RF, the frequency domain display of that signal appears. The next thing you have to do is press the Frequency/Span button below RF and configure Center Frequency and Span to get a usable display.

The other way to access the frequency domain display of a signal is to apply it to an analog channel input, then press Math and FFT. Here we see the time domain displayed in split-scrren format with the frequency domain including its array of harmonics.

The frequency domain is very useful because it displays the signal’s fundamental and its harmonics, showing relative amplitude and spectral location.

Here is a sine wave displayed in the frequency domain. Notice that all the power exists at a single frequency, known as the fundamental. The only other energy that is displayed is the noise floor, which appears as an irregular roughly horizontal fluctuating line at the bottom of the screen. This represents the wide-spectrum thermal noise level, which obscures any signal that falls below it. It does not represent any malfunction of the equipment, but is just a consequence of its sensitivity to random charge-carrier motion.

When we switch the AFG output to square wave, notice what it looks like in the time domain. There is a high level and a low level, with near instantaneous transitions. These very fast rise and fall times are in essence high-frequency components, which generate large amplitude harmonics, visible in the frequency domain. Notice that they diminish in amplitude farther in frequency from the fundamental, until they are lost below the noise floor.

Now we’ll define the X- and Y-axes in still another way, displaying the same square-wave signal as a spectrogram. To do this, we press the RF button bringing up its menu, then the soft key adjacent to Spectrogram, which opens the Spectrogram menu. The top soft key toggles Spectrogram On.

Here, in split-screen format, is the standard frequency domain in the lower display and the Spectrogram at the top. Notice that the display starts at the bottom and slowly moves to the top. You might think that it is taking time to load, but that is not what is happening. Actually, for a Spectrogram, frequency is plotted along the X-axis as in frequency domain, but time is plotted along the Y-axis. If we toggle the Spectrogram Off and On, it starts over. After it fills to the top, the older parts of the signal disappear at the top and new information appears at the bottom, so a signal that is changing in time is shown in that way. The number of seconds can be seen at the top. It takes about 30 seconds for information to make its way from the bottom to the top.

What about amplitude? It could be shown on a third Z-axis, perpendicular to the X- and Y-axes. But this is not possible in the two-dimensional space of the flatscreen. The way amplitude is shown is by color. A hot color such as red represents high amplitude and a cool color such as blue represents low amplitude. If we press Autoset, the harmonics are scaled out of the display so this may be more clearly seen. The speckled texture in the large low-amplitude blue area is the noise floor.

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