What is an oscilloscope and much more
The oscilloscope is one of the most important and most used measuring instruments. Its essence is that it displays the waveform of the measured voltage signal over time. While the analog oscilloscope allowed the determination of basic time and amplitude parameters (or phase using the X-Y mode), mainly by simple reading and recalculation from a screen grid, digital oscilloscopes have become, in cooperation with internal and external applications, a device that provides very sophisticated tools and the resulting results. The possibilities are now so vast that we could perhaps fill a book.
At the outset, it should be said that even a digital oscilloscope is still an oscilloscope and thus retains some of its features. As such, it has its limits, and one of the essential points is the use of an oscilloscope fast enough for the problem at hand and the correct connections. Do not change the ratios at the point to be measured so that the oscilloscope screen displays a signal corresponding to the signal that is present at that point even without the oscilloscope connected. For example, a measurement in a switching power supply without a differential probe will either lead to the destruction of the measured object or to the grounding of the relevant location due to the connection of the oscilloscope ground to the protective conductor. Such results are then completely "wrong".
Measuring with an oscilloscope
Three main factors play a role in oscilloscope measurements. Oscilloscope bandwidth, sampling rate and transducer resolution. Oscilloscopes are equipped with 8-bit converters for their conversion speed and in recent years with 12-bit converters. However, due to real technologies, the number of effective bits is 1-2 bits less. The total accuracy in the vertical axis is then given in units of percent. In addition, the vertical axis is also loaded by the characteristics of the oscilloscope's input circuitry, so the overall accuracy is given in units of percent. For frequencies from 20 % of the indicated bandwidth, this error is in the order of one percent. The bandwidth definition of oscilloscopes assumes a maximum 3dB drop, which, however, represents an error of almost 30% in the amplitude measurement in the voltage domain. The actual input characteristics are then very far from the ideal frequency response curves according to Eq:
where AU is the indicated amplitude
A is the signal amplitude
fBW is the bandwidth
The sampling rate defines the accuracy of signal reconstruction from discrete points and determines how fast the oscilloscope is able to display the change. An undersampled signal (aliasing type error) reconstructs the signal poorly, the edges are reconstructed with kinks (similar kinks will appear even when DSP corrections are applied to the fastest oscilloscopes). The ubiquitous bandwidth parameter also plays a role here, especially for edge velocity measurements. Since the oscilloscope inputs have their own time constant due to their impedance, the oscilloscope's own rise time is included in the measurement result.
The resulting rise (or fall) edge time is expressed by the relation:
where ts is the actual rise time
fBW is the bandwidth
The resulting bias of the result can be taken as the maximum possible error because the bandwidth is usually given with a margin that reduces the error. In the case that the measuring apparatus includes a probe, a term should be included in the previous relation.
Advantageously, this error of the whole chain can be measured and possibly eliminated in the result. In Figure 1, the signal with an edge of about 200 ps is measured as 1.243 ns (1 ns is the delay due to the 350 MHz oscilloscope BW). In Fig. 1, the signal with an edge of about 200 ps is measured as 1.243 ns (1ns is the delay due to the BW of the 350 MHz oscilloscope) with a direct SMA cable connection and a 50 Ohm impedance termination.
Figure 2 shows the distortion of the measured signal after connecting the 500 MHz passive probes (channel 3) and the 200 MHz on channel 2 (blue waveform) has the edge obviously the slowest (theoretically +2 ns). As can be seen further in Fig. 2, the originally optimal fast edge signal is completely distorted by the change in impedance of the entire measurement circuit after the 500 MHz and 200 MHz probes are connected. Therefore, if we measure on the signal path (here the ideal SMA cable connection) using an incorrect method, we change the originally error-free signal in the circuit to a signal that is very likely to not allow the device to operate correctly. The measurement error is highly dependent on the circuit used, the oscilloscope settings and the signal being measured.
Oscilloscope functions and how to choose an oscilloscope
The current possibilities of measuring functions are very extensive. Measurement of basic parameters such as period, frequency, leading and trailing edge, pulse width is already in the cheapest models, while higher classes add statistical functions, histograms, trend evaluation. However, from the user's point of view, it is sometimes very difficult to trace where a given value is measured. For example, measuring leading edge velocity can be an example of this. If, for example, 100 edges are recorded in the oscilloscope's memory, which edge is actually being measured? Unfortunately, it depends on the manufacturer. However, measurements are most often taken either on the first edge in memory or on the first edge on the screen. Better oscilloscopes allow you to turn on indicators to show where the measurement is taking place, while offering some method to measure at a defined point. Because details make the difference, you can tell a smart oscilloscope by selecting the area where you want to make an rms measurement, for example. Digitization has also significantly expanded the possibilities of creating mathematical channel(s). Basic models will offer no more than the sum, difference, product of channels plus possibly an FFT (see below). Mid-range can offer equation creation using measured parameters, constants, multiple math operations even between multiple channels - powers, square roots, goniometric functions, integral and derivative. With the derivative, very often the result is at first sight not matching the idea, here unfortunately there is again the effect of low resolution, the noise of the converters does great damage here. Most often mathematics is used to measure performance. This is a rather interesting and extensive issue. When measuring the switching power of fast semiconductors and other similar tasks, the fundamental problem is the time delay between the voltage and current paths (the current probe usually has a longer propagation time).
Differences in measured values can reach hundreds of percent. The best oscilloscopes offer special ready-made analytical measurement tools just for power analysis, jitter, eye diagram measurements. You can have multiple math channels and use a math channel within a math channel.
One of the first complex functions that was implemented in oscilloscopes is the FFT, the fast Fourier transform. This is now appearing as a standard in the lower classes of oscilloscopes. The difference can be found mainly in the number of points from which the oscilloscope calculates the FFT and in the windowing, magnification and measurement options over this mathematical channel. Very often the FFT is limited to only a small portion of the acquisition memory. The value of the spectral analysis information is determined in an oscilloscope by the number of points to calculate (generally it must be 2n, the more the better the resolution in the frequency domain), then by the number of periods of the signal to calculate (in 2n samples there should be an integer number of periods, almost impossible in an oscilloscope. Otherwise, one whole period is generally sufficient, but if we sample 1.5 periods, that half period is actually extra and will burden the calculation with error. Therefore, it is necessary to set the time base so that the FFT calculation takes place over several tens of periods. The fewer the periods, the more emphasis on the use of windows to correct for this non-integerity of periods). It is also interesting to note that when oscilloscopes have FFTs, the first (and sometimes only) scale that appears is in decibels. This scale is very suitable for RF applications, but with oscilloscopes the good feeling is spoiled by the amount of noise caused by the small number of effective bits of the transducers. So sometimes it is better to set the scale to linear, if for no other reason than that decibels are not very fast for most ordinary electronics users. Scaling in mV is more friendly to them. Figure 3 shows a rectangular waveform composed of 1, 3 and 5 harmonic components. The FFT performed correctly shows the individual amplitudes, with cursor two placed at the end of the analyzed spectrum - 1.25 GHz. This corresponds to the sampling theorem, the oscilloscope has a sampling rate of 2.5 GSa/s. However, the image is also there for a second side view - if we feed a rectangular 100 MHz signal to an oscilloscope with a 500 MHz bandwidth, the displayed signal on the screen will look similar. Only the 1st, 3rd and 5th harmonics will pass through the input circuits. The other harmonics will be attenuated by the system. Alternatively, one of the averaging methods can be used to reduce the noise. Using external mathematical processing, the oscilloscope data can also be made into a vector analyzer with support for phase spectrum, demodulation, etc. However, dedicated vector/spectrum analysers are equipped with higher resolution transducers, so the "quality" of the results is at a higher level. Even so, the oscilloscope sometimes has the edge in this area due to its sampling speed and depth of memory.
