The math channel undoubtedly adds a new method to the analysis of the signal. Thank you for your attention and support to this series of articles. Although math is challenging, once the math channel is loaded into the library, it is always available to us. In the process of explaining the RMS value of AC signals in this article, two examples need to be studied.
The first example discusses drawing the voltage RMS curve of an AC signal. The formula for calculating the voltage RMS of a single AC signal is sqrt(integral((A)^2)/T). The following .psdata file contains voltage RMS math channels. (For related documents, please click the Hongke pico oscilloscope forum to download)
Figure 1 Voltage RMS math channel
First, we need to "square" (A^2) AC voltage. This step can invert the negative part of the waveform (full-wave rectification). The integral "integral" in the formula adds up the "area" enclosed by the curve, it generates a sloping line whose slope increases with time, and then divides it by the sweep time T to become a horizontal line. Finally, "Sqrt" will calculate the square root of the horizontal line to display the RMS value.
Figure 2 RMS formula explanation
Since the mathematical formula in the software is just divided by zero, there will be larger values and some fluctuations, we can ignore these situations. After this, the RMS waveform will rise to about 570mV. When using triggers, the pre-trigger time should be set to greater than 0% (the trigger marker is on the far left of the screen) to ensure that the time is always positive and the waveform is meaningful.
In addition, it is necessary to collect enough signal waveforms so that the math channel waveforms can converge to a value. If the measurement function is used, only the ruler placed on the convergent part of the math channel can give accurate measurement values. When zooming in to observe the waveform, the convergence speed of the RMS math channel is not very fast. You can zoom in near the starting point, or increase the scale to zoom in the waveform vertically. The scale ratio of the math channel is not automatically proportional to the input signal channel, so you may need to adjust it to match.
The second example explores the process of a three-phase motor accelerating from a standstill, how we draw the current RMS curve. For measuring three-phase AC current at the same time, we are equipped with a dedicated AC three-phase flexible current probe (you can also use 3 current clamps). Suppose I am using a three-phase flexible probe and a DC current clamp. Because there is no related custom probe settings, I need to convert the captured voltage values on channels A, B, C, and D into current (the probe sensitivity is 1 mV / A ). Therefore, channels A, B, C, and D need to be multiplied by 1000, and converted to amperes using formulas A, B, C and D * 1000, as shown in Figure 3.
Figure 3 Three-phase voltage is converted into current
To calculate the current RMS of the motor winding, we use the following mathematical channel formula: (sqrt(integral(A^2)/T)+sqrt(integral(B^2)/T)+sqrt(integral(C^2)/T ))*1000. The following .psdata file contains current RMS math channels. (For related documents, please click the Hongke pico oscilloscope forum to download)
Figure 4 Current RMS value of a three-phase motor
Carefully observe this mathematical channel formula, it is similar to the previous formula for a single AC signal, because it is repeated three times for a three-phase motor. Note that since the initial setup of the probe captures voltage rather than current, the end of the formula requires *1000 to be converted to amperes. You can load this formula into your math channel library for future use in other three-phase signals, such as fuel pumps and VVT actuators that use three-phase motors.