For example, if noise exists at MHz in Fig. This is because neither signal of In addition, a cyclic waveform does not have any frequency component that is lower than the fundamental frequency. If you find noise in any of these frequencies, it is considered to be caused by a frequency-divided signal not the original signal.
In this case, the harmonics are the integral multiples of frequency-divided signal frequency. However, if two or more circuits are operating at the same clock signal that has been frequency-divided, the harmonics of the clock signal and the harmonics of the frequency-divided signal overlap with each other, making it difficult to tell them apart.
How the digital signal waveform and the included harmonics are related to each other? You can see that the sine waveform of the original fundamental wave is getting closer to a rectangular waveform as each harmonic is added to it. In contrast, when subtracting the higher-order harmonics from an ideal rectangular waveform, it is getting closer to sine wave.
However the change is gentle. As an example, Fig. So the even harmonics are also included as shown in Fig. As above, the relatively lower frequency lower-order components among the harmonics of digital signal are important to maintain the signal waveform, while the higher frequency higher-order components can be considered as less important. However, as described in Section Harmonics in signal, the higher-order harmonics have higher frequencies and thus have a nature of being easily emitted and causing noise.
Therefore, noise suppression is implemented by eliminating the higher-order harmonics to the extent of not causing any problems to the signal waveform. Usually up to the 3rd to 7th harmonics are maintained and any higher-order harmonics are eliminated. The digital signal without harmonics has a waveform with rounded corners like this instead of having decent square corners. EMI suppression filters for signals are the filters that are used for this purpose.
In Fig. Therefore, the waveform in the figure b contains up to the 7th harmonics MHz. EMI suppression filters will be further described in later sections.
Let's look at the trend of the levels of harmonics included in digital signal. If the voltage waveform of digital signal has a perfect trapezoidal wave as shown in Fig. Figure b shows an envelope of the harmonics included in the trapezoidal wave. As shown in the figure, if the frequency is plotted in a logarithmic axis, the envelope of the harmonics forms a simple polygonal line with two inflection points A, B. The narrower the pulse width becomes, the more A shifts towards the higher frequency side.
B is a frequency point determined by the signal rise fall time t r. The shorter this period becomes, the more B shifts towards the higher frequency side. Provided that the rise time and fall time are the same for the sake of simplifying the trend. Region c. Therefore, it is desired to shift Points A and B to the lower frequency side from the viewpoint of noise suppression. Please refer to the reference [Reference 2] , which shows the theoretical formula that expresses this trend.
The above frequency characteristics merely indicate the general trend. The individual harmonic levels can be affected by duty cycle etc. The voltage waveforms measured by an oscilloscope are shown on the left side of the figure, while the spectrums measured by a spectrum analyzer are shown in the middle. The same harmonics as those indicated in Fig. On the right side of the figure, the frequency axis of the spectrums in the middle is converted into logarithmic axis so that those can be compared with the envelope of Fig.
For your reference, red lines indicate the theoretical envelopes. You may say that the envelope of Fig. In the higher frequency range above MHz, the actual measurements are smaller than the theoretical values. This is considered to be because the signal generator used for the experiment could not output accurate trapezoidal waves due to its upper limit in the frequency generation.
In order to design a circuit causing less nose, it is advantageous to avoid these trends and shift Points A and B towards the low frequency side. If you cannot avoid the above trends in your design, it will be easier to perform noise suppression if the signal line is provided with pads to attach EMI suppression filters. When observing harmonics of an actual digital signal, it is hard to observe Region a. The left side of the figure shows the assumed signal waveform, and the middle shows the calculation results of the harmonic spectrum.
Just like Fig. The right graphs show each spectrum with dots and superimpose the envelope shown in Fig. The level of spectrum has been calculated in root-mean-square value on the assumption of using a spectrum analyzer for measurement. The same is applied to all of the following data. Point B of the envelope calculated from the formula in Fig. The one under the condition b is approx. The calculation results of Fig. In addition, it was confirmed that Point B is not visible within the display range of the graph up to 1GHz.
In contrast, the calculation results of Fig. An inflection point, which is considered as Point B possibly exists around here. Comparing the spectrums in the middle with each other, b with a slow signal rise has smaller harmonic levels than the others in the entire frequency range except for the very small range in the lower frequency side.
The difference reaches as large as over 20dB at MHz. From the above calculation results, it is clear that slowing down the signal rise speed is effective for suppressing the harmonics. In order to create a circuit that causes less noise, it is effective to choose an IC that is as slow as possible to the extent of not causing any problems to the circuit operation. It is also effective to equip EMI suppression filters for the signal. One type of typical digital signals that easily cause noise is clock signal.
The levels of the even harmonics are disposed to change significantly in accordance with duty ratio. The changes in the odd harmonics are also large in the high frequency range, where the orders of harmonics are high. These calculation results show that the even harmonics and odd harmonics line up along the green line and yellow line respectively, indicating a different trend between the even orders and odd orders. In contrast, Fig.
There is no large change in the general shape of the spectrum, which is still in line with the envelope shown in Fig. However, the influences seem significant when looking at each spectrum separately. You need to note this disposition since it can cause a serious influence on the reproducibility of noise measurement. Regarding the decision of pass or fail for noise regulation, it is considered to be fail even if only one part of the spectrum exceeds.
Careful measurements are required if such a component of significant variation is close to the limit. The above mentioned disposition of harmonics is based on the premise that the voltage waveform has a rectangular waveform. You need to note that even though an actual circuit has a rectangular waveform for the voltage waveform, the current waveform may be different.
That means the noise emission can show a different trend depending on whether it is mainly from the voltage or the current. The voltage waveform is close to an ideal digital pulse, and the values of the harmonic spectrum are close to those of the envelope shown in Fig. In contrast, the current only flows at the rising and falling moments as shown in the figure. The spectrum of such waveform has a constant level up to a high frequency of several MHz depending on the rise time as shown in the figure.
Therefore, if there is a noise emission due to the current, the noise is likely to be caused by high frequencies. In the results of noise measurements shown in Fig. Therefore it can be considered that the cause of noise emission in this experiment has been the electric current as one of the causes of indicating differences in the frequency distributions between the noise source and the emitted noise.
As opposed to this experiment, there are cases that voltage causes a noise emission. A harmonic is one of an ascending series of sonic components that sound above the audible fundamental frequency. The higher frequency harmonics that sound above the fundamental make up the harmonic spectrum of the sound. Harmonics can be difficult to perceive distinctly as single components, nevertheless, they are there.
Harmonics have a lower amplitude than the fundamental frequency. Harmonics are integer multiples of the fundamental frequency. Overtones are frequencies of a waveform that are higher than, but not directly related to , the fundamental frequency.
Two tones produced by different instruments might have the same fundamental frequency and thus the same pitch e. It is the presence of harmonics and overtones within a soundwave that helps to produce the sounds unique sound. The timbre describes those characteristics of sound which allow the ear to distinguish sounds that have the same fundamental pitch.
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