It is known that in coils with H/D ratio is greater than one, the frequency of the standing wave the frequency of LC resonance, so to combine them you need to use artificial methods of increasing the latter. One of the methods, modulation of the fundamental frequency with lower multiples of the fundamental. Modulation splits the energy of the first harmonic in the spectrum, consisting of frequencies in the left and right region, if you count the fundamental frequency centre. We are interested in only the right side of the spectrum, in which frequencies will be formed by the following rule: \[F = f + {f \cdot i \over N} \quad N \in 2, 3, 4, 5, ... \] where: \(F\) is the frequency of the spectrum, \(f\) is the basic frequency of the LC resonance (resonancia frequency coils), \(i\) is the number of modulation harmonics (integer), \(N\) — the multiplicity of the modulation frequency. More clearly all of this is depicted in the following figure. On the left side shows the pulses applied to the inductor coil, and the right range of frequencies formed by these pulses. The harmonic number \(i\) is shown in white.

Generally speaking, if we consider the ideal pulse packet, as the figure on the left, the even harmonics at the modulation should be absent. But in reality, the coil has its q-factor, therefore bundles its amplitude increases gradually, and at its end gradually decreases. Tutu steel is obtained, which means that — in the spectrum will be even harmonics, as shown in the diagram on the right.

It is seen that if the fundamental frequency is not modulated (figure 1.1), then the spectrum will consist only of a single frequency — the main. This mode is \(N=1\) is set to calculator by default. If the fundamental frequency be modulated two times smaller (\(N=2\)), the range will consist of the following frequencies: \(f+f\frac12,\, f+f\frac22,\ f+f\frac32\), etc. As you can see, for such a modulation of the pulse sequence just removed every even-numbered pulse. If the modulation is a frequency of four times less basic \(N=4\), the range will consist of the following frequencies: \(f+f\frac14,\, f+f\frac24,\ f+f\frac34\) etc. For this modulation is a sequence of four pulse need to remove every 3rd and 4th. Etc.

It should be noted that any frequency from the spectrum can be combined with frequency standing wave that can do calculator. When you select the "Multiplicity of modulation frequency" greater than unity (\(N \gt 1\)), the chart calculator will display the harmonics from figures 1 and 2. If you select "Harmonic modulation" for example from 1 to 3, then this graph will be presented to the harmonics of the orange from the bottom up: the bottom of the first, the middle second, top third. To the left of the graph given the value of the resonant frequency of the coil at the selected point of intersection. To obtain the graph of the fundamental frequency, in left field, "Harmonic modulation" you need to put zero.

How to make a modulation with a frequency ratio of 3, 5, 7, etc. from the main? We will not consider a variant, when the pulses of the oscillator fractional (although in the end you could do that), and go by changing the duty cycle of the pulse packet. So for example, for \(N=3\) from a sequence of three pulse we remove every third, and for \(N=5\) — every 4-th and 5-th pulses.

You can do another thing: for \(N=3\) from the sequence in three pulses to remove every 2nd and 3rd, and for \(N=3\) from the sequence of five pulses to remove every 3rd, 4th and 5th. In these cases, the overall energy spectrum will be less, and the amplitude of the higher harmonics grow relative to the lower.