The fact that, as we saw above, φ is expressed by the equation $\phi^2=\phi+1$, allows us to observe, multipling by $\phi^{n-2}$ both members of equality, as: $\phi^n=\phi^{n-1}+\phi^{n-2}$ , by summing up the two con ¬ secutive's powers <p, we obtain the power of the next series. semiialelor Mixing radio is strongly connected to this phenomenon.

Following observations are offered peiitru especially those interested in physics and electro Aplicada possible the number of gold technique.

Modulation in amplitude, in its 'balanced', produces what is called in technical terms in the dual-band modulation with suppressed carry

The mere gathering of amplitude, point by point, so that the resultant wave will be the algebraic sum is mixing so-called 'linear'. On an oscilloscope, it will lead to a wave which is the sum of two signals originating. Amplitudiiiea oscilloscope displays the screen vertical axis and time on the horizontal axis (time domain analysis)

Another way is in line aiializei in frequency domain, amplitudiiie / frequency instead of amplitude / time. Appropriate measurement tool is a spectral analysis. It will then display two 'peaks', each corresponding to the original wave frequency, along the spectral uiiei hours. Thus, while the oscilloscope indicate iioua

waveform, formed by summing up the originals, the spectral analyzer is displayed inside the wave-source, meaning the two original frequencies. To transmit voice through a wireless radio, "carry" is required modulation signal amplitudiiiii conducted with the speech waveform. This means, mathematically, to multiply the two where, instead they gather. Just as we learned school that we can multiply two powers of the same base exponendi gathering them, and here, when gather two voltages in the environment where new-linear (logarithmic), in a joiictiunea PN diode or a traiizistor, act like them multiplied. Multiplication is logarithmic meeting. In the field of radio, this is called mixing.

Waves interact and carry out the oscilloscope is a high frequency wave, modulated in intensity by a low frequency voice signal. An analyzer spec ¬ Tral but produces four 'peaks' separate frequency. Appear two frequencies originate, plus one, which is their sum, and, mirroring "its initial frequency difference. Thus, multiplying the second time in the field which coincides with the translation simultaiia up and down in frequency domain. These two new frequencies are called the upper band and lower band. They occur whenever two or more radio waves to modulate each other, it explains how low-frequency sound waves are translated, "clinging to" carry wave that is audible outside the area. This beam where ( electromagnetic, sonic not) of high frequency is what is transmitted by the antenna. Thus, if the mode of a 1 kHz tone (produced at the microphone) with a carrier frequency of 1MHz, we have four outputs: 1 kHz, 1 MHz, 1.001 MHz ( amount, upper band) and 0.999 MHz (the difference, lower band).

Audio frequency of 1 KHz is preajoasa, so it is filtered and transmitted to the other three frequencies. Note that the new band frequently only depend on Addition and Subtraction to the audio signal and carrier. There is a harmonic relationship between them.