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In electronics, a frequency multiplier is an electronic circuit that generates an output signal whose output frequency is a harmonic (multiple) of its input frequency. Frequency multipliers consist of a nonlinear circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent bandpass filter selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output. Frequency multipliers are often used in frequency synthesizers and communications circuits. It can be more economical to develop a lower frequency signal with lower power and less expensive devices, and then use a frequency multiplier chain to generate an output frequency in the microwave or millimeter wave range. Some modulation schemes, such as frequency modulation, survive the nonlinear distortion without ill effect (but schemes such as amplitude modulation do not). Frequency multiplication is also used in nonlinear optics. The nonlinear distortion in crystals can be used to generate harmonics of laser light. ==Theory== A pure sine wave has a single frequency ''f'' : If the sine wave is applied to a linear circuit, such as a distortionless amplifier, the output is still a sine wave (but may acquire a phase shift). However, if the sine wave is applied to a nonlinear circuit, the resulting distortion creates harmonics; frequency components at integer multiples ''nf'' of the fundamental frequency ''f''. The distorted signal can be described by a Fourier series in ''f''. : The nonzero ''ck'' represent the generated harmonics. The Fourier coefficients are given by integrating over the fundamental period ''T'': : These harmonics can be selected by a bandpass filter. The power in the distorted signal is spread across all the resulting harmonics.〔See Parseval's theorem.〕 An ideal halfwave rectifier, for example, has all nonzero coefficients. An approximate circuit could use a diode. From a conversion efficiency standpoint, the nonlinear circuit should maximize the coefficient for the desired harmonic and minimize the others. Consequently, the transcribing function is often specially chosen. Easy choices are to use an even function to generate even harmonics or an odd function for odd harmonics. See Even and odd functions#Harmonics. A full wave rectifier, for example, is good for making a doubler. To produce a times-3 multiplier, the original signal may be input to an amplifier that is over driven to produce nearly a square wave. This signal is high in 3rd order harmonics and can be filtered to produce the desired x3 outcome. YIG multipliers often want to select an arbitrary harmonic, so they use a stateful distortion circuit that converts the input sine wave into an approximate impulse train. The ideal (but impractical) impulse train generates an infinite number of (weak) harmonics. In practice, an impulse train generated by a monostable circuit will have many usable harmonics. YIG multipliers using step recovery diodes may, for example, take an input frequency of 1 to 2 GHz and produce outputs up to 18 GHz.〔For example, the old Hewlett Packard 83590A.〕 Sometimes the frequency multiplier circuit will adjust the width of the impulses to improve conversion efficiency for a specific harmonic. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Frequency multiplier」の詳細全文を読む スポンサード リンク
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