# Frequency Multiplier

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## frequency multiplier

[¦frē·kwən·sē ′məl·tə‚plī·ər]## Frequency Multiplier

an electronic or, less frequently, electromagnetic device for delivering an output wave with a frequency that is an exact integral multiple of the input frequency. The ratio of the output frequency *f*_{out} to the input frequency *f*_{in} is called the frequency multiplication ratio *m*(*m* ≥ 2, and can be as large as several tens).

It is a characteristic property of frequency multipliers that if *f*_{in}is changed within a certain finite range, the factor *m* remains constant, as do some other parameters, such as the resonant frequencies of oscillatory circuits and resonators used as components of frequency multipliers. From this it follows that if for some reason the input frequency is increased by a sufficiently small increment Δ*f*_{in}, the increment Δ*f*_{out} will be such that Δ*f*_{in}/*f*_{in} = Δ*f*_{ou}/*f*_{out}. This means that the relative instability of the oscillation frequency remains unchanged upon multiplication. This important property permits frequency multipliers to be used for increasing the frequency of stable oscillations (usually obtained from a quartz driving oscillator) in various radio transmitters, radar, and measuring equipment.

The most widely used types of frequency multipliers consist of a nonlinear device (such as a transistor, varactor, varicap, coils with ferrite cores, or an electron tube) and one or several electric filters. The nonlinear device changes the waveform of input oscillations. Consequently, the oscillation spectrum at the output of the device exhibits components with frequencies that are multiples of *f*_{in}. These complex oscillations enter the input of the filter, which extracts the component that has the specified frequency and suppresses all other components. In real filters this suppression is incomplete, and unwanted, or spurious, harmonics with numbers other than *m* appear at the output of the frequency multiplier. This problem is alleviated if the nonlinear devices generate practically only the *m*th harmonic of *f*_{in}. In this case the filter may sometimes be omitted; some frequency multipliers of this type use tunnel diodes and special electron beam devices. At *m* > 5, it is advantageous, from the point of view of power consumption, to use multistage frequency multipliers, in which the output oscillations of one stage serve as input oscillations for the next stage.

The operation of certain frequency multipliers is based on the synchronization of self-excited oscillators. Oscillations excited in such an oscillator have the frequency *f*_{0} ≈ *mf*_{in}, and become exactly equal to *mf*_{in} when acted upon by oscillations of a frequency *f*_{in} that enter the input of the oscillator. The disadvantage of such frequency multipliers is the comparatively narrow range of values for *f*_{in} that can be used for synchronization. In addition to the types mentioned, radio pulse frequency multipliers have also found some application. Here, the radio pulses are shaped by the input oscillations of the frequency *f*_{in} and are then fed to the input of an electrical filter.

The primary problem encountered in designing frequency multipliers is the reduction of phase instability of the output oscillations, caused by the random character of phase changes. Phase instability increases the relative frequency instability of the output as compared with the same value of the input. A rigorous design of frequency multipliers involves the integration of nonlinear differential equations.

### REFERENCES

Zhabotinskii, M. E., and Iu. L. Sverdlov.*Osnovy teorii i tekhniki umnozhitelei chastoty*. Moscow, 1964.

Rizkin, I. Kh.

*Umnozhiteli i deliteli chastoty*. Moscow, 1966.

Bruevich, A. N.

*Umnozhiteli chastoty*. Moscow, 1970.

*Radioperedaiushchie ustroistva na poluprovodnikovykh priborakh*. Moscow, 1973.

I. KH. RIZKIN