# 6.7: Frequency Multiplier

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There are three main types of microwave frequency multipliers. One uses a nonlinear resistive element to generate harmonics and a bandpass filter selects the appropriate harmonic for the output (see Figure 6.6.2(a)) [33]. A second type uses a reactive element but is inherently narrow band. A third type uses a mixer.

An example is the diode frequency multiplier shown in Figure 6.6.2(b). If unbiased, the diode conducts current only during the positive half-cycle of the input signal, creating a voltage across the diode that is rich in harmonics. If no external bias is applied, some of the positive voltage swing is required to turn the diode on. This type of multiplier is referred to as a resistive frequency multiplier. The transistor circuit in Figure 6.6.2(c) uses the resistive multiplier principle to achieve frequency multiplication. Now the bandpass filter is the tuned circuit in the collector leg of the amplifier. The transistor is biased to realize a strong nonlinearity and the base-emitter junction has an exponential current-voltage characteristic.

If the input signal is

$\label{eq:1}x(t)=A\cos(\omega_{t}+\phi)$

then the output at the $$n$$ harmonic is

$\label{eq:2}y(t)=A_{n}\cos(n\omega_{t}+n\phi)$

One of the issues with all frequency multipliers is the multiplication of the phase noise on the input signal. If $$\phi$$ represents the phase noise on the original signal, then the phase noise of the output signal will be increased by a factor $$n$$. That is, even if the frequency multiplier introduces no noise of its own, the signal-to-noise (i.e., phase noise) ratio of a signal will be reduced by a factor $$n$$. The amplitude of the output signal, $$A_{n}$$, will usually be much less than that of the input signal unless the nonlinear circuit incorporates an amplifier. The increase in phase noise and power loss (without amplification) are the major drawbacks of using a resistive nonlinear element to produce frequency multiplication.

The bandwidth of a resistive frequency multiplier is limited by the maximum bandwidth of a filter that will select just one harmonic at the output. That is, if the input signal is at $$10\text{ GHz}$$ and with $$10\times$$ multiplication the output will be at $$100\text{ GHz}$$. The useful fractional input bandwidth is $$1/n =\frac{1}{10}$$ of the input signal, otherwise two harmonics could appear simultaneously in the output.

Another type of frequency multiplier uses a reactive element such as the nonlinear capacitance of a reverse-biased semiconductor diode (i.e., a varactor diode) [34]. This mixer is called a reactive frequency multiplier or a parametric frequency multiplier. The nonlinear reactive element is part of a resonant input circuit at the input frequency and also part of a resonant output circuit at the output frequency. The efficiency of this type of mixer is higher than for a resistive mixer but the bandwidth is much lower.

A third type of frequency multiplier uses a mixer. Some, but not all, mixers can be used to realize frequency multiplication by applying the same signal to the two input ports. The suitable mixer circuits are the balanced mixers but not the mixers that rely on filtering to separate LO, RF, and IF signals.

A further type of frequency multiplier uses a phase-locked loop. Frequency division in the feedback loop results in frequency multiplication of the input signal. Yet another type uses flip-flops working on a microwave frequency binary clock signal and this is the type often used in modern RFICs to provide a square wave drive to a switching mixer.

6.7: Frequency Multiplier is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.