such as diodes may be added to enhance the production of harmonic frequencies. Since the power in the harmonics declines rapidly, usually a frequency multiplier is tuned to only a small multiple (twice, three times, or five times) of the input frequency. Usually amplifiers are inserted in a chain of frequency multipliers to ensure adequate signal level at the final frequency. Since the tuned circuits have a limited bandwidth, if the base frequency is changed significantly (more than one percent or so), the multiplier stages may have to be adjusted; this can take significant time if there are many stages. Microelectromechanical (MEMS) frequency doubler An electric-field driven micromechanical cantilever resonator is one of the most fundamental and widely studied structures in MEMS, which can provide a high Q and narrow bandpass filtering function. The inherent square-law nonlinearity of the voltage-to-force transfer function of a cantilever resonator's capacitive transducer can be employed for the realization of frequency doubling effect. Due to the low-loss attribute (or equivalently, a high Q) offered by MEMS devices, improved circuit performance can be expected from a micromechanical frequency doubler than semiconductor devices utilized for the same task. Graphene based frequency multipliers Graphene based FETs have also been employed for frequency doubling with more than 90% converting efficiency. In fact, all ambipolar transistors can be used for designing frequency multiplier circuits. Graphene can work over a large frequency range due to its unique characteristics. Phase-locked loops with frequency dividers A phase-locked loop (PLL) uses a reference frequency to generate a multiple of that frequency. A voltage controlled oscillator (VCO) is initially tuned roughly to the range of the desired frequency multiple. The signal from the VCO is divided down using frequency dividers by the multiplication factor. The divided signal and the reference frequency are fed into a phase comparator. The output of the phase comparator is a voltage that is proportional to the phase difference. After passing through a low pass filter and being converted to the proper voltage range, this voltage is fed to the VCO to adjust the frequency. This adjustment increases the frequency as the phase of the VCO's signal lags that of the reference signal and decreases the frequency as the lag decreases (or lead increases). The VCO will stabilize at the desired frequency multiple. This type of PLL is a type of frequency synthesizer. Fractional-N synthesizer In some PLLs the reference frequency