Frequency multiplier

# Frequency multiplier

Discussion

Encyclopedia
In electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, a frequency multiplier is an electronic circuit
Electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow...

that generates an output signal whose output frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

is a harmonic
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

of its input frequency. Frequency multipliers consist of a nonlinear
Linear circuit
A linear circuit is an electronic circuit in which, for a sinusoidal input voltage of frequency f, any output of the circuit is also sinusoidal with frequency f...

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 synthesizer
Frequency synthesizer
A frequency synthesizer is an electronic system for generating any of a range of frequencies from a single fixed timebase or oscillator. They are found in many modern devices, including radio receivers, mobile telephones, radiotelephones, walkie-talkies, CB radios, satellite receivers, GPS systems,...

s and communications circuits. It can be more economic 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
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

or millimeter wave range. Some modulation schemes, such as frequency modulation
Frequency modulation
In telecommunications and signal processing, frequency modulation conveys information over a carrier wave by varying its instantaneous frequency. This contrasts with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant...

, survive the nonlinear distortion without ill effect (but schemes such as amplitude modulation
Amplitude modulation
Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent...

do not).

Frequency multiplication is also used in nonlinear optics
Nonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...

. The nonlinear distortion in crystals can be used to generate harmonics of laser light.

## Theory

A pure sinewave at frequency f has no harmonics. If it goes through a linear amplifier, the result continues to be pure (but may acquire a phase shift).

If the sinewave is run through a stateless nonlinear circuit (transcribing function), the resulting distortion creates harmonics. The distorted signal can be described by a Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

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. 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 to for odd harmonics. See Even and odd functions#Harmonics. A full wave rectifier, for example, is good for making a doubler. On the other hand, a tripler may over drive an amplifier to symmetrically distort the positive and negative peaks.

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
Dirac comb
In mathematics, a Dirac comb is a periodic Schwartz distribution constructed from Dirac delta functions...

. 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. Sometimes the frequency multiplier circuit will adjust the width of the impulses to improve conversion efficiency for a specific harmonic.

### Spark generator

Before amplifiers, frequency multipliers were the way to generate radio frequencies.
• Spark gap transmitter
• Arc converter
Arc converter
The arc converter, sometimes called the arc transmitter or Poulsen arc after its inventor Danish engineer Valdemar Poulsen, is a device that used an electric arc to convert direct current electricity into radio frequency alternating current...

### Class C amplifier and multiplier

Efficiently generating power becomes more important at high power levels. Linear Class A amplifiers are at best 25 percent efficient. Push-pull Class B amplifiers are at best 50 percent efficient. The basic problem is the amplifying element is dissipating power. Switching Class C amplifiers are nonlinear, but they can be better than 50 percent efficient because an ideal switch does not dissipate any power.

A clever design can use the nonlinear Class C amplifier for both gain and as a frequency multiplier.

### Step recovery diode

Generating a large number of useful harmonics requires a fast nonlinear device.

Step recovery diode
Step recovery diode
In electronics, a step recovery diode is a semiconductor junction diode having the ability to generate extremely short pulses. It is also called snap-off diode or charge-storage diode or memory varactor, and has a variety of uses in microwave electronics as pulse generator or parametric...

s.

### Varactor diode

Resistive loaded varactors. Regenerative varactors. Penfield.

Frequency multipliers have much in common with frequency mixer
Frequency mixer
In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...

s, and some of the same nonlinear devices are used for both: transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s operated in Class C
Class C
The term Class C may refer to:* Class C amplifier, a category of electronic amplifier*Class C , a defunct class in minor league baseball in North America* Class C stellar classification for a carbon star...

and diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear currentâ€“voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s. In transmitting circuits many of the amplifying devices (vacuum tubes or transistors) operate nonlinearly and create harmonics, so an amplifier stage can be made a multiplier by tuning the tuned circuit at the output to a multiple of the input frequency. Usually the power (gain
Gain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...

) produced by the nonlinear device drops off rapidly at the higher harmonics, so most frequency multipliers just double or triple the frequency, and multiplication by higher factors is accomplished by cascading doubler and tripler stages.

### Previous

Frequency multipliers use circuits tuned to a harmonic of the input frequency. Non-linear elements 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 amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

s 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.

## PLLs with frequency dividers

In digital electronics, frequency multipliers are often used along with frequency dividers and phase-locked loops to generate any desired frequency from an external reference frequency. The frequency multiplication is carried out in the phase-locked loop's feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

loop, by using a frequency divider on the output of the voltage controlled oscillator (VCO). This divided-down output is fed-back to the input comparator
Comparator
In electronics, a comparator is a device that compares two voltages or currents and switches its output to indicate which is larger. They are commonly used in devices such as Analog-to-digital converters .- Input voltage range :...

and compared to the reference frequency. Since the divided down frequency is smaller than the reference frequency, the comparator generates a voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points â€” or the difference in electric potential energy per unit charge between two points...

signal to the VCO, telling it to increase the output frequency. It continues to do this via the feedback loop, raising the VCO output frequency, until the divided-down frequency from the VCO output is equal to the reference frequency. At this point the comparator stabilizes and generates no more signals to the VCO, or only minor changes to maintain stability. The output frequency from the VCO will be stable at the input reference frequency multiplied by the value of the feedback divider.

A PLL with a frequency divider in its feedback loop acts as a frequency multiplier and is a type of frequency synthesizer
Frequency synthesizer
A frequency synthesizer is an electronic system for generating any of a range of frequencies from a single fixed timebase or oscillator. They are found in many modern devices, including radio receivers, mobile telephones, radiotelephones, walkie-talkies, CB radios, satellite receivers, GPS systems,...

.

### Integer-N synthesizer

In a configuration with an integer-N divider, its VCO
Voltage-controlled oscillator
A voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...

's output frequency is N times its reference, or input, frequency.

### Fractional-N synthesizer

Periodic changes in the integer value of an integer-N frequency divider will effectively result in a multiplier with both whole number and fractional component. Such a multiplier is called a fractional-N synthesier after its fractional component. Fractional-N synthesizers provide an effective means of achieving fine frequency resolution with lower values of N, allowing loop architectures with tens of thousands of times less phase noise than alternative designs with lower reference frequencies and higher integer N values. They also allow a faster settling time because of their higher reference frequencies, allowing wider closed and open loop bandwidths.

#### Delta sigma synthesizer

A delta sigma synthesizer adds a randomization to programmable-N frequency divider of the fractional-N synthesizer. This is done to shrink sidebands created by periodic changes of an integer-N frequency divider.