# Frequency mixer

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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 are applied to a mixer, and it produces new signals at the sum and difference of the original frequencies. Other frequency components may also be produced in a practical frequency mixer.

Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter.

## Contents

Mixers are widely used to shift signals from one frequency range to another, a process known as heterodyning, for convenience in transmission or further signal processing. For example, a key component of a superheterodyne receiver is a mixer used to move received signals to a common intermediate frequency. Frequency mixers are also used to modulate a carrier signal in radio transmitters.

A superheterodyne receiver, often shortened to superhet, is a type of radio receiver that uses frequency mixing to convert a received signal to a fixed intermediate frequency (IF) which can be more conveniently processed than the original carrier frequency. It was invented by US engineer Edwin Armstrong in 1918 during World War I. Virtually all modern radio receivers use the superheterodyne principle.

In communications and electronic engineering, an intermediate frequency (IF) is a frequency to which a carrier wave is shifted as an intermediate step in transmission or reception. The intermediate frequency is created by mixing the carrier signal with a local oscillator signal in a process called heterodyning, resulting in a signal at the difference or beat frequency. Intermediate frequencies are used in superheterodyne radio receivers, in which an incoming signal is shifted to an IF for amplification before final detection is done.

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. Most radio systems in the 20th century used frequency modulation (FM) or amplitude modulation (AM) for radio broadcast.

## Types

The essential characteristic of a mixer is that it produces a component in its output, which is the product of the two input signals. A device that has a non-linear (e.g. exponential) characteristic can act as a mixer. Passive mixers use one or more diodes and rely on their non-linear relation between voltage and current, to provide the multiplying element. In a passive mixer, the desired output signal is always of lower power than the input signals.

In mathematics, an exponential function is a function of the form

A diode is a two-terminal electronic component that conducts current primarily in one direction ; it has low resistance in one direction, and high resistance in the other. A diode vacuum tube or thermionic diode is a vacuum tube with two electrodes, a heated cathode and a plate, in which electrons can flow in only one direction, from cathode to plate. A semiconductor diode, the most commonly used type today, is a crystalline piece of semiconductor material with a p–n junction connected to two electrical terminals. Semiconductor diodes were the first semiconductor electronic devices. The discovery of asymmetric electrical conduction across the contact between a crystalline mineral and a metal was made by German physicist Ferdinand Braun in 1874. Today, most diodes are made of silicon, but other materials such as gallium arsenide and germanium are used.

Active mixers use an amplifying device (such as a transistor or vacuum tube) to increase the strength of the product signal. Active mixers improve isolation between the ports, but may have higher noise and more power consumption. An active mixer can be less tolerant of overload.

A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power. It is composed of semiconductor material usually with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits.

In electronics, a vacuum tube, an electron tube, or valve or, colloquially, a tube, is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.

Mixers may be built of discrete components, may be part of integrated circuits, or can be delivered as hybrid modules.

An integrated circuit or monolithic integrated circuit is a set of electronic circuits on one small flat piece of semiconductor material that is normally silicon. The integration of large numbers of tiny MOS transistors into a small chip results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete electronic components. The IC's mass production capability, reliability, and building-block approach to circuit design has ensured the rapid adoption of standardized ICs in place of designs using discrete transistors. ICs are now used in virtually all electronic equipment and have revolutionized the world of electronics. Computers, mobile phones, and other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs.

Mixers may also be classified by their topology:

• An unbalanced mixer, in addition to producing a product signal, allows both input signals to pass through and appear as components in the output.
• A single balanced mixer is arranged with one of its inputs applied to a balanced (differential) circuit so that either the local oscillator (LO) or signal input (RF) is suppressed at the output, but not both.
• A double balanced mixer has both its inputs applied to differential circuits, so that neither of the input signals and only the product signal appears at the output. [1] Double balanced mixers are more complex and require higher drive levels than unbalanced and single balanced designs.

A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to the two inputs. It is an analog circuit with two inputs and and one output in which the output is ideally proportional to the difference between the two voltages

Selection of a mixer type is a trade off for a particular application.

Mixer circuits are characterized by their properties such as conversion gain (or loss), and noise figure. [2]

Nonlinear electronic components that are used as mixers include diodes, transistors biased near cutoff, and at lower frequencies, analog multipliers. Ferromagnetic-core inductors driven into saturation have also been used. In nonlinear optics, crystals with nonlinear characteristics are used to mix two frequencies of laser light to create optical heterodynes.

### Diode

A diode can be used to create a simple unbalanced mixer. This type of mixer produces the original frequencies as well as their sum and their difference. The significant property of the diode here is its non-linearity (or non-Ohmic behavior), which means its response (current) is not proportional to its input (voltage). The diode does not reproduce the frequencies of its driving voltage in the current through it, which allows the desired frequency manipulation. The current I through an ideal diode as a function of the voltage V across it is given by

${\displaystyle I=I_{\mathrm {S} }\left(e^{qV_{\mathrm {D} } \over nkT}-1\right)}$

where what is important is that V appears in e's exponent. The exponential can be expanded as

${\displaystyle e^{x}=\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}}$

and can be approximated for small x (that is, small voltages) by the first few terms of that series:

${\displaystyle e^{x}-1\approx x+{\frac {x^{2}}{2}}}$

Suppose that the sum of the two input signals ${\displaystyle v_{1}+v_{2}}$ is applied to a diode, and that an output voltage is generated that is proportional to the current through the diode (perhaps by providing the voltage that is present across a resistor in series with the diode). Then, disregarding the constants in the diode equation, the output voltage will have the form

${\displaystyle v_{\mathrm {o} }=(v_{1}+v_{2})+{\frac {1}{2}}(v_{1}+v_{2})^{2}+\dots }$

The first term on the right is the original two signals, as expected, followed by the square of the sum, which can be rewritten as ${\displaystyle (v_{1}+v_{2})^{2}=v_{1}^{2}+2v_{1}v_{2}+v_{2}^{2}}$, where the multiplied signal is obvious. The ellipsis represents all the higher powers of the sum which we assume to be negligible for small signals.

Suppose that two input sinusoids of different frequencies are fed into the diode, such that ${\displaystyle v_{1}=\sin at}$ and ${\displaystyle v_{2}=\sin bt}$. The signal ${\displaystyle V_{0}}$ becomes:

${\displaystyle v_{\mathrm {o} }=(\sin at+\sin bt)+{\frac {1}{2}}(\sin at+\sin bt)^{2}+\dots }$

Expanding the square term yields:

${\displaystyle v_{\mathrm {o} }=(\sin at+\sin bt)+{\frac {1}{2}}(\sin ^{2}at+2\sin at\sin bt+\sin ^{2}bt)+\dots }$

Ignoring all terms except for the ${\displaystyle \sin at\sin bt}$ term and utilizing the prosthaphaeresis (product to sum) identity,

${\displaystyle \sin a\sin b={\frac {\cos(a-b)-\cos(a+b)}{2}}}$

yields,

${\displaystyle v_{\mathrm {o} }=\cos((a-b)t)-\cos((a+b)t)+\dots }$

demonstrating how new frequencies are created from the mixer.

### Switching

Another form of mixer operates by switching, with the smaller input signal being passed inverted or non inverted according to the phase of the local oscillator (LO). This would be typical of the normal operating mode of a packaged double balanced mixer, with the local oscillator drive considerably higher than the signal amplitude.

The aim of a switching mixer is to achieve linear operation over the signal level by means of hard switching, driven by the local oscillator. Mathematically, the switching mixer is not much different from a multiplying mixer. Instead of the LO sine wave term, we would use the signum function. In the frequency domain, the switching mixer operation leads to the usual sum and difference frequencies, but also to further terms e.g. ±3fLO, ±5fLO, etc. The advantage of a switching mixer is that it can achieve (with the same effort) a lower noise figure (NF) and larger conversion gain. This is because the switching diodes or transistors act either like a small resistor (switch closed) or large resistor (switch open), and in both cases only a minimal noise is added. From the circuit perspective, many multiplying mixers can be used as switching mixers, just by increasing the LO amplitude. So RF engineers simply talk about mixers, while they mean switching mixers.

The mixer circuit can be used not only to shift the frequency of an input signal as in a receiver, but also as a product detector, modulator, phase detector or frequency multiplier. [3] For example, a communications receiver might contain two mixer stages for conversion of the input signal to an intermediate frequency and another mixer employed as a detector for demodulation of the signal.

## Related Research Articles

An electronic mixer is a device that combines two or more electrical or electronic signals into one or two composite output signals. There are two basic circuits that both use the term mixer, but they are very different types of circuits: additive mixers and multiplicative mixers. Additive mixers are also known as "analog adders" to distinguish from the related digital adder circuits.

Heterodyning is a signal processing technique invented by Canadian inventor-engineer Reginald Fessenden that creates new frequencies by combining or mixing two frequencies. Heterodyning is used to shift one frequency range into another, new one, and is also involved in the processes of modulation and demodulation. The two frequencies are combined in a nonlinear signal-processing device such as a vacuum tube, transistor, or diode, usually called a mixer. In the most common application, two signals at frequencies f1 and f2 are mixed, creating two new signals, one at the sum f1 + f2 of the two frequencies, and the other at the difference f1 − f2. These frequencies are called heterodynes. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. Heterodyne frequencies are related to the phenomenon of "beats" in acoustics.

A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator generates a periodic signal, and the phase detector compares the phase of that signal with the phase of the input periodic signal, adjusting the oscillator to keep the phases matched.

In telecommunications, a third-order intercept point (IP3) is a specific figure of merit associated with the more general Third Order Intermodulation (TOI) distortion, which is a measure for weakly nonlinear systems and devices, for example receivers, linear amplifiers and mixers. It is based on the idea that the device nonlinearity can be modeled using a low-order polynomial, derived by means of Taylor series expansion. The third-order intercept point relates nonlinear products caused by the third-order nonlinear term to the linearly amplified signal, in contrast to the second-order intercept point that uses second-order terms. (IP3) is the generally accepted unambiguous term for the third-order intercept point, although one occasionally sees the use of TOI for this figure-of-merit; such use is considered as incorrect by experts in the field.

A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction.

In electronics, ring modulation is a signal-processing function, an implementation of frequency mixing, performed by blending two signals, where one is typically a sine wave or another simple waveform and the other is the signal to be modulated. A ring modulator is an electronic device for ring modulation. A ring modulator may be used in music synthesizers and as an effects unit.

A product detector is a type of demodulator used for AM and SSB signals. Rather than converting the envelope of the signal into the decoded waveform like an envelope detector, the product detector takes the product of the modulated signal and a local oscillator, hence the name. A product detector is a frequency mixer.

A phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a voltage signal which represents the difference in phase between two signal inputs. It is an essential element of the phase-locked loop (PLL).

In electronics, a Schmitt trigger is a comparator circuit with hysteresis implemented by applying positive feedback to the noninverting input of a comparator or differential amplifier. It is an active circuit which converts an analog input signal to a digital output signal. The circuit is named a "trigger" because the output retains its value until the input changes sufficiently to trigger a change. In the non-inverting configuration, when the input is higher than a chosen threshold, the output is high. When the input is below a different (lower) chosen threshold the output is low, and when the input is between the two levels the output retains its value. This dual threshold action is called hysteresis and implies that the Schmitt trigger possesses memory and can act as a bistable multivibrator. There is a close relation between the two kinds of circuits: a Schmitt trigger can be converted into a latch and a latch can be converted into a Schmitt trigger.

In electronics, a common collector amplifier is one of three basic single-stage bipolar junction transistor (BJT) amplifier topologies, typically used as a voltage buffer.

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency.

A network, in the context of electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to linear network analysis.

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.

Ripple in electronics is the residual periodic variation of the DC voltage within a power supply which has been derived from an alternating current (AC) source. This ripple is due to incomplete suppression of the alternating waveform after rectification. Ripple voltage originates as the output of a rectifier or from generation and commutation of DC power.

A parametric oscillator is a driven harmonic oscillator in which the oscillations are driven by varying some parameter of the system at some frequency, typically different from the natural frequency of the oscillator. A simple example of a parametric oscillator is a child pumping a playground swing by periodically standing and squatting to increase the size of the swing's oscillations. The child's motions vary the moment of inertia of the swing as a pendulum. The "pump" motions of the child must be at twice the frequency of the swing's oscillations. Examples of parameters that may be varied are the oscillator's resonance frequency and damping .

The harmonic mixer and subharmonic mixer are a type of frequency mixer, which is a circuit that changes one signal frequency to another. The ordinary mixer has two input signals and one output signal. If the two input signals are sinewaves at frequencies f1 and f2, then the output signal consists of frequency components at the sum f1+f2 and difference f1f2 frequencies. In contrast, the harmonic and subharmonic mixers form sum and difference frequencies at a harmonic multiple of one of the inputs. The output signal then contains frequencies such as f1+kf2 and f1kf2 where k is an integer.

In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal. The term complex is used because mathematically this effect can be expressed as a complex number.

In electronics, the Gilbert cell is a type of mixer. It produces output signals that are proportional to the product of two input signals. Such circuits are widely used for frequency conversion in radio systems. The advantage of this circuit is the output current is an accurate multiplication of the (differential) base currents of both inputs. As a mixer, its balanced operation cancels out many unwanted mixing products, resulting in a "cleaner" output.

Piezoresponse force microscopy (PFM) is a variant of atomic force microscopy (AFM) that allows imaging and manipulation of piezoelectric/ferroelectric materials domains. This is achieved by bringing a sharp conductive probe into contact with a ferroelectric surface and applying an alternating current (AC) bias to the probe tip in order to excite deformation of the sample through the converse piezoelectric effect (CPE). The resulting deflection of the probe cantilever is detected through standard split photodiode detector methods and then demodulated by use of a lock-in amplifier (LiA). In this way topography and ferroelectric domains can be imaged simultaneously with high resolution.

A phase detector characteristic is a function of phase difference describing the output of the phase detector.

## References

1. Poole, Ian. "Double balanced mixer tutorial". Adrio Communications. Retrieved 30 July 2012.
2. D.S. Evans, G. R. Jessop, VHF-UHF Manual Third Edition, Radio Society of Great Britain, 1976, page 4-12
3. Paul Horowitz, Winfred Hill The Art of Electronics Second Edition, Cambridge University Press 1989, pp. 885–887.