Analog multiplier

Under an analog multiplier , engl. analog multiplier , electrical engineering understands a building block that forms the product of two analog signals . Operations related to multiplication such as squaring and square root can be implemented on the basis of this function with the help of additional elements.

function

Functional implementation of an analog multiplier

A multiplier generally works according to the following function:

${\displaystyle x=a\cdot b}$

or often with differential inputs and output offset correction:

${\displaystyle x=(a_{1}-a_{2})\cdot (b_{1}-b_{2})+c}$

In terms of circuit technology, the simple implementation form for a quadrant makes use of the fact that the multiplication of two positive factors can be traced back to the logarithm of the two factors, subsequent addition and to form the product on a final exposure :

${\displaystyle x=a\cdot b=e^{\ln(a\cdot b)}=e^{\ln a+\ln b}}$

Analog multipliers implemented in this way are only suitable for one quadrant, since the logarithm of negative numbers is not real. Extensions that allow a multiplication in four quadrants work with a bias and are based on the exponential transfer function of bipolar transistors . They are implemented in integrated circuits in the form of the Gilbert multiplier cell .

Principle structure

Schematic circuit with operational amplifiers

In the basic circuit diagram of an analog multiplier shown on the right, the two positive input voltages v ₁ and v ₂ are multiplied with one another in order to obtain the product in the form of the output voltage v _out . The resistances all have the same value R , the operational amplifiers are assumed to be ideal and the diodes have a reverse current I _s , a temperature voltage of V _T ≈26 mV and an emission coefficient of n = 1..2. After the summation at point v _a , the following voltage arises:

${\displaystyle v_{a}=nV_{T}\ln \left[\left({\frac {v_{1}}{RI_{s}}}+1\right)\left({\frac {v_{2}}{RI_{s}}}+1\right)\right]}$

Exposure will

${\displaystyle v_{b}=-RI_{s}\left(e^{\frac {v_{a}}{nV_{T}}}-1\right)=-{\frac {v_{1}\cdot v_{2}}{RI_{s}}}-(v_{1}+v_{2})}$

educated. The undesired second term is compensated for by the last stage, an addition stage. With which v _out becomes:

${\displaystyle v_{out}=-\left(-{\frac {v_{1}\cdot v_{2}}{RI_{s}}}-(v_{1}+v_{2})+(v_{1}+v_{2})\right)={\frac {v_{1}\cdot v_{2}}{RI_{s}}}}$

results.

Analog multiplier with MOS-FETs

There are also other circuit variants, such as with metal-oxide-semiconductor field effect transistors . The product is formed from the two positive input voltages v ₁ and v ₂ , and a constant positive reference voltage v _{ref is also} required to generate the output voltage

${\displaystyle v_{out}={\frac {R_{2}}{R_{1}}}{\frac {v_{1}v_{2}}{V_{ref}}};\qquad V_{ref},v_{1},v_{2}>0}$

to build.

Integrated multiplier circuits

Analog multipliers are often developed as an integrated circuit (IC) for a specific application (such as rms value formation). There are also a number of universally applicable components such as the AD834 from Analog Devices , a 4-quadrant multiplier. Such universal components often contain attenuator or amplifier circuits at inputs and outputs so that a signal can be scaled within the specified voltage limits.

Although analog multipliers have a lot in common with operational amplifiers , they are considerably more susceptible to interference such as noise and voltage offset , as these are multiplied by. In the high frequency range, oscillation tendencies are difficult to control due to phase shifts. The design of a universal, broadband analog multiplier is therefore far more complex than that of a comparable operational amplifier. Expensive special techniques such as laser trimming must be used in their manufacture . As a result, such modules are expensive and are usually only used when there is no cheaper solution.

Differentiation between voltage-controlled amplifiers and analog multipliers

If the voltage of one input is kept constant, the multiplier scales the signal at the second input proportionally to the level of the fixed voltage. In this case one speaks of a voltage controlled amplifier . Obvious areas of application are electronic volume control and automatic gain control . Although analog multipliers are often used in such circuits, voltage-controlled amplifier circuits are not necessarily full-fledged analog multipliers. With some ICs for electronic volume control, the input for the control signal often allows a higher input voltage with a significantly limited bandwidth.

In contrast, the inputs of a real multiplier are symmetrical, i.e. they have identical properties. The real multiplier is used for mixing or in circuits for the discrete Fourier transform .

A four- quadrant multiplier is a circuit in which input and output signals can assume both positive and negative voltage values. Many multiplier circuits only work over 2 quadrants (an input has only one polarity) or one quadrant (inputs and outputs have only one polarity, mostly positive).

application areas

• modulator
• Demodulator
• Discriminator
• Mixer (electronics)
• Voltage controlled amplifier
• Compander
• Noise reduction
• Analog computer
• Analog signal processing
• Automatic gain control
• Rms value formation
• Analog filter

Withdrawal of the analog multiplier

The function of an analog multiplier can often be better realized with the help of digital technology in the form of a digital multiplier . Especially in the area of ​​low signal frequencies, digital solutions are cheaper and more effective, and the circuit function can also be adapted using software / firmware . With increasing frequencies, the costs of a digital solution grow faster than that of an analog one.

In addition, digital signal processing is still on the advance. As a result, more and more functions that were originally used by analog multipliers are being taken over by digital signal processors, such as the rms value formation of a signal.

In addition, numerous functions such as tone control and AGC can be implemented in microcontroller-controlled circuits with the aid of digital potentiometers (see also digital-to-analog converter ) without the need to recalculate the digitized value.

Nevertheless, the high possible speed of the analog multiplier at low cost is a reason for its use in RF technology as e.g. B. modulator or demodulator , as a mixer or for rms value formation .

Web links

• Data sheet of the four-quadrant multiplier AD834 (PDF file; 358 kB)

Individual evidence

1. ↑ Analog Multipliers ( Memento of the original from September 19, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 297 kB), School of Electronics and Communications Engineering