ADL5391

Data Sheet

Rev. A | Page 10 of 15

THEORY OF OPERATION

BASIC THEORY

The multiplication of two analog variables is a fundamental

signal processing function that has been around for decades. By

convention, the desired transfer function is given by

W = αXY/U + Z

(1)

where:

X and Y are the multiplicands.

U is the multiplier scaling factor.

α is the multiplier gain.

W is the product output.

Z is a summing input.

All the variables and the scaling factor have the dimension of volts.

In the past, analog multipliers, such as the AD835, were

implemented almost exclusively with a Gilbert Cell topology

or a close derivative. The inherently asymmetric signal paths

for X and Y inevitably create amplitude and delay imbalances

between X and Y. In the ADL5391, the novel multiplier core

provides absolute symmetry between X and Y, minimizing

scaling and phasing differences inherent in the Gilbert Cell.

The simplified block diagram of the ADL5391 shows a main

multiplier cell that receives inputs X and Y and a second

multiplier cell in the feedback path around an integrating buffer.

The inputs to this feedback multiplier are the difference of the

output signal and the summing input, W − Z, and the internal

scaling reference, U. At dc, the integrating buffer ensures that

the output of both multipliers is exactly 0, therefore

(W − Z)xU = XY, or W = XY/U + Z

(2)

By using a feedback multiplier that is identical to the main

multiplier, the scaling is traced back solely to U, which is

an accurate reference generated on-chip. As is apparent in

Equation 2, noise, drift, or distortion that is common to both

multipliers is rejected to first-order because the feedback

multiplier essentially compensates the impairments generated

in the main multiplier.

The scaling factor, U, is fixed by design to 1.12 V. However, the

multiplier gain, α, can be adjusted by driving the GADJ pin with

a voltage ranging from 0 V to 2 V. If left floating, then α = 1 or

0 dB, and the overall scaling is simply U = 1 V. For VGADJ = 0 V,

the gain is lowered by approximately 4 dB; for VGADJ = 2 V, the

gain is raised by approximately 6 dB. Figure 5 shows the

relationship between α(V/V) and VGADJ.

The small-signal bandwidth from the inputs X, Y, and Z to

the output W is a single-pole response. The pole is inversely

proportional to α. For α = 1 (GADJ floating), the bandwidth is

about 2 GHz; for α > 1, the bandwidth is reduced; and for α < 1,

the bandwidth is increased.

All input ports, X, Y, and Z, are differential and internally

500 Ω up to 100 MHz, rolling off to 50 Ω at 2 GHz. All inputs

can be driven in single-ended fashion and can be ac-coupled. In

dc-coupled operation, the inputs can be biased to a common

the input pins to accommodate the lower common mode is

subtracted from the 50 mA total available from the internal

internally from VREF to the input pins.

Calibration

The dc offset of the ADL5391 is approximately 20 mV but

changes over temperature and has variation from part to part

(see Figure 4). It is generally not of concern unless the ADL5391

is operated down to dc (close to the point X = 0 V or Y = 0 V),

where 0 V is expected on the output (W = 0 V). For example,

when the ADL5391 is used as a VGA and a large amount of

attenuation is needed, the maximum attenuation is determined

by the input dc offset.

Applying the proper voltage on the Z input removes the W offset.

Calibration can be accomplished by making the appropriate cross

plots and adjusting the Z input to remove the offset.

Additionally, gain scaling can be adjusted by applying a dc voltage

to the GADJ pin, as shown in Figure 5.

BASIC CONNECTIONS

Multiplier Connections

The best ADL5391 performance is achieved when the X, Y, and

Z inputs and W output are driven differentially; however, they

can be driven single-ended. Single-ended-to-differential

transformations (or differential-to-single-ended transformations)

can be done using a balun or active components, such as the

AD8313, the AD8132 (both with operation down to dc), or the

AD8352 (for higher drive capability). If using the ADL5391

single-ended without ac coupling capacitors, the reference

voltage of 2.5 V needs to be taken into account. Voltages above

2.5 V are positive voltages and voltages below 2.5 V are negative

voltages. Care needs to be taken not to load the ADL5391 too

heavily, the maximum reference current available is 50 mA.