AD8310

Rev. F | Page 9 of 24

THEORY OF OPERATION

(

)

O

IN

SLOPE

OUT

P

P

V

V

−

=

Logarithmic amplifiers perform a more complex operation than

classical linear amplifiers, and their circuitry is significantly

different. A good grasp of what log amps do and how they do it

can help users avoid many pitfalls in their applications. For a

complete discussion of the theory, see the AD8307 data sheet.

The essential purpose of a log amp is not to amplify (though

amplification is needed internally), but to compress a signal of

wide dynamic range to its decibel equivalent. It is, therefore, a

measurement device. An even better term might be logarithmic

converter, because the function is to convert a signal from one

domain of representation to another via a precise nonlinear

transformation:

⎟⎟

⎠

⎜⎜

⎝

=

X

Y

OUT

V

V

V

log

⎞

⎛

IN

V

(1)

where:

VOUT

is the output voltage.

VY

is the slope voltage. The logarithm is usually taken to

base ten, in which case VY is also the volts-per-decade.

VIN

is the input voltage.

VX

is the intercept voltage.

Log amps implicitly require two references (here VX and VY)

that determine the scaling of the circuit. The accuracy of a log

amp cannot be any better than the accuracy of its scaling

references. In the AD8310, these are provided by a band gap

reference.

VOUT

5VY

4VY

3VY

2VY

VY

–2VY

VOUT =0

LOG VIN

VSHIFT

LOWER INTERCEPT

VIN =10–2VX

–40dBc

VIN =102VX

+40dBc

VIN =104VX

+80dBc

VIN =VX

0dBc

Figure 21. General Form of the Logarithmic Function

While Equation 1, plotted in Figure 21, is fundamentally

correct, a different formula is appropriate for specifying the

calibration attributes or demodulating log amps like the

AD8310, operating in RF applications with a sine wave input.

(2)

where:

VOUT

is the demodulated and filtered baseband (video or RSSI)

output.

VSLOPE

is the logarithmic slope, now expressed in V/dB

(25 mV/dB for the AD8310).

PIN

is the input power, expressed in dB relative to some

reference power level.

PO

is the logarithmic intercept, expressed in dB relative to the

same reference level.

A widely used reference in RF systems is dB above 1 mW in

50 Ω, a level of 0 dBm. Note that the quantity (PIN − PO) is dB.

The logarithmic function disappears from the formula, because

the conversion has already been implicitly performed in stating

the input in decibels. This is strictly a concession to popular

convention. Log amps manifestly do not respond to power

(tacitly, power absorbed at the input), but rather to input

voltage. The input is specified in dBV (decibels with respect to

1 V rms) throughout this data sheet. This is more precise,

although still incomplete, because the signal waveform is also

involved. Many users specify RF signals in terms of power

(usually in dBm/50 Ω), and this convention is used in this data

sheet when specifying the performance of the AD8310.

PROGRESSIVE COMPRESSION

High speed, high dynamic-range log amps use a cascade of

nonlinear amplifier cells to generate the logarithmic function

as a series of contiguous segments, a type of piecewise linear

technique. The AD8310 employs six cells in its main signal

path, each having a small-signal gain of 14.3 dB (×5.2) and a

−3 dB bandwidth of about 900 MHz. The overall gain is about

20,000 (86 dB), and the overall bandwidth of the chain is

approximately 500 MHz, resulting in a gain-bandwidth product

(GBW) of 10,000 GHz, about a million times that of a typical

op amp. This very high GBW is essential to accurate operation

under small-signal conditions and at high frequencies. The

AD8310 exhibits a logarithmic response down to inputs as

small as 40 μV at 440 MHz.

Progressive compression log amps either provide a baseband

video response or accept an RF input and demodulate this

signal to develop an output that is essentially the envelope of the

input represented on a logarithmic or decibel scale. The

AD8310 is the latter kind. Demodulation is performed in a total

of nine detector cells. Six are associated with the amplifier

stages, and three are passive detectors that receive a progres-

sively attenuated fraction of the full input. The maximum signal

frequency can be 440 MHz, but, because all the gain stages are

dc-coupled, operation at very low frequencies is possible.