AD8310
Rev. F | Page 9 of 24
THEORY OF OPERATION
(
)
O
IN
SLOPE
OUT
P
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
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
01084-021
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.