AD8307ANZ datasheet(11/24 Pages) AD

No. de pieza	AD8307ANZ

Descripción Electrónicos	Low Cost DC-500 MHz, 92 dB Logarithmic Amplifier

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AD8307

Rev. C | Page 11 of 24

of A. At the next critical point (labeled 3 in Figure 24), the input

is again A times larger and VOUT has increased to (3A–2)EK, that

is, by another linear increment of (A–1)EK.

Further analysis shows that right up to the point where the

input to the first cell is above the knee voltage, VOUT changes by

(A–1)EK for a ratio change of A in VIN. This can be expressed as

a certain fraction of a decade, which is simply log10(A). For

example when A = 5, a transition in the piecewise linear output

function occurs at regular intervals of 0.7 decade (log10(A), or

14 dB divided by 20 dB). This insight allows us to immediately

write the volts per decade scaling parameter, which is also the

scaling voltage, VY, when using base 10 logarithms, as

()

)

(

log

1

10 A

E

A

V

in

Change

Decades

V

in

Change

Linear

V

K

IN

OUT

Y

−

=

(4)

Note that only two design parameters are involved in

determining VY, namely, the cell gain A and the knee voltage EK,

while N, the number of stages, is unimportant in setting the

slope of the overall function. For A = 5 and EK = 100 mV, the

slope would be a rather awkward 572.3 mV per decade

(28.6 mV/dB). A well designed log amp has rational scaling

parameters.

The intercept voltage can be determined by using two pairs of

transition points on the output function (consider Figure 24).

The result is

())

1

/

1

(

−

+

=

A

N

K

X

A

E

V

(5)

For the case under consideration, using N = 6, calculate

VZ = 4.28 μV. However, be careful about the interpretation of

this parameter, since it was earlier defined as the input voltage

at which the output passes through zero (see Figure 21). Clearly,

in the absence of noise and offsets, the output of the amplifier

chain shown in Figure 23 can be zero when, and only when,

VIN = 0. This anomaly is due to the finite gain of the cascaded

amplifier, which results in a failure to maintain the logarithmic

approximation below the lin-log transition (point 1 in Figure 24).

Closer analysis shows that the voltage given by Equation 5

represents the extrapolated, rather than actual, intercept.

DEMODULATING LOG AMPS

Log amps based on a cascade of A/1 cells are useful in baseband

applications because they do not demodulate their input signal.

However, baseband and demodulating log amps alike can be

made using a different type of amplifier stage, called an A/0 cell.

Its function differs from that of the A/1 cell in that the gain

above the knee voltage EK falls to zero, as shown by the solid

line in Figure 25. This is also known as the limiter function, and

a chain of N such cells are often used to generate hard limited

output in recovering the signal in FM and PM modes.

SLOPE = A

SLOPE = 0

AEK

0

EK

INPUT

A/0

tanh

Figure 25. A/0 Amplifier Functions (Ideal and Tanh)

The AD640, AD606, AD608, AD8307, and various other

Analog Devices, Inc. communications products incorporating a

logarithmic IF amplifier all use this technique. It becomes

apparent that the output of the last stage can no longer provide

the logarithmic output, since this remains unchanged for all inputs

above the limiting threshold, which occurs at VIN = EK/AN−1.

Instead, the logarithmic output is now generated by summing

the outputs of all the stages. The full analysis for this type of log

amp is only slightly more complicated than that of the previous

case. It is readily shown that, for practical purposes, the intercept

voltage VX is identical to that given in Equation 5, while the

slope voltage is

()

A

AE

V

K

Y

10

log

=

(6)

Preference for the A/0 style of log amp, over one using A/1 cells,

stems from several considerations. The first is that an A/0 cell

can be very simple. In the AD8307 it is based on a bipolar

transistor differential pair, having resistive loads, RL, and an

emitter current source, IE. This exhibits an equivalent knee

voltage of EK = 2 kT/q and a small signal gain of A = IERL/EK.

The large signal transfer function is the hyperbolic tangent

(see dotted line in Figure 25). This function is very precise, and

the deviation from an ideal A/0 form is not detrimental. In fact,

the rounded shoulders of the tanh function result in a lower

ripple in the logarithmic conformance than that obtained using

an ideal A/0 function.

An amplifier built of these cells is entirely differential in

structure and can thus be rendered very insensitive to

disturbances on the supply lines and, with careful design, to

temperature variations. The output of each gain cell has an

associated transconductance (gm) cell, which converts the

differential output voltage of the cell to a pair of differential

currents, which are summed simply by connecting the outputs

of all the gm (detector) stages in parallel. The total current is

then converted back to a voltage by a transresistance stage to

generate the logarithmic output. This scheme is depicted, in

single sided form, in Figure 26.

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