AD8307_15 datasheet(11/24 Pages) AD

Part #	AD8307

Description	Low Cost, DC to 500 MHz, 92 dB Logarithmic Amplifier

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Manufacturer	AD [Analog Devices]

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AD8307

Rev. D | Page 11 of 24

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 the user 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, because 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 (labeled 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 logarith-

mic IF amplifier all use this technique. It becomes apparent that

the output of the last stage can no longer provide the logarithmic

output because 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 the dashed 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 composed 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 that converts the differen-

tial 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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