Datasheet AD641 (Analog Devices) - 9

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AD641 FUNDAMENTALS OF LOGARITHMIC CONVERSION
IY, the Slope Current, is 1 mA. The current output can readily The conversion of a signal to its equivalent logarithmic value be converted to a voltage with a slope of 1 V/decade, for ex- involves a nonlinear operation, the consequences of which can be ample, using one of the 1 kΩ resistors provided for this purpose, very confusing if not fully understood. It is important to realize in conjunction with an op amp, as shown in Figure 21. from the outset that many of the familiar concepts of linear circuits are of little relevance in this context. For example, the
1mA PER DECADE R2
incremental gain of an ideal logarithmic converter approaches
R1
infinity as the input approaches zero. Further, an offset at the
48.7
V output of a linear amplifier is simply equivalent to an offset at
C1 AD846
the input, while in a logarithmic converter it is equivalent to a
330pF
change of amplitude at the input—a very different relationship.
OUTPUT VOLTAGE 1V PER DECADE
We assume a dc signal in the following discussion to simplify the
FOR R2 = 1k
V
100mV PER dB
concepts; ac behavior and the effect of input waveform on cali-
15 14 13 12 11 FOR R2 = 2k
V bration are discussed later. A logarithmic converter having a
LOG LOG +V SIG S OUT COM +OUT
voltage input VIN and output VOUT must satisfy a transfer func-
AD641
tion of the form
SIG –VS ITC BL2 –OUT 6 7 8 9 10
VOUT = VY LOG (VIN/VX) Equation (1) Figure 21. Using an External Op Amp to Convert the where VY and VX are fixed voltages which determine the scaling AD641 Output Current to a Buffered Voltage Output of the converter. The input is divided by a voltage because the argument of a logarithm has to be a simple ratio. The logarithm
Intercept Stabilization
must be multiplied by a voltage to develop a voltage output. Internally, the intercept voltage is a fraction of the thermal volt- These operations are not, of course, carried out by explicit com- age kT/q, that is, VX = VXOT/TO, where VXO is the value of VX putational elements, but are inherent in the behavior of the at a reference temperature TO. So the uncorrected transfer converter. For stable operation, V function has the form: X and VY must be based on sound design criteria and rendered stable over wide temperature IOUT = IY LOG (VIN TO/VXOT) Equation (3) and supply voltage extremes. This aspect of RF logarithmic amplifier design has traditionally received little attention. Now, if the amplitude of the signal input VIN could somehow be rendered PTAT, the intercept would be stable with tempera- When VIN = VX, the logarithm is zero. VX is, therefore, called ture, since the temperature dependence in both the numerator the Intercept Voltage, because a graph of VOUT versus LOG and denominator of the logarithmic argument would cancel. (VIN)—ideally a straight line—crosses the horizontal axis at this This is what is actually achieved by interposing the on-chip point (see Figure 20). For the AD641, VX is calibrated to ex- attenuator, which has the necessary temperature dependence to actly 1 mV. The slope of the line is directly proportional to VY. cause the input to the first stage to vary in proportion to abso- Base 10 logarithms are used in this context to simplify the rela- lute temperature. The end limits of the dynamic range are now tionship to decibel values. For VIN = 10 VX, the logarithm has a totally independent of temperature. Consequently, this is the pre- value of 1, so the output voltage is VY. At VIN = 100 VX, the ferred method of intercept stabilization for applications where output is 2 VY, and so on. VY can therefore be viewed either as the input signal is sufficiently large. the Slope Voltage or as the Volts per Decade Factor. When the attenuator is not used, the PTAT variation in VX will The AD641 conforms to Equation (1) except that its two out- result in the intercept being temperature dependent. Near 300K puts are in the form of currents, rather than voltages: (+27°C) it will vary by 20 LOG (301/300) dB/°C, about 0.03 dB/ °C. Unless corrected, the whole output function would drift up IOUT = IY LOG (VIN/VX) Equation (2) or down by this amount with changes in temperature. In the AD641 a temperature compensating current IYLOG(T/TO) is
VYLOG (VIN/VX) IDEAL
added to the output. This effectively maintains a constant inter-
ACTUAL
cept VXO. This correction is active in the default state (Pin 8
2VY
open circuited). When using the attenuator, Pin 8 should be grounded, which disables the compensation current. The drift
SLOPE = VY
term needs to be compensated only once; when the outputs of two AD641s are summed, Pin 8 should be grounded on at least
YY
one of the two devices (both if the attenuator is used).
+ Conversion Range
Practical logarithmic converters have an upper and lower limit on the input, beyond which errors increase rapidly. The upper
0
limit occurs when the first stage in the chain is driven into limit-
ACTUAL INPUT ON V
ing. Above this, no further increase in the output can occur and
I N = VX V V I N = 10VX I N = 100VX LOG SCALE –
the transfer function flattens off. The lower limit arises because
IDEAL
a finite number of stages provide finite gain, and therefore at Figure 20. Basic DC Transfer Function of the AD641 low signal levels the system becomes a simple linear amplifier. –8– REV. D Document Outline FEATURES PRODUCT DESCRIPTION PIN CONFIGURATIONS AD641--SPECIFICATIONS ELECTRICAL CHARACTERISTICS THERMAL CHARACTERISTICS ABSOLUTE MAXIMUM RATINGS ESD CAUTION REVISION HISTORY AD641--TYPICAL DC PERFORMANCE CHARACTERISTICS TYPICAL AC PERFORMANCE CHARACTERISTICS CIRCUIT DESCRIPTION CIRCUIT OPERATION FUNDAMENTALS OF LOGARITHMIC CONVERSION INTERCEPT STABILIZATION CONVERSION RANGE EFFECT OF WAVEFORM ON INTERCEPT LOGARITHMIC CONFORMANCE AND WAVEFORM SIGNAL MAGNITUDE INTERCEPT AND LOGARITHMIC OFFSET OPERATION OF A SINGLE AD641 ACTIVE CURENT-TO-VOLTAGE CONVERSION EFFECT OF FREQUENCY ON CALIBRATION SOURCE RESISTANCE AND INPUT OFFSET USING HIGHER SUPPLY VOLTAGES USING THE ATTENUATOR OPERATION OF CASCADED AD641s ELIMINATING THE EFFECT OF FIRST STAGE OFFSET PRACTICAL APPLICATIONS RSSI APPLICATIONS 250 MHz RSSI CONVERTER WITH 58 dB DYNAMIC RANGE OUTLINE DIMENSIONS ORDERING GUIDE