Datasheet AD8307 (Analog Devices) - 9

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Data Sheet AD8307 LOG AMP THEORY
Logarithmic amplifiers perform a more complex operation than describing VOUT for all values of VIN continues indefinitely in both that of classical linear amplifiers, and their circuitry is significantly directions. The dotted line shows that the effect of adding an different. A good grasp of what log amps do and how they work offset voltage, VSHIFT, to the output is to lower the effective intercept can prevent many pitfalls in their application. The essential purpose voltage, VX. Exactly the same alteration can be achieved by raising of a log amp is not to amplify, though amplification is utilized to the gain (or signal level) ahead of the log amp by the factor, achieve the function. Rather, it is to compress a signal of wide VSHIFT/VY. For example, if VY is 500 mV per decade (25 mV/dB), dynamic range to its decibel equivalent. It is thus a measurement an offset of 150 mV added to the output appears to lower the device. A better term may be logarithmic converter, because its intercept by two-tenths of a decade, or 6 dB. Adding an offset to basic function is the conversion of a signal from one domain of the output is thus indistinguishable from applying an input level representation to another via a precise nonlinear transformation. that is 6 dB higher. Logarithmic compression leads to situations that can be confusing The log amp function described by Equation 1 differs from that or paradoxical. For example, a voltage offset added to the output of a linear amplifier in that the incremental gain δVOUT/δVIN is a of a log amp is equivalent to a gain increase ahead of its input. very strong function of the instantaneous value of VIN, as is In the usual case where all the variables are voltages, and regardless apparent by calculating the derivative. For the case where the of the particular structure, the relationship between the variables logarithmic base is δ, can be expressed as V  V OUT Y  (2) V  V ( log V /V ) (1) V V OUT Y IN X IN IN where: That is, the incremental gain is inversely proportional to the VOUT is the output voltage. instantaneous value of the input voltage. This remains true VY is the slope voltage; the logarithm is usually taken to base 10 for any logarithmic base, which is chosen as 10 for all decibel (in which case VY is also the volts per decade). related purposes. It follows that a perfect log amp is required to VIN is the input voltage. have infinite gain under classical small signal (zero amplitude) VX is the intercept voltage. conditions. Less ideally, this result indicates that whatever All log amps implicitly require two references, in this example, means are used to implement a log amp, accurate response V under small signal conditions (that is, at the lower end of the X and VY, which determine the scaling of the circuit. The abso- lute accuracy of a log amp cannot be any better than the accuracy dynamic range) demands the provision of a very high gain of its scaling references. Equation 1 is mathematically incomplete bandwidth product. A further consequence of this high gain is in representing the behavior of a demodulating log amp, such that in the absence of an input signal, even very small amounts as the AD8307, where V of thermal noise at the input of a log amp cause a finite output IN has an alternating sign. However, the basic principles are unaffected, and this can be safely used as the for zero input. This results in the response line curving away starting point in the analyses of log amp scaling. from the ideal shown in Figure 21 toward a finite baseline, which can be either above or below the intercept. Note that the
VOUT 5V
value given for this intercept can be an extrapolated value, in
Y
which case the output cannot cross zero, or even reach it, as is
4VY V
the case for the AD8307.
SHIFT 3VY
While Equation 1 is fundamentally correct, a simpler formula is
LOWER INTERCEPT
appropriate for specifying the calibration attributes of a log amp
2VY
like the AD8307, which demodulates a sine wave input.
VY
VOUT = VSLOPE (PIN – P0) (3)
LOG VIN V
where:
OUT = 0 VIN = VX VIN = 102VX VIN = 104VX
021
VIN = 10–2VX
VOUT is the demodulated and filtered baseband (video or
–40dBc 0dBc
2-
+40dBc +80dBc
108 0 RSSI) output.
–2V
V
Y
SLOPE is the logarithmic slope, now expressed in V/dB (typically between 15 mV/dB and 30 mV/dB). Figure 21. Ideal Log Amp Function PIN is the input power, expressed in decibels relative to some Figure 21 shows the input/output relationship of an ideal log amp, reference power level. conforming to Equation 1. The horizontal scale is logarithmic and P0 is the logarithmic intercept, expressed in decibels relative to spans a wide dynamic range, shown in Figure 21 as over 120 dB, or the same reference level. six decades. The output passes through zero (the log intercept) at the unique value V The most widely used reference in RF systems is decibels above IN = VX and ideally becomes negative for inputs below the intercept. In the ideal case, the straight line 1 mW in 50 Ω, written dBm. Note that the quantity (PIN – P0) is Rev. F | Page 9 of 24 Document Outline FEATURES APPLICATIONS FUNCTIONAL BLOCK DIAGRAM GENERAL DESCRIPTION TABLE OF CONTENTS REVISION HISTORY SPECIFICATIONS ABSOLUTE MAXIMUM RATINGS ESD CAUTION PIN CONFIGURATION AND FUNCTION DESCRIPTIONS TYPICAL PERFORMANCE CHARACTERISTICS LOG AMP THEORY PROGRESSIVE COMPRESSION DEMODULATING LOG AMPS INTERCEPT CALIBRATION OFFSET CONTROL EXTENSION OF RANGE INTERFACES ENABLE INTERFACE INPUT INTERFACE OFFSET INTERFACE OUTPUT INTERFACE THEORY OF OPERATION BASIC CONNECTIONS INPUT MATCHING NARROW-BAND MATCHING SLOPE AND INTERCEPT ADJUSTMENTS APPLICATIONS INFORMATION BUFFERED OUTPUT FOUR-POLE FILTER 1 µW TO 1 kW 50 Ω POWER METER MEASUREMENT SYSTEM WITH 120 dB DYNAMIC RANGE OPERATION AT LOW FREQUENCIES OUTLINE DIMENSIONS ORDERING GUIDE