Datasheet AD8307 (Analog Devices) - 10

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AD8307 Data Sheet
just 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
T AEK U SLOPE = 1
(tacitly, power absorbed at the input), but rather to input voltage.
A/1 P T
The use of dBV (decibels with respect to 1 V rms) is more precise,
OU
though still incomplete, because waveform is involved as well.
SLOPE = A
Because most users think about and specify RF signals in terms
0
of power, more specifically, in dBm re: 50 Ω, this convention is 023
EK INPUT
82- used in specifying the performance of the AD8307. 010 Figure 23. A/1 Amplifier Function
PROGRESSIVE COMPRESSION
Let the input of an N-cell cascade be VIN, and the final output Most high speed, high dynamic range log amps use a cascade of be VOUT. For small signals, the overall gain is simply AN. A nonlinear amplifier cells (see Figure 22) to generate the logarithmic six-stage system in which A = 5 (14 dB) has an overall gain function from a series of contiguous segments, a type of piecewise of 15,625 (84 dB). The importance of a very high small signal linear technique. This basic topology immediately opens up the gain in implementing the logarithmic function has been noted; possibility of enormous gain bandwidth products. For example, however, this parameter is only of incidental interest in the design the AD8307 employs six cells in its main signal path, each having of log amps. a small signal gain of 14.3 dB (×5.2) and a −3 dB bandwidth of From this point forward, rather than considering gain, analyze about 900 MHz. The overall gain is about 20,000 (86 dB) and the overall nonlinear behavior of the cascade in response to a the overall bandwidth of the chain is some 500 MHz, resulting simple dc input, corresponding to the V in the incredible gain bandwidth product (GBW) of 10,000 GHz, IN of Equation 1. For very small inputs, the output from the first cell is V about a million times that of a typical op amp. This very high 1 = AVIN. The output from the second cell is V GBW is an essential prerequisite for accurate operation under 2 = A2 VIN, and so on, up to V small signal conditions and at high frequencies. In Equation 2, N = AN VIN. At a certain value of VIN, the input to the Nth cell, V however, the incremental gain decreases rapidly as V N − 1, is exactly equal to the knee voltage EK. Thus, VOUT = AEK IN increases. and because there are N − 1 cells of Gain A ahead of this node, The AD8307 continues to exhibit an essentially logarithmic calculate V response down to inputs as small as 50 μV at 500 MHz. IN = EK /AN − 1. This unique situation corresponds to the lin-log transition (labeled 1 in Figure 24). Below this input,
STAGE 1 STAGE 2 STAGE N–1 STAGE N
the cascade of gain cells acts as a simple linear amplifier, whereas
V
for higher values of VIN, it enters into a series of segments that
X V A A A A W
lie on a logarithmic approximation (dotted line). 2 -02 82 010
VOUT
Figure 22. Cascade of Nonlinear Gain Cells
(4A–3) E
To develop the theory, first consider a scheme slightly different
K 2 3
from that employed in the AD8307, but simpler to explain and
(3A–2) E 3 K
mathematically more straightforward to analyze. This approach
(A–1) EK
is based on a nonlinear amplifier unit, called an A/1 cell, with
(2A–1) E 2 K
the transfer characteristic shown in Figure 23.
1 RATIO AE
The local small signal gain δV
K OF A
OUT/δVIN is A, maintained for all inputs up to the knee voltage E
LOG V
K, above which the incremental
IN 0
gain drops to unity. The function is symmetrical: the same drop 024
E
2-
K/AN–1 EK/AN–2 EK/AN–3 EK/AN–4
in gain occurs for instantaneous values of V 0108 IN less than –EK. The Figure 24. First Three Transitions large signal gain has a value of A for inputs in the range −EK ≤ VIN ≤ +EK, but falls asymptotically toward unity for very large Continuing this analysis, the next transition occurs when the inputs. In logarithmic amplifiers based on this amplifier function, input to the N − 1 stage just reaches EK, that is, when VIN = both the slope voltage and the intercept voltage must be traceable EK/AN − 2. The output of this stage is then exactly AEK, and it is to the one reference voltage, EK. Therefore, in this fundamental easily demonstrated (from the function shown in Figure 23) that analysis, the calibration accuracy of the log amp is dependent the output of the final stage is (2A − 1)EK (labeled 2 in Figure 24). solely on this voltage. In practice, it is possible to separate the Thus, the output has changed by an amount (A − 1)EK for a basic references used to determine VY and VX and, in the case of change in VIN from EK/AN − 1 to EK/AN − 2, that is, a ratio change of A. the AD8307, VY is traceable to an on-chip band gap reference, At the next critical point (labeled 3 in Figure 24), the input is whereas VX is derived from the thermal voltage kT/q and is later again A times larger and VOUT has increased to (3A − 2)EK, that temperature corrected. is, by another linear increment of (A − 1)EK. Rev. F | Page 10 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