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AD8309ARU-REEL Fiches technique(PDF) 8 Page - Analog Devices |
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AD8309ARU-REEL Fiches technique(HTML) 8 Page - Analog Devices |
8 / 20 page REV. B AD8309 –8– As a consequence of this high gain, even very small amounts of thermal noise at the input of a log amp will cause a finite output for zero input, resulting in the response line curving away from the ideal (Figure 19) at small inputs, toward a fixed baseline. This can either be above or below the intercept, depending on the design. Note that the value specified for this intercept is invariably an extrapolated one: the RSSI output voltage will never attain a value of exactly zero in a single supply implementation. Voltage (dBV) and Power (dBm) Response While Equation 1 is fundamentally correct, a simpler formula is appropriate for specifying the RSSI calibration attributes of a log amp like the AD8309, which demodulates an RF input. The usual measure is input power: VOUT = VSLOPE (PIN – P0 ) (3) VOUT is the demodulated and filtered RSSI output, VSLOPE is the logarithmic slope, expressed in volts/dB, PIN is the input power, expressed in decibels relative to some reference power level and P0 is the logarithmic intercept, expressed in decibels relative to the same reference level. The most widely used convention in RF systems is to specify power in decibels above 1 mW in 50 Ω, written dBm. (However, that the quantity [PIN – P0 ] is simply dB). The logarithmic function disappears from this formula because the conversion has already been implicitly performed in stating the input in decibels. Specification of log amp input level in terms of power is strictly a concession to popular convention: they do not respond to power (tacitly “power absorbed at the input”), but to the input voltage. In this connection, note that the input impedance of the AD8309 is much higher that 50 Ω, allowing the use of an im- pedance transformer at the input to raise the sensitivity, by up to 13 dB. The use of dBV, defined as decibels with respect to a 1 V rms sine amplitude, is more precise, although this is still not unambiguous complete as a general metric, because waveform is also involved in the response of a log amp, which, for a complex input (such as a CDMA signal) will not follow the rms value exactly. Since most users specify RF signals in terms of power—more specifi- cally, in dBm/50 Ω—we use both dBV and dBm in specifying the performance of the AD8309, showing equivalent dBm levels for the special case of a 50 Ω environment. Progressive Compression High speed, high dynamic range log amps use a cascade of nonlinear amplifier cells (Figure 20) to generate the logarithmic function from a series of contiguous segments, a type of piece- wise-linear technique. This basic topology offers enormous gain- bandwidth products. For example, the AD8309 employs in its main signal path six cells each having a small-signal gain of 12.04 dB ( ×4) and a –3 dB bandwidth of 850 MHz, followed by a final limiter stage whose gain is typically 18 dB. The overall gain is thus 100,000 (100 dB) and the bandwidth to –10 dB point at the limiter output is 525 MHz. This very high gain- bandwidth product (52,500 GHz) is an essential prerequisite to accurate operation under small signal conditions and at high frequencies: Equation (2) reminds us that the incremental gain decreases rapidly as VIN increases. The AD8309 exhibits a loga- rithmic response over most of the range from the noise floor of –91 dBV, or 28 µV rms, (or –78 dBm/50 Ω) to a breakdown- limited peak input of 4 V (requiring a balanced drive at the differential inputs INHI and INLO). A VX STAGE 1 STAGE 2 STAGE N –1 STAGE N VW A A A Figure 20. Cascade of Nonlinear Gain Cells Theory of Logarithmic Amplifiers To develop the theory, we will first consider a somewhat differ- ent scheme to that employed in the AD8309, but which is sim- pler to explain, and mathematically more straightforward to analyze. This approach is based on a nonlinear amplifier unit, which we may call an A/1 cell, having the transfer characteristic shown in Figure 21. We here use lowercase variables to define the local inputs and outputs of these cells, reserving uppercase for external signals. The small signal gain ∆V OUT/ ∆V IN is A, and is maintained for inputs up to the knee voltage EK, above which the incremental gain drops to unity. The function is symmetrical: the same drop in gain occurs for instantaneous values of VIN less than –EK. The large signal gain has a value of A for inputs in the range –EK < VIN < +EK, but falls asymptotically toward unity for very large inputs. In logarithmic amplifiers based on this simple function, both the slope voltage and the intercept voltage must be traceable to the one reference voltage, EK. Therefore, in this fundamental analy- sis, the calibration accuracy of the log amp is dependent solely on this voltage. In practice, it is possible to separate the basic refer- ences used to determine VY and VX. In the AD8309, VY is trace- able to an on-chip band-gap reference, while VX is derived from the thermal voltage kT/q and later temperature-corrected by a precise means. Let the input of an N-cell cascade be VIN, and the final output VOUT. For small signals, the overall gain is simply A N. A six- stage system in which A = 5 (14 dB) has an overall gain of 15,625 (84 dB). The importance of a very high small-signal ac gain in implementing the logarithmic function has already been noted. However, this is a parameter of only incidental interest in the design of log amps; greater emphasis needs to be placed on the nonlinear behavior. SLOPE = A SLOPE = 1 AEK 0 EK INPUT A/1 Figure 21. The A/1 Amplifier Function Thus, rather than considering gain, we will analyze the overall nonlinear behavior of the cascade in response to a simple dc input, corresponding to the VIN of Equation (1). For very small inputs, the output from the first cell is V1 = AVIN; from the second, V2 = A 2 V IN, and so on, up to VN = A N V IN. At a certain value of VIN, the input to the Nth cell, VN–1, is exactly equal to the knee voltage EK. Thus, VOUT = AEK and since there are N–1 cells of gain A ahead of this node, we can calculate that VIN = EK /A N–1. This unique point corresponds to the lin-log transition, |
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