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AD8307AR-REEL Arkusz danych(PDF) 8 Page - Analog Devices |
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AD8307AR-REEL Arkusz danych(HTML) 8 Page - Analog Devices |
8 / 20 page AD8307 –8– REV. A voltage. The use of dBV (decibels with respect to 1 V rms) would be more precise, though still incomplete, since waveform is involved, too. Since most users think about and specify RF signals in terms of power—even more specifically, in dBm re 50 Ω —we will use this convention in specifying the performance of the AD8307. Progressive Compression Most 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 immediately opens up the possibility of enormous gain-bandwidth products. For example, the AD8307 employs six cells in its main signal path, each having a small-signal gain of 14.3 dB ( ×5.2) and a –3 dB bandwidth of about 900 MHz; the overall gain is about 20,000 (86 dB) and the overall bandwidth of the chain is some 500 MHz, resulting in the incredible gain-bandwidth product (GBW) of 10,000 GHz, about a million times that of a typical op amp. This very high GBW is an essential prerequisite to accurate operation under small-signal conditions and at high frequencies. Equation 2 reminds us, however, that the incremental gain will decrease rapidly as VIN increases. The AD8307 continues to exhibit an essentially logarithmic response down to inputs as small as 50 µV at 500 MHz. A VX STAGE 1 STAGE 2 STAGE N –1 STAGE N VW A A A Figure 20. Cascade of Nonlinear Gain Cells To develop the theory, we will first consider a slightly different scheme to that employed in the AD8307, but which is simpler 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. The local small-signal gain ∂V OUT/∂VIN is A, main- tained for all 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 ampli- fier function, both the slope voltage and the intercept voltage must be traceable to the one reference voltage, EK. Therefore, in this fundamental analysis, the calibration accuracy of the log amp is dependent solely on this voltage. In practice, it is possible to separate the basic references used to determine VY and VX and SLOPE = A SLOPE = 1 AEK 0 EK INPUT A/1 Figure 21. The A/1 Amplifier Function in the case of the AD8307, VY is traceable to an on-chip band- gap reference, while VX is derived from the thermal voltage kT/q and later temperature-corrected. 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 gain in implementing the logarithmic function has been noted; how- ever, this parameter is of only incidental interest in the design of log amps. From here onward, 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 situation corresponds to the lin-log transition, labeled 1 on Figure 22. Below this input, the cascade of gain cells is acting as a simple linear amplifier, while for higher values of VIN, it enters into a series of segments which lie on a logarithmic approximation (dotted line). VOUT LOG VIN 0 RATIO OF A EK/AN–1 EK/AN–2 EK/AN–3 EK/AN–4 (A-1) EK (4A-3) EK (3A-2) EK (2A-1) EK AEK Figure 22. The First Three Transitions Continuing this analysis, we find that the next transition occurs when the input to the (N–1) stage just reaches EK; that is, when VIN = EK /A N–2. The output of this stage is then exactly AE K, and it is easily demonstrated (from the function shown in Figure 21) that the output of the final stage is (2A–1) EK (labeled on Figure 22). Thus, the output has changed by an amount (A–1)EK for a change in VIN from EK /A N–1 to E K /A N–2, that is, a ratio change of A. At the next critical point, labeled , we find the input is again A times larger and VOUT has increased to (3A–2)EK, that is, by another linear increment of (A–1)EK. 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 (that is, log10(A), or 14 dB divided by 20 dB). This insight allows us to immediately write the Volts per Decade scaling parameter, which is also the Scaling Voltage VY, when using base-10 logarithms, as: VY = Linear Change in VOUT Decades Change in VIN = A −1 ()E K log10 A () (4) |
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