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AD8307 Datasheet(PDF) 11 Page - Analog Devices |
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AD8307 Datasheet(HTML) 11 Page - Analog Devices |
11 / 24 page AD8307 Rev. D | Page 11 of 24 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 (log10(A), or 14 dB divided by 20 dB). This insight allows the user to immediately write the volts per decade scaling parameter, which is also the scaling voltage, VY, when using base 10 logarithms, as () ) ( log 1 10 A E A V in Change Decades V in Change Linear V K IN OUT Y − = = (4) Note that only two design parameters are involved in determining VY, namely, the cell gain A and the knee voltage, EK, while N, the number of stages, is unimportant in setting the slope of the overall function. For A = 5 and EK = 100 mV, the slope would be a rather awkward 572.3 mV per decade (28.6 mV/dB). A well designed log amp has rational scaling parameters. The intercept voltage can be determined by using two pairs of transition points on the output function (consider Figure 24). The result is ()) 1 / 1 ( − + = A N K X A E V (5) For the case under consideration, using N = 6, calculate VZ = 4.28 μV. However, be careful about the interpretation of this parameter, because it was earlier defined as the input voltage at which the output passes through zero (see Figure 21). Clearly, in the absence of noise and offsets, the output of the amplifier chain shown in Figure 23 can be zero when, and only when, VIN = 0. This anomaly is due to the finite gain of the cascaded amplifier, which results in a failure to maintain the logarithmic approximation below the lin-log transition (labeled 1 in Figure 24). Closer analysis shows that the voltage given by Equation 5 represents the extrapolated, rather than actual, intercept. DEMODULATING LOG AMPS Log amps based on a cascade of A/1 cells are useful in baseband applications because they do not demodulate their input signal. However, baseband and demodulating log amps alike can be made using a different type of amplifier stage, called an A/0 cell. Its function differs from that of the A/1 cell in that the gain above the knee voltage EK falls to zero, as shown by the solid line in Figure 25. This is also known as the limiter function, and a chain of N such cells are often used to generate hard-limited output in recovering the signal in FM and PM modes. SLOPE = A SLOPE = 0 AEK 0 EK INPUT A/0 tanh Figure 25. A/0 Amplifier Functions (Ideal and Tanh) The AD640, AD606, AD608, AD8307, and various other Analog Devices, Inc., communications products incorporating a logarith- mic IF amplifier all use this technique. It becomes apparent that the output of the last stage can no longer provide the logarithmic output because this remains unchanged for all inputs above the limiting threshold, which occurs at VIN = EK/AN−1. Instead, the logarithmic output is now generated by summing the outputs of all the stages. The full analysis for this type of log amp is only slightly more complicated than that of the previous case. It is readily shown that, for practical purposes, the intercept voltage, VX, is identical to that given in Equation 5, while the slope voltage is () A AE V K Y 10 log = (6) Preference for the A/0 style of log amp over one using A/1 cells stems from several considerations. The first is that an A/0 cell can be very simple. In the AD8307, it is based on a bipolar transistor differential pair, having resistive loads, RL, and an emitter current source, IE. This exhibits an equivalent knee voltage of EK = 2 kT/q and a small signal gain of A = IERL/EK. The large signal transfer function is the hyperbolic tangent (see the dashed line in Figure 25). This function is very precise, and the deviation from an ideal A/0 form is not detrimental. In fact, the rounded shoulders of the tanh function result in a lower ripple in the logarithmic conformance than that obtained using an ideal A/0 function. An amplifier composed of these cells is entirely differential in structure and can thus be rendered very insensitive to disturbances on the supply lines and, with careful design, to temperature variations. The output of each gain cell has an associated transconductance (gm) cell that converts the differen- tial output voltage of the cell to a pair of differential currents, which are summed simply by connecting the outputs of all the gm (detector) stages in parallel. The total current is then converted back to a voltage by a transresistance stage to generate the logarithmic output. This scheme is depicted in single-sided form in Figure 26. |
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