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AD8309ARU-REEL7 데이터시트(PDF) 9 Page - Analog Devices |
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AD8309ARU-REEL7 데이터시트(HTML) 9 Page - Analog Devices |
9 / 20 page REV. B AD8309 –9– labeled x 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 logarith- mic approximation. Continuing this analysis, we find that the next transition occurs when the input to the (N–1)th stage just reaches EK, that is, when VIN = EK /A N–2. The output of this stage is then exactly AEK. It is easily demonstrated (from the function shown in Figure 21) that the output of the final stage is (2A–1)EK (la- beled ≠ 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. 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 At the next critical point, labeled z, the input is 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 reaches the knee volt- age, VOUT changes by (A–1)EK for a ratio change of A in VIN. Expressed as a certain fraction of a decade, this 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 us to immedi- ately state the “Volts per Decade” scaling parameter, which is also the “Scaling Voltage” VY when using base-10 logarithms: V Linear Change inV Decades Change inV AE A Y OUT IN K == ( –) log ( ) 1 10 (4) Note that only two design parameters are involved in determin- ing 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 practical log amp will provide more rational scaling parameters. The intercept voltage can be determined by solving Equation (4) for any two pairs of transition points on the output function (see Figure 22). The result is: V E A X K NA = + (/[ –]) 11 (5) For the example under consideration, using N = 6, VX evaluates to 4.28 µV, which thus far in this analysis is still a simple dc voltage. A/0 SLOPE = 0 SLOPE = A EK AEK 0 INPUT Figure 23. A/0 Amplifier Functions (Ideal and tanh) Care is needed in the interpretation of this parameter. It was earlier defined as the input voltage at which the output passes through zero (see Figure 19). Clearly, in the absence of noise and offsets, the output of the amplifier chain shown in Figure 20 can only be zero when VIN = 0. This anomaly is due to the finite gain of the cascaded amplifier, which results in a failure to main- tain the logarithmic approximation below the “lin-log transition” (Point x in Figure 22). 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 (pulse) applications, because they do not demodulate their input signal. Demodulating (detecting) log-limiting amplifiers such as the AD8309 use a different type of amplifier stage, which we will call 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 23. This is also known as the limiter function, and a chain of N such cells is often used alone to generate a hard limited output, in recovering the signal in FM and PM modes. The AD640, AD606, AD608, AD8307, AD8309, AD8313 and other Analog Devices communications products incorporating a logarithmic IF amplifier all use this technique. It will be appar- ent that the output of the last stage cannot now provide a loga- rithmic output, since this remains unchanged for all inputs above the limiting threshold, which occurs at VIN = EK /A N–1. Instead, the logarithmic output is 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 can be shown that, for practical purpose, the intercept voltage VX is identical to that given in Equation (5), while the slope voltage is: V AE A Y K = log ( ) 10 (6) An A/0 cell can be very simple. In the AD8309 it is based on a bipolar-transistor differential pair, having resistive loads RL and an emitter current source IE. This amplifier limiter cell exhibits an equivalent knee-voltage of EK = 2kT/q and a small-signal gain of A = IERL /EK. The large signal transfer function is the hyperbolic tangent (see dotted line in Figure 23). 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 func- tion beneficially result in a lower ripple in the logarithmic con- formance than that which would be obtained using an ideal A/0 function. A practical amplifier chain built of these cells is differ- ential in structure from input to final output, and has a low |
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