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AD641AP Scheda tecnica(PDF) 8 Page - Analog Devices |
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AD641AP Scheda tecnica(HTML) 8 Page - Analog Devices |
8 / 16 page REV. C AD641 –8– FUNDAMENTALS OF LOGARITHMIC CONVERSION The conversion of a signal to its equivalent logarithmic value involves a nonlinear operation, the consequences of which can be very confusing if not fully understood. It is important to realize from the outset that many of the familiar concepts of linear circuits are of little relevance in this context. For example, the incremental gain of an ideal logarithmic converter approaches infinity as the input approaches zero. Further, an offset at the output of a linear amplifier is simply equivalent to an offset at the input, while in a logarithmic converter it is equivalent to a change of amplitude at the input—a very different relationship. We assume a dc signal in the following discussion to simplify the concepts; ac behavior and the effect of input waveform on cali- bration are discussed later. A logarithmic converter having a voltage input VIN and output VOUT must satisfy a transfer func- tion of the form VOUT = VY LOG (VIN/VX) Equation (1) where VY and VX are fixed voltages which determine the scaling of the converter. The input is divided by a voltage because the argument of a logarithm has to be a simple ratio. The logarithm must be multiplied by a voltage to develop a voltage output. These operations are not, of course, carried out by explicit com- putational elements, but are inherent in the behavior of the converter. For stable operation, VX and VY must be based on sound design criteria and rendered stable over wide temperature and supply voltage extremes. This aspect of RF logarithmic amplifier design has traditionally received little attention. When VIN = VX, the logarithm is zero. VX is, therefore, called the Intercept Voltage, because a graph of VOUT versus LOG (VIN)—ideally a straight line—crosses the horizontal axis at this point (see Figure 20). For the AD641, VX is calibrated to ex- actly 1 mV. The slope of the line is directly proportional to VY. Base 10 logarithms are used in this context to simplify the rela- tionship to decibel values. For VIN = 10 VX, the logarithm has a value of 1, so the output voltage is VY. At VIN = 100 VX, the output is 2 VY, and so on. VY can therefore be viewed either as the Slope Voltage or as the Volts per Decade Factor. The AD641 conforms to Equation (1) except that its two out- puts are in the form of currents, rather than voltages: IOUT = IY LOG (VIN/VX) Equation (2) ACTUAL 0 INPUT ON LOG SCALE YY 2VY IDEAL VYLOG (VIN/VX) VIN = VX VIN = 100VX VIN = 10VX ACTUAL SLOPE = VY IDEAL + – Figure 20. Basic DC Transfer Function of the AD641 IY, the Slope Current, is 1 mA. The current output can readily be converted to a voltage with a slope of 1 V/decade, for ex- ample, using one of the 1 k Ω resistors provided for this purpose, in conjunction with an op amp, as shown in Figure 21. 9 12 8 13 7 14 6 15 10 11 LOG OUT LOG COM SIG +OUT +VS –VS ITC BL2 SIG –OUT AD641 C1 330pF 1mA PER DECADE AD846 R1 48.7 R2 OUTPUT VOLTAGE 1V PER DECADE FOR R2 = 1k 100mV PER dB FOR R2 = 2k Figure 21. Using an External Op Amp to Convert the AD641 Output Current to a Buffered Voltage Output Intercept Stabilization Internally, the intercept voltage is a fraction of the thermal volt- age kT/q, that is, VX = VXOT/TO, where VXO is the value of VX at a reference temperature TO. So the uncorrected transfer function has the form: IOUT = IY LOG (VIN TO/VXOT) Equation (3) Now, if the amplitude of the signal input VIN could somehow be rendered PTAT, the intercept would be stable with tempera- ture, since the temperature dependence in both the numerator and denominator of the logarithmic argument would cancel. This is what is actually achieved by interposing the on-chip attenuator, which has the necessary temperature dependence to cause the input to the first stage to vary in proportion to abso- lute temperature. The end limits of the dynamic range are now totally independent of temperature. Consequently, this is the pre- ferred method of intercept stabilization for applications where the input signal is sufficiently large. When the attenuator is not used, the PTAT variation in VX will result in the intercept being temperature dependent. Near 300K (+27 °C) it will vary by 20 LOG (301/300) dB/°C, about 0.03 dB/ °C. Unless corrected, the whole output function would drift up or down by this amount with changes in temperature. In the AD641 a temperature compensating current IYLOG(T/TO) is added to the output. This effectively maintains a constant inter- cept VXO. This correction is active in the default state (Pin 8 open circuited). When using the attenuator, Pin 8 should be grounded, which disables the compensation current. The drift term needs to be compensated only once; when the outputs of two AD641s are summed, Pin 8 should be grounded on at least one of the two devices (both if the attenuator is used). Conversion Range Practical logarithmic converters have an upper and lower limit on the input, beyond which errors increase rapidly. The upper limit occurs when the first stage in the chain is driven into limit- ing. Above this, no further increase in the output can occur and the transfer function flattens off. The lower limit arises because a finite number of stages provide finite gain, and therefore at low signal levels the system becomes a simple linear amplifier. |
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