Datasheet AD8309 (Analog Devices) - 9

AD8309
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 V
SLOPE = 0
IN, it enters into a series of segments which lie on a logarith- mic approximation.
AEK
Continuing this analysis, we find that the next transition occurs
A/0
when the input to the (N–1)th stage just reaches E
SLOPE = A
K, that is,
OUTPUT
when VIN = EK /AN–2. The output of this stage is then exactly AE
0
K. It is easily demonstrated (from the function shown in
EK INPUT
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 Figure 23. A/0 Amplifier Functions (Ideal and tanh) amount (A–1)EK for a change in VIN from EK /AN–1 to EK /AN–2, Care is needed in the interpretation of this parameter. It was that is, a ratio change of A. 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
VOUT
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-
(4A-3) EK
tain the logarithmic approximation below the “lin-log transition” (Point ① in Figure 22). Closer analysis shows that the voltage
(3A-2) EK (A-1) E
given by Equation (5) represents the extrapolated, rather than
K
actual, intercept.
(2A-1) EK Demodulating Log Amps AE RATIO K
Log amps based on a cascade of A/1 cells are useful in baseband
OF A
(pulse) applications, because they do not demodulate their input
LOG VIN 0
signal. Demodulating (detecting) log-limiting amplifiers such as
EK/AN–1 EK/AN–2 EK/AN–3 EK/AN–4
the AD8309 use a different type of amplifier stage, which we Figure 22. The First Three Transitions will call an A/0 cell. Its function differs from that of the A/1 cell in that the gain above the knee voltage E At the next critical point, labeled ③, the input is A times larger K falls to zero, as shown by the solid line in Figure 23. This is also known as the limiter and VOUT has increased to (3A–2)EK, that is, by another linear function, and a chain of N such cells is often used alone to increment of (A–1)EK. Further analysis shows that, right up to generate a hard limited output, in recovering the signal in FM the point where the input to the first cell reaches the knee volt- and PM modes. 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 log The AD640, AD606, AD608, AD8307, AD8309, AD8313 and 10(A). other Analog Devices communications products incorporating a For example, when A = 5 a transition in the piecewise linear logarithmic IF amplifier all use this technique. It will be appar- output function occurs at regular intervals of 0.7 decade (log10(A), ent that the output of the last stage cannot now provide a loga- or 14 dB divided by 20 dB). This insight allows us to immedi- rithmic output, since this remains unchanged for all inputs ately state the “Volts per Decade” scaling parameter, which is above the limiting threshold, which occurs at V also the “Scaling Voltage” V IN = EK /AN–1. Y when using base-10 logarithms: Instead, the logarithmic output is generated by summing the Linear Change inV outputs of all the stages. The full analysis for this type of log amp OUT A 1 E V K = =( – ) Y (4) is only slightly more complicated than that of the previous case. Decades Change inVIN log ( 10 A) It can be shown that, for practical purpose, the intercept voltage Note that only two design parameters are involved in determin- VX is identical to that given in Equation (5), while the slope ing VY, namely, the cell gain A and the knee voltage EK, while voltage is: N, the number of stages, is unimportant in setting the slope of the overall function. For A = 5 and EK = 100 mV, the slope A EK = would be a rather awkward 572.3 mV per decade (28.6 mV/dB). VY (6) log ( 10 A) A well designed practical log amp will provide more rational scaling parameters. An A/0 cell can be very simple. In the AD8309 it is based on a bipolar-transistor differential pair, having resistive loads R The intercept voltage can be determined by solving Equation L and an emitter current source I (4) for any two pairs of transition points on the output function E. This amplifier limiter cell exhibits an equivalent knee-voltage of E (see Figure 22). The result is: K = 2kT/q and a small-signal gain of A = IERL /EK. The large signal transfer function is the E hyperbolic tangent (see dotted line in Figure 23). This function V K = X (5) is very precise, and the deviation from an ideal A/0 form is not (N + / 1 [ A– ] 1 ) A detrimental. In fact, the “rounded shoulders” of the tanh func- For the example under consideration, using N = 6, VX evaluates tion beneficially result in a lower ripple in the logarithmic con- to 4.28 µV, which thus far in this analysis is still a simple dc formance than that which would be obtained using an ideal A/0 voltage. function. A practical amplifier chain built of these cells is differ- ential in structure from input to final output, and has a low REV. B –9–