Datasheet AD8309 (Analog Devices) - 7

AD8309 THEORY OF OPERATION
references. Note that (1) is mathematically incomplete in rep- The AD8309 is an advanced IF signal processing IC, intended resenting the behavior of a demodulating log amp such as the for use in high performance receivers, combining two key func- AD8309, where VIN has an alternating sign. However, the basic tions. First, it provides a large voltage gain combined with pro- principles are unaffected. gressive compression, through which an IF signal of high dynamic Figure 19 shows the input/output relationship of an ideal log range is converted into a square-wave (that is, hard limited) amp, conforming to Equation (1). The horizontal scale is loga- output, from which frequency and phase information modulated rithmic, and spans a very wide dynamic range, shown here as on this input can be recovered by subsequent signal processing. over 120 dB, that is, six decades of voltage or twelve decades of For this purpose, the noise level referred to the input must be input-referred power. The output passes through zero (the very low, since it determines the detection threshold for the receiver. “log-intercept”) at the unique value VIN = VX and becomes Further, it is often important that the group delay in this ampli- negative for inputs below the intercept. In the ideal case, the fier be essentially independent of the signal level, to minimize straight line describing VOUT for all values of VIN would con- the risk of amplitude-to-phase conversion. Finally, it is also desir- tinue indefinitely in both directions. The dotted line shows that able that the amplitude of the limited output be well defined and the effect of adding an offset voltage VSHIFT to the output is to temperature stable. In the AD8309, this amplitude can be con- lower the effective intercept voltage VX. trolled by the user, or even completely shut off, providing greater flexibility.
VOUT 5V
The second function is to provide a demodulated (baseband)
Y
output proportional to the decibel value of the signal input,
4VY
which may be used to measure the signal strength. This output,
VSHIFT
which typically runs from a value close to the ground level to a
3VY
few volts above ground, is called the Received Signal Strength
LOWER INTERCEPT
Indication, or RSSI. The provision of this function requires the
2VY
use of a logarithmic amplifier (log amp). For this output to be suitable for measuring signal strength, it is important that its
VY
scaling attributes are well controlled.
LOG VIN VOUT = 0
These are the logarithmic slope, specified in mV/dB, and the
VIN = 10–2VX V V IN = VX IN = 102VX VIN = 104VX
intercept, often specified as an equivalent power level at the
–40dBc 0dBc +40dBc +80dBc
amplifier input, although a log amp is inherently a voltage- responding device. (See further discussion, below). Also
–2VY
important is the law conformance, that is, how well the RSSI approximates an ideal function. Many low quality log amps Figure 19. Ideal Log Amp Function provide only an approximate solution, resulting in large errors in Exactly the same modification could be achieved raising the gain law conformance and scaling. All Analog Devices log amps are (or signal level) ahead of the log amp by the factor VSHIFT/VY. designed with close attention to matters affecting accuracy of For example, if VY is 400 mV/decade (that is, 20 mV/dB, as for the overall function. the AD8309), an offset of 120 mV added to the output will In the AD8309, these two basic signal-processing functions are appear to lower the intercept by two tenths of a decade, or 6 dB. combined to provide the necessary voltage gain with progressive Adding an offset to the output is thus indistinguishable from compression and hard limiting, and the determination of the applying an input level that is 6 dB higher. logarithmic magnitude of the input (RSSI). This combination is The log amp function described by (1) differs from that of a called a log limiting amplifier. A good grasp of how this product linear amplifier in that the incremental gain DVOUT/DVIN is a works will avoid many pitfalls in their application. very strong function of the instantaneous value of VIN, as is
Log-Amp Fundamentals
apparent by calculating the derivative. For the case where the The essential purpose of a logarithmic amplifier is to reduce a logarithmic base is e, it is easy to show that signal of wide dynamic range to its decibel equivalent. It is thus ∆VOUT V primarily a measurement device. The logarithmic representation Y = (2) leads to situations that may be confusing or even paradoxical. ∆ VIN VIN For example, a voltage offset added to the RSSI output of a log That is, the incremental gain of a log amp is inversely propor- amp is equivalent to a gain increase ahead of its input. tional to the instantaneous value of the input voltage. This re- When all the variables expressed as voltages, then, regardless of mains true for any logarithmic base. A “perfect” log amp would the particular structure, the output can be expressed as be required to have infinite gain under classical “small-signal” (zero-amplitude) conditions. This demonstrates that, whatever VOUT = VY log (VIN /VX) (1) means might be used to implement a log amp, accurate HF where VY is the “slope voltage.” VIN is the input voltage, and VX response under small signal conditions (that is, at the lower end is the “intercept voltage.” The logarithm is usually to base-10, of the full dynamic range) demands the provision of a very high which is appropriate to a decibel-calibrated device, in which gain-bandwidth product. A wideband log amp must therefore use case VY is also the “volts-per-decade.” It will be apparent from many cascaded gain cells each of low gain but high bandwidth. (1) that a log amp requires two references, here VX and VY, that For the AD8309, the gain-bandwidth (–10 dB) product is determine the scaling of the circuit. The absolute accuracy of a 52,500 GHz. log amp cannot be any better than the accuracy of its scaling REV. B –7–