LMH2100 Datasheet, PDF (23/32 Pages) National Semiconductor (TI) – 50 MHz to 4 GHz 40 dB Logarithmic Power Detector for CDMA and WCDMA

• Values for the parameters in this formula.
The values for the parameters in the model can be obtained
in various ways. They can be based on measurements of the
detector transfer function in a precisely controlled environ-
ment (parameter extraction). If the parameter values are sep-
arately determined for each individual device, errors like part-
to-part spread are eliminated from the measurement system.
Obviously, errors may occur when the operating conditions of
the detector (e.g. the temperature) become significantly dif-
ferent from the operating conditions during calibration (e.g.
room temperature). Subsequent sections will discuss exam-
ples of simple estimators for power measurements that result
in a number of commonly used metrics for the power mea-
surement error: the LOG-conformance error, the temperature
drift error, the temperature sensitivity and differential power
error.
2.2 LOG-Conformance Error
Probably the simplest power measurement system that can
be realized is obtained when the LOG-detector transfer func-
tion is modelled as a perfect linear-in-dB relationship between
the input power and output voltage:
in which K_SLOPE represents the LOG-slope and P_INTERCEPT the
LOG-intercept. The estimator based on this model imple-
ments the inverse of the model equation, i.e.
The resulting power measurement error, the LOG-confor-
mance error, is thus equal to:
The most important contributions to the LOG-conformance
error are generally:
• The deviation of the actual detector transfer function from
an ideal Logarithm (the transfer function is nonlinear in
dB).
• Drift of the detector transfer function over various
environmental conditions, most importantly temperature;
K_SLOPE and P_INTERCEPT are usually determined for room
temperature only.
• Part-to-part spread of the (room temperature) transfer
function.
The latter component is conveniently removed by means of
calibration, i.e. if the LOG slope and LOG-intercept are de-
termined for each individual detector device (at room temper-
ature). This can be achieved by measurement of the detector
output voltage - at room temperature - for a series of different
power levels in the LOG-linear range of the detector transfer
function. The slope and intercept can then be determined by
means of linear regression.
An example of this type of error and its relationship to the
detector transfer function is depicted in Figure 6.
30014015
FIGURE 6. LOG-Conformance Error and LOG-Detector
Transfer Function
In the center of the detector's dynamic range, the LOG-con-
formance error is small, especially at room temperature; in
this region the transfer function closely follows the linear-in-
dB relationship while K_SLOPE and P_INTERCEPT are determined
based on room temperature measurements. At the tempera-
ture extremes the error in the center of the range is slightly
larger due to the temperature drift of the detector transfer
function. The error rapidly increases toward the top and bot-
tom end of the detector's dynamic range; here the detector
saturates and its transfer function starts to deviate significant-
ly from the ideal LOG-linear model. The detector dynamic
range is usually defined as the power range for which the LOG
conformance error is smaller than a specified amount. Often
an error of ±1 dB is used as a criterion.
2.3 Temperature Drift Error
A more accurate power measurement system can be ob-
tained if the first error contribution, due to the deviation from
the ideal LOG-linear model, is eliminated. This is achieved if
the actual measured detector transfer function at room tem-
perature is used as a model for the detector, instead of the
ideal LOG-linear transfer function used in the previous sec-
tion.
The formula used for such a detector is:
V_OUT,MOD = F_DET(P_IN,T_O)
where T_O represents the temperature during calibration (room
temperature). The transfer function of the corresponding es-
timator is thus the inverse of this:
In this expression V_OUT(T) represents the measured detector
output voltage at the operating temperature T.
The resulting measurement error is only due to drift of the
detector transfer function over temperature, and can be ex-
pressed as:
Unfortunately, the (numeric) inverse of the detector transfer
function at different temperatures makes this expression
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