LMH2110 Datasheet, PDF (17/33 Pages) National Semiconductor (TI) – 8 GHz Logarithmic RMS Power Detector with 45 dB Dynamic Range

LMH2110
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SNWS022C – JANUARY 2010 – REVISED MARCH 2013
³^{1 T v(t)2}
V_RMS2
P=
T⁰
R
dt =
R
where
• T is the time interval over which is averaged
• v(t) is the instantaneous voltage at time t
• R is the resistance in which the power is dissipated
• V_RMS is the equivalent RMS voltage
(1)
According to aforementioned formula for power, an exact power measurement can be done via measuring the
RMS voltage (V_RMS) of a signal. The RMS voltage is described by:
³ ^{VRMS =}
1
T
v(t)²dt
(2)
Implementing the exact formula for RMS can be difficult though. A simplification can be made in determining the
average power when information about the waveform is available. If the signal shape is known, the relationship
between RMS value and, for instance, the peak value of the RF signal is also known. It thus enables a
measurement based on measuring peak voltage rather than measuring the RMS voltage. To calculate the RMS
value (and therewith the average power), the measured peak voltage is translated into an RMS voltage based on
the waveform characteristics. A few examples:
• Sine wave: V_RMS = V_PEAK/ √2
• Square wave: V_RMS = V_PEAK
• Saw-tooth wave: V_RMS = V_PEAK/ √3
For more complex waveforms it is not always easy to determine the exact relationship between RMS value and
peak value. A peak measurement can then become impractical. An approximation can be used for the V_RMS to
V_PEAK relationship but it can result in a less accurate average power estimate.
Depending on the detection mechanism, power detectors may produce a slightly different output signal in
response to the earlier mentioned waveforms, even though the average power level of these signals are the
same. This error is due to the fact that not all power detectors strictly implement the definition for signal power,
being the root mean square (RMS) of the signal. To cover for the systematic error in the output response of a
detector, calibration can be used. After calibration a look-up table corrects for the error. Multiple look-up tables
can be created for different modulation schemes.
Types of RF Detectors
This section provides an overview of detectors based on their detection principle. Detectors that will be discussed
are:
• Peak Detectors
• LOG Amp Detectors
• RMS Detectors
Peak Detectors
A peak detector is one of the simplest types of detectors. According to the naming, the peak detector “stores” the
highest value arising in a certain time window. However, usually a peak detector is used with a relative long
holding time when compared to the carrier frequency and a relative short holding time with respect to the
envelope frequency. In this way a peak detector is used as AM demodulator or envelope tracker (Figure 47).
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