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Ponderings on Power Measurements
Joseph L. Cahak
Copyright 2013 Sunshine Design Engineering Services
Pondering on Power
A power measurement is a scalar quantity and is a measure of power detected. These
measurements can be made a variety of ways. Most of us are familiar with the notion that voltage (volts) multiplied
by current (amps) is power (watts) and power multiplied by time is energy. At DC or low frequencies these power
measurements from the current or voltage is relatively easy and not very complicated. As we get to higher frequencies
the typical means of measuring voltage or current breakdown and are not accurate. The power measurement inaccuracies
are due to frequency response of the detectors at high frequency and also the impedance match of the detectors as
well as the instantaneous frequency response of the detector network. All power sensors are broadband sensors. They
cannot discriminate between individual signals in a multiple signal environment. These signals can add or subtract
from the total power as a combination of the power depending if the signals are in or out of phase.
Power measurement in the RF and Microwave frequency range are typically made with thermister, thermocouple or diode
based instruments. The thermister or thermocouple based power sensors are most accurate for “true” or RMS power.
True power is properly integrated (modulation envelope) over time to give the’ true’ power no matter the waveform
shape. If the signal is a CW (continuous wave) signal that does not vary in signal strength or frequency, the measurement
is relatively easy and the RMS value is easy to compute. In the case of more complicated modulated signals or complex
waveforms, computing or measuring True RMS power gets more difficult and complicated. To better understand this
we will review the methods of measuring RF Power.
Figure 1 - Power Sensor type and Range courtesy Agilent Technologies
Thermister and Thermocouple Devices
The most accurate methods of measuring True
RF power is with devices called a thermister or a thermocouple. These devices converts RF power to thermal power
(heat) and the thermal power is converted to a resistance or a voltage difference measurement that can be measured
and converted to the power measured. There are issues associated with this method of measuring RF power.
Figure 2 - Thermister Power Meter Schematic courtesy Agilent Technologies
The first issue with this method is a limited dynamic range that it will accurately measure over. Most of
the sensors in the market today that use thermister based sensors have a measurement range of -30 to +20 dBm.
Some measure higher power levels with an attached calibrated attenuator. Microprocessors and EEPROM calibration
tables are used to perform power correction for temperature and frequency response.
With RF power to
thermal conversion, there is a small time lag for the thermal response from the RF power. While this is a small
sensor with a small thermal mass in the sensor, nonetheless this equates to a small lag in the power response. This
property will affect accuracy of rapidly varying signals, and signals with complex modulation. Finally, there is
a frequency response associated with the sensor and also the impedance match of the interface to the sensor. These
responses can be calibrated and removed using a cal factor for the sensor.
Figure 3 - Thermistor temperature response courtesy Agilent Technologies
Another method of measuring power is with a diode sensor. These diode
sensors have a faster response time than thermister based sensors, but due to the diode characteristics, they have
more impedance match issues than the thermister. The diode has low impedance compared to the 50 ohm characteristic
Impedance of most RF instruments and RF networks in use today. This means that some form of matching network must
be used to improve the match into the sensor and DC isolation (blocking). These components have frequency sensitivity.
Figure 4 - Diode Power Sensor courtesy Agilent Technologies
The diode is sensitive to VSWR and is more prone to measurement error due to these issues. Another issue
is the non-linearity of the diodes. What that means is at higher power levels the diodes conduct and the current
is no longer square law proportional to the voltage of the detected signal. This has ramification with measuring
complex signal environments. Recall the power equation from voltage:
Power = V2/R = I2*R
This implies that while the diode is in the square law region the voltage output from the rectification
is directly proportional to the power in that region only. Outside that region, the power is not directly linear
Figure 5 - Universal Power Sensor Range courtesy Anritsu
Making power measurements in the quasi and linear regions of the diode response is less accurate when the
signal input is modulated with wide bandwidth signals or multiple tone signals. To make these measurements, the
instrument must have the dynamic measurement power range and the frequency response to be quantifiable, repeatable
and correctable. For the diode sensors, extensive EEPROM correction tables are used for the frequency, signal levels
and temperatures at which the power measurements will be made. In many cases these corrections are not adequate
for very wideband devices such as Ultra Wideband USB or some of the other digital modulation formats. Most sensors
have an instantaneous bandwidth that they can respond to which typically range from 10 MHz to 30 MHz for
most power sensors available on the market. This is not important for most measurement markets. With modulation
formats wider than this and higher in power than the square law region, pulsed power or sensor instantaneous bandwidth
can have varying amounts of error. Recall the comment above regarding operation above the square law region. The
trick that can be used to gain some level of better power accuracy for modulated signals with diode sensors is to
keep the power within the square law region (-70 to -20 dBm).
Figure 6 - Universal Wide Power Range Sensor courtesy Anritsu
Figure 7 - E4412/13 Sensor Architecture courtesy Agilent Technologies
Figure 8 - Sensor for E4412/13 Power Sensor courtesy Agilent Technologies
Figure 9 - Diode Sensor Error with harmonic signal present courtesy Agilent Technologies
Analog Devices has recently come out with a replacement for the Schottky diodes to measure power. The ADL6010
is a coplanar input for measuring power from 500MHz to 50GHz. It features built-in linearization for added accuracy.
One trend is communication power measurements is to use DSP (digital signal
processing) architecture to process the signals and get a better measure of power with complex formats and frequency
components. These can also provide the ability to measure the peak or envelope power and crest power on multiple
tones or modulated signal measurements. They can also offer wider bandwidths than traditional sensors. Capability
is only limited by the sampling rate, bit depth and accuracy of the ADC’s or Sigma-D samplers.
Figure 10 - DSP Power Measurement courtesy Agilent Technologies
Peak Envelope Power and Peak or Crest Power
Other RF Power measurements are
peak envelope power (PEP) and peak or crest power. These are used to measure the power of multi tone and digitally
modulated waveforms to get the instantaneous power maximum of the system. There are many instances where a power
measurement that takes the peak power value of the envelope is needed. All digitally modulated waveforms, AM and
single sideband (SSB) use this measurement. The peak measurement is also the crest power, which would be compared
to the average power to calculate the crest factor of the RF device, which is the ratio of the peak power level
above average power. These peaks can damage power amplifiers if not contained in amplitude.
or Video Bandwidth
Instantaneous or video bandwidth (VBW) is the response after rectification of
the signal and the detection circuitry response and ability to integrate the RMS power. This video modulated rectification
result is used to calculate the power. If the detection circuitry downstream of the rectification has poor frequency
response, the accuracy of the power measurement will degrade. Typical video bandwidth range is 10 MHz up to 100
MHz video or instantaneous bandwidth. The user must be aware of the signal measurement equipment requirements to
account for this signal bandwidth and to thereby ensure accurate power measurements of modulated signals. If measuring
pulsed power the Video or instantaneous bandwidth should be at least 5x the pulse repetition rate.
The quality or accuracy of the power measurement depends not only on
the power sensor calibration factors previously mentioned. Another significant source of measurement error is the
sensor impedance match and the match of the device port under test. This mismatch error is computed with the formula
Mismatch Error= 10log(1±ρgρl)2 . The + and – represent the max and minimum mismatch for the measurement mismatch
loss of power measured. ρg and ρl are the generator and load reflection coefficient.
Figure 11 - Power Mismatch Curves for Anritsu Detector courtesy Anritsu
Agilent Application Notes:
Anritsu Product or Application Notes
- 4 Steps for Making Better Power Measurements App Note 64-4D 5965-8167E
- Fundamentals of RF and Microwave Power Measurements (Part 1) 1449_1_5988-9213EN
- Fundamentals of RF and Microwave Power Measurements (Part2) 1449_2_5988-9213EN
- Fundamentals of RF and Microwave Power Measurements (Part 3) 1449_3_5988-9213EN
- Fundamentals of RF and Microwave Power Measurements (Part 4) 1449_4_5988-9213EN
- Power Measurement Basics 5965-7919E
- ML2400A Series Power Meter -15000-00004 rev C
- Accurate Power Measurements on Modern Communication Systems
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Ramona, CA 92065
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Posted October 8, 2013