Power is proportional to the square of voltage or current, so it really shouldn’t be too difficult to measure. Indeed, thermocouple- and thermistor-based power meters measure the true average power of RF signals regardless of their distortion, modulation, or duty cycle.
However, the increasing use of complex digital modulation requires a better understanding of the statistical distribution of power levels within the overall signal. An average power measurement may be very accurate, but it doesn’t provide sufficient information about the signal detail that is important to the correct operation of modern communications systems.
There are three main ways in which digitally modulated signals have affected power meter development. First, digital modulation is fast—whether spread spectrum code division multiple access (CDMA) or frequency hopping time division multiple access (TDMA). In both cases, a fast video bandwidth is required or the sampled sensor reading cannot accurately represent the power signal. Video bandwidth, or simply sensor bandwidth, is the modulation frequency at which the sensor output is down 3 dB. The actual RF bandwidth of the sensor typically is from 10 to 40 GHz compared to the video bandwidth that ranges from a few kilohertz to 100 MHz.
Commenting on this point, Ian Messer, product manager at Hewlett-Packard, said, “Although the measurement of average power will continue to dominate the requirements of power meters and sensors, the development of new communications formats will place new demands on power meters. For example, wideband CDMA (W-CDMA) will require more statistical analysis, and the high crest factors (peak-to-average ratio) inherent in W-CDMA signals require power sensors capable of measuring high instantaneous power levels.”
The second factor is the growing need to describe these complex signals statistically. At the 1999 Wireless Symposium, Ben Zarlingo of Hewlett-Packard, chairman of the Test and Measurement sessions, discussed the greatly increased use of complementary cumulative distribution functions (CCDFs) to describe W-CDMA signals. He said that during the 1998 symposium the term was seldom referred to, but this year three papers featured it.
And the third factor is sensitivity. Specifically referring to W-CDMA, Steve Stanton, product marketing manager for the wireless communications test business unit at Tektronix, said, “The broadband noise characteristics of digitally modulated signals will drive measurements to lower power levels with greater dynamic range.” When received power levels are considered along with transmitter power variations, measurement dynamic range exceeds that of most diode sensors.
The trend among power-meter manufacturers is to use high video bandwidth diode sensors to measure digitally modulated signals. Many meters acquire samples that represent instantaneous power and can be averaged, analyzed statistically, or displayed in an oscilloscope-like power-vs-time waveform. Meters with built-in graphic displays provide a detailed view of the power waveform as well as alphanumeric measurement results. One implication of high-speed power sampling is the need for fast digital signal processing.
Given a diode sensor that has sufficient video bandwidth to follow fast pulsed power, several manufacturers sample the diode output and apply the relevant correction factor before averaging. According to the Boonton 4400A power meter brochure, each individual sample is converted to power before averaging. For more information on power sensors, see the sidebar accompanying this article.
A variation of the process breaks the measurement range into many bins of contiguous small ranges and averages the readings within each bin separately. Then, at the end of the measurement time, the relevant correction factors are applied to the bins, and all the measurements are averaged together. This approach is used by Giga-tronics and can be very fast because it reduces data processing.
Measuring Communications Signals
Statistical analysis of acquired data is becoming an expected feature of RF power meters. Describing noise-like signals statistically characterizes them more fully than an average power measurement. If you can be certain that the same power distribution has been applied throughout a series of tests, the results should be more consistent.
Figure 1
is a CCDF plot generated by an HP89441A Vector Signal Analyzer. The 0-dB label at the left edge of the graph corresponds to the average signal power. The X axis then shows peak power above average. The ordinate and abscissa of a point on the CCDF curve represent the percentage of the time that the signal power is at or above the X-axis value. CCDF plots illustrate the effects of distortion and gain, for example, on amplified signals with complex modulation.
Boonton’s Model 4500A develops a histogram with 4,096 discrete power levels. Associated with each histogram bin is a 31-bit counter. This means that over 2,100,000,000 samples can be accumulated in each bin, allowing very infrequent events to be acquired over long time intervals. Consequently, statistical analysis will be based upon very representative data.
Another distinguishing feature of modern meters is the signal processing prowess. In addition to careful ordering of acquisition, correction, and averaging, some meters use random, repetitive, and direct sampling methods. Random sampling may undersample the power waveform, but because any correlation between the sampling clock and the signal frequency has been destroyed in the sampling process, aliasing does not occur.
“To measure the maximum available dynamic range, a sensor and a meter must have bandwidth high enough to accurately track signal amplitude variations in the range of the sensor above -20 dBm,” commented Steve Reyes, marketing manager at Giga-tronics. He continued, “The Model 8650A provides a 20 MHz sample rate for CW measurements and a randomly varied sample rate of 2.5 to 5 MS/s for modulated signals. The random sample rate allows an undersampled condition and minimizes aliasing.”
In a power meter used for sampling CDMA waveform power, the requirement is to acquire statistically independent samples, not to reconstruct the original waveform. The samples acquired via random sampling accomplish this goal.
Manufacturers not applying random sampling rely upon an inherent lack of correlation between the source and the sample clock to avoid aliasing. Were aliasing to occur in a power meter, its effect would distort the average power reading because all parts of the input waveform would not be represented equally in the sampled data.
For TDMA signals, most meters use direct or repetitive sampling because they need to derive timing information about the width of the RF bursts. If the signal is sufficiently repetitive, then repetitive or equivalent time sampling will provide high time resolution at low cost. Otherwise, direct sampling must be used at a high rate.
“Providing the capability to identify the start of a burst and lock to the signal results in an automatic time gate setting for measuring total average power between the 3-dB points of the burst,” commented Mr. Reyes. Average pulse power traditionally has been measured by finding the duty cycle of the pulse and applying that to the overall average power reading. This method will be in error if the edges of the pulse are not rectangular.
Digital power meters also may produce incorrect pulse power readings if they are incorrectly synchronized. If averaging of accumulated samples is done periodically, it is possible for successive averages to include different portions of the pulse if the meter averaging is not aligned to the pulse repetition rate. Whether a meter is relying upon successive cycles of the measured waveform or can compute power on a single-shot basis makes a big difference to how well it suits an application.
One reason that manufacturers provide so many types of power sensors was explained by Steve Stanton. “The Tektronix/Rohde & Schwarz NRV-Z31 Power Sensor measures the peak envelope power in TDMA radio systems—for example, GSM, DECT, and PCS1900. This tailored design suppresses envelope overshoots permitted by the relevant standards, allowing accurate measurement of the envelope peak.”
As an example of the kinds of diode sensors that are available, consider the Giga-tronics range of sensors. It includes models designed for continuous wave (CW) signals, pulse modulation with >350-ns pulse width, and three general-purpose detectors: 40-kHz or 1.5-MHz video bandwidths with an 87-dB dynamic range and 10- MHz bandwidth with an 80-dB range.
Other manufacturers offer similar sensor capabilities. Wide dynamic range up to 90 dB adds to user convenience and removes range-dependent errors by eliminating the need to change ranges.
Other Types of Power Measurements
Power meters are used in a variety of applications, not just in measuring digitally modulated communications signals. High-definition television and cable TV are areas where signals are amplified and distributed widely, so it is important to know the power levels at different points in the system.
Bird Electronic produces power meters used in the semiconductor industry to measure RF levels in manufacturing processes. These meters typically deal with considerably higher power levels than sensitive communications signal meters. They use couplers to sample the large signal. The much smaller sample then is applied to the actual sensor and measured.
Power measurement is but one function of combined counter/power meter/instruments and dedicated transmitter analyzers. According to Steve Gledhill, marketing communications manager at IFR, “The Model 3410A Hand-Held Power Meter incorporates a 2.6-GHz frequency counter as well as a 2.6-GHz power meter. It is aimed at field measurements on microwave point-to-point links where testing is carried out at the top of the tower.
“The Model 2310 TETRA Signal Analyzer has a digital IF, low-noise receiver and local oscillator, and high linearity to meet the requirements of design proving and conformance testing,” he continued. “As well as transmitter power, it measures power profile, adjacent channel power, power in a nonactive slot, and frequency and modulation accuracy.”
If you are shopping for a new RF power meter, make sure you understand the range of applications to which it will be applied. Each application has its own implications that will help you narrow the choices among analog or digital technology, peak or average reading meters, direct coupling or the need for attenuation, statistical analysis, and thermocouple, diode, or thermistor sensors. Beyond these decisions, multipurpose instruments may give you the opportunity to solve many related measurement problems conveniently, in a single product.
Additional Resources
“Fundamentals of RF and Microwave Power Measurements,” Application Note 64-1A, Hewlett-Packard, 1998.
“Power Measurement Techniques for Modulated Signals,” Application Note, Giga-tronics.
“RF Peak Power Measurement,” Product Brochure , Boonton Electronics, 1998.
Sidebar
Historically, thermocouples were one of the first sensors to be used. They produce such a small output voltage that wide dynamic range and high accuracy have only recently become available at a reasonable cost. Very low-level signal processing involves chopper amplifiers, averaging, filtering, and much attention to thermal effects. However, when these considerations are all addressed, the thermocouple sensor power meter is a truly universal instrument. Voltage out is proportional to power in because the sensor inherently has a square law transfer function. The dynamic range is about 50 dB from -30 dBm to +20 dBm.
Very small thermocouple sensors may have a thermal time constant as small as 100 µs, the time required to reach 63% of the final response to a step input. But depending upon the range (sensitivity) and the amount of averaging that is required to reduce noise, the meter’s response time may be a few tens of milliseconds to several seconds.
To improve response time, Anritsu developed high-output MA242XA Series thermopile-based sensors. A thermopile comprises many series-connected thermocouples. A higher output requires less signal conditioning and allows 100× faster measurement rates compared to conventional thermocouple-based meters.
Thermocouples actually sense the heat dissipation caused by the applied RF power. They give the correct average power reading for any mix of CW signals or switched signals, regardless of wave shape, distortion, or harmonics. A peak reading can be obtained, but only for a slowly changing signal.
Most thermocouple meters operate open-loop which means that their accuracy is precisely known only at the calibration points. This is one reason that their accuracy generally is not considered to be as good as that of thermistor-based meters.
Thermistors are semiconductor devices with a negative temperature coefficient of resistance. The devices are quite nonlinear and typically used in a bridge circuit.
As the bridge becomes unbalanced because applied RF power has caused a thermistor to change its resistance, a compensating DC or low-frequency current is applied to restore the thermocouple to its original operating point. The amount of DC power required is a measure of the RF power initially applied. The technique is called DC substitution. The measurement range typically is from -20 dBm to +10 dBm.
Because the compensating DC power can be measured very accurately and the bridge balance maintained precisely, thermistor meters can be used as transfer standards. The U.S. National Institute for Standards and Technology (NIST) accepts thermistor sensors as an accurate means of transferring power-measurement parameters within its measurement services program.
RF power sensors are incorporated into input circuits designed to maintain a low standing wave ratio (SWR) over a wide frequency range. This means that the circuit appears to the input RF as a pure resistance. Thermistors respond directly to the RF current flowing through them. Thermocouples sense the temperature rise in a very closely coupled resistor through which the RF current flows. Both thermocouples and thermistors are relatively slow to respond to a step change in the power level.
In contrast, diodes rectify the RF voltage appearing across them. Because of the nonlinear relationship between low-level voltage and current in a diode, the rectified output follows a square law curve. This means that for small RF signals from -70 dBm to -20 dBm, diodes measure power directly.
The development of RF power-sensing diodes has received a great deal of attention This has resulted in diodes with increased dynamic range and high video bandwidth—the speed with which a sensor can follow a change in RF power level. HP claims a dynamic range of more than 90 dB (-70 dBm to +20 dBm) for the E-Series Diode Power Sensors and a 100-MHz video bandwidth for peak power sensors.
The diodes described here are not simple 1N4004 rectifier diodes. Highly specialized Schottky and, more recently, planar-doped barrier diodes have been designed with an accurate square law region over a large dynamic range. Most manufacturers claim a range from about -70 dBm to -20 dBm for true square law operation. Some sensors use GaAs rather than silicon.
The terminology may be confusing. The region above -20 dBm can be referred to as nonlinear because the relationship between log (input power) and detected output voltage is not linear. From -70 dBm to -20 dBm, it is linear. However, it is more common to refer to the region above -20 dBm as the linear region because output voltage is linearly proportional to input voltage.
Actually, there are three regions: square law and linear with a transition region between them extending from -20 dBm to approximately 0 dBm. See Figures 2a and 2b.
For power levels above -20 dBm, correction factors are required to extend square law behavior. The resulting corrected device really does have a very large dynamic range, but cannot be used for other than CW measurements when combined with a simple, average-reading meter. A two-tone example illustrates this point.
Two-Tone Example
Consider the case of two signals 1 MHz apart (at frequencies F and F + 1 MHz), each at a power level of 0 dBm (1 mW). Figure 3 shows the modulation envelope, which for F>> 1 MHz will have peaks repeating with a 1 MHz frequency and a peak amplitude twice that of the input waveforms. Figure 4 represents the sin2 envelope of the corresponding power signal. A thermocouple responds to power regardless of modulation, so it will measure 2 mW. A diode sensor operating in the square law region also will respond to the resultant of the incident waveforms. In this case, each signal has an amplitude across 50 W of 223.6 mV rms or for sine waves 316.2 mV peak. The peak amplitude of the envelope is twice that of the original waveforms, 632.4 mV, and its rms value is 632.4/The typical power range of a thermocouple sensor is -30 dBm to +20 dBm, so it could be used directly to measure the signals in the example—2 mW is +3 dBm. However, 3 dBm is outside a diode sensor’s -70 dBm to -20 dBm square law range. Either the sensor has to be suitably corrected to read the higher power level or an attenuator must be used.
For some corrected diode power meters, correction is done after the average power is calculated. A CW sine-wave signal with an rms amplitude of 316.2 mV, or 447.2-mVpeak, produces 2 mW of power in a 50-W load. As a result, a manufacturer could construct a voltage-to-power correction-factor table that ensured the meter read 2 mW whenever the diode input was 447.2 mV peak. Because a CW signal is being used, it doesn’t matter that the diode output is averaged by the slow meter response before the correction factor is applied.
In the two-tone example, the peak voltage of the 0.5-MHz modulated envelope is 632.4 mV, twice the peak of an individual signal. If the diode output corresponding to this peak is averaged with other diode outputs as the power level varies and a correction factor applied to that averaged value, the answer will be wrong. Above -20 dBm, different correction factors are required. A power measurement cannot be corrected after the sensor readings have been averaged.
By changing the order of correcting and averaging, measuring complex power waveforms has become routine for many power meters. For example, the Giga-tronics Models 8540C and 8560A apply correction factors before averaging.
In a discussion about power meter accuracy, Ray Beers, product marketing manager at Anritsu, commented that diode square-law correction in the linear region depends upon the applied RF power waveform being sinusoidal. For power levels above -20 dBm, diode correction factors cannot account for a distorted RF waveform regardless of when averaging is done.
Some sensors are made with integral attenuators. The difference between an integral or external 30-dB attenuator which would shift a diode’s square law region to
-40 dBm to +10 dBm is calibration accuracy. The output from a sensor is digitized and corrected by calibration values stored in EEPROMs on-board the sensor package.
You may have to enter the frequency range of interest into the power meter, but you don’t need to enter calibration data. The meter reading automatically compensates for frequency-dependent dips and peaks as well as temperature changes.
Anritsu’s ML2430A Series power meters allow you to develop a calibration factor table that accounts for frequency-dependent nonlinearities throughout the test setup. Correction factors for the assembly of antennas, couplers, cable, limiters, and switches are stored in the sensor EEPROM.
RF Power Meter Products
RF Meter With Statistics
The 4530 Series RF Power Meter makes peak and CW power measurements with up to 20-MHz video bandwidth, depending upon the sensor used. Statistical features include histograms and cumulative distribution functions for analysis of complex signal such as CDMA and high-definition TV. The effective sampling rate is up to 50 MS/s for repetitive signals and 1.25 MS/s maximum for single-shot capture. Measurement of average, maximum, and minimum power; the peak-to-average power ratio; and RF voltage and display of power vs time also are provided. GPIB and RS-232-C ports are standard; a second channel is optional. Single-channel 4531A: $3,650; dual-channel 4532A: $5,650. Boonton Electronics, (973) 386-9696.
Modulation, W, and V Meter
The Model NRVD Dual-Channel Power Meter measures average power, peak envelope power, pulse power, AM depth of modulation, and AC and DC voltage. The two channels operate independently, but their outputs also can be related to each other to derive reflection coefficient, SWR, or return loss, for example. Power from 400 pW to several kilowatts can be measured at frequencies up to 26.5 GHz depending on the type of sensor used. Features include storage of 20 instrument setups, 13 digital filters for noise suppression, and a 50-MHz, 0-dBm calibration generator. From $5,295. Tektronix, (800) 426-2200.
V-Band Power Sensor
The HP V8486A V-Band Power Sensor measures power from 50 to 75 GHz with an uncertainty from 4.4 to 7.3%. The specifications include power range from -30 dBm to +20 dBm, 1.06 maximum SWR, and <±1% linearity error from -30 dBm to +10 dBm. The sensor is compatible with EIA WR-15 waveguide and UG-385/U flanges. True average power readings are ensured by operating the modified barrier integrated diode (MBID) in its square-law region. A 50-MHz calibration port eliminates the variation encountered with different sensor/meter combinations and provides traceability to NIST. $4,495. Hewlett-Packard, (800) 452-4844, ext. 6248.
Dual-Sensor Power Meter
The single-channel ML2437A and dual-channel ML2438A Power Meters feature a graphics display panel, softkey control of menus, high-speed GPIB output of more than 600 readings/s, and compatibility with both thermocouple and diode sensors. A custom operation mode provides full control of triggering and trigger delay, sample integration time, and averaging. Three types of sensors with on-board EEPROM calibration factors complement the meters: 90-dB dynamic range diode power sensors, 60-dB range thermal power sensors, and 87-dB, high-accuracy diode sensors. Measurement to 60 GHz is possible depending upon the sensor type. ML2437A: from $3,400; ML2438A: from $4,550. Anritsu, (408) 778-2000.
Fast-Sampling Power Meter
The single- or dual-channel 8650A Series Universal Power Meters feature a 20-MS/s maximum uniform sampling rate for CW signals and a 2.5- to 5-MS/s random sampling rate for modulated signals. Random sampling minimizes aliasing effects caused by undersampling complex signals such as third-generation wideband CDMA. Statistical power measurement analysis, automatic burst measurement, time gating, and peak hold functions are provided. A range of high-frequency RF diode sensors supports power measurement up to 40 GHz with a 10-MHz video bandwidth and an 80-dB dynamic range. Single-channel: $3,310; dual-channel: $4,870. Giga-tronics, (800) 726-4442.
Rugged, High Power Meter
The Model APM-16 RF Wattmeter measures the average power of complex digitally modulated CDMA, TDMA, or frequency division multiple access as well as CW signals with an accuracy of ±4% of reading ±1% of full scale. Reflected and forward power readings with crest factors of at least 10 dB are accommodated by reversing the direction of the element. The APM-16 is battery-powered and housed in a rugged cast aluminum case and features a mirrored-scale, shock-mounted meter with scales of 25, 50, and 100. A large range of elements covers power from 1 to 1,000 W and frequency from 2 to 2,300 MHz. Call company for price. Bird Electronic, (440) 248-1200.
Meter With Power Reference
The Model PM2002 Dual-Channel Power Meter features a 10-kHz to 40-GHz frequency range and a -70 dBm to +44 dBm power range, both dependent upon the sensor used. The dynamic range is 90 dB for diode sensors and 50 dB for thermocouple sensors. The meter can emulate the HP437, HP438, and Boonton 4220A should a replacement for these instruments be required. User-selectable filter times from 0.05 to 20 s and ±99.99-dB display offset are included along with automatic zero correction. $3,600. Amplifier Research, (215) 723-8181.
Copyright 1999 Nelson Publishing Inc.
May 1999
Types of RF Power Sensors