The Sharp End of RF Power Measurement

It’s not only the highways that are becoming more crowded. The answer to the problems and opportunities of modern life increasingly seems to involve wireless communications. Sure, there are cell phones with their various technologies and the anticipated higher data rates that 3G will bring. But what about Bluetooth, 802.11, HomeRF, and other wireless proposals?

These communications facilities add noise to an already busy spectrum. Although some services are temporarily solving that problem by going to higher frequencies, wireless schemes still must operate within strict power limits to minimize interfering with other users.

The normal operation of wireless channels depends on tight power control. For example, excessive power-amplifier output compression will distort modulation in code division multiple access (CDMA) systems with a high peak-to-average power ratio, causing unreliable communications. Also in CDMA systems, the transmitted power from each user is remotely adjusted to ensure all channels are received at the base station with about equal powers. These types of applications rely on accurate measurement of RF power.

Seeing the Trees for the Forest

Faced with the need to measure RF power, you may not know where to start. Power meters and sensors have been available for many years, and there are many models to choose from. When wireless progress has demanded new sensor or meter technologies, they have been developed and added to the products that already existed. The result is a wide choice of meters and sensors that can easily confuse even experienced users.

You can narrow the field initially by determining whether you need to make terminated or through power measurements. Bird is the major manufacturer of through-type meters that use a coupler to redirect a small part of the total power to a measuring element. You could use a coupler with a terminating-type meter, but a Bird meter is mechanically simpler and includes the relevant calibration factors.

Most other manufacturers make terminating-type meters that appear as a 50-W load to the incident signal. You can buy high-power sensors with built-in attenuators to use with these meters, but 44 dBm (about 25 W) is a typical maximum average power. Attenuating sensors must dissipate the signal’s average power, so there is a limit to the amount of heat that can be handled in a practical-size sensor.

All types of sensors can be used with suitable attenuation to measure higher power signals, but built-in attenuators provide better accuracy because most modern sensors have an EPROM-stored table of calibration values. Sensors with integral attenuators will include the attenuator and cal factor in their calibration.

These sensors have much higher peak power ratings expressed as allowable pulse areas. For example, the Boonton type 51300 Thermocouple Sensor will handle pulse areas of 300 W-µs up to 150 W maximum. For very high power levels, it’s better to couple part of the signal to the sensor, as Bird does, rather than try to attenuate the signal. Bird average power sensors measure greater than 1 kW.

If you’ve decided you don’t require a coupler-type meter, you need to consider what type of sensor best matches your signals.

Thermal
The basic types of sensor technologies and power measurements are listed in Table 1 (below). There actually are two types of thermal sensors, thermocouple and thermistor, but thermistor sensors are almost exclusively used as power transfer standards. They don’t have a wide dynamic range but are quite accurate because of the power-balancing bridge circuitry used in thermistor meters.

Thermocouples, on the other hand, are open-loop sensors calibrated with an external power source. Most meter manufacturers provide a NIST-traceable, integral 50-MHz, 1-mW reference source. Boonton has a 1-GHz calibration source in the 4400A and 4500A Meters, and 1 GHz is optional on the Giga-tronics 8650A Meter.

Thermal sensors produce an output because of the heat generated by RF energy dissipated in a 50-W load. In response to a change in their temperature, thermistors change resistance. Thermocouples generate a small output voltage because of the Seebeck effect.

A thermocouple sensor can detect power changes from about 1 µW (-30 dBm) through 100 mW (+20 dBm). At the lower levels, many cycles of averaging will be necessary to reduce noise. Because thermocouple sensors have thermal time constants several milliseconds long, it can take as much as a few seconds for the average power reading to stabilize.

The most important feature of thermal sensors is their independence from types of modulation. Thermocouples measure power, and it doesn’t matter how the power was generated. They will average it correctly, provided the signal never falls outside of the sensor’s dynamic range.

Constant amplitude (CW) and frequency modulated (FM) or phase modulated (PM) signals always have the same amplitude and are the least challenging types of signals. The average power of a pulsed carrier waveform such as radar will be measured correctly by a thermocouple sensor. But many meters estimate pulse power by dividing the average power by duty cycle. This approach works best for well-defined pulses with fast rise and fall times.

If the edges of the pulses are slow compared to the sensor time constant, significant power may be contributed to the average reading before or after the nominal pulse period. Overshoot also contributes to the inaccuracies of measuring pulse power this way. But, if all you need to do is measure average power, regardless of the type of modulation, thermocouple sensors are accurate within their dynamic range limitations.

Diodes
Diode sensors, like thermal ones, require a separate calibration source. They operate by rectifying the RF signal, but they also behave like nonlinear resistors. Diode sensors can have very short time constants from a few microseconds to hundreds of nanoseconds and track the RF modulation envelope to give peak power readings.

The bandwidth of the sensor corresponding to its time constant is called its video or modulation bandwidth. This is not to be confused with the much larger RF bandwidth—the actual frequency of the RF signal being detected.

If a video bandwidth-reducing filter is added, a diode sensor can measure true rms average power directly from about -70 dBm to -20 dBm—the so-called square-law area. In this region, a Maclaurin expansion of the diode equation is dominated by the V² term, hence the square-law terminology. Diode sensors operating in this region measure power correctly regardless of modulation.

The amount of filtering is chosen to match the type of signal you have and the measurement speed you require. If slow, unrepeated modulation is present, you can’t make fast average power measurements. To provide one number that represents the average value of the modulation envelope may take several seconds. In most cases, modulation speed is kilohertz or megahertz, so achieving a few hundred readings/s is possible.

The problem presented by diode sensors occurs as the power level exceeds -20 dBm. Above this level, the diode curve shown in Figure 1 progressively deviates from the square law and becomes more linearly related to input power. A straight line on the log-log plot of Figure 1 indicates a constant exponential relationship. That is, a log-log plot of the equation y = x² would be a straight line with a slope of 2.

Because the diode equation also has a term that is linear in current, as the input current (power) increases, the effect is to reduce the slope of the curve gradually because the contribution from the linear term approaches that from the square-law term. For example, at a power level of +20 dBm, the diode output indicates a power level almost 14 dB too low. Of course, different manufacturers have developed different types of diodes, but the -20 dBm level generally is used as the upper cutoff of everyone’s diode sensor square-law region. Some manufacturers treat -30 dBm as the beginning of the transition region.

According to Ronald Swanson, a senior design engineer at Boonton Electronics, “We almost exclusively use dual diode detectors with one responding to the positive signal and the other to the negative. It produces a balanced circuit with twice the output voltage of a single diode that correctly measures power when even-harmonic distortion is present and gives a nearly perfect true rms output through most of its power range.”

Discussion of diode sensor linearity can be confusing because the words linear and nonlinear appear to be used interchangeably. What they mean depends on the context. In terms of power-in to voltage-out, the square-law region is the linear part of the transfer curve—here we’re talking about the straight-line relationship on the log-log plot. If you’re talking about the diode equation, the nonlinear, second-order (square-law) region is between -70 dBm and -20 dBm. Above -20 dBm, the linear term dominates.

Boldly Going Beyond -20 dBm

Why not compensate the diode to work properly above -20 dBm? This is a common approach taken to extend the dynamic range, but it causes complications. Agilent Technologies warns that the Model E4412A or E4413A Sensors only can be used for CW signals over the -70-dBm to +20-dBm dynamic range. This is because the sensor output is averaged and then compensated to read correctly on signal levels outside the square-law region.

If some of the time the power is above -20 dBm and some of the time below -20 dBm, it’s not possible to correct the output after it has been averaged. It is practical, however, to separately compensate each reading in a sampled data system. Each corrected sample then can be included in an average.

For example, Agilent’s E4416A/17A Meters provide up to a 20-MS/s sampling rate when used with E9320-type Sensors with 300-kHz to 5-MHz video bandwidths. This combination of meter and sensor measures both average and peak power from -67 to +20 dBm.

Sampled data systems with fast sensors are the key to the statistical power measurements required for modern digitally modulated communications signals. Once the modulation envelope data has been captured, it’s relatively straightforward to calculate the average, the peak, or a complete statistical power distribution.

Giga-tronics samples at a random rate between 2.5 and 5.0 MHz. Because power is a scalar quantity, the phase of a sample is unimportant. Only sample magnitude affects the power reading. So, undersampling a fast modulation envelope is as valid as oversampling a slow one. Using a random rate avoids aliasing.

The downside of random sampling is that you cannot accurately determine the shape of the modulation envelope from a single waveform. Instead, the Giga-tronics Model 8650A develops a graphical representation from successive bursts of the signal. For example, a graphical display of the modulation envelope can be helpful when setting up time gates used to define the position and duration of a pulse power measurement.

Fast diode sensor meters can trigger measurement start/stop timing on the rising and falling edges of a pulse. Separate delays can be set to exclude specific parts of the pulse and include others. Features vary with manufacturer and model, but dealing directly with pulse power is more accurate and foolproof than working with duty-cycle estimates.

Note c in Table 1 refers to the noise reduction that can be achieved by using only the video bandwidth you require and not more. This is another consideration in choosing one sensor over another.

Some meters offer user-selectable video bandwidth filtering, and other meters automatically reduce video bandwidth at lower power levels. They provide maximum bandwidth for large, fast peak excursions. Bandwidth reduction at lower levels may affect statistical measurements for low average power signals as well as limit achievable measurement rates. 
Reduced video bandwidth doesn’t affect measurement accuracy within a diode sensor’s square-law region. Power meters are optimized for measurements down to -70 dBm by narrowing the bandwidth. A wide video bandwidth increases the noise floor and decreases dynamic range. Depending on the bandwidth used, dynamic range can be reduced by up to 10 dB.

Multipath Architecture
Anritsu and Agilent have produced multipath diode sensors that combine two (Agilent E9300) or three (Anritsu MA2481A) diode/attenuator sections. See Figure 2. The idea is to split and attenuate the input signal so at least one diode/attenuator section will be operating in its square-law area. Decision-making circuitry in some meters chooses which section’s output to use according to the signal level. In this way, the average power of a wide dynamic range signal can be measured without compensating for non-square-law behavior. The sensors only are suitable for average power measurements.

The new Agilent E9320 Series of sensors uses a multipath architecture but with selectable filtering and two separate outputs. The result is a single sensor that can be used for either average or peak power measurements.

Advantages cited for multipath average power measurement include faster and lower-noise operation because a lower video bandwidth can be used: It’s not necessary to track fast modulation peaks above -20 dBm.

Agilent also claims that its two-path scheme avoids increased reflections of the test signal’s harmonics above the square-law region encountered by compensated single diodes. In addition, because several diodes are used in series in each of the diode/attenuator sections, higher peak power can be handled without damage. Competitors counter that the break points between sections cause higher noise and slower measurements at medium power-signal levels while simpler sensors do not have these problems.

But Is It Correct?

According to Giga-tronics, the eight most likely causes of power meter measurement error are the following:

• Mismatch, sensor-to-source.
• Instrumentation linearity.
• Calibration factor uncertainty.
• Sensor power linearity.
• Calibrator uncertainty.
• Calibrator-to-sensor mismatch.
• Zero error (last 15 dB of dynamic range).
• Noise (last 15 dB of dynamic range).

You can get a good idea of the values involved by carefully reading a sensor specification sheet. For example, the Anritsu standard diode sensor type MA2475A is representative of conventional diode sensors. It has a frequency range from 10 MHz to 50 GHz, -70- to +20-dBm dynamic range, and <0.004-ms (<4-µs) rise time. Sensor linearity ranges from 1.8% below 18 GHz to 3.5% closer to 50 GHz.

Similarly, voltage standing wave ratio (VSWR) varies from a maximum of <1.9:1 below 50 MHz to a minimum of <1.12:1 from 0.15 to 2 GHz and up again to <1.63:1 from 40 to 50 GHz. Lower VSWR is available in sensors that include a 3-dB attenuator. The attenuator provides better matching at the expense of 3 dB less dynamic range.

A VSWR of 1.9:1 corresponds to a reflection coefficient (G) of 0.31 while G is only 0.057 for a VSWR of 1.12:1. These values become important when combined with the reflection coefficient of the source being measured. The percent uncertainty due to mismatch is given by:

% uncertainty = 100 × [(1 ± G₁ × G₂ )² -1]      (1)

where: G₁ is the reflection coefficient of the source 
G₂ is the reflection coefficient of the sensor

For a source with a good 1.25:1 VSWR, for example, the percent uncertainty corresponding to the MA2475A Sensor between 10 MHz and 50 MHz is +7%, -6.8% of reading. That is, the error uncertainty is not symmetrical but is about 7% in this case. Between 150 MHz and 2 GHz, the uncertainty reduces to ±1.27%.

It’s easy to see that if your source does not have the low VSWR of this example and you are measuring near either end of this sensor’s frequency range, your errors will be noticeable. Some sensors have large VSWR only at one end. However, when mismatch uncertainty is combined with the other sources of error in the list, most measurements cannot be guaranteed to be better than a few percent accurate.

This may seem like a large error, but as Angus Robinson, Anritsu’s market segment manager for power meters pointed out, the error is reasonable when compared to your alternatives. “Power meters are selected in production facilities in preference to integrated radio test sets because they have much better accuracy and faster measurement speed. Typical power-meter accuracy is 4.5% over the full -60- to +20-dBm dynamic range. By contrast, a test set typically will have 12% accuracy over just a 20- or 30-dB dynamic range,” he said.

Follow your manufacturer’s recommendations for determining measurement accuracy to get the best from your equipment. For example, upon request, Giga-tronics will provide a paper describing how to calculate the relevant uncertainties by hand. Alternatively, the company has developed an Accuracy Audit program available on CD.

Summary

While it is true that there are many sensors to choose from, there is a logical process to find the one best for you. Assuming you can use a terminating meter, the sequence of questions to consider might be:

• Average or peak power?
• Type of modulation and level?
• Measurement speed?
• RF bandwidth and connector type?

Sensors have to be used with meters, so if you don’t already have a meter, you need to decide what features you require. These may include statistics, time gating, graphical display, and single- or dual-channel operation. When you have selected a meter manufacturer, you will be limited to only that manufacturer’s sensors. If you need a special meter feature, you may have to compromise on the sensor and vice versa.

Take the time to explore solutions from a few manufacturers. They all offer a number of meters and many different sensors that can address most applications. But, the detailed interaction of each meter-sensor-signal combination only can be fully understood by thorough evaluation.

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Published by EE-Evaluation Engineering
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February 2001