Measuring RF Power Sensor Nonlinearity

Measuring RF Power Sensor Nonlinearity  RF power sensor linearity is a commonly misunderstood topic. To obtain the most accurate power measurements, though, you need to understand what linearity is, the sources of nonlinearity, and how to measure the linearity of your RF power sensors.
 
Types of RF power sensors

There are three main types of RF power sensors:
• Diode sensors have the fastest response times (microseconds) and the largest dynamic range (-70 to +20 dBm), but have the worst linearity specs. Nonlinearity ranges from 1.5% to 5%, depending on design. They are best used for making peak power measurements and very wide dynamic range measurements.
• Thermoelectric sensors have response times in the millisecond range and typically a 50 dBm dynamic range (-30 dBm to +20 dBm). Their nonlinearity is negligible over most of their range, but may be up to 3% at the top end of the range. They are best used for making true average power measurements.
• Thermistor sensors are the most accurate and most linear of the three RF power sensor types. Typically, the nonlinearity of a thermistor RF power sensor is 0.1%. This makes them ideal for use as transfer standards.

What is linearity?
A perfectly linear RF power sensor is one whose output varies in direct proportion to a change in input power. That is to say the output voltage of a perfectly linear RF power sensor will double when the input power is doubled. The linearity specification describes the extent to which a sensor's actual response can vary from the ideal response.

RF power sensors exhibit two types of nonlinear behavior:
• Ranging nonlinearity is a symptom of multi-path sensors, which effectively combine a number of sensors with different sensitivities.
• Design-related nonlinearity is caused by either a diode sensor being operated over a wide range without multiple paths, or by nonlinearities in the thermopile and other thermal responses of thermoelectric bolometer sensors.  These tend to be related to some exponent applied to the power input, but probably not exactly the square.

The nonlinearity of an RF power sensor is a combination of both types on nonlinearity, and when you measure the nonlinearity of a sensor, your measurements will include both types of non-linear behavior.  This chart shows a linear response of the two different kinds of nonlinearity. Both start off with k=1.0, but degrade as power increases.

 
The square response introduces error proportional to the square of power, and therefore stays pretty good for the first few decades (data goes from -30 to +30 dBm). 
The range response changes slope every decade, the way a ranging meter could.  A linearity test will see both types of nonlinearity, and the actual response may look something like a combination of both responses.
 

Compensating for nonlinearity
The most common way to compensate for RF power sensor nonlinearity is to measure the nonlinearity over the power range of the sensor and then build a lookup table. These values are then input to a power meter, which then uses them to correct for nonlinearity by retrieving a correction value from the table based on the input power level. The meter then adjusts the measured value and displays the corrected value.

Measuring nonlinearity
There are several methods that you can use to measure RF power sensor nonlinearity, including:
• Direct comparison to an RF thermistor standard such as the TEGAM M1130A.
• Control the input power level to the RF sensor with a highly accurate RF source such as the Fluke 9640A.
• Use a variable attenuator such as the Agilent 84904K with a 11713B switch driver to precisely adjust signal level.
• Use a vector network analyzer like the Agilent N5244A PNA-X.

Each of these methods typically uses a test frequency of 50 MHz, and while each method is reliable, there are some tradeoffs. These include equipment specifications, reusability, and cost.

We feel that direct comparison to an RF thermistor standard, such as the TEGAM M1130A is the best approach. The TEGAM M1130A has a linearity accuracy of 0.004 dB, and will by far yield the most accurate results.

By contrast, the Fluke 9640A has 0.05 dB accuracy to 128 MHz with 0.02 dB attenuation accuracy to 55 dB, and the accuracy of variable attenuators is even worse. The accuracy of the Agilent 84904, for example, is 0.12 dB. Attenuators can be characterized at a national lab like NPL to achieve an accuracy of around 0.001 dB, but these characterizations can be expensive and require a lot of time to complete.

Using a vector network analyzer is the least appealing option. VNA receiver amplitude accuracy is only about 0.05 dB, and VNAs have output power limitations.