Radio frequency (RF) circuit elements that are traditionally considered to be linear frequently exhibit nonlinear properties that affect the intended operation of many other RF systems. Devices such as RF connectors, antennas, attenuators, resistors, and dissimilar metal junctions generate nonlinear distortion that degrades primary RF system performance. The communications industry is greatly affected by these unintended and unexpected nonlinear distortions. The high transmit power and tight channel spacing of the communication channel makes communications very susceptible to nonlinear distortion.

To minimize nonlinear distortion in RF systems, specialized circuits are required to measure the low-level nonlinear distortions created from traditionally linear devices, i.e., connectors, cables, antennas, etc. Measuring the low-level nonlinear distortion is a difficult problem. The measurement system requires the use of high-power probe signals and the capability to measure very weak nonlinear distortions. Measuring the weak nonlinear distortion becomes increasingly difficult in the presence of higher-power probe signals, as the high-power probe signal generates distortion products in the measurement system.

Measurement Requirements

Nonlinearities in RF and microwave systems can take many forms. Historically, nonlinearities are found in circuit elements such as diodes, transistors, amplifiers, mixers, and others. In addition, nonlinearities have been found in other circuit components and are generated by different mechanisms.

One of the less common nonlinear mechanisms is passive intermodulation (PIM) distortion, which occurs in antennas, cables, connectors, metal-to-metal junctions, and various components. A recent development has led to the exploitation of nonlinearities in electronic circuits to detect and track nonlinear targets.

Circuit elements exhibit nonlinear properties either by design or by consequence. By design,P-N junctions, such as diodes, are inherently nonlinear, and this property is exploited for their use in frequency mixers, which are used to up-convert or down-convert signals from one frequency to another.

The operation of mixing two signals together to create a new frequency is a nonlinear operation. By consequence, many RF and microwave circuit elements exhibit unintended nonlinear properties.

An example is the RF amplifier. Amplifiers are intended to operate linearly, boosting the input signal without creating extraneous frequencies at the output. In practice, creating a linear amplifier is not possible and additional frequency content is generated that distorts the desired signal. Much research has been done to linearize amplifiers. The unintended frequency content generated by the nonlinear properties of the amplifier interferes with other radar and communication systems, as well as affects the sensitivity of the receiver.

There are other nonlinear effects that are subtler and do not manifest as often. Among these is PIM, which is observed when high-power signals interact with components that are weakly nonlinear. Such components do not exhibit measurable nonlinear distortion under normal conditions. In communication systems, the PIM produced can fall close to the fundamental band and interfere with adjacent communication channels. To combat this, much research has gone into linearizing communication systems. For close-in intermodulation distortion (IMD), the frequency separation between the fundamental signal and PIM is too small to effectively filter out. Additionally, the communication channels change frequency quickly to accommodate multiple users. So, adaptable filters with large Q values would be needed; however, re-configurable, high Q filters do not exist. For this reason, adaptive techniques are used to predict and cancel the nonlinearities. Such techniques include predistortion, feedforward linearization, channel equalization, etc.

Measuring weakly nonlinear RF circuit components requires specialized RF hardware, which itself must be highly linear and devoid of any self-generated nonlinearities. If the measurement system is not highly linear, the measurements will reflect the distortions caused by the test hardware in addition to the device under test (DUT).

Commercially available high-dynamic-range PIM measurement systems are accessible today. These systems are typically designed for specific frequencies, usually around the cell band. They use a two-tone test setup and achieve up to 170 dBc of dynamic range using high Q filters that are fixed in frequency, but lack frequency agility. A commercially available nonlinear vector network analyzer, PNA-X, demonstrates far more flexibility than the fixed frequency PIM testing systems, and has the ability to vary tone spacings and tone amplitudes. The PNA-X system also tracks intermodulation (IM) products and harmonics, keeping track of all the nonlinear terms; however, it lacks the dynamic range necessary to measure nonlinear distortion from weakly nonlinear devices, as they are specified to generate harmonics lower than 60 dBc.

An alternate approach to measuring low-level nonlinear distortion from weakly nonlinear targets uses the second harmonic to characterize the non-linearities of passive RF circuit elements. The measurement system achieves the high dynamic range, of the order of 175 dBc, necessary to measure weakly nonlinear devices while covering a 20% bandwidth, something the PNA-X and other commercially available systems cannot accomplish. The measurement system is also low-complexity, not requiring complicated feedforward cancellation circuits.

Creating a High-Dynamic-Range Harmonic Measurement System

To measure harmonics generated by devices that are not traditionally nonlinear, a high-dynamic-range (DR) measurement system must be developed. The measurement system must create a highly linear probe signal and must have the ability to measure very weak nonlinear signals in the presence of the large fundamental probe signal.

There are two important aspects of designing a high-DR harmonic measurement system: the use of a high-DR receiver to measure the weak nonlinear signals in the presence of the highpower probe signal, and generation of a highly linear probe signal used to probe a DUT. Both the receiver and probe signal generator have their unique problems that must be addressed to generate high-fidelity, linearized signals.

Figure 1. Block diagram of the linear/nonlinear measurement system with specific test locations.

The measurement system was developed to measure second harmonic responses from weakly nonlinear targets. The system also collects data on the linear, fundamental responses from DUTs. The system was designed to measure both the pass-through and reflected linear and second harmonic response. This allows for full characterization of devices. The linear frequency range spans 800 to 1000 MHz and the second harmonic frequency range is 1600 to 2000 MHz. A block diagram of the measurement system is shown in Figure 1. The second diplexer is flipped to give the harmonics traveling in the reverse direction a path to a 50-| termination. Wherever possible, all inputs and outputs are terminated in 50 | at both the fundamental frequency and second harmonic.

A National Instruments (NI) PXI-5651 signal generator was used to create the probe signal. Next, Mini-Circuits RBF-272 diplexers were used in a low-pass configurations to linearize the probe signal and filter out any second harmonic generated by the signal generator. To boost the power of the probe signal, a Mini-Circuits power amplifier (PA) was used. The probe signal is amplified to 10 W (+40 dBm). The power amplifier is a nonlinear device and generates significant harmonics that need to be filtered. The NI chassis and RF components are shown in Figure 2.

Figure 2. The Nl chassis with computer, signal generator, and spectrum analyzer.

Since the fundamental frequency power is at 10 W, high-power custom diplexers from Reactel were used. The high-power diplexers are rated up to 100 W continuous wave input power. They are cavity diplexers that provide greater than 80 dB of rejection in the stop band. The passband attenuation is less than 0.4 dB. In addition to the diplexers, an isolator is used to isolate the power amplifier output from the DUT and avoid mismatches. The insertion loss of the isolator is 0.2 dB; thus, the power delivered to the DUT was approximately +39 dBm.

Test results from a single diplexer showed the diplexers’ ability to pass the fundamental frequencies, from 800 to 1000 MHz, and attenuate the second harmonics, from 1600 to 2000 MHz.

One cavity diplexer attenuates all harmonics, from 1600 to 2000 MHz, by at least 80 dB with less than 0.4 dB attenuation at the fundamental frequencies, from 800 to 1000 MHz.

The high-frequency path of the diplexer was also tested. Again, the diplexer attenuates the unwanted fundamental frequencies (here it is from 800 to 1000 MHz) by more than 80 dB and it passes the desired harmonic frequencies, 1600 to 2000 MHz, with less than 0.4 dB of loss. Since the diplexers have very little loss in the pass band, they do not absorb a significant amount of pass band energy.

The receiver hardware is straightforward. The probe signal, at the fundamental frequency, is separated from the second harmonic using another high-power diplexer. The spectrum analyzer has an 80-dBc dynamic range; coupling this with the 80-dB of loss provided by the Reactel diplexer yields a system dynamic range of over 200-dBc; however, the theoretical 200-dBc dynamic range is unachievable, as in practice, the system would be noise-limited before 200-dBc can be achieved. The noise floor of the receiver is measured to be less than 135 dBm. With the probe signal measured to be greater than 40 dBm and the noise floor below 135 dBm, the system's dynamic range is estimated to be greater than 175 dB.

System Test Results

Figure 3. Devices tested for second harmonic characterization.

The high-DR measurement system was used to measure the second harmonic response from a variety of circuit elements. The passive devices tested are shown in Figure 3. The two-port devices were tested for their input and output harmonic generation while the one-port devices could only be tested for their reflected harmonic generation.

Since the spectrum analyzer has one input port, the fundamental and second harmonic at the output of the DUT must be measured via two separate measurements. Therefore, the loading conditions of the two measurements are slightly different. The spectrum analyzer is matched to 50 W throughout the bands of interest with an input reflection coefficient of less than 20 dB, which provides a 99% power transfer. The differences between the loading conditions for the fundamental and second harmonic measurements is therefore expected to be negligible compared to using a 50 W termination.


As the frequency spectrum gets more crowded and the demand for wireless communication increases, nonlinear distortions generated by passive elements become more relevant. Commercially available nonlinear measurement systems are expensive and either lack the dynamic range needed to make the sensitive measurements, or are fixed in frequency and do not provide the flexibility required. Robust feed-forward systems have been constructed that provide both the flexibility and dynamic range needed to make the sensitive measurements, but these systems are complex and require iterative tuning and optimization algorithms.

The alternate method for characterizing nonlinear distortion from weakly nonlinear devices uses absorptive diplexers to separate the harmonic response from the high-power probe signal, thus increasing the system's dynamic range. The method is also capable of measuring the reflected harmonic from devices. The method is relatively simple to implement and it is cost-effective for measuring weak nonlinear responses of circuit elements.

The method demonstrated the capability of achieving 175-dBc dynamic range over a 22% bandwidth. The system is capable of producing over 10W (+40 dBm) of probe signal power while measuring second harmonics generated by a DUT as low as 135 dBm, resulting in the 175 dBc dynamic range. These passive RF circuit elements are not traditionally thought to exhibit nonlinearities, which require a high-DR nonlinear measurement system.

This work was done by Ram M. Narayanan of Penn State University; Kyle A. Gallagher, Anthony F. Martone, and Kelly D. Sherbondy of the US Army Research Laboratory Sensors Directorate; and Gregory J. Maz-zaro of The Citadel. For more information, visit the Army Research Lab Sensors Directorate here .

Aerospace & Defense Technology Magazine

This article first appeared in the February, 2019 issue of Aerospace & Defense Technology Magazine.

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