Jonathan R. Wilkerson

Electro-Thermal Theory of Intermodulation Distortion in Lossy Microwave Components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.

Distributed Passive Intermodulation Distortion on Transmission Lines

A theoretical treatment of distributed electro-thermally induced intermodulation distortion is developed for microstrip transmission lines. The growth of passive intermodulation distortion (PIM) along the length of a line is derived accounting for both loss and electrical dispersion. PIM dependencies on width, length, thickness, and substrate parameters are analyzed leading to design guidelines for low distortion lines. Single metal silver transmission lines are fabricated on sapphire and fused-quartz substrates to isolate the electro-thermal effect and validate the model. Electro-thermal PIM is measured in a two-tone test with tone separation ranging from 4 Hz to 10 kHz.

Automated Broadband High-Dynamic-Range Nonlinear Distortion Measurement System

This paper presents an intermodulation distortion measurement system based on automated feedforward cancellation that achieves 113 dB of broadband spurious-free dynamic range for discrete tone separations down to 100 Hz. For 1-Hz tone separation, the dynamic range is 106 dB, limited by carrier phase noise. A single-tone cancellation formula is developed requiring only the power of the probing signal and the power of the combined probe and cancellation signal so that the phase shift required for cancellation can be predicted. The technique is applied to a two-path feedforward cancellation system in a bridge configuration. The effects of reflected signals and of group delay on system performance is discussed. Spurious frequency content and interchannel coupling are analyzed with respect to system linearity. Feedforward cancellation and consideration of electromagnetic radiation coupling and reverse-wave isolation effects extends the dynamic range of spectrum and vector analyzers by at least 40 dB. Application of the technique to the measurement of correlated and uncorrelated nonlinear distortion of an amplified wideband code-division multiple-access signal is presented.

Electro-Thermal Passive Intermodulation Distortion in Microwave Attenuators

This paper explores the generation of passive intermodulation distortion products through the self heating of resistive elements in a microwave attenuator. A compact electrothermal resistor model requiring only two physical parameters is developed for platinum resistors and applied to a resistive attenuator pi network to predict electrothermal PIM. The electrothermal model is verified by comparing measured and predicted results when the attenuator is excited by a two tone signal at 400MHz with tone spacing from 1 to 100 Hz

Passive Intermodulation Distortion in Antennas

An analytic formulation of passive intermodulation distortion (PIM) in antennas is presented for PIM introduced by electro-thermal modulation of conductivity by current-related losses. A silver rectangular patch antenna was fabricated using a sapphire substrate isolating the thermal process from other possible sources. Two-tone testing at 990 MHz using a sweep of the tone separation from 3 Hz to 100 kHz is reported. Both transmitted and reflected PIM are characterized using a high dynamic range two-tone test system incorporating an analog canceler achieving a dynamic range of 125 dB at 1-Hz tone separation for reflection measurements, and 100 dB at 10-Hz tone separation for transmission measurements with each tone set to 32.3 dBm.

Acoustic-RF anechoic chamber construction and evaluation

The use of sound as a means to gather information about our environment has been developed with limited scope over the past several decades. The primary application of this technology has been ultrasound and ultrasonic ranging. Recent developments in nonlinear acoustics have proven that two-tone measurements and directional high frequency parametric arrays can extract much more information about the size, shape, and density of objects under inspection. However, acoustic measurements are difficult to make in the laboratory environment due to excessive ambient noise. For these reasons, the Electronics Research Laboratory at NC State University has constructed an acoustic-RF anechoic chamber as a means to make these measurements and further research in nonlinear acoustics and acoustic detection and imaging.

Why it is so hard to find small radio frequency signals in the presence of large signals

The essence of radar, radio and wireless sensor engineering is extracting small information-bearing signals. This is notoriously difficult and engineers compensate by transmitting high power signals, reducing range, and spacing wireless systems in frequency and time. New understandings of passive intermodulation distortion, thermal effects, time-frequency effects, and noise are presented. It is seen that the familiar frequency-domain-based abstractions have missed important underlying physics. Through greater understanding, RF engineers can develop microwave systems with far lower levels of distortion and noise.

Wideband high dynamic range distortion measurement

This paper presents an intermodulation distortion measurement system based on automated feedfoward cancellation that achieves 95 dB of broadband dynamic range. A single tone cancellation formula is developed requiring only the power of the probing signal and the power of the combined probe and cancellation signal to predict the required phase shift for cancellation. This formula is applied to a two path feedfoward cancellation system, combined with the DUT probe path in a bridge configuration. The dynamic range and cancellation capabilities of this system are confirmed by measuring the passive intermodulation distortion generated by a low PIM microwave chip termination. The cancellation method extends the intermodulation distortion measurement dynamic range by at least 20 dB.

Investigation of close-in passive intermodulation distortion on antennas

Passive intermodulation distortion (PIM) generated on antennas is experimentally investigated and shown to agree with calculations based on an electro-thermal origin. Two-tone testing is used in the investigations with tone spacings ranging from 3 Hz to 100 kHz. The two-tone measurement system has a minimum spurious-free dynamic range of 125 dB at 3 Hz tone separation. Results show that at least some of the PIM generated by an antenna is due to electro-thermal effects but it is apparent that there are sources of PIM that cannot be described by electro-thermal effects alone.