Creating frequency scalable nonlinear transmission line based vector network analysers

Mixers tend to be the down converter of choice in the rf domain, due mainly to their simpler local oscillator (LO) drive system and enhanced spur management advantages. At microwave and millimetre wave frequencies – where receiver compression and cost are of major concern – harmonic sampling is often used. Where the frequency band spans the rf, microwave and millimetre wave spectra, harmonic samplers and mixers can be used in tandem to optimise performance across the VNA's frequency range. Sampler based reflectometers make use of equivalent time sampling or harmonic mixing to 'time stretch' coupled versions of the waves incident on, and reflected from, a DUT, prior to digitising them. This approach results in a simplified VNA architecture with reduced cost in comparison with one employing fundamental mixing. This is a direct result of the nature of the equivalent time sampling process, in which the frequency range of the LO (or strobe) is confined to an octave, whilst its harmonics effect the down conversion of the coupled high frequency signals. The LO source required for strobing the samplers operates in a lower frequency range than that which would be required in a fundamental mixer VNA, although at the expense of increased conversion loss. The periodic nature of the incident and reflected waves allows them to be down converted using equivalent time sampling, also known as undersampling, harmonic sampling or super Nyquist sampling (see fig 1). Samples of a sinusoidal rf waveform of period Trf appear at the output of an ideal switch gated at a rate of TLO. The sampled IF waveform, VIF(t), is the product of the sinusoidal rf waveform VRF(t) and the ideal switch conductance, g(t). Fig 2 shows the low pass filtering of the IF waveform results in a 'time stretched' replica of the rf waveform. It can also be shown that gating time, Tg, has a considerable effect on the magnitude response of the ideal switch – by reducing the gating time of the switch, rf bandwidth is increased at the expense of reduced conversion efficiency. Practical implementations of samplers for VNAs have traditionally relied on Schottky diodes as switches and step recovery diodes (SRD) for pulse generation. One such implementation – a sampling circuit due to Grove – has been used extensively in a range of instruments, including microwave VNAs, sampling oscilloscopes and frequency counters. Here, a voltage pulse is used to gate Schottky diodes over a brief time interval, Tg. During this interval, the Schottky diodes are driven into conduction and charge sampling capacitors. The charge on the capacitors results in an output waveform related to the polarity and amplitude of the rf input. While SRDs make it possible to extend a VNA's rf bandwidth to 65GHz, their limited fall time and a lack of LO frequency scalability prevents their use at higher frequencies. In addition, the dynamic range of transmission measurements in an SRD based sampling VNA is limited by the lack of broadband devices for isolating test channels. These observations, coupled with the fact that such frequency dependent leakage phenomena cannot be calibrated out, impose limitations on the dynamic range of an SRD based sampling VNA. These, in turn, prevent the full characterisation of highly reflective devices, such as high pass filters, and devices where weak coupling among constituents must be measured fully as a function of frequency (such as weak crosstalk). Overcoming limitations These limitations can be overcome by making use of samplers based on nonlinear transmission lines (NLTL). NLTLs – distributed devices that support the propagation of nonlinear electrical waves – are comprised of high impedance transmission lines loaded with varactor diodes so as to form a propagation medium whose phase velocity, and thus time delay, is a function of the instantaneous voltage. For a step like waveform propagating along an NLTL, the trough of the wave travels at a faster phase velocity than the peak. This results in compression of the fall time and as a result, the formation of a steep wave front that approaches that of a shock wave. In order to extend the bandwidth of a VectorStar VNA to 110GHz, an external reflectometer was designed based on NLTL samplers and harmonic generators. The reflectometer was integrated with the VNA. The measured raw directivity of the VNA and its external reflectometer is better than 6dB across the entire frequency range. Raw directivity, coupled with a vanishing thermal gradient across the external reflectometer and LO level control, contributes to long term measurement stability. On the other hand, the measured dynamic range exceeds 100dB from 70kHz to 110GHz, making possible the characterisation of highly reflective devices and weak crosstalk. Finally, the measured LO power leakage out of the test port of the reflectometer is less than -40dBm in the LO frequency range from 5 to 10GHz. This is achieved by careful design of the LO driver circuits which are isolated from the test port by at least 65dB in the 5 to 10GHz range. LO leakage could be filtered further, since it is out of band. NLTL based reflectometers could be used to extend the frequency range of a VNA into the millimetre waves. Its small form factor and light weight make it a prime candidate for use in multiport on wafer measurements and near field scanning. In addition, the ability to locate the reflectometer close to a DUT enhances test port power and improves the VNA's raw directivity, leading to long term measurement stability. A key advantage of the miniature reflectometer is its unobtrusive nature; leaving the rf path starting in the base VNA and leading to the test port, intact. The end result is continuous frequency coverage, demonstrated here from 70kHz to 110GHz: a range limited only by the bandwidth of the coaxial connector and the number of NLTL multiplier chains. This, combined with an NLTL based sampling bridge, allows the frequency range of a VNA to be extended without the use of combiners, while enhancing the directivity of the analyser. This is in contrast with existing VNA frequency extensions, in which a large external combiner is used to concatenate two frequency bands, with the added deterioration in raw directivity and additional insertion loss. Karam Noujeim, engineering fellow, Jon Martens, fellow hardware development engineer, and Tom Roberts, senior hardware development engineer, are with Anritsu's Microwave Measurements Division.