### Introduction

Dynamic range is a vector network analyzer (VNA) specification and refers to the signal-to-noise ratio (SNR) of the system. It is essentially the ratio of the incident power to the noise power and is defined at each frequency. Recently, the time-domain reflectometer (TDR) has been increasingly used to make VNA measurements, specifically the measurement of scattering parameters, or s-parameters. Engineers using the TDR therefore began to ask, “what is the dynamic range of a TDR?”

Normally, for the TDR, this would be an esoteric question, but for sparameter measurements, it’s a very important question. It is analogous to asking what the spatial resolution is for a VNA making time-domain impedance measurements.

Since the VNA is inherently quieter than the TDR, the dynamic range is the most important factor in the measurement of TDR based s-parameters.

### TDR Dynamic Range

The dynamic range of TDR-based instruments is calculated according to the following formula (see [2]):1

The first term in equation (1) deals with the definition of the overall noise only; the second term deals with steps vs. impulses; the third term the acquisition speed; the fourth with the effects of denoising; and the last two terms deal with the response of the pulser/sampler and the fixturing/cabling effects:

The variables that go into the dynamic range equation are provided in table 1 for both the LeCroy SPARQ product, produced until 2018, and the new WavePulser 40iX product introduced in 2019. There were many improvements made in the new product, including dynamic range.

One of the main architectural changes is the use of an impulse instead of a step waveform. The advantage of the impulse is that its frequency content is ideally flat, while the frequency content of the step is proportional

to 1/f as seen in equation (1).2 Because of this impulsive stimulus, the amplitude is expressed as the amplitude of the step that results from integrating the impulse in the units of webers (Wb), where 1Wb = 1 V · s. While the low-frequency amplitude is much smaller, the content at 40GHz is many times larger, although the SPARQ compensated for this somewhat by having a very peaked response of +12dB at 40GHz. And despite slightly higher noise in the WavePulser 40iX, the 10x improvement in sample rate adds 10dB of dynamic range. The shorter path from the pulser/sampler chip to the device under test (DUT) also improves things.

The use of wavelet denoising techniques provides an additional 10dB of dynamic range (a conservative estimate that depends on the DUT.

Plots of dynamic range versus frequency are shown on a linear frequency scale for theWavePulser 40iX in figure 1a and for the SPARQ in figure 1b. Both plots show three curves with the preview mode curve corresponding to Tw = 1 s, and the normal and extra mode curves corresponding to Tw = 10 s and Tw = 100 s respectively. For each mode, the total measurement time (acquisition time) is provided. Here, it is seen that the WavePulser 40iX is three times faster. This is because it employs a pulser/sampler per port, whereas the SPARQ product employed one pulser/sampler and one sampler module that had to be routed through a switchyard to make the variety of required measurements. Therefore, the WavePulser 40iX need only drive each port of the DUT, while sampling on all four ports (for a total of four acquisitions), whereas the SPARQ required twelve acquisitions.

In figure 2, the dynamic range is plotted for the WavePulser 40iX in figure 2a and for the SPARQ in figure 2b on a logarithmic scale, which highlights the log-linear 1/f nature of the dynamic range with a step-like stimulus. Note that all the plots are shown starting from 1GHz, with the general expectation that the dynamic range is constant from DC to 1GHz.

### Conclusion

The WavePulser 40iX provides nearly 10dB dynamic range improvement at 40GHz over the SPARQ, while simultaneously improving the speed of the measurement by a factor of three. Both the old SPARQ product and the new WavePulser 40iX provide the highest dynamic range TDR based s-parameter measurement instruments on the market and are shown to be more than adequate for signal integrity measurements.