PicoVNA 106 6 GHz Vector Network Analyzer
21
© 2017 Pico Technology
pv106ug r1
To facilitate the use of the Inverse Fourier Transform to compute the time domain response, the samples in
the frequency domain must be harmonically related and consist of 2
n
points. For this reason, the TDR facility
in the PicoVNA 106 makes available special 512, 1024, 2048 and 4096-frequency-point calibrations with a
stop frequency of up to 6000 MHz. The resulting alias-free range is a function of the number of frequency
points (
N
) and the total frequency span. It is given by the expression:
So, the available ranges on the PicoVNA 106 are approximately 100 ns, 171 ns, 341 ns and 683 ns.
The transform returns twice the number of points of the calibration in the time domain. Therefore the above
ranges provide time resolutions of approximately 98ps to 84ps.
4.7.7.2.2
Bandpass method
The bandpass method provides only magnitude information so it is not possible to distinguish between
inductive and capacitive reactances. Also, the time resolution is only half as good as in the lowpass
mode.
However, the method can be used for circuits where there is no DC path and hence is suitable for AC-
coupled circuits such as bandpass filters. This method is not currently supported by the PicoVNA 106.
4.7.7.3
Windowing
The bandwidth of the network analyzer is limited by the frequency range, so the frequency domain data will
be truncated at the bandwidth of the analyzer. Also the analyzer gathers data at discrete frequencies. The
result of the sampled nature of the data and the truncation in the frequency domain is to produce a sin(
x
)/
x
response when transformed to the time domain. This appears as ringing on both the displayed impulse
response and the step response. To overcome this problem, a technique known as windowing can be
applied to the frequency domain data before implementing the Inverse Fourier Transform.
The windowing function progressively reduces the data values to zero as the edge of the frequency band is
approached, thus minimizing the effect of the discontinuities. When the modified data is transformed, the
ringing is reduced or removed depending on the selected windowing function. However, the windowing
function reduces the bandwidth and so increases the width of the pulse in impulse response mode and
slows the edge in step response mode. A balance must be made between the width of the pulse, or speed of
the edge, and the amount of ringing to be able to determine closely spaced discontinuities. The PicoVNA
106 allows you to choose a rectangular window (no bandwidth reduction), a Hanning window (raised
cosine), or a Kaiser–Bessel window. The order of the Kaiser–Bessel window is configurable.
4.7.7.4
Aliasing
The sampled nature of the data means it is subject to the effects of aliasing. The result is repetition of time-
domain response at the effective sampling rate in the frequency domain. This limits the maximum time
delay and hence maximum cable length that can be observed. In the PicoVNA 106 this is 683ns
(approximately 138m of cable).
