Aerospace and Electronic Systems Magazine December 2017 - 48

Sensitivity and Linearity Requirements of an OTH Radar Receiving System

Figure 2.

Spectral output of a modelled 16-bit ADC (blue) after propagation of an
input filtered wideband noise signal (red) through the model, showing
the emergence of quantization noise at a predictable level.

Figure 4.

When a signal of fn /4 is input to the ADC model, odd harmonics are
produced. At 3/4 fn , 5/4 fn , etc. Because of the aliasing properties, all
energy including the quantization noise appears at fn /4 and 3/4 fn.

Figure 3.

Figure 5.

0.289 times the quantization step size. In the model, we used a 16bit ADC with peak voltage of 0.6V which equates to -122.5 dBW,
and if we assume this is distributed evenly over the 50 MHz equates
to a NSD of -199 dBW/Hz in agreement with the ADC modelling.
When a -30 dBW tone at an arbitrary frequency in conjunction
with the same low noise floor of -190 dBW/RBW is applied to our
ideal ADC different behavior is observed in the output, Figure 3.
Using the same processing numbers and ADC used with the noise,
in this case spurious (distortion) products appear to be limiting the
noise floor well above the -167 dBW/RBW level of the quantization noise. The distortion level appears independent of the number
of incoherent averages indicating the spectrum is formed from many
closely spaced discrete signals rather than broadband noise, since

increasing incoherent averages would shrink the envelope (variance)
of quantization noise, resulting in peak values receding towards the
nominal quantization noise spectral density as it did before.
A contention is that these distortion products are harmonics of
the original tone, but as a noninteger fraction of the Nyquist frequency ( fn), the higher harmonics wrap to fill the spectrum with spurs.
If this contention is true, then a tone injected at an integer fraction
of fn should provide a simpler spectrum since harmonics will fall
on original signals when they wrap. This contention is borne out in
Figure 4. where all distortion is contained in odd harmonics.
When a small dithering signal is added to the input tone, the perfect harmonic relation is destroyed, the spur level is reduced and the
base spectrum becomes limited by a mixture of noise from quantization and the dither signal. By adjusting the size of the dither, the noise
and distortion can be reduced to a peak spur level around -164.5 dBW/

Spectral output of a modelled 16-bit ADC (blue) after propagation of an
input tone (red) through the model, showing the emergence of distortion
products at levels up to -152 dBW. The spurious signal peak levels are
largely independent of incoherent average number indicating discrete
rather than noise like properties.

46

ADC behavior with the signal as in Figure 3 with an additional dither
signal, showing reduction of harmonics towards a noise floor set by a
combination of quantization and dither noise.

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017



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