NETWORK ANALYSIS FOR DIGITAL ENGINEERS - Advanced Signal Integrity for High-Speed Digital Design - page 378

200 Sample points

S 21 , measured

( S 21 , measured)*

1.0

0.8

0.6

800 Sample points

0.4

0.2

Zero padding

0 20 50 + / − 100 − 50 − 20 0

Frequency, GHz

Discontinuity caused
by the zero padding
Figure 9-25 Zero-padded spectrum. Bandwidh of measured response is 20 GHz and
zero-padded to 100 GHz to ensure 5-ps resolution in the time domain.

2.0

1.5

1.0

Ripple caused
by zero padding

0.5

0.0

2.75 3.00 3.25 3.50 3.75 4.00

Time, ns

Figure 9-26 Impulse response calculated from the inverse FFT of the 20-GHz padded
to 100-GHz S 21 data shown in Figure 9-25.

Note that the zero padding has introduced a small amount of ringing into the
impulse response. The error is caused by the discontinuous spectrum where the
measured data stops and the zero padding begins. This error can be minimized
by increasing the bandwidth of the measured data, extrapolating the real and
imaginary parts of the measured data instead of zero padding or smoothing the
zero-padding discontinuity.