SFRA45 User Manual
9-2
For a sampled signal, the formulae become:
i = n-1
a1 = 1/n
v[i].cos(2
ci/n)
i = 0
i = n-1
b1 = 1/n
v[i].sin(2
ci/n)
i = 0
where n is the number of samples for an integral number
of complete cycles of the input waveform, and c is the
number of cycles.
Having computed the real and quadrature components, the
magnitude and phase of each channel can be derived:
mag =
(a12 + b12)
= tan-1(b1/a1)
The relative gain and phase of the circuitry under test at
that particular frequency is derived from the real and
quadrature components by vector division:
vector gain = (a + jb) {ch2} / (a + jb) {ch1}
gain = magnitude (vector gain)
phase = tan-1(b/a (vector gain))
The gain is usually quoted in dB:
dB = 20 log10(gain)
To look at differences in gain from a nominal value, an
offset gain can be applied either manually or by pressing
ZERO.
