PSM1700 PsimetriQ user manual
11-2
For a sampled signal, the formulae become:
i = n-1
a
1
= 1/n
v[i].cos(2ci/n)
i = 0
i = n-1
b
1
= 1/n
v[i].sin(2ci/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 = (a
1
2
+ b
1
2
)
= tan
-1
(b
1
/a
1
)
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 log
10
(gain)
The phase difference can be expressed as a delay time:
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