HSP50016 Datasheet, PDF (24/31 Pages) Intersil Corporation – Digital Down Converter

HSP50016
f_S = f₁’R
f₁’ = 2f”
-f”/2
-f”/4
0
f”/4
f”/2
-f’
-f’
4
8
-f_S
-f_S
4R
8R
f’
f’
8
4
f_S
f_S
8R
4R
A. OUTPUT OF FIR FILTERS: SIGNAL OVERSAMPLED BY 2
-f”/2
-f”/4
0
f”/4
f”/2
-f’
-f’
4
8
-f_S
-f_S
4R
8R
f’
f’
8
4
f_S
f_S
8R
4R
B. FIRST OPERATION IN FORMATTER:
UP CONVERT BY SAMPLE FREQUENCY / 4
-f”/2
-f”/4
0
f”/4
f”/2
-f’
-f’
4
8
-f_S
-f_S
4R
8R
f’
f’
8
4
f_S
f_S
8R
4R
C. SECOND OPERATION IN FORMATTER: I OUTPUT = I + Q
FIGURE 17. QUADRATURE TO REAL CONVERSION OF AN OUTPUT SIGNAL
Up Conversion by f”/2
This operation allows the user to exchange the positions of
the upper and lower halves of a down converted signal
while leaving each half unchanged. Quadrature up
conversion by f”/2 is performed by multiplying the output
signal by e^{j2πnf’’/2} = cos(2pnf”/2) + j sin(2pnf”/2). When
sampled at a rate of f”, cos(2pnf”/2) takes on the values 1,
-1, 1, -1,... and sin(2pnf”/2) always = 0. Thus, the up
convert LO sequence is:
e^jπn = 1 + j0, -1 + j0, 1 + j0, …
(EQ. 24)
This sequence is multiplied by the output of the I and Q
branches of the filter:
w(n) = cos((ω_k - ω_c)n) + jsin((ω_k - ω_c)n)
= e^j(ωk ^{- ω}c⁾ⁿ,
(EQ. 25)
yielding an output sequence:
y = (RE(w(n)), IM(w(n))),
-RE(w(n+1)), - IM(w(n+1))),
RE(w(n+2)), IM(w(n+2))), …
(EQ. 26)
The Formatter contains the circuitry to shift the quadrature
output spectrum up by one half of the output sample
frequency f”. This operation is independent of the function of
the Phase Generator and Mixer. The spectra of the outputs
of the Filter and Formatter are shown in Figure 18.
The setup is identical to the down conversion configuration,
except that the Up Convert Bit is set in Control Word 4.
-f”/2 -f”/4 0 f”/4 f”/2
A. OUTPUT OF FIR FILTERS
-f”/2 -f”/4 0 f”/4 f”/2
B. FILTER OUTPUT UP CONVERTED BY
OUTPUT SAMPLE FREQUENCY / 2
FIGURE 18. UP CONVERSION BY F” / 2
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