TMC2249AH5C1 Fairchild Semiconductor, TMC2249AH5C1 Datasheet - Page 12

• Manufacturer Part Number: TMC2249AH5C1
• Manufacturer: Fairchild Semiconductor

Specifications of TMC2249AH5C1

• Function: Digital Mixer
• Operating Temperature (max): 70C
• Operating Temperature (min): 0C
• Package Type: MQFP
• Pin Count: 120
• Mounting: Surface Mount
• Lead Free Status / Rohs Status: Not Compliant

PRODUCT SPECIFICATION
Complex Arithmetic Functions
The TMC2249A can also be used to perform complex arith-
metic functions. The basic function performed by the device,
ignoring the delay controls,
SUM = ( A B) + ( C D)
can realize in two steps the familiar summation:
(P+jR)(S+jT)=(PS-RT) + j(PT+SR)
by loading the TMC2249A as follows:
where H and L indicate a logic HIGH and LOW.
Thus we can perform a complex multiplication in two clock
cycles. Notice that the user must switch the two components
of the second input vector between the B and D inputs to
obtain the second complex summation.
Calculating a Butterfly
Taking advantage of the complex multiply which we imple-
mented above using the TMC2249A, we can expand slightly
to calculate a Radix-2 Butterfly, the core of the Fast Fourier
Transform algorithm. To review, the Butterfly is calculated
as shown in Figure 6.
Where
X=A+B(W
Y=A–B(W
and W
for the N-point transform, which is:
W
with Re and Im indicating the real and imaginary parts of the
vector.
12
Step
N
1
2
r
N
r
Figure 6. Signal Flow of Radix-2 Butterfly
is the complex phase coefficient, or "twiddle factor"
A
(1)
P
P
A
B
=
=
=
N
N
r
r
),
)
B
S
T
(2)
TMC2249A Inputs
e
cos(2 /N) + j(sin(2 /N))
Re(W) + jIm(W)
W
j(2 /N)
C
R
R
N
r
D
S
T
NEG1 NEG2
-1
L
L
H
L
Resultant
X
Y
(PT+SR)
(PS-RT)
Output
Expanding the complex vectors A and B to calculate X and
Y, we get:
X
lm(B)lm(W)+j(Re(B)lm(W)+lm(B)Re(W)))
lm(B)lm(W))+j(lm(A)+Re(B)lm(W)+lm(B)Re(W))
and,
Y
lm(B)lm(W)+j(Re(B)lm(W)+lm(B)Re(W)))
Re(B)Re(W)+lm(B)lm(W))+j(lm(A)-Re(B)lm(W)-
lm(B)Re(W))
The butterfly is then neatly implemented in four clocks, as
follows:
Notice again that the components of the second vector must
be switched by the user on the second half of the computa-
tion, as well as the parts of the vector presented to the cas-
cade input.
Quadrature Modulation
The TMC2249A can also be used to advantage as a digital-
domain complex frequency synthesizer, as demonstrated in
Figure 7.
Here, orthogonal sinusoidal waveforms are generated digi-
tally in the TMC2330A Coordinate Transformer. These
quadrature phase coefficients are then multiplied with two
input signals, such as digitized analog data.
The TMC2249A then adds these products, which can be out-
put directly to a high-speed digital-to-analog converter such
as the Fairchild TDC1012 for direct waveform synthesis.
This 12-bit, 20MHz DAC is ideally suited to waveform gen-
eration, featuring extremely low glitch energy for low spuri-
ous harmonics and distortion.
Step
1
2
3
4
=
=
=
=
=
=
Re(B) Re(W) Im(B) Im(W) Re(A)
Re(B) Re(W) Im(B) Im(W) Re(A)
Re(B) Im(W) Im(B) Re(W) Im(A)
Re(B) Im(W) Im(B) Re(W) Im(A)
A
B
(Re(A)+jlm(A))+(Re(B)Re(W)-
(Re(A)+Re(B)Re(W)-
Re(X)+jlm(X)
(Re(A)+jlm(A))-(Re(B)Re(W)-
(Re(A)-
Re(Y)+jlm(Y)
TMC2249A Inputs
C
D
Input
CAS
NEG1
H
H
L
L
REV. 1.0.2 7/6/00
NEG2
H
L
L
H
TMC2249A
Result-
Output
Re(X)
Re(Y)
Im(X)
Im(Y)
ant