參數(shù)資料
型號： SA1630
廠商： NXP Semiconductors N.V.
英文描述： IF Quadrature Transceiver(IF正交收發(fā)器)
中文描述： 中頻正交收發(fā)器（中頻正交收發(fā)器）
文件頁數(shù)： 27/36頁
文件大?。?/td> 477K
代理商： SA1630
Philips Semiconductors
Application note
AN2003
SA1630 IF transceiver demonstration board
1999 Jan 05
27
Quadrature phase error only
So, now let’s take a look at the effects of quadrature phase error by itself, while assuming all the other sources of error are ideal. This is done by
assuming the following:
G
e
= 1 (channel mixer gains and baseband input signal amplitudes are perfectly matched)
Θ
not = 0 (quadrature phase error)
(70)
(71)
I(0) = Q(0) = 0 (there is no input offset error)
(72)
I = Q = M (the baseband input signal amplitudes are equal)
(73)
Substituting Equations (70) and (71) into Equations (42) and (43) gives:
A =
1
/
2
G * 1 * cos
Θ
=
1
/
2
G cos
Θ
B =
1
/
2
G * 1 * sin
Θ
=
1
/
2
G sin
Θ
(74)
(75)
Substituting Equations (72), (73), (74), and (75) into Equations (39), (40), and (41) yields:
C = 0 + 0 + 0 = 0
(76)
USB = –
1
/
2
G M cos
Θ
cos
ω
h
t +
1
/
2
G M sin
Θ
sin
ω
h
t +
1
/
2
G M cos
ω
h
t
LSB =
1
/
2
G M cos
Θ
cos
ω
l
t –
1
/
2
G M sin
Θ
sin
ω
l
t +
1
/
2
G M cos
ω
l
t
(77)
(78)
Grouping the phase error terms together in Equation (77) gives:
USB = –
1
/
2
G M (cos
Θ
cos
ω
h
t – sin
Θ
sin
ω
h
t) +
1
/
2
G M cos
ω
h
t
(79)
Using the trigonometric angle sum and difference relation in Equation (6) yields:
USB = –
1
/
2
G M [cos (
Θ
+
ω
h
t) – cos
ω
h
t]
(80)
Applying the trigonometric function sum and difference relation in Equation (15) gives:
USB = –
1
/
2
G M [–2 sin
1
/
2
(
Θ
+
ω
h
t +
ω
h
t) sin
1
/
2
(
Θ
+
ω
h
t –
ω
h
t) ]
(81)
Collecting terms gives:
USB = G M [sin (
ω
h
t +
Θ
/2)] (sin
Θ
/2)
(82)
Applying the small angle approximation in Equation (19) yields:
USB
GM2sin
h
t
2
(83)
Now let’s work on the LSB equation in a similar fashion. Grouping the phase error terms in Equation (78) together yields:
LSB =
1
/
2
G M (cos
Θ
cos
ω
l
t – sin
Θ
sin
ω
l t) +
1
/
2
G M cos
ω
l
t
(84)
Again, using the trigonometric angle sum and difference relation in Equation (6) yields:
LSB =
1
/
2
G M [cos (
Θ
+
ω
l
t) + cos
ω
l
t]
(85)
Using the trigonometric function sum and difference relation in Equation (14) gives:
LSB =
1
/
2
G M [2 cos
1
/
2
(
Θ
+
ω
l
t +
ω
l
t) cos
1
/
2
(
Θ
+
ω
l
t –
ω
l
t)]
(86)
Collecting terms yields:
LSB = G M cos (
Θ
/2) cos (
ω
l
t +
Θ
/2)
(87)
Applying the small angle approximation in Equation (20) gives:
LSB = G M cos (
ω
l t +
Θ
/2)
(88)
Now let’s compare these equation to the datasheet specifications.
From Equations (83) and (88) :
mag (USB) = G M (
Θ
/2)
(89)
mag (LSB) = G M
(90)
Substituting Equations (89) and (90) into Equation (64) gives:
SBS = 20 log [G M (
Θ
/2) / G M ] = 20 log (
Θ
/2)
(91)
If the phase error is given in degrees instead of radians
SBS = 20 log (
Θ
*
π
/360)
(92)
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