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參數資料
| 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： | 30/36頁 |
| 文件大?。?/td> | 477K |
| 代理商： | SA1630 |
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Philips Semiconductors
Application note
AN2003
SA1630 IF transceiver demonstration board
1999 Jan 05
30
EFFECT OF SIMULTANEOUS QUADRATURE PHASE AND AMPLITUDE ERRORS ON THE SIDEBAND
SIGNALS
Upper sideband
Again applying the small angle approximations of Equations (19) and (20) to Equations (42) and (43) yields:
A =
1
/
2
G G
e
B =
1
/
2
G G
e
Θ
(120)
(121)
Substituting Equations (120) and (121) into the expression for the upper sideband signal in Equation (40), and assuming the baseband input
signals are equal, I = Q = M (recall, the ac amplitude mismatches are lumped into the mismatch ratio G
e
) gives:
USB = –
1
/
2
G G
e
M cos
ω
h
t +
1
/
2
G G
e
Θ
M sin
ω
h
t +
1
/
2
G M cos
ω
h
t
(122)
Factoring out common terms gives:
USB =
1
/
2
G M [G
e
Θ
sin
ω
h
t + cos
ω
h
t – G
e
cos
ω
h
t]
(123)
Grouping common quadrature component terms gives:
USB =
1
/
2
G M [ (G
e
Θ
) sin
ω
h
t + (1–G
e
) cos
ω
h
t]
(124)
Therefore,
mag(USB)
1
e
)
2
(1
G
e
)
2
(125)
Equation (125) shows that the magnitude of the upper sideband signal incorporates a (1–G
e
) term due to the effects of amplitude mismatch as
was derived in Equation (65), as well as a new (G
e
Θ
) term which reflects the interaction of having both amplitude mismatch error and
quadrature phase error simultaneously.
Also note, if we assume no quadrature phase error (
Θ
= 0) and perfect baseband signal amplitude and mixer gain matching, Equation (125) still
indicates the complete suppression of the upper sideband signal as previously derived in Equation (53).
Mag(USB)
1
0)
2
(1
1)
2
0
(126)
Lower sideband
The lower sideband signal can then be analyzed in a similar fashion. Substituting Equations (120) and (121) into the expression for the lower
sideband signal in Equation (41) and again assuming the baseband input signals are equal I = Q = M (recall, the ac amplitude mismatches are
lumped in to the mismatch ratio, G
e
) gives:
LSB =
1
/
2
G G
e
M cos
ω
l
t –
1
/
2
G G
e
Θ
M sin
ω
l
t +
1
/
2
G M cos
ω
l
t
(127)
Factoring out common terms gives:
LSB =
1
/
2
G M [G
e
cos
ω
l
t + cos
ω
l
t – G
e
Θ
sin
ω
l
t]
(128)
Grouping common quadrature component terms gives:
LSB =
1
/
2
G M [(1+G
e
) cos
ω
l
t – (G
e
Θ
) sin
ω
l
t]
(129)
Therefore,
mag(LSB)
1
G
e
)
2
(G
e
)
2
(130)
Equation (130) shows that the magnitude of the lower sideband signal incorporates a (1+G
e
) term due to the effects of amplitude mismatch as
was derived in Equation (66), as well as a new (G
e
Θ
) term which reflects the interaction of having both amplitude mismatch error and
quadrature phase error simultaneously.
Also note, if we assume no quadrature phase error (
Θ
= 0) and perfect baseband signal amplitude and mixer gain matching, Equation (130)
indicates the magnitude of the lower sideband signal is:
mag(LSB)
1
1)
2
(1
0)
2
GM
(131)
as previously derived in Equation (54).
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