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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)： | 23/36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
23
Quantitative analysis
The following is a very detailed quantitative analysis of the
relationships between amplitude mismatch and quadrature phase
error on carrier and sideband suppression. Additional insight is
obtained by considering several different scenarios and sets of
assumptions. The various results are then compared against each
other and also against the SA1630 datasheet specifications for
carrier and sideband suppression. It is meant for those interested in
how these types of relationships are derived and therefore all
calculation steps have been included for this reason. If these
derivations are not of interest to you, equations (130), (132) and
Figures 24, 25, and 26 provide a reasonable summarization of the
results of this analysis.
The in-phase and quadrature baseband input signals are defined by:
I(0) + I sin
ω
bb
t
Q(0) + Q cos
ω
bb
t
Where
I(0) and Q(0) represent DC offsets
I and Q represent the ac magnitude of the baseband signals
ω
bb = 2 *
π
* F
bb
Fbb represents the baseband frequency
t represents time
The gain and phase error will be arbitrarily assigned to the in-phase
channel.
The gain of the in-phase channel mixer is therefore defined by
G * G
e
, where G is the gain of the in-phase and quadrature mixers,
and G
e
is the in-phase mixer gain and/or baseband input amplitude
mismatch error ratio relative to the quadrature mixer gain and/or
baseband input amplitude. G
e
= 1 would indicate perfectly matched
baseband input signal amplitudes and mixer gains.
The in-phase and quadrature local oscillator signals are defined by:
sin (
ω
c
+
Θ
) and cos (
ω
c
t), respectively.
Where
ω
c
= 2 *
π
* F
c
F
c
represents the local oscillator and/or carrier frequency.
Θ
is the quadrature phase error relative to the quadrature local
oscillator signal.
t represents time.
Summary of trigonometric relationships
Angle sum and difference relations
sin (a+b) = sin a cos b + cos a sin b
(4)
sin (a–b) = sin a cos b – cos a sin b
(5)
cos (a+b) = cos a cos b – sin a sin b
(6)
cos (a–b) = cos a cos b + sin a sin b
(7)
Function product relations
sin a sin b =
1
/
2
cos (a–b) –
1
/
2
cos (a+b)
cos a cos b =
1
/
2
cos (a–b) +
1
/
2
cos (a+b)
sin a cos b =
1
/
2
sin (a+b) +
1
/
2
sin (a–b)
cos a sin b =
1
/
2
sin (a+b) +
1
/
2
sin (a–b)
(8)
(9)
(10)
(11)
Function sum and difference relations
sin a + sin b = 2 sin
1
/
2
(a+b) cos
1
/
2
(a–b)
sin a – sin b = 2 cos
1
/
2
(a+b) sin
1
/
2
(a–b)
cos a + cos b = 2 cos
1
/
2
(a+b) cos
1
/
2
(a–b)
cos a – cos b =– 2 sin
1
/
2
(a+b) sin
1
/
2
(a–b)
(12)
(13)
(14)
(15)
Pythagorean relation
(sin a)
2
+ (cos a)
2
= 1
(16)
Half angle relations
sina
2
1
cosa
2
(17)
cosa
2
1
cosa
2
(18)
Small angle approximations
sin a = a
(19)
cos a = 1
(20)
where “a” is given in radians.
Function properties
sin –a = –sin a
(21)
cos –a = cos a
(22)
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