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)： 24/36頁
文件大?。?/td> 477K
代理商： SA1630
Philips Semiconductors
Application note
AN2003
SA1630 IF transceiver demonstration board
1999 Jan 05
24
I channel mixer output calculation
The in-phase channel mixer output is then:
I mixer output = [I(0) + I sin
ω
bb t] * [GG
e
sin (
ω
c
t +
Θ
)]
Using the trigonometric identity in Equation (4), sin (
ω
c
+
Θ
) t can be rewritten as:
Sin (
ω
c
t +
Θ
) = sin
ω
c
t cos
Θ
+ cos
ω
c
t sin
Θ
(23)
(24)
Substituting Equation (24) into Equation (23) gives:
I mixer output = [I(0) + I sin
ω
bb
t] * [GG
e
cos
Θ
sin
ω
c
t + GG
e
sin
Θ
cos
ω
c
t]
(25)
Expanding Equation (25) gives:
I mixer output = I(0) GG
e
cos
Θ
sin
ω
c
t + I(0) GG
e
sin
Θ
cos
ω
c
t
+ I GG
e
cos
Θ
sin
ω
bb
t sin
ω
c
t + I GG
e
sin
Θ
sin
ω
bb
t cos
ω
c
t
(26)
Using the identity in Equation (8)
sin
ω
bb
t sin
ω
c
t =
1
/
2
cos (
ω
bb
t –
ω
c
t) –
1
/
2
cos (
ω
bb
t +
ω
c
t)
(27)
Using the function property in Equation (22) allows Equation (27) to be rewritten as:
sin
ω
bb
t sin
ω
c
t =
1
/
2
cos (
ω
c
t –
ω
bb
t) –
1
/
2
cos (
ω
c
t +
ω
bb
t)
(28)
Using the identity in Equation (10)
sin
ω
bb
t cos
ω
c
t =
1
/
2
sin (
ω
bb
t +
ω
c
t) +
1
/
2
sin (
ω
bb
t –
ω
c
t)
(29)
Using the function property in Equation (21) allows Equation (29) to be rewritten as:
sin
ω
bb
t cos
ω
c
t =
1
/
2
sin (
ω
c
t +
ω
bb
t) –
1
/
2
sin (
ω
c
t –
ω
bb
t)
(30)
Substituting (28) and (30) into (26) and defining the following:
A =
1
/
2
GG
e
cos
Θ
B =
1
/
2
GG
e
sin
Θ
ω
h
=
ω
c
+
ω
bb
ω
l
=
ω
c
–
ω
bb
gives the following:
I mixer output = 2A I(0) sin
ω
c
t + 2B I(0) cos
ω
c
t + A I cos
ω
l
t – A I cos
ω
h
t
+ B I sin
ω
h
t – B I sin
ω
l
t
(31)
Q channel mixer output calculation
The quadrature channel mixer output is much easier to derive because we have associated all the gain and phase error terms with the I channel
mixer. The quadrature channel mixer output is:
Q mixer output = [Q(0) + Q cos
ω
bb
t] * [G cos
ω
c
t]
(32)
Expanding Equation (32) gives:
Q mixer output = G Q(0) cos
ω
c
t + G Q cos
ω
bb
t cos
ω
c
t
(33)
Using the trigonometric function product relation in Equation (9)
Q mixer output = G Q(0) cos
ω
c
t + G Q [
1
/
2
cos (
ω
bb
t –
ω
c
t) +
1
/
2
cos (
ω
bb
t +
ω
c
t)]
(34)
Using the function properties given in Equations (21) and (22), Equation (33) can be rewritten as:
Q mixer output = G Q(0) cos
ω
c
t + G Q
1
/
2
cos (
ω
c
t –
ω
bb
t) + G Q
1
/
2
cos (
ω
c
t +
ω
bb
t)
Inserting the definitions for
ω
l
and
ω
h
given previously yields:
Q mixer output = G Q(0) cos
ω
c
t +
1
/
2
G Q cos
ω
l
t +
1
/
2
G Q cos
ω
h
t
(35)
(36)
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