LINEAR TECHNOLOGY LT5575 Technical data
L DESIGN FEATURES
a
Z IP
2
0
2
2
=
DIPLEXER
ADC
ADC
0°
I/Q DEMOD
AGC
BAND
FILTER
LOWPASS
FILTERS
BASEBAND
AMPLIFIERS
LNARF AT
1920 MHz–1980 MHz
FROM Tx
2110 MHz–2170 MHz
LO AT
1920 MHz–1980 MHz
90°
LO
RF TONE POWER = P
S
RF PASSBAND
SINGLE TONE EXAMPLE MODULATED SIGNAL EXAMPLE
DOWNCONVERSION
LO
RF PASSBAND
DC DUE TO 2ND ORDER
DISTORTION = a2PSZ
0
0 Hz 0 Hz
BASEBAND PSEUDO-RANDOM POWER
DUE TO 2ND ORDER DISTORTION
= 3a
2
2
Z0P
S
2
RF SIGNAL POWER = P
S
Understanding IP2 and IP3 Issues
in Direct Conversion Receivers for
WCDMA Wide Area Basestations
Introduction
A direct conversion receiver architecture offers several advantages over the
traditional superheterodyne. It eases
the requirements for RF front end
bandpass filtering, as it is not susceptible to signals at the image frequency.
The RF bandpass filters need only
attenuate strong out-of-band signals
to prevent them from overloading
the front end. Also, direct conversion
eliminates the need for IF amplifiers
and bandpass filters. Instead, the RF
input signal is directly converted to
baseband, where amplification and
filtering are much less difficult. The
overall complexity and parts count of
the receiver are reduced as well.
Direct conversion does, however,
come with its own set of implementation issues. Since the receive LO
signal is at the same frequency as
the RF signal, it can easily radiate
from the receive antenna and violate
regulatory standards. Also, a thorough
understanding of the impact of the
IP2 and IP3 issues is required. These
parameters are critical to the overall
performance of the receiver and the key
component is the I/Q demodulator.
Unwanted baseband signals can be
generated by 2nd order nonlinearity of
the receiver. A tone at any frequency
entering the receiver gives rise to a DC
offset in the baseband circuits. Once
generated, straightforward elimination
of DC offset becomes very problematic.
That is because the frequency response
of the post-downconversion circuits
must often extend to DC. The 2nd order
nonlinearity of the receiver also allows
a modulated signal—even the desired
signal—to generate a pseudo-random
block of energy centered about DC.
direct conversion receivers are susceptible to such 2nd order mechanisms
regardless of the frequency of the
incoming signal. So minimizing the
10
Unlike superheterodyne receivers,
effect of finite 2nd order linearity is
critical.
effect of 3rd order distortion on a direct
conversion receiver. In this case, two
signals separated by an appropriate
frequency must enter the receiver in
order for unwanted products to appear
at the baseband frequencies.
Second Order Distortion (IP2)
The second order intercept point (IP2)
of a direct conversion receiver system
is a critical performance parameter. It
is a measure of second order non-linearity and helps quantify the receiver’s
susceptibility to single- and 2-tone
interfering signals. Let’s examine how
this nonlinearity affects sensitivity.
Figure 1. Direct conversion receiver architecture
Later in this article we consider the
Figure 2. Effects of 2nd order distortion
by Doug Stuetzle
We can model the transfer function
of any nonlinear element as a Taylor
series:
y(t) = x(t) + a2x2 (t) + a3x3(t) + …
where x(t) is the input signal consisting of both desired and undesired
signals. Consider only the second order
distortion term for this analysis. The
coefficient a2 is equal to
where IP2 is the single tone intercept
point in watts. Note that the 2-tone
IP2 is 6dB below the single-tone IP2.
The more linear the element, the
smaller a2 is.
Linear Technology Magazine • June 2008
DESIGN FEATURES L
P
Z
E A t t
S
=
{ }
1
0
2
• ( ) cos ω
P
Z
E A t E
t
S
= •
{ }
•
+
1 1 2
2
0
2
( )
cos ω
P
Z
E A t
S
=
{ }
1
2
0
2
• ( )
P
A
Z
S
=
2
0
2
E A t Z P
S20
2( )
{ }
=
y t A t t
a A t t
Higher Orde
( ) ( )cos
( ) cos
=
+
+…
ω
ω
2
2
rr Terms
A t t
a A t
a A t t
=
+
+
( ) cos
( )
( ) cosωω
1
2
1
2
2
2
2
2
2
……
DC OFFSET a A a P Z
S
= =
1
2
2
2
2 0
•
P
Z
E a A t
BB
=
1 1
2
0
2
2
2
• ( )
P
a
Z
E A t
BB
=
( )
{ }
2
2
0
4
4
• ( )
E A t E A t
4 2
2
3( ) • ( )
{ }
=
{ }
P
a
Z
E A t
BB
=
( )
{ }
3
4
2
2
0
2
2
• ( )
P a Z P
BB S
=
( ) ( )
3
220
2
y t A t t
a A t t B t t
u
( ) ( )cos
( ) cos ( ) cos
=
+ +
+
ω
ω ω
2
2
……
=
+ +
Higher Order Terms
A t t
a A t a
( ) cos
( )
ω
1
2
1
2
2
2
2
AA t t
a A t B t t t
A t
u
2
2
2
2
( ) cos
( ) ( )cos cos
( ) co
ω
ω ω+ …
= ss
( ) ( )cos( )
ω
ω ω
t
a A t B t t
u
+…
+ − …
2
ADC
0°
I/Q DEMOD
GAIN = 30dB
GAIN = 20dB
EQUIVALENT
PSEUDO-RANDOM
DISTORTION
AT –118.7dBm
TOTAL Rx
THERMAL NOISE
= –101.2dBm
WCDMA
INTERFERER
AT –40dBm
WCDMA
INTERFERER
AT –20dBm
DISTORTION
AT –98.2dBm
90°
Every signal entering the nonlinear
element generates a signal centered
at zero frequency. Even the desired
signal gives rise to distortion products
at baseband. To illustrate this, let the
input signal be represented by x(t) =
A(t)cosωt, which may be a tone or a
modulated signal. If it is a tone, then
A(t) is simply a constant. If it is a
modulated signal, then A(t) represents
the signal envelope.
By definition, the power of the desired signal is
where E{β} is the expected value of
β. Since A(t) and cosωt are statistically independent, we can expand
E{(A(t)cosωt)2} as E{A2(t)} • E{cos2ωt}.
By trigonometry
The expected value of the second
term is simply ½, so the power of the
desired signal simplifies to:
[1]
In the case of a tone, A(t) may be
replaced by A. The signal power is, as
expected, equal to
In the more general case, the desired signal is digitally modulated by
a pseudo-random data source. We
can represent it as bandlimited white
noise with a Gaussian probability
distribution. The signal envelope A(t)
is now a Gaussian random variable.
The expected value of the square of the
envelope can be expressed in terms of
the power of the desired signal as:
[2]
Now substitute x(t) into the Taylor
terms of the desired signal power, we
must relate E{A4(t)} to E{A2(t)}. For a
Gaussian random variable, the follow-
ing relation is true:
series expansion to find y(t), which is
the output of the nonlinear element:
expressed as
terms of the desired signal power:
Consider the 2nd order distortion
term ½a2[A(t)]2. This term appears
centered about DC, whereas the other
2nd order term appears near the 2nd
harmonic of the desired signal. Only
the term near DC is important here,
as the high frequency tone is rejected
by the baseband circuitry.
In the case where the signal is a
to DC, and any modulated signal into
a baseband signal that makes 2nd
order performance critical to direct
conversion receiver performance. Unlike other nonlinear mechanisms, the
signal frequency does not determine
where the distortion product falls.
tone, the 2nd order result is a DC
offset equal to:
nonlinear element give rise to a beat
note/term. Let
[3]
If the desired signal is modulated,
then the 2nd order result is a modulated baseband signal. The power of
x(t) = A(t)cosωt + B(t)cosωut,
where the first term is the desired
signal and the second term is an unwanted signal.
this term is
This can be expanded to:
[4]
In order to express this result in
[5]
The distortion power can then be
Now express the expected value in
[6]
It is the conversion of any given tone
Any two signals entering the
Linear Technology Magazine • June 2008
Figure 3. 2nd Order distortion due to WCDMA carrier
The second order distortion term of
interest is a2A(t)B(t)cos(ω– ωu)t. This
term describes the distortion product
centered about the difference frequency between the two input signals. In the
case of two unwanted tones entering
the element, the result includes a tone
at the difference frequency. If the two
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