AN-1364: Differential Filter Design for a Receive Chain in Communication Systems (Rev. 0) PDF

AN-1364
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Differential Filter Design for a Receive Chain in Communication Systems
by Mercy Chen
INTRODUCTION
RF engineers often see single-ended 50 Ω systems in design.
Some of them feel that the differential circuit is not easy to
design, test, and debug. Meanwhile, for better performance the
differential system is often applied in communication systems
especially in the IF stage. Among those difficulties, a differential
filter is a key concern. This application note looks at some basic
filter key specifications concepts, a few types of frequently used
filter responses, a Chebyshev Type 1 filter application, and
step-by-step instructions on how to transfer a single-ended
filter design to a differential filter design. A differential filter
design example is in this application note as well as a few points
on how to optimize differential circuit PCB design.
Rev. 0 | Page 1 of 10
AN-1364
Application Note
TABLE OF CONTENTS
Introduction ...................................................................................... 1
Designing a Band-Pass Filter .......................................................7
Revision History ............................................................................... 2
Application Example .....................................................................7
Differential Circuit Advantages .................................................. 3
Differential Filter Layout Consideration ....................................8
Filters .............................................................................................. 3
References .................................................................................... 10
Designing a Low-Pass Filter ........................................................ 6
REVISION HISTORY
7/15—Revision 0: Initial Version
Rev. 0 | Page 2 of 10
Application Note
AN-1364
This section discusses differential circuit advantages in RF
signal chain applications compare to single-ended circuits.
The user can reach a higher signal amplitude with a differential
circuit than with a single-ended circuit. With the same power
supply voltage, a differential signal can provide double the
amplitude compared to a single-ended signal; it provides better
linearity performance and SNR performance.
a
VOD = 1 – 0 = 1
VCC
+1
VOUT+
0
VOUT–
+1
VOCM
DIFFERENTIAL OUTPUT VOD p-p = 1 – (–1) = 2
Figure 3. Differential Amplifier
VOUT  VOUT   VOUT   [Cn (VIN  )n  Cn (VIN  )n
(3)
VOUT   C0  C1 cos t  C 2 (cos t )2  C 3 (cos t )3  
(4)
Therefore, in the communication system, for better
performance consideration, a differential circuit is preferred.
Differential circuits are fairly immune to outside EMI and
crosstalk from nearby signals. This is because the received
voltage is doubled, and theoretically, the noise affects the tightly
coupled traces equally. Therefore, they cancel each other out.
Differential signals also tend to produce less EMI. This is
because the changes in signal levels (dV/dt or dI/dt) create
opposing magnetic fields, again canceling each other out.
FILTERS
Filter Specification
Cutoff frequency, corner frequency, or break frequency is a
boundary in a system's frequency response at which energy
flowing through the system begins to reduce (attenuate or
reflect) rather than passing through.
0
Differential signals can reject even order harmonics. For
example, use continuous wave (CW) passes through one gain
stage.
1
4
6
8
10
GAIN (dB)
2
2
m1
3dB CUTOFF
FREQUENCY
–10
If using one single-ended amplifier, the output can be expressed
as shown in Figure 2, Equation 1, and Equation 2.
–2
(6)
Ideally, the output does not have any even order harmonics.
Figure 1. Differential Output Amplitude
–4
VOUT–
where … indicates that the sequence continues.
VOD = 0 – 1 = –1
b
–6
VIN– = –Acos ωt
VOUT  2C1 cos t  2C3 (cos t )3  
0
VEE
VOUT+
VOUT   C0  C1(  cos t )  C 2 ( cos t )2  C 3 ( cos t )3   (5)
13221-001
VIN–
VIN+
VIN+ = Acos ωt
13221-003
If using one differential amplifier, the input and output are
shown in Figure 3, Equation 3, Equation 4, Equation 5, and
Equation 6.
DIFFERENTIAL CIRCUIT ADVANTAGES
12
–20
–30
VOUT
–40
m1
FREQUENCY = 219MHz
dB(S(6,5)) = –3.014dB
Figure 2. Single-Ended Amplifier
–50
VOUT   CnVIN n
(1)
VOUT  C0  C1 cos t  C 2 (cos t )2  C 3 (cos t )3  
(2)
where … indicates that the sequence continues.
Rev. 0 | Page 3 of 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
FREQUENCY (GHz)
Figure 4. 3 dB Cutoff Frequency Point
0.9
1.0
13221-004
–2
VIN = Acos ωt
13221-002
–1
AN-1364
Application Note
In-band ripple is the fluctuation of insertion loss within the
pass band.
Group delay is a measure of the time delay of the amplitude
envelopes of the various sinusoidal components of a signal
through a device under test, and is a function of frequency for
each component.
1
IN-BAND RIPPLE
12
0
10
–1
8
DELAY (ns)
–2
–3
0
20
40
60
80
100 120 140 160 180 200 220
FREQUENCY (MHz)
13221-005
4
–4
–20
0
100
0
0.2
0.3
0.4
0.5
0.6
0.7
FREQUENCY (GHz)
0.8
0.9
1.0
13221-006
–100
0.1
200
Figure 7. Group Delay
200
–200
100
FREQUENCY (GHz)
Phase linearity is the direct proportionality of phase shift to
frequency over the frequency range of interest.
0
2
0
Figure 5. In-Band Ripple
PHASE (Degrees)
6
Figure 6. Phase Linearity
Rev. 0 | Page 4 of 10
300
400
13221-007
GAIN (dB)
ΔdB
Application Note
AN-1364
Filter Comparison
Table 1. Filters Comparison
Filter
Butterworth
Elliptic
S21 Response
See Figure 8
See Figure 9
Pros
Very good flatness in pass band
Rolls off very quickly in close in stop band
Bessel
Chebyshev Type I
See Figure 10
See Figure 11
Chebyshev Type II
See Figure 12
Maximum flat group/phase delay
Rolls off quickly in stop band; no
equalized ripple in stop band
No ripple in pass band
Cons
Rolls off slowly in stop band
Has equalized ripple in both pass band and stop band, this affects
the stop band rejection performance
Very slow roll off in stop band
Has equalized ripple in pass band
Roll off is not very fast; has equalized ripple in stop band
0
0
–10
–20
GAIN (dB)
GAIN (dB)
–20
–30
–40
–40
–60
–50
–80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
FREQUENCY (GHz)
–100
13221-008
–70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
FREQUENCY (GHz)
13221-011
–60
Figure 11. Chebyshev Type I Filter S21 Response
Figure 8. Butterworth Filter S21 Response
10
0
0
–10
GAIN (dB)
GAIN (dB)
–20
–40
–20
–30
GAIN =
C
1 + C2
–40
–60
–50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
FREQUENCY (GHz)
PASS BAND
–60
0.1
1
ω/ω0
Figure 9. Elliptiv Filter S21 Response
10
Figure 12. Chebyshev Type II Filter S21 Response
0
The IF filter designed in the communication receive chain is
basically a low-pass filter or band-pass filter; it is used for
rejecting the aliasing signals together with spurs generated by
active components. The spurs include functions such as
harmonics and IMD products. With the filter, the receive chain
can provide clean and good SNR signals for ADC to analyze.
–0.5
–1.0
–1.5
The Chebyshev Type I filter was chosen as the topology because
it has good in-band flatness, quick roll off in stop band, and no
equiripple in stop band.
–2.0
–2.5
–3.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
FREQUENCY (GHz)
0.9
1.0
13221-010
GAIN (dB)
STOP BAND
13221-012
0
13221-009
–80
Figure 10. Bessel Filter S21 Response
Rev. 0 | Page 5 of 10
AN-1364
Application Note
DESIGNING A LOW-PASS FILTER
C1SCALED = 1.433/(2π × 100 × 106 × 200) = 11.4 pF
Because the receive IF filter is used to reject spurs and aliasing
signals, using a faster stop band roll-off is better; however, faster
roll-off means higher-order components. Nevertheless, a highorder filter is not recommended because following reasons:
L2SCALED = (1.594 × 200)/(2π × 100 × 106) = 507.4 nH
11.4pF
RL
200Ω
Figure 13. Single-Ended Filter Example
Convert the single-ended filter into a differential filter (see
Figure 14).
RS/2 = 100Ω
Define the response needed by specifying the required
attenuation at a selected frequency point.
Use low-cost filter software, such as MathCad®, MATLAB®, or
ADS to design the single-ended low-pass filter.
Alternatively, design the filter by manually. RF Circuit Design by
Chris Bowick (see the References section) offers a useful guide.
RS/2 = 100Ω
Cn
2πf c R L
(8)
LSCALED =
Ln RL
2πf c
(9)
RL
200Ω
253.7nH
Using the real world value for each component, the filter is
updated as shown in Figure 15.
RS/2 = 100Ω
250nH
12pF
VS
RS/2 = 100Ω
(7)
CSCALED =
11.4pF
Figure 14. Converting Single-Ended Filter into Differential Filter
To determine the orders of the filter, normalize the frequency of
interest by dividing it with the cutoff frequency of the filter.
For example, if the in-band ripple needs to be 0.1 dB, the 3 dB
cutoff frequency is 100 MHz. At 250 MHz the rejection needs to
be 28 dB, the frequency ratio is 2.5. A third-order low-pass filter
can meet this requirement. If the source impedance of the filter
is 200 Ω, the load impedance of the filter is also 200 Ω, RS/RL is
1; use a capacitor as the first component. Then the user receives
a normalized C1 = 1.433, L2 = 1.594, C3 = 1.433, if the fc is
100 MHz, use Equation 7 and Equation 8 to finalized results
253.7nH
11.4pF
VS
To determine the maximum amount of ripple in the pass band,
keep the specification to the maximum limit of the system
requirement, this can help get faster roll-off in stop band.
f
fc
11.4pF
VS
In general, use a seventh-order or lower filter. Meanwhile, with
the same order components, if bigger in-band ripple isn’t a
problem, faster roll-off in stop band is a payout.
Frequency ratio =
507.4nH
13221-013
RS
200Ω
Difficulty for tuning at the design and debug stage.
Difficulty in mass production, because capacitors and
inductors have part-to-part variation; it is difficult for
filters on each PCB board to have the same response.
Large PCB size.
13221-014
•
The circuit is shown in Figure 13.
12pF
250nH
RL
200Ω
13221-015
•
•
C3SCALED = 11.4 pF
Figure 15. Final Differential Filter
Note that if the output impedance of the mixer or IF amplifier
and the input impedance of ADC are capacitive, it is better to
consider using a capacitor as the first component and a
capacitor as the last component. Also, it is important to tune
the first capacitor and last stage capacitor value at a higher rate
(at least 0.5 pF) than the capacitance of the output impedance
of the mixer or IF amplifier and input impedance of ADC.
Otherwise, it is very difficult to tune the filter response.
where:
CSCALED is the final capacitor value.
LSCALED is the final inductor value.
Cn is a low-pass prototype element value.
Ln is a low-pass prototype element value.
RL is the final load resistor value.
fc is the final cutoff frequency.
Rev. 0 | Page 6 of 10
Application Note
AN-1364
4.
DESIGNING A BAND-PASS FILTER
In communication systems when the IF frequency is quite high,
some low frequency spurs also need to be filtered out, like half
IF spur. For this kind of application, design a band-pass filter.
For a band-pass filter, it is not necessary to be symmetrical for
low frequency rejection and high frequency rejection. The easy
way to design a band-pass antialiasing filter is to design a lowpass filter first, then add one shunt inductor in parallel with
the shunt capacitor at the final stage of the filter to limit low
frequency components (a shunt inductor is a high-pass
resonance pole). If one stage high-pass inductor is not enough,
add one more shunt inductor in parallel with the first stage
shunt capacitor to get more rejection for low frequency spurs.
After adding the shunt inductor, tune all components again, to
receive the right out of band rejection specification and then
finalize the filter components value.
For subsystem level simulation, add the ADL5201 DGA
S-parameter file at the input, use the voltage control
voltage source to model the AD6641 ADC at the output
of the filter. To change the low-pass filter into a band-pass
filter, add two shunt inductors: L7 in parallel with C9 and
L8 in parallel with C11. C12 represents the AD6641 input
capacitance. R3 and R4 are two load resistors put at the
input of AD6641 to be the load of filter. The AD6641 input
is high impedance. After tuning, see Figure 21.
The simulation results with ideal components is shown in
Figure 16.
5.
m5
m6
20
0
–20
GAIN (dB)
Note that in general for a band-pass filter, serial capacitors are
not recommended because they increase tuning and debugging
difficulty. The capacitance value is usually quite small, it is
heavily affected by parasitic capacitance.
–40
–60
APPLICATION EXAMPLE
–80
Center frequency: 368.4 MHz
Bandwidth: 240 MHz
Input and output impedance: 150 Ω
In-band ripple: 0.2 dB
Insertion loss: 1 dB
Out of band rejection: 30 dB at 614.4 MHz
0
3.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 16. Filter Transmission Response with Ideal Inductors
6.
Replace all ideal inductors with the inductor S-parameter
files of the intended device (for example, Murata
LQW18A). The insertion loss is a little bit higher than
using ideal inductors. The simulation result changes
slightly as shown in Figure 17.
m1
m2
20
GAIN (dB)
0
–20
–40
–60
Start with a single-ended, low-pass filter design (see
Figure 18).
Change the single-ended filter into a differential filter.
Keep the source and load impedance the same, shunt all
capacitors, and cut all serial inductors in half and put them
in the other differential path (see Figure 19).
Optimize the components ideal value with real world value
(see Figure 20).
m1
FREQUENCY = 248MHz
dB(S(2,1)) = 17.968dB
m2
FREQUENCY = 488MHz
dB(S(2,1)) = 17.730dB
–80
0
0.1
0.2
0.3
0.4
0.5
0.6
FREQUENCY (GHz)
0.7
0.8
0.9
1.0
13221-021
2.
0.1
FREQUENCY (GHz)
To build the example design, use the following steps:
1.
m6
FREQUENCY = 488MHz
dB(S(4,3)) = 18.475dB
–100
Following are some of the band-pass filter design specifications
taken from a real communication system design:
•
•
•
•
•
•
m5
FREQUENCY = 248MHz
dB(S(4,3)) = 18.527dB
13221-020
This section describes an application example of filter design
between the ADL5201 and AD6641. The ADL5201 is a high
performance IF digitally controlled gain amplifier (DGA),
which is designed for base station real IF receiver applications
or digital predistortion (DPD) observation paths; it has a 30 dB
gain control range, very high linearity whose OIP3 reaches
50 dBm, and a voltage gain of about 20 dB. The AD6641 is a
250 MHz bandwidth DPD observation receiver that integrates a
12-bit 500 MSPS ADC, a 16,000 × 12 FIFO, and a multimode
back end that allows users to retrieve the data through a serial
port. This filter example is a DPD application.
Figure 17. Filter Transmission Response with Murata LQW18A Inductors
Rev. 0 | Page 7 of 10
AN-1364
Application Note
+
–
TERM3
NUM = 3
Z = 150Ω
L15
74nH
+
C12
2.8pF
C13
4.8pF
C14
2.8pF
–
TERM4
NUM = 4
Z = 150Ω
13221-016
L13
74nH
Figure 18. Single-Ended Low-Pass Filter
+
–
TERM3
NUM = 3
Z = 150Ω
L15
37nH
+
C12
2.8pF
C13
4.8pF
C14
2.8pF
–
L14
37nH
TERM4
NUM = 4
Z = 150Ω
13221-017
L13
37nH
L16
37nH
Figure 19. Differential Low-Pass Filter with Ideal Components
+
–
TERM3
NUM = 3
Z = 150Ω
L15
36nH
+
C12
2.7pF
C13
4.3pF
C14
2.7pF
–
L14
36nH
TERM4
NUM = 4
Z = 150Ω
13221-018
L13
36nH
L16
36nH
Figure 20. Differential Low-Pass Filter with Real World Value
+
–
TERM3
NUM = 3
Z = 150Ω
L9
47nH
R3
75Ω
L11
33nH
R2
+
4
1
S4P
SNP8 2
C9
2.7pF
3 REF
C8
8.2pF
L7
68nH
C10
3.9pF
L10
47nH
C11
3.9pF
L8
56nH
R4
75Ω
L12
33nH
C12
1.3pF
R1
–
TERM4
NUM = 4
Z = 150Ω
VCVS
SRC2
G=1
13221-019
C7
8.2pF
Figure 21. Differential Band-Pass Filter
The differential traces in a pair need to be of an equal length.
This rule originated from the fact that a differential receiver
detects where the negative and positive signals cross each other
at the same time—the crossover point. Therefore, the signals
arrive at the receiver at the same time for proper operation.
The traces within a differential pair need to be routed close to
each other, the coupling between the neighboring lines within a
pair is small if the distance between them is >2× the dielectrical
thickness. Also, this rule is based upon the fact that because the
differential signals are equal and opposite, and if external noise
equally interferes with these signals, the noise nullifies.
Similarly, any unwanted noise induced by the differential
signals into adjacent conductors cancels each other out if traces
are routed side by side.
Use a wide pair-to-pair spacing to minimize crosstalk between
pairs.
If using copper fill on the same layer, increase the clearance
from the differential traces to the copper fill. A minimum
clearance of 3× the trace width from the trace to the copper fill
is recommended.
Reduce intra pair skew in a differential pair by introducing
small meandering corrections close to the source of the skew
(see Figure 22).
MATCH NEAR LENGTH MISMATCH
The trace separation within a differential pair needs to be
constant over its entire length. If the differential traces are
routed close together, then they impact the overall impedance.
If this separation is not maintained from the driver to the
receiver, there are impedance mismatches along the way,
resulting in reflections.
Rev. 0 | Page 8 of 10
AVOID
Figure 22. Using Meandering Corrections
13221-022
DIFFERENTIAL FILTER LAYOUT CONSIDERATION
Application Note
AN-1364
Avoid tight (90°) bends when routing differential pairs (see
Figure 23).
PREFERRED
13221-023
AVOID
Figure 23. Avoid 90° Bends
Using symmetric routing when routing differential pairs (see
Figure 25).
AVOID STUBS
PREFERRED
One example of the differential filter PCB layout is Analog
Devices, Inc., receiver reference design board (see Figure 26).
Figure 26 shows a fifth-order filter between the ADL5201 and
the AD6649. The AD6649 is 14-bit 250 MHz pipeline ADC that
has very good SNR performance.
13221-025
If test points are required, avoid introducing trace stubs and
place the test points symmetrically (see Figure 24).
Consider relaxing the filter component value tuning workloads
on the printed circuit board (PCB); it is important to keep the
parasitic capacitance and inductance as low as possible. The
parasitic inductance may not be significant compared to the
design value of the inductor in the filter design. The parasitic
capacitance is more critical for a differential IF filter. The
capacitors in the IF filter designs are only a few picofarads, if the
parasitic capacitance reaches a few tenths of picofarads, it
affects the filter response significantly. To avoid parasitic
capacitance, it is good practice to avoid any ground or power
planes under the differential routing region and under power
supply chokes.
Figure 24. Avoiding Trace Stubs
13221-024
PREFERRED
AVOID
13221-026
Figure 25. Symmetric Routing Guidelines
Figure 26. Example of Differential Circuit PCB Layout Design
Rev. 0 | Page 9 of 10
AN-1364
Application Note
REFERENCES
Bowick, Chris. RF Circuit Design. Newnes. 1997.
Calvo, Carlos. “The Differential-Signal Advantage for Communications System Design.” Analog Devices, Inc.
©2015 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
AN13221-0-7/15(0)
Rev. 0 | Page 10 of 10
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