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High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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High-Frequency Filters(Part 1)
Dr. José Ernesto Rayas-Sánchez
2Dr. J. E. Rayas-Sánchez
Outline
Filter design at high frequencies
General characteristics of filters
Methods for filter design at high-frequencies
The insertion loss method
Example of a low-pass prototype filter design
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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3Dr. J. E. Rayas-Sánchez
Filter Design at High-Frequencies
Lumped inductors and capacitors are unsuitable for frequencies above 500 MHz
At high-frequencies, we use distributed elements
An impedance-normalized low-pass filter is the basic building block
We also use a normalized frequency
Transformations are used to convert lumped elements to distributed elements (e.g. Richards transformation, Kuroda identities, etc.)
Transfer function is usually attenuation or insertion loss (instead of voltage gain)
4Dr. J. E. Rayas-Sánchez
Types of Filters
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
j
c /
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Types of Filtering Profiles
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
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Filter Response Parameters
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Filter Response Parameters (cont)
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
22
||1||
21
o
oav Z
VP
2||1log10log10 L
inc
PP
IL factor) (shape dB3
dB60
BWBW
SF
Q) (loaded 1
dB3dB3dB3 LU
CLD ff
fBW
Q
bandwidth relative :dB3BWratio) loss(power LR
L
inc
PP
P
8Dr. J. E. Rayas-Sánchez
General Methods for Filter Design
The Image Parameter method
The Insertion Loss method
CAD techniques
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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9Dr. J. E. Rayas-Sánchez
The Insertion Loss Method
It uses network synthesis techniques from a completely specified frequency response
The characterizing response is the power-loss ratio (or the insertion loss)
General procedure:
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
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Power-Loss Ratio Characterization
12
LR )1(load the todeliveredpower
source thefrompower
refinc
inc
L
inc
PPP
PP
P
2
LR )(1log10log10 PIL
2LR)(1
1
P
It can be shown that () is an even function of ( () can be represented by even series of the form k0+k22+k44 +…)
Since | ()| ≤ 1, it can be expressed as
then)()(
)()(
22
22
NMM
)()(
12
2
LR
NM
P
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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11Dr. J. E. Rayas-Sánchez
Power-Loss Ratio Filtering Profiles
Maximally Flat profile (or Binomial or Butterworth)
N: filter order
Chebyshev profile
N
c
kP2
2LR 1
c
NTkP22
LR 1
TN(x) is the Chebyshev
polynomial of order N
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
12Dr. J. E. Rayas-Sánchez
Normalized Low-Pass Prototypes
Series source
Shunt source
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Normalized Low-Pass Prototypes (cont)
Series source
Shunt source
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
inductor series a is if econductanc load Scaled
capacitor shunt a is if resistance load Scaled1
N
N
N g
gg
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Attenuation for L-P Prototypes (Butterworth)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Element Values L-P Prototypes (Butterworth)
(Assuming g0 = 1 and c = 1)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
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Attenuation for L-P Prototypes (Chebyshev)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
(0.5dB ripple)
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Attenuation for L-P Prototypes (Chebyshev)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
(3dB ripple)
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Element Values L-P Prototypes (Chebyshev)
(Assuming g0 = 1 and c = 1)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
(In this case, c is at 0.5dB)
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Element Values L-P Prototypes (Chebyshev)
(Assuming g0 = 1 and c = 1)
(D. M. Pozar, Microwave Engineering, Wiley, 2005)
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De-Normalized Element Values L-P Prototypes
The final element values for a low-pass prototype are obtained from (R0 is the actual source resistance):
c
kk
gRL
0
c
kk R
gC
0
resistance load a toscorrespond if
econductanc load a toscorrespond if /
1
1
10
10
N
N
N
N
L g
g
gR
gRR
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Example: Low-Pass Filter Prototype
Design a low-pass filter with the following specifications:
Cut-off frequency at 3 GHz
For a 75- system
Minimum attenuation of 20 dB at 5 GHz
Butterworth filtering profile
Use a series voltage source topology
22Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
Solution:
RS = RL = 75C1 = C5 = 0.437pF
C3 = 1.41pF
L2 = L4 = 6.44nH
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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Example: Low-Pass Filter Prototype (cont)
ADS simulation:
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Example: Low-Pass Filter Prototype (cont)
ADS simulation results:
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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25Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
ADS simulation results (cont):
26Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
ADS simulation results (cont):
1|||| 221
211 SS
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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27Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
APLAC simulation:Port1
75
Port2
751.41pFC30.437pFC1
6.44nH
L2
6.44nH
L4
0.437pF
Sweep "Low-Pass Filter 5th-order"LOOP 100 FREQ LIN 0.1GHz 10GHzWINDOW=0 grid Y "" "" 0 1WINDOW=1 grid Y "" "" -80 0
Show W=0 Y=Mag(S(1,1)) Y=Mag(S(2,1))Show W=1 Y=MagdB(S(1,1)) Y=MagdB(S(2,1))EndSweep
C5
28Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
APLAC simulation results:
100.000M 2.575G 5.050G 7.525G 10.000G0.00
0.25
0.50
0.75
1.00
f/HzMag(S(1,1)) Mag(S(2,1))
2.810G 2.906G 3.003G 3.099G 3.196G-3.70
-3.39
-3.08
-2.78
-2.47
f/HzMagdB(S(1,1)) MagdB(S(2,1))
100.000M 2.575G 5.050G 7.525G 10.000G-80.00
-60.00
-40.00
-20.00
0.00
f/HzMagdB(S(1,1)) MagdB(S(2,1))
2.797G 2.904G 3.010G 3.116G 3.223G0.68
0.70
0.71
0.72
0.73
f/HzMag(S(1,1)) Mag(S(2,1))
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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29Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
SPICE simulation 1:Fifth-Order Low-Pass Filter
Vs 1 0 DC 0 AC 1RS 1 2 75C1 2 0 0.437pFC5 4 0 0.437pFC3 3 0 1.41pFL2 2 3 6.44nHL4 3 4 6.44nHRL 4 0 75
.controlAC LIN 100 0.1GHz 10GHzAv = mag(v(4)/v(1))Av_dB = db(Av)plot Av plot Av_dB.endc.end
30Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
SPICE simulation 2:Fifth-Order Low-Pass Filter
Vs 1 0 DC 0 AC 1RS 1 2 75C1 2 0 0.437pFC5 4 0 0.437pFC3 3 0 1.41pFL2 2 3 6.44nHL4 3 4 6.44nHRL 4 0 75
.controlAC LIN 100 0.1GHz 10GHzAv = 2*mag(v(4)/v(1))Av_dB = db(Av)plot Av plot Av_dB.endc.end
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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31Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
SPICE simulation 3:Fifth-Order Low-Pass Filter
Vs 1 0 DC 0 AC 1RS 1 2 0.01C1 2 0 0.437pFC5 4 0 0.437pFC3 3 0 1.41pFL2 2 3 6.44nHL4 3 4 6.44nHRL 4 0 1K
.controlAC LIN 100 0.1GHz 10GHzAv = mag(v(4)/v(1))Av_dB = db(Av)plot Avplot Av_dB.endc.end
32Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
SPICE simulation 4:Fifth-Order Low-Pass Filter
Vs 1 0 DC 0 AC 1RS 1 2 75C1 2 0 0.437pFC5 4 0 0.437pFC3 3 0 1.41pFL2 2 3 6.44nHL4 3 4 6.44nHRL 4 0 75
.controlAC LIN 100 0.1GHz 10GHzAv = mag(v(4)/v(2))Av_dB = db(Av)plot Avplot Av_dB.endc.end
High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez
April 28, 2017
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33Dr. J. E. Rayas-Sánchez
Example: Low-Pass Filter Prototype (cont)
SPICE simulation 5:Fifth-Order Low-Pass Filter
Vs 1 0 DC 0 AC 1RS 1 2 150C1 2 0 0.437pFC5 4 0 0.437pFC3 3 0 1.41pFL2 2 3 6.44nHL4 3 4 6.44nHRL 4 0 150
.controlAC LIN 100 0.1GHz 10GHzAv = 2*mag(v(4)/v(1))Av_dB = db(Av)plot Avplot Av_dB.endc.end