High-Frequency Filters - ITESO - Iniciodesi.iteso.mx/.../rf_electronics_course/Lectures/Filters_1.pdf · High-Frequency Filters (Part 1) ... 60dB BW BW S F ... Design a low-pass filter

High-Frequency Filters (Part 1)Dr. José Ernesto Rayas-Sánchez

April 28, 2017

1

1

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


April 28, 2017

2


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)


Types of Filters

(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)

j

c /


April 28, 2017

3


Types of Filtering Profiles



Filter Response Parameters



April 28, 2017

4


Filter Response Parameters (cont)


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


General Methods for Filter Design

The Image Parameter method

The Insertion Loss method

CAD techniques


April 28, 2017

5


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)


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


April 28, 2017

6


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



Normalized Low-Pass Prototypes

Series source

Shunt source



April 28, 2017

7


Normalized Low-Pass Prototypes (cont)

Series source

Shunt source


inductor series a is if econductanc load Scaled

capacitor shunt a is if resistance load Scaled1

N

N

N g

gg


Attenuation for L-P Prototypes (Butterworth)



April 28, 2017

8


Element Values L-P Prototypes (Butterworth)

(Assuming g0 = 1 and c = 1)



Attenuation for L-P Prototypes (Chebyshev)


(0.5dB ripple)


April 28, 2017

9


Attenuation for L-P Prototypes (Chebyshev)


(3dB ripple)


Element Values L-P Prototypes (Chebyshev)



(In this case, c is at 0.5dB)


April 28, 2017

10


Element Values L-P Prototypes (Chebyshev)




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


April 28, 2017

11


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


Example: Low-Pass Filter Prototype (cont)

Solution:

RS = RL = 75C1 = C5 = 0.437pF

C3 = 1.41pF

L2 = L4 = 6.44nH


April 28, 2017

12



ADS simulation:



ADS simulation results:


April 28, 2017

13



ADS simulation results (cont):



ADS simulation results (cont):

1|||| 221

211 SS


April 28, 2017

14



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



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))


April 28, 2017

15



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





.controlAC LIN 100 0.1GHz 10GHzAv = 2*mag(v(4)/v(1))Av_dB = db(Av)plot Av plot Av_dB.endc.end


April 28, 2017

16




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





.controlAC LIN 100 0.1GHz 10GHzAv = mag(v(4)/v(2))Av_dB = db(Av)plot Avplot Av_dB.endc.end


April 28, 2017

17





.controlAC LIN 100 0.1GHz 10GHzAv = 2*mag(v(4)/v(1))Av_dB = db(Av)plot Avplot Av_dB.endc.end

Documents

High-Frequency Filters - ITESO - Iniciodesi.iteso.mx/.../rf_electronics_course/Lectures/Filters_1.pdf · High-Frequency Filters (Part 1) ... 60dB BW BW S F ... Design a low-pass filter