high-frequency filters - iteso€¦ · maximally flat profile (or binomial or butterworth) n:...

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

May 12, 2020

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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


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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 /


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Types of Filtering Profiles



Filter Response Parameters



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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


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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


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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



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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)



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Element Values L-P Prototypes (Butterworth)

(Assuming g0 = 1 and c = 1)



Attenuation for L-P Prototypes (Chebyshev)


(0.5dB ripple)


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Attenuation for L-P Prototypes (Chebyshev)


(3dB ripple)


Element Values L-P Prototypes (Chebyshev)



(In this case, c is at 0.5dB)


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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:

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

gk = (cLk)/R0

gk = (cCk)R0

R0 is the actual source resistance = reference impedance Z0


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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


Example: Low-Pass Filter Prototype (cont.)

ADS simulation:


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ADS simulation results:



ADS simulation results (cont.):


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ADS simulation results (cont.):

1|||| 221

211 SS

high-frequency filters - iteso€¦ · maximally flat profile (or binomial or butterworth) n:...

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