3 Design of Rf and Microwave Filters
-
Upload
akmal-nurhakim -
Category
Documents
-
view
238 -
download
2
description
Transcript of 3 Design of Rf and Microwave Filters
-
Design of RF and Microwave Filters2009
Microwave & Millimeter-wave Lab.
*Contents
1. Introduction ; types of Filters 2. Characterization of Filters 3. Approximate Design Methods 4. Lowpass Prototype Network 5. Impedance Scaling and Frequency Mapping 6. Immittance Inverters
Microwave & Millimeter-wave Lab.
*1. Introduction 1.1 Types of Filters A. Lowpass Filters B. Highpass Filters
C. Bandpass Filters D. Bandstop Filters
Microwave & Millimeter-wave Lab.
*2. Filter Characterization(1) Two-port Network ;
Fig. 1 Two-port Network
Microwave & Millimeter-wave Lab.
*2. Filter Characterization(2) Fig. 2 Characteristics of ideal bandpass filter Characteristics of ideal bandpass filters ; not realizable approximation required
Microwave & Millimeter-wave Lab.
*2. Filter Characterization(3) Practical specifications ;1) Passband ; lower cutoff frequency - upper cutoff frequency 2) Insertion loss : ; must be as small as possible 3) Return Loss : ; degree of impedance matching 4) Ripple ; variation of insertion loss within the passband
Microwave & Millimeter-wave Lab.
*2. Filter Characterization(4) 5) Group delay
; time to required to pass the filter 6) Skirt frequency characteristics ; depends on the system specifications 7) Power handling capability
Microwave & Millimeter-wave Lab.
*3. Approximate Design Methods 1) based on Amplitude characteristics A. Image parameter method B. Insertion loss method a) J-K inverters b) Unit element - Kuroda identity 2) based on Linear Phase characteristics
Microwave & Millimeter-wave Lab.
*3.1 Filter design(the insertion loss method) Definition of Power Loss Ratio (PLR) ; impedance matching as well as frequency selectivity Fig. 3 General filter network network synthesis procedures are required
Microwave & Millimeter-wave Lab.
*3.1 Filter Design(2)Approximation methods : 1) Maximally Flat (Butterworth) response 2) Chebyshev response 3) Elliptic Function response
Microwave & Millimeter-wave Lab.
*3.2 Approximation Methods A. Maximally flat response Where, ; passband tolerance ; order of filterUsually degree of freedom=1 (order N)Fig. 4 Comparison Between Maximally Flat and Chebyshev response
1
1.5
0.5
1
0
c
PLR
Chebyshev
Maximally flat
Microwave & Millimeter-wave Lab.
*3.2 Approximation Methods(2)B. Chebyshev response : equal ripple response in the passband : Chebyshev Polynomial of order
Microwave & Millimeter-wave Lab.
*3.2 Approximation Methods(3)Fig. 5 Chebyshev and Elliptic Function response; ripple (0.01 dB, 0.1 dB, etc.); order of filter degree of freedom=2 (ripple and order)
Microwave & Millimeter-wave Lab.
*3.2 Approximation Methods(4)C. Elliptic Function response equal ripple passband in both passband and stopband
: stopband minimum attenuation : transmission zero at stopband
degree of freedom=3 (order N, ripple, transmission zero at stopband )
Microwave & Millimeter-wave Lab.
*4. Lowpass Prototype Filter ; normalized to 1 Fig. 5 Lowpass prototype
Microwave & Millimeter-wave Lab.
*4. Lowpass Prototype Filter(2) Maximally Flat response ;
Equal Ripple response ;
Microwave & Millimeter-wave Lab.
*4. Lowpass Prototype Filter(3)Table1. Element values for Butterworth and chebyshev filters
TypeElement NoButterworth0.1 dB rippleChebyshev0.5 dB rippleChebyshev10.61801.14681.705821.61801.37121.229632.00001.97502.540841.61801.37121.229650.61801.14681.7058
Microwave & Millimeter-wave Lab.
*5. Impedance and freq. mapping5.1 Impedance Scaling
Impedance level 50 ; same reflection coefficient maintained series branch(impedance) elements ; shunt branch(admittance) elements ;
Microwave & Millimeter-wave Lab.
*5. Impedance and freq. mapping(2)5.2 Frequency Expansion
cutoff frequency 1 lowpass cutoff frequency
mapping function ;
series and shunt branch elements ;
Microwave & Millimeter-wave Lab.
*5. Impedance and freq. mapping(3)Fig. 6 Various mapping relations derived from lowpass prototype network
Microwave & Millimeter-wave Lab.
*5.3 Lowpass to Highpass transformation(lowpass cutoff freq. 1 highpass cutoff freq. ) mapping function ; series branch(impedance) elements ;
shunt branch(admittance) elements ; Fig. 7 Highpass filter derived from lowpass prototype 5. Impedance and freq. mapping(4)
Microwave & Millimeter-wave Lab.
*5.4 Lowpass to bandpass transformation (low cutoff freq. , high cutoff freq. ) mapping function ;
5. Impedance and freq. mapping(5)
Microwave & Millimeter-wave Lab.
*series branch element : impedance
shunt branch element : admittance
Fig. 8 Bandpass filter derived from thelowpass prototype 5. Impedance and freq. mapping(6)
Microwave & Millimeter-wave Lab.
*Example : Design a bandpass filter having a 0.5dB equal-ripple response, with N=3. The f0 is 1GHz, bandwidth is 10%, and the input and output impedance 50.
step 1 : from the element values of lowpass prtotype (0.5dB ripple Chebyshev)
step 2 : apply impedance scaling 5. Impedance and freq. mapping(7)
Microwave & Millimeter-wave Lab.
*step 3 : apply bandpass transformation 5. Impedance and freq. mapping(8)
Microwave & Millimeter-wave Lab.
*5.5 Lowpass to bandstop transformation (low cutoff freq. , high cutoff freq. ) mapping function ;
inverse of bandpass mapping function5. Impedance and freq. mapping(9)
Microwave & Millimeter-wave Lab.
*series branch element : admittance
shunt branch element : impedance
Fig. 9 Bandstop network derived from thelowpass prototype 5. Impedance and freq. mapping(10)
Microwave & Millimeter-wave Lab.
*5.6 Immitance Inverters K ; impedance inverter J ; admittance inverterex. simplest form of inverter : /4 transformer series LC J-inverter + shunt LC shunt LC K-inverter + series LC Fig. 10 Immitance inverter 5. Impedance and freq. mapping(11)
Microwave & Millimeter-wave Lab.
*5.7 Bandpass filters using J-, K-inverters Fig. 11 Equivalent Network for lowpass prototype and bandpass network Reflection coefficient ;lowpass :bandpass :If (mapping relation) 5. Impedance and freq. mapping(12)
Microwave & Millimeter-wave Lab.
*Fig. 12 Lowpass network and bandpass network 5. Impedance and freq. mapping(13)
Microwave & Millimeter-wave Lab.
*From the partial fraction expansion including bandpass mapping relation
: fractional bandwidth, : center freq.
In the same manner, J-inverter values are derived as 5. Impedance and freq. mapping(14)
Microwave & Millimeter-wave Lab.
*Typical immittance inverters ; Fig. 13 Impedance(K-) inverters 5. Impedance and freq. mapping(15)
Microwave & Millimeter-wave Lab.
*Fig. 14 Admittance(J-) inverters 5. Impedance and freq. mapping(16)
Microwave & Millimeter-wave Lab.
*6. LC filters, Distributed filters 6.1 LC filters A. C-coupled bandpass filters Fig. 14 Bandpass filter network using ideal J-inverters Fig. 15 Bandpass filter network containing practical inverters
Microwave & Millimeter-wave Lab.
*Fig. 16 Inverter of first and last stages By equating the real and imaginary part of and6. LC filters, Distributed filters(2)
Microwave & Millimeter-wave Lab.
*B. L-coupled bandpass filter Fig.17 C-coupled Bandpass filter Fig.18 L-coupled Bandpass filter 6. LC filters, Distributed filters(3)
Microwave & Millimeter-wave Lab.
*Design a LC bandpass filter. The f0 is 2.8 GHz, bandwidth is 500 MHz, and the input and output impedance 50. step 1 : from the element values of lowpass prototypestep 2 : apply impedance scaling step 3 : apply bandpass transformation using J-invertersStep 4 : simulation6. LC filters, Distributed filters(4)
Microwave & Millimeter-wave Lab.
*Simulated results:6. LC filters, Distributed filters(3)
Microwave & Millimeter-wave Lab.
* Step 5 : Realization
Insertion loss < 3.1 dBRetrun loss > 15.5 dBAttenuation @ 3.3 GHz : 15 dB
Microwave & Millimeter-wave Lab.
* Step 6. improvement
C-couplingLC filterL-couplingLC filter+=
Microwave & Millimeter-wave Lab.
*Measured results27 dB
Microwave & Millimeter-wave Lab.
*6.2 Distributed filters At microwave frequencies :
Resonators made of Lumped elements are lossy(low Q) or bulky Distributed Resonators
Distributed resonators ; quarter-wavelength or half-wavelength transmission lines such as microstrip lines, coaxial lines and waveguides 6. LC filters, Distributed filters(3)
Microwave & Millimeter-wave Lab.
*A. Combline filters : cellular base stations as well as portable phone
Fig. 19 (a) Top view of Combline FilterFig. 19 (b) Side view of Combline Filter6. LC filters, Distributed filters(3)
Select box and type. Control handles change width & height of box.
Fig. 17(b) Side View of Combline Filter
tuning screw
L
conductor
Microwave & Millimeter-wave Lab.
* Instead of lumped element inductors distributed inductors (L < /4) are used.
Overall equivalent circuit :Fig. 20 Coupled lineFig. 21 Equivalent circuit of Fig.20Fig. 22 Equivalent circuit of Fig. 19
*************