无线系统的微波与射频设计5

jX K j
C
LK
1 jC K
'
CK
'
1
C LK
1
jBK j
C
CK
1 jL
' K
L
' K

C C K
3. Band pass Transformation
0
1 1
0 0
1 2
0 1 0 2 1 0 0
M N
2
M
2
2
2
PLR 1
M
N
2 2
Maximally flat response (Butterworth)
1 k c
2
PLR

2N
Where N is the order of the filter c is the cutoff frequency
N
PLR
Linear phase response:
1 P A C
2N

The group delay
2N A1 P2 N 1 d C

②attenuation within the stopband of the filter.
Classifications by response:
Low-Pass, high-pass, bandpass, bandstop
LPF HPF BPF BSF
Application:
In receivers
③ IF
IF
g N 1 1,
the load is matched the prototype realizes Impedance transformer.
g N 1 1,
Process: Filter specifications →Low-pass prototype design
C Y B
Rs R0, RL R0 RL
EXAMPLE 5.2, page 162.
2. Low-pass to High-pass Transformation

c
0 0

1 c
1 c
0 0
The negative sign is needed to convert L C and C L
How ?
1. Richard’s Transformation
Foundation:
jX L jL jLtgBl
jBC jC jCtgBl
1 tg l
The Richard’s-transformation has the same cutoff frequency with the low-pass filter prototype. At the frequency away from c, the impedance of the stubs will no longer match the original lumped-element impedance. So dose the filter response.
1. Characterization by Power Loss Ratio 2. Maximally Flat Low–pass Filter prototype. 3. Equal–Ripple Low–pass Filter prototype.
1. Characterization by Power Loss Ratio
LK
'
LK 0
CK '

0 LK
LK "

0CK
" CK

CK 0
Band Stop Transformation
§ 5.3 Low-pass and high-pass using Transmission line stub
At MW:
①lumped elements are available only for a limited frequency range.
PLR
1 k TN C
2 2
Where TN(x)is a Chebyshev polynomical of order N. The ripple of amplitude in the pass band is 1+k2.
For c
2 k 2 4 C 2
d
→a maximally flat function.
Low-pass Filter Prototype
①normalized in terms of impedance and frequency. ②simplifies the design of filters for arbitrary frequency, impedance and type (BPF,BSP,LPF,HPF).
Maximally flat response (Butterworth)
Equal-ripple response (Chebyshev)
Linear phase response Low-pass Filter Prototype
2. Maximally Flat Low–pass Filter prototype 3. Equal–Ripple Low–pass Filter prototype
Microwave and RF Design of Wireless Systems
Chapter 5
Filter
Dr. Zhang Yonghong
Functions:
Filters are used to control the frequency response.
①allowing transmission at frequency within the passband of the filter.
impedance transformer.
§5.2 Filter Scaling and Transformation
1．Impedance Scaling and Frequency Scaling (for LPF) 2．Low-pass to High-pass 3．Band pass Transformation
1. Impedance Scaling and Frequency Scaling (for LPF)
C

Series inductors Shunt capacitors:
' '
L
' K

R0 L K
c
CK R0 c
Z
Z X R
Y
Y B R
C
' K
L Z X
①rejection signals outside the operating band. ②attenuating undesired mixer products. ③Setting the IF bandwidth of the receiver.
In transmitters
①to control the spurious response of upconverting mixers. ②to select the desired sidebands. ③to limit the bandwidth of the radiated signal.
→scalling and conversion →Impedance
2. Maximally Flat Low–pass Filter prototype
Zin h LK , CK , g N 1
Z in 1 Z in 1
, From the filter Prototype.
Beginning with a shunt capacitor
Beginning with a series inductor
Feature:
①all of the element values for the ladder–type circuits is normalized. ②the element values are different according to different response.
Passband:
0 c
The power loss ratio at the band edge c: 1 k 2 IF k=1, then PLR=3dB
For c
PLR
k c
2

2N
Equal-ripple response (Chebyshev)
②The valve of lumped element is too small to be realized at microwave.
③The electrical distance between filter components is not negligible.
④Open or short transmission line stub can be used as reactive elements.
PLR 1 k T
2
2 N

0 TN 0 1
'
for N odd for N even
For filter prototype, N is odd,
PLR h Lk , Ck , g N 1
g N 1 1 g 0 g N 1 1
N is even,
1. Characterization by Power Loss Ratio
Power Loss ratio: PLR
P in PLoad 1 1
2
ILdB 10 lg PLR
Because of the causal properties of networks, 2 is an even function of , Therefore, writing 2 as a polynomial in 2

PLR
1 1
2
h Lk , CK , g N 1 1 k
' 2
2N
Solving the equation,
Lk , C k
will be known. g N 1 1
3. Equal–Ripple Low–pass Filter prototype

0
0 12

2 0 0 1
2 1 0
Fraction bandwidth of the passband
jX K
j 0 LK L 1 ' Lk j j 0 K j LK j ' 0 0 CK
§5.5 Bandpass Filters using Transmission Line Response
§5.1 Filter Design by the Insertion Loss Method
Ideal filters have
Zero insertion loss in the passband; Infinite attenuation in the stopband ; Linear phase response in the passband. Compromises must be made. The insertion loss method allow a high degree of control over the passband and stopband amplitude and phase characteristics.
§5.1 Filter Design by the Insertion Loss Method
§5.2 Filter Scaling and Transformation
§5.3 Low-pass and high-pass using Transmission line stub §5.4 Stepped-Impedance low-pass Filters