• High pass filter (passive)
Transfer |H()| function 1
• Filters used in electronics can be constructed from resistors, inductors, capacitors, transmission line sections, and resonating structures (e.g., piezoelectric crystal, Surface Acoustic Wave (SAW) devices, mechanical resonators, etc.).
射频电路设计基础
11
3B. RF Microwave Filters
2
1.0 Basic Filter Theory
3
Introduction
• An ideal filter is a linear 2-port network that provides perfect transmission of signal for frequencies in a certain passband region, infinite attenuation for frequencies in the stopband region, and a linear phase response in the passband (to reduce signal distortion).
• An active filter may contain a transistor, FET, and an op-amp.
Filter LPF HPF BPF
Active Passive Active Passive
5
Filter Frequency Response
• Frequency response implies the behavior of the filter with respect to steady-state sinusoidal excitation (e.g., energizing the filter with a sine voltage or current source and observing its output).
4
Categorization of Filters
• Low pass filter (LPF), high pass filter (HPF), bandpass filter (BPF), bandstop filter (BSF), arbitrary type, etc.
• In each category, the filter can be further divided into active and passive types.
6
Filter Frequency Response (cont’d)
• Low pass filter (passive)
V1()
Filter H()
V2() ZL
|H()|
1
Transfer
function
H V2 V1
(1.1a)
Complex value
Arg(H()) c
A()/dB
• Low pass filter (passive) continued...
A()/dB
Passband
50
40
30
20
10
3Hale Waihona Puke 0cTransition band
Stopband
Cut-off frequency (3 dB)
V1()
Filter H()
V2()
ZL
9
Filter Frequency Response (cont’d)
• In an active filter, there can be amplification of the signal power in the passband region; a passive filter do not provide power amplification in the passband.
50
40
Real value
c
30 20 10 3
Atten nA ua 2tL i0oo 1g 0V V1 2 (1.1b)
0
c
7
Filter Frequency Response (cont’d)
• Low pass filter (passive) continued...
• For the impedance matched system, using s21 to observe the filter response is more convenient, as this can be easily measured using a vector network analyzer (VNA).
• There are various approaches to displaying the frequency response:
– Transfer function H() (the traditional approach) – Attenuation factor A() – S-parameters, e.g., s21() – Others, such as ABCD parameters, etc.
• The goal of filter design is to approximate the ideal requirements within acceptable tolerance with circuits or systems consisting of real components.
Vs
Zc
a1
Zc
Zc b2
Zc
Filter
Zc Zc
20log|s21()|
0 dB
Arg(s21())
Transmission line is optional
c
s11ab11a20 s21ba21a20
Complex value
8
Filter Frequency Response (cont’d)