無(wú)線(xiàn)系統(tǒng)的微波與射頻設(shè)計(jì)

1、Microwave and RF Design of Wireless Systems,Chapter 5 Filter,Dr. Zhang Yonghong,Filters are used to control the frequency response.,Functions:,allowing transmission at frequency within the passband of the filter. attenuation within the stopband of the filter.,Classifications by response: Low-Pass, h

2、igh-pass, bandpass, bandstop LPF HPF BPF BSF,Application:,In receivers rejection signals outside the operating band. attenuating undesired mixer products. Setting the IF bandwidth of the receiver.,In transmitters to control the spurious response of upconverting mixers. to select the desired sideband

3、s. to limit the bandwidth of the radiated signal.,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 5.5 Bandpass Filters using Transmission Line Response,5.1 Filter Desig

4、n 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 c

5、haracteristics.,Characterization by Power Loss Ratio Maximally Flat Lowpass Filter prototype. EqualRipple Lowpass Filter prototype.,3. EqualRipple Lowpass Filter prototype,1. Characterization by Power Loss Ratio,2. Maximally Flat Lowpass Filter prototype,Maximally flat response (Butterworth) Equal-r

6、ipple response (Chebyshev) Linear phase response Low-pass Filter Prototype,1. Characterization by Power Loss Ratio,Power Loss ratio:,Because of the causal properties of networks, 2 is an even function of ,Therefore, writing 2 as a polynomial in 2,Maximally flat response (Butterworth),Where N is the

7、order of the filter c is the cutoff frequency,Passband:,The power loss ratio at the band edge c:,IF k=1, then PLR=3dB,Equal-ripple response (Chebyshev),Where TN(x)is a Chebyshev polynomical of order N.,The ripple of amplitude in the pass band is 1+k2.,Linear phase response:,The group delay,a maximal

8、ly flat function.,Low-pass Filter Prototype,normalized in terms of impedance and frequency. simplifies the design of filters for arbitrary frequency, impedance and type (BPF,BSP,LPF,HPF).,Beginning with a shunt capacitor,Beginning with a series inductor,Feature:,all of the element values for the lad

9、dertype circuits is normalized. the element values are different according to different response.,2. Maximally Flat Lowpass Filter prototype, From the filter Prototype.,3. EqualRipple Lowpass Filter prototype,For filter prototype,N is odd,5.2 Filter Scaling and Transformation,1Impedance Scaling and

10、Frequency Scaling (for LPF) 2Low-pass to High-pass 3Band pass Transformation,1. Impedance Scaling and Frequency Scaling (for LPF),Series inductors,Shunt capacitors:,EXAMPLE 5.2, page 162.,2. Low-pass to High-pass Transformation,3. Band pass Transformation,Fraction bandwidth of the passband,Band Stop

11、 Transformation, 5.3 Low-pass and high-pass using Transmission line stub,At MW:,lumped elements are available only for a limited frequency range. The valve of lumped element is too small to be realized at microwave. The electrical distance between filter components is not negligible. Open or short t

12、ransmission line stub can be used as reactive elements.,How ?,Foundation:,1. Richards Transformation,The Richards-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

13、 impedance. So dose the filter response.,2. Kurodas Identities,It use redundant transmission line sections to achieve a more practical microwave filter.,Function: Physically separate transmission line stubs. Transform series stubs into shunt stubs, or vice versa. Change impractical characteristic Im

14、pedances into more realizable ones.,Example 5.4 page 172,The series stub would be difficult to implement in microstrip form. The redundant elements do not affect filter performance since they are matched to the source and load impedance. The passband characteristic are very similar. The distributed

15、element filter has a much sharp cutoff response. The distributed element filter has a periodic response. Similar procedures can be used for LPF and BSF, not useful for HPF and BPF.,5.4 Stepped-Impedance low-pass Filters,at,at,hi-Z and low-Z LPF,Example 5.5 page 176,Feature: easy to design. take up l

16、ess space than LPF using stubs. electrical performance is not as good as that of stub filter. Limited to applications where a sharp select off is not required.,Compared with the lumped-element filter, the Response: passband characteristic are similar. at higher frequency, the lumped-element circuit

17、gives more attenuation. have other passband at higher frequency, not be perfectly periodic because the section are not commensurate in length., 5.5 Bandpass Filters using Transmission Line Resonators,The can be used to transform between series-connected and shunt-connected elements.,Thus, a series LC resonator can be transformed to a parallel LC resonator, or vise versa.,Note: For a narrow passband width, the response is the same as that of a lumped element BPF.,Required characteristic impedance of the stub lines are often unrea