EE 524 PR PROJECT 1
MICROSTRIP LOWPASS AND HIGHPASS FILTER DESIGN
SUBMITTED BY: Göksenin BOZDAĞ SUBMITTED TO: Asst. Prof. Dr. Sevinç AYDINLIK BECHTELER December-2011 1
CONTENTS
ABSTRACT………………………………………………………………………………….......................
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A)MICROSTRIP CHEBSYSEHEV LOWPASS FILTER..………………………………………….. FILTER..…………………………………………..
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1.CHEBSYSEHEV RESPONSE………………………………………………..………………………
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2.CHEBSYSEHEV 2.CHEBSYSEHEV LOWPASS FILTER DESIGN…………………………………………… DESIGN………………………………………………….. ……..
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B) MICROSTRIP CHEBSYSEHEV HIGHPASS FILTER ..………………………………………….
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1.MICROSTRIP HIGHPASS FILTER DESIGN…………………………………………… DESIGN……………………………………………………… …………
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C)REFERENCES………………………………………………………………………………………………….
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ABSTRACT The ambition of the project is designing Microstrip Chebsysehev Low Pass and High Pass Filters. Some of the line calculations and design simulations have been done by the computer program, QUCS. Realization of the filters have not been done but the realization procedure and realization results will be added to this report as soon as it is possible. th
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Finally, 5 degree Microstrip Chebsysehev Low Pass and 3 degree Microstrip Chebsysehev High Pass Filters are designed designed and simulated.
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A) MICROSTRIP CHEBSYSEHEV LOWPASS FILTER 1)CHEBSYSEHEV 1)CHEBSYSEHEV RESPONSE The Chebysehev response that exhibits the equal-ripple passband and maximally flat stopband. The amplitude-squared transfer function that describes this type type of response is
LAr represents the ripple in dB and ɛ represents the ripple constant.
Tn(Ω) is a Chebysehev function of the first kind of order n.
General Response of Lowpass Chebysehev
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While desining this type of lowpass filters we use some coefficients. The coefficients are got by calculation according to the formula given below or more generally look-up tables are used.
Where
For the required passband ripple LAr in dB, the minimum stopband attenuation LAs in dB at Ω = Ωs, the degree of a Chebyshev lowpass prototype, which will meet this specification, can be found by
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2)CHEBSYSEHEV 2)CHEBSYSEHEV LOWPASS FILTER DESİGN Example: Design a lowpass filter whose input and output output are matched to a 50 Ω impedance and cut-off frequency 2,5 GHz, equi-ripple 0.5 dB, and rejection of at least 40 dB at approximately twice of the cut-off frequency. Solution: Firstly, we determine the degree of filter according to the formula. LAs = 40 dB
LAr = 0.5 dB
Then, n ≥4.8 So we can use n=5 coefficients from the table
According to table g1=g5=1.7058, g2=g4=1.2296, g3=2.5408.
Π type lowpass prototype
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Secondly; Lumped elements are changed with their microstrip equivalents. (Richard’s Transformation). Replacing Replacing inductors and capacitors capacitors by series and shunt stubs.
Third step is using unit elements converting short circuits to open circuits. (Kudora’s 2
Identities) N =1 + (Z2/Z1)
While Kuroda’s identities are applying, unit elements are put both left and right sight.
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For this figure we should calculate N . 2
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N Z1=1 and (1/N Z2)=1.7058 Then; N =1+(Z2/Z1) = 1.5862 2
(second identity is used)
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(Z1N ) = 1 Z1= 1/ 1.5862 = 0.6304
(1/ N Z2) = 1.7058 Z2 = 0.3696
When we put the calculated values, we get the circuit circuit below.
Now we use the first identity for short circuits at center. 2
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Z2/N =0.3696 and Z1/N =1.2296 Then; N = 1 + (Z 2/Z1) =1.3006 Z1 and Z2 are calculated as Z2=0.4807 Z1=1.5992 Lastly, we have to convert outer short circuits to open circuits so we again add unit elements and we again apply Kuroda’s first identity. 2
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Z2/N = 1 and Z1/N = 0.6304 Then; N = 1 + (Z2/Z1) = 2.5863 Z1 and Z2 are calculated as Z 2=2.5863 Z1=1.6304
All shorts are converted to opens by applying Kuroda’s identities twice. 8
At fourth step, all impedances are de-normalized, microstrip equivalents are calculated.
Impedance (Ω) Z1=Z5=2.5859*50=129.299 L1=L4=1.6304*50=81.5200 Z2=Z4=0.4793*50=23.9659 L2=L3=1.5992*50=79.9600 Z3=0.3936*50 =19.6800
Width (mm) 0.305 1.080 8.190 1.130 10.48
Eeff 3.00596 3.16777 3.76791 3.17625 3.85611
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Length (mm) Q c=c/(fc*8*√
) = 8.65166
Q c=c/(fc*8*√
) = 8.42780
Q c=c/(fc*8*√
) = 7.72753
Q c=c/(fc*8*√
) = 8.41655
Q c=c/(fc*8*√
) = 7.63865
Figure 1 Chebsyshev Lowpass Lowpass Filter fc=2.5 GHz Er=4.5 Er=4.5 t=1.5 mm
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Figure 2 S11 and S12 response of the designed fi lter. According to this figure we can obviously see see that both lo pass characteristics and cut-off frequency sliding are acceptable. 11
B) MICROSTRIP CHEBSYSEHEV HIGHPASS FILTER While designing highpass filter, we fallow a different procedure from lowpass filter. For constructing highpass design procedure, we are helped by optimum distributed highpass filter circuit scheme and its’ look-up look-up table. The type of filter consists of a cascade cascade of shunt short-circuited stubs of electrical length Q c at some specified frequency fc (usually the cutoff frequency of high pass), separated by connecting lines (unit elements) of electrical length 2Q c. Although the filter consists of only n stubs, it has an insertion function of degree 2 n – 1 in frequency so that its highpass response has 2 n – 1 ripples. Characteristic response of the filter is calculated by the formula given below.
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For highpass applications, the filter has a primary passband from Q c to π - Q c with a cutoff at Q c. The harmonic passbands occur periodically, centered at Q = 3π/2, 5π/2.
1)MICROSTRIP HIGHPASS FILTER DESIGN Example: Design a highpass filter whose input input and output are matched matched to a 50 Ω impedance and cut-off frequency 2,5 GHz with equi-ripple 0.1 dB. Solution: Let we assume that our filter is third degree and Qc is 35 degree. Of course we can choose another filter degree and Qc degree but for third degree necessary impedances can not be get from the used substrate FR4 ( Er=4.5 Er=4.5 t=1.5 mm).
Impedances are de-normalized as Zi=Z0/Yi Zi,i+1=Z0/Yi,i+1. Generally length of short stubs are Qc and length of lines are 2Qc in design procedure of this filter type. On the other hand, according to my simulation results, I get the optimum results when I take take length of short stubs stubs are λ/8 and length of lines are 2λ/8. Additionaly, instead instead of using square root of Eff, I used Eff.
Impedance (Ω) Z1=Z3=50/0.40104=124.6758 L1,2=L2,3=50/1.05378=47.448 Z2=50/0.48294=103.5325
Width (mm) 0.31969 3.07166 0.57839
Eeff 3.01026 3.43108 3.07357 13
Length (mm) Q c=c/(fc*8* ) = 4.9830 Q c=2c/(fc*8* )= 8.7436 Q c=c/(fc*8* ) = 4.8803
Figure 3 Chebsyshev Highpass Filter fc=2.5 GHz Er=4.5 t=1.5 mm
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Figure 4 S11 and S12 response of the designed highp ss filter. According to this figure we can obviously see see that bo h highpass characteristics and cu -off frequency sliding are acceptable. (fc=2.5 GHz)
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Figure
Chebsyshev Highpass Filter fc=3 GHz Er=4.5 t=1.5 mm
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Figure 6 S11 and S12 response of the designed highp ss filter. According to this figure we can obviously see see that bo h highpass characteristics and c t-off frequency sliding are acceptable. (fc=3 GHz)
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E) REFERENCES
Books
1. Microstrip Filters for RF/Microwave Applications, Jia-Sheng Hong, M. J. Lancaster 2. RF Circuit Design, R.Ludwig – P. Bretechko 3. Microwave Engineering, David M. Pozar
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