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EKT 441 MICROWAVE COMMUNICATIONS

EKT 441 MICROWAVE COMMUNICATIONS. CHAPTER 5: MICROWAVE FILTERS PART II. Filter Realization Using Distributed Circuit Elements (1). Lumped-element filter realization using surface mounted inductors and capacitors generally works well at lower frequency (at UHF, say < 3 GHz).

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EKT 441 MICROWAVE COMMUNICATIONS

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  1. EKT 441MICROWAVE COMMUNICATIONS CHAPTER 5: MICROWAVE FILTERS PART II

  2. Filter Realization Using Distributed Circuit Elements (1) • Lumped-element filter realization using surface mounted inductors and capacitors generally works well at lower frequency (at UHF, say < 3 GHz). • At higher frequencies, the practical inductors and capacitors loses their intrinsic characteristics. • Also a limited range of component values are available from manufacturer. • Therefore for microwave frequencies (> 3 GHz), passive filter is usually realized using distributed circuit elements such as transmission line sections. • Here we will focus on stripline microwave circuits. f2

  3. Zo l l C L Zo Zc ,  Zc ,   Zo Zo Filter Realization Using Distributed Circuit Elements (2) • Recall in the study of Terminated Transmission Line Circuit that a length of terminated Tline can be used to approximate an inductor and capacitor. • This concept forms the basis of transforming the LC passive filter into distributed circuit elements.    

  4. Zo Connection physical length cannot be ignored at microwave region, comparable to  How do we implement series Tline connection ? (only practical for certain Tline configuration) Zo Filter Realization Using Distributed Circuit Elements (3) • This approach is only approximate. There will be deviation between the actual LC filter response and those implemented with terminated Tline. • Also the frequency response of distributed circuit filter is periodic. • Other issues are shown below. Thus some theorems are used to facilitate the transformation of LC circuit into stripline microwave circuits. Chief among these are the Kuroda’s Identities (See Appendix)

  5. Zin Zin l l  C L Zc ,  Zc ,   More on Approximating L and C with Terminated Tline: Richard’s Transformation (3.1.1a) (3.1.1b) Wavelength at cut-off frequency For LPP design, a further requirment is that: (3.1.1c)

  6. More on Approximating L and C with Terminated Tline: Richard’s Transformation

  7. l Z1 Kuroda’s Identities Note: The inductor represents shorted Tline while the capacitor represents open-circuit Tline. • As taken from [2]. l   Z2/n2 l l   n2Z1 Z2 l l 1: n2   Z2/n2 Z2 l l n2: 1   n2Z1 Z1

  8. g3 1.000H g1 1.000H Zo=1 g4 1 g2 2.000F Example 5.7 – LPF Design Using Stripline • Design a 3rd order Butterworth Low-Pass Filter. Rs = RL= 50Ohm, fc = 1.5GHz. Step 1 & 2: LPP Length = c/8 for all Tlines at  = 1 rad/s

  9. Example 5.7 – LPF Design Using Stripline • Design a 3rd order Butterworth Low-Pass Filter. Rs = RL= 50Ohm, fc = 1.5GHz. Step 3: Convert to Tlines using Richard’s Transformation Length = c/8 for all Tlines at  = 1 rad/s

  10. Example 5.7 Cont… Step 4: Add extra Tline on the series connection Extra T-lines Length = c/8 for all Tlines at  = 1 rad/s

  11. Example 5.7 Cont… Step 5: apply Kuroda’s 1st Identity. Step 6: apply Kuroda’s 2nd Identity. Similar operation is performed here

  12. Example 5.7 Cont… After applying Kuroda’s Identity. Length = c/8 for all Tlines at  = 1 rad/s Since all Tlines have similar physical length, this approach to stripline filter implementation is also known as Commensurate Line Approach.

  13. Example 5.7 Cont… Step 5: Impedance and frequency denormalization. Microstrip line using double-sided FR4 PCB (r = 4.6, H=1.57mm) Length = c/8 for all Tlines at f = fc = 1.5GHz Zc/Ω/8 @ 1.5GHz /mm W /mm 50 13.45 2.85 25 12.77 8.00 100 14.23 0.61

  14. Example 5.7 Cont… Step 6: The layout (top view)

  15. Example 5.8 Design a low pass filter for fabrication using microstrip lines. The specifications are: cutoff freq of 4 GHz, third order, impedance of 50 ohms and a 3dB equal ripple characteristics g1 = 3.3487 = L1 g2 = 0.7117 = C2 g3 = 3.3487 = L3 g4 = 1.0000 = RL

  16. Example 5.8 (cont)

  17. Example 5.8 (cont)

  18. Example 5.8 (cont)

  19. Example 5.8 (cont)

  20. Kuroda’s Identities Note: The inductor represents shorted Tline while the capacitor represents open-circuit Tline. • As taken from [2].

  21. Kuroda’s Identities Note: The inductor represents shorted Tline while the capacitor represents open-circuit Tline. • As taken from [2].

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