1. BITS Pilani Pilani Campus EEE G581 RF & Microwave Engineering SONU BALIYAN 2017H1240098P

2. BITS Pilani Pilani Campus

3. BITS Pilani, Pilani Campus RF FILTERS RF filters represent a class of electronic filter, designed to operate on signals in the MHz to GHz frequency ranges (medium frequency to extremely high frequency). This frequency range is used by most broadcast radio, television, wireless communication (cellphones, Wi-Fi, etc.),So microwave devices will include some kind of filtering on the signals transmitted or received.

4. BITS Pilani, Pilani Campus An ideal filter is a linear two port network that provides perfect transmission of signal for frequencies in a certain pass band region and high attenuation in stopband.

5. BITS Pilani, Pilani Campus Filter Characteristics Important parameters: ■ SWR or S11 ■ Insertion Loss (S21 or S12) ■ Attenuation in the stopband (S21) ■ Group delay ■ Power Handling Capability ■ Size & Weight ■ Tunability

6. BITS Pilani, Pilani Campus Filter Classification Classification may be according to one of the following:  Frequency selection (LP, HP, BP, or BS)  Response (Chebysheve, Maximally flat,…..etc)  Technology (Lumped, Waveguide, SAW, …etc)  Frequency band (Narrow band or Broadband)  Reflection type or absorbing type

7. BITS Pilani, Pilani Campus Image Parameter Method of Filter Design Figure shows an arbitrary, reciprocal two-port network with Image impedances defined as follows: - Zi1 = input impedance at 1 when 2 is terminated with Zi2 Zi2 = input impedance at 2 when 1 is terminated with Zi1

8. BITS Pilani, Pilani Campus ABCD for T and  network

9. BITS Pilani, Pilani Campus Image impedance in T and  network 9 Image impedance Propagation constant Substitute ABCD in terms of Z 1 and Z 2

10. BITS Pilani, Pilani Campus Composite filter 10

11. BITS Pilani, Pilani Campus Constant-k section for Low-pass filter using T- network 11 If we define a cutoff frequency And nominal characteristic impedance Then Z i T = Z o when  =0

12. BITS Pilani, Pilani Campus continue 12 Propagation constant, we have - Two regions can be considered.   <  c : passband of filter -- Z iT become real and  is imaginary (  = j  ) since  2 /  c 2 -1<1.   >  c : stopband of filter--- Z iT become imaginary and  is real (  =  ) since  2 /  c 2 -1<1. cc  Mag cc      passband stopband

13. BITS Pilani, Pilani Campus Constant-k section for Low-pass filter using  -network 13 Z i  = Z o when  =0 Propagation constant is the same as T-network

14. BITS Pilani, Pilani Campus Constant-k section for high-pass filter using T-network 14 If we define a cutoff frequency And nominal characteristic impedance Then Z i T = Z o when  =

15. BITS Pilani, Pilani Campus Constant-k section for high-pass filter using  -network 15 Z i  = Z o when  = Propagation constant is the same for both T and  -network

16. BITS Pilani, Pilani Campus Composite filter 16

17. BITS Pilani, Pilani Campus m-derived filter T-section 17 Constant-k section suffers from very slow attenuation rate and non- constant image impedance. Thus we replace Z 1 and Z 2 to Z’ 1 and Z’ 2 respectively. Let’s Z’ 1 = m Z 1 and Z’ 2 to obtain the same Z iT as in constant-k Solving for Z’ 2, we have

18. BITS Pilani, Pilani Campus Low -pass m-derived T-section 18 For constant-k section and Propagation constant where

19. BITS Pilani, Pilani Campus continue 19 If we restrict 0 < m < 1 and Thus, both equation reduces to Then When  <  c, e  is imaginary. Then the wave is propagated in the network. When  c <  <  op, e  is positive and the wave will be attenuated. When  =  op, e  becomes infinity which implies infinity attenuation. When  >  op, then e  become positif but decreasing.,which meant decreasing in attenuation.

20. BITS Pilani, Pilani Campus Comparison between m-derived section and constant-k section 20 M-derived section attenuates rapidly but after  >  op, the attenuation reduces back. By combining the m-derived section and the constant- k will form so called composite filter.This is because the image impedances are nonconstant.

21. BITS Pilani, Pilani Campus High -pass m-derived T-section 21 and Propagation constant where

22. BITS Pilani, Pilani Campus continue If we restrict 0 < m < 1 and Thus, both equation reduces to Then When   op, e  is becoming negative and the wave will be propagted. Thus  op <  c

23. BITS Pilani, Pilani Campus continue 23    op cc M-derived section seem to be resonated at  =  op due to serial LC circuit. By combining the m-derived section and the constant-k will form composite filter which will act as proper highpass filter.

24. BITS Pilani, Pilani Campus m-derived filter  -section 24 Note that The image impedance is

25. BITS Pilani, Pilani Campus Low -pass m-derived  -section 25 For constant-k section Then and Therefore, the image impedance reduces to The best result for m is 0.6which give a good constant Z i   This type of m-derived section can be used at input and output of the filter to provide constant impedance matching to or from Z o.

26. BITS Pilani, Pilani Campus Composite filter 26

27. BITS Pilani, Pilani Campus Composite filter 27 m<0.6 for m-derived section is to place the pole near the cutoff frequency(  c ) For 1/2  matching network, we choose the Z’ 1 and Z’ 2 of the circuit so that

28. BITS Pilani, Pilani Campus Matching between constant-k and m- derived 28 The image impedance Z iT does not match Z i  The matching can be done by using half-  section as shown below and the image impedance should be Z i1 = Z iT and Z i2 =Z i  It can be shown that Note that

29. BITS Pilani, Pilani Campus Example #1 29 Design a low-pass composite filter with cutoff frequency of 2GHz and impedance of 75 . Place the infinite attenuation pole at 2.05GHz, and plot the frequency response from 0 to 4GHz. For high f- cutoff constant -k T - section or Rearrange for  c and substituting, we have

30. BITS Pilani, Pilani Campus continue 30 For m-derived T section sharp cutoff

31. BITS Pilani, Pilani Campus continue 31 For matching section m=0.6

32. BITS Pilani, Pilani Campus continue 32 A full circuit of the filter

33. BITS Pilani, Pilani Campus continue 33 Pole due to m=0.2195 section Pole due to m=0.6 section