Fabrication Processes for RF and Microwave Circuits
3.7 Supplementary Problems
712.7 nm
729.0 nm 0.0 nm
0.0 nm 20 μm
20 μm
20 μm
20 μm
20 μm 20 μm 15
15
15
15
15 15 10
10
10
10
10
10
(a)
(b)
5
5
5
Typical surface peaks
Generally smoother surface
5
5
5
Figure 3.39 AFM scans of surface of gold conductor: (a) untreated gold surface and (b) gold surface after chemical polishing.
3.7 Supplementary Problems
Q3.1 The complex relative permittivity of a particular dielectric material is 2.32−j0.007. Determine the loss tangent and Qof the material.
Q3.2 The phase change through a 50 mm length of dielectric at 950 MHz is 144∘. If the dielectric material has aQof 125, what is the complex relative permittivity of the material?
Q3.3 Measurements on a 3 cm thick block of dielectric material at a particular frequency show the transmission loss through the block is 0.35 dB, and the transmission phase change is 0.3 rad. What is the propagation constant of the material?
Q3.4 A microstrip line having a characteristic impedance of 70Ωis fabricated on a 0.635 mm thick alumina substrate (𝜀r=9.8). Determine the dielectric loss (in dB/m) in the line at 8.5 GHz, given that the loss tangent of the alumina is 0.0008.
Q3.5 The following data apply to a 50Ωmicrostrip line fabricated on an LTCC substrate that has a relative permittivity of 9.8:
Substrate: thickness=1.5 mm
Conductor: copper (𝜎=5.76×107S/m) RMS surface roughness=0.31μm
If the loss of a 50 mm length of the line at 2.4 GHz is 0.120 dB, determine the loss tangent of the dielectric.
Q3.6 A 50Ωmicrostrip line designed for use at 94 GHz has the following parameters:
Substrate:𝜀r=9.8 tan𝛿=0.0005 h=0.2 mm
k k RMS surface roughness=0.605μm
Determine the total line loss in dB/mm.
Q3.7 A 12 GHz resonant cavity supporting the TE101 mode is made from a length of rectangular copper waveg- uide having internal dimensions ofa=22.86 mm andb =10.16 mm. Determine the unloadedQof the cavity (𝜎copper=5.76×107S/m).
Q3.8 A 40 GHz resonant cavity is made from a length of circular copper waveguide having an internal diameter of 50 mm.
The cavity supports the TE013mode. Determine:
(i) The required length of the unloaded cavity (ii) The unloadedQof the cavity.
(𝜎copper=5.76×107S/m).
Q3.9 An aperture-coupled resonant cavity is to be constructed from a length of short-circuitedX-band rectangular waveguide (as shown in Figure 3.18), that has internal dimensions ofa=22.86 mm andb=10.16 mm, and is to support the dominant TE101mode. The coupling iris is a centred circular hole in a transverse plate.
Determine:
(i) The required radius of the aperture if the cavity is 19 mm long, and is to resonate at 10 GHz
(ii) The required length of the cavity if the radius of the aperture is 3 mm, and the resonance is to occur at 12 GHz.
(Use a Smith chart to confirm the answers.)
Q3.10 The following data were obtained when the loss tangent of a low-loss dielectric having a relative permittivity of 6 was measured using a resonant cavity perturbation method:
Resonant frequency of unloaded cavity=9.6 GHz Q-factor of the unloaded cavity=3500
Change in resonant frequency when specimen loaded=3%
Change inQ-factor when specimen loaded=4.2%
Determine:
(i) The resonant frequency of the loaded cavity (ii) TheQ-factor of the loaded cavity
(iii) The loss tangent andQof the dielectric
Q3.11 A 60 GHz high-Qcavity is to be made from a length of circular waveguide supporting the TE011mode. The waveg- uide has a diameter of 25 mm. One end of the cavity is terminated by a short circuit and the other by a transverse plate with a small coupling iris. Determine the required length of the cavity if the iris has a normalized susceptance of –j5.2.
Q3.12 The following data apply to a 50Ωmicrostrip line used in an antenna feed system:
Substrate: 𝜀r=9.8
h=0.3 mm tan𝛿=0.0015
Conductor: Copper (𝜎=5.87×107S/m)
If the system specification requires that the loss in the microstrip feed line should not exceed 0.08 dB/mm at 25 GHz, determine the maximum acceptable RMS surface roughness of the conductor.
k k
References 125
Q3.13 Draw a graph showing how the total loss (in dB/mm) of the microstrip line specified in Q3.12 varies as a function ofΔ/𝛿for 0.5≤Δ/𝛿≤2.
Q3.14 Repeat the graph in Q3.13, but for a line of 70Ωcharacteristic impedance. Comment upon the result.
References
1 Harrop, P.J. (1972).Dielectrics. London: Butterworth.
2 Hammerstad, E.O. and Bekkadal, F. (1975).A Microstrip Handbook, ELAB Report, STF44 A74169. University of Trond- heim Norway.
3 Sain, A. and Melde, K.L. (2013). Broadband characterization of coplanar waveguide interconnects with rough conductor surfaces.IEEE Transactions on Components, Packaging and Manufacturing Technology3 (6): 1038–1046.
4 Iwai, T. and Mizatani, D. (2015). Motoaki Tani measurement of high-frequency conductivity affected by conductor sur- face roughness using dielectric rod resonator method.Proceedings of IEEE International Symposium on Electromagnetic Compatibility, Dresden, Germany (Auguest 2015), pp. 634–639.
5 Gold, G. and Helmreich, K. (2015). Surface impedance concept for modelling conductor roughness.Proceedings of IEEE International Microwave Symposium, Phoenix, AZ (May 2015).
6 Cruickshank, D.B. (2011).Microwave Materials for Wireless Applications. Norwood, MA: Artech House.
7 Pitt, K.E.G. (ed.) (2005).Handbook of Thick Film Technology. Port Erin, Isle of Man, UK: Electrochemical Publications Ltd.
8 Tian, Z., Free, C.E., Aitchison, C., Barnwell, P., and Wood, J. (2002). Multilayer thick-film microwave components and measurements.Proceedings of 35th International Symposium on Microelectronics, Denver, CO (4–6 September 2002).
9 Tian, Z., Free, C.E., Barnwell, P., Wood, J., and Aitchison, C. (2001). Design of novel multilayer microwave coupled line structures using thick-film technology.Proceedings of 31st European Microwave Conference, London (24–26 September 2001).
10 Osman, N. and Free, C.E. (2014). Miniature rectangular ring band-pass filter with embedded barium strontium titanate capacitors.Proceedings of Asia Pacific Microwave Conference, Sendai, Japan (November 2014), pp. 306–308.
11 Chen, X.-P., Wu, K. et al. (2014).IEEE Microwave Magazine15 (5): 108–116.
12 Chen, X.-P. and Wu, K. (2014). Substrate integrated waveguide filters: design techniques and structure innovations.IEEE Microwave Magazine15 (6): 121–133.
13 Chen, X.-P. and Wu, K. (2014). Substrate integrated waveguide filters: practical aspects and design considerations.IEEE Microwave Magazine15 (7): 75–83.
14 Schorer, J., Bornemann, J., and Rosenberg, U. (2014). Comparison of surface mounted high quality filters for combina- tion of substrate integrated and waveguide technology.Proceedings of 2014 Asia Pacific Microwave Conference, Sendai, Japan (4–7 November 2014), pp. 929–931.
15 Gaynor, M.P. (2007).System-in-Package: RF Design and Applications. Norwood, MA: Artech House.
16 Henry, M., Osman, N., Tick, T., and Free, C.E. (2008). Integrated air-filled waveguide Antennas in LTCC for G-band operation.Proceedings of Asia Pacific Microwave Conference, Hong Kong (December 2008).
17 Belhaj, M.M., Wei, W., Palleecchi, E., Mismer, C., Roch-jeune, I., and Happy, H. (2014). Inkjet printed flexible trans- mission lines for high frequency applications up to 67 GHz.Proceedings of 9th European Microwave Integrated Circuit Conference, Rome, Italy (6–7 October 2014), pp. 584–587.
18 Kim, S., Shamim, A., Georgiadis, A. et al. (2016). Fabrication of fully inkjet-printed Vias and SIW structures on thick polymer substrates.IEEE Transactions on Components, Packaging and Manufacturing Technology6 (3): 486–496.
19 Nikfalazar, M., Zheng, Y., Wiens, A., Jakoby, R., Friederich, A., Kohler, C., and Binder, J.R. (2014).Proceedings of 44th European Microwave Conference, Rome, Italy (6–9 October 2014), pp. 504–507.
20 Chen, M.Y., Pham, D., Subbaraman, H. et al. (2012). Conformal ink-jet printed C-band phased-Array antenna incorpo- rating carbon nanotube field-effect transistor based reconfigurable true-time delay lines.IEEE Transactions on Microwave Theory and Techniques60 (1): 179–184.
k k 22 Collin, R.E. (1992).Foundations for Microwave Engineering. New York: McGraw-Hill.
23 Karbowiak, A.E. (1965).Trunk Waveguide Communication. London: Chapman and Hall.
24 Orloff, N.D., Obrzut, J., Long, C.J. et al. (2014). Dielectric characterization by microwave cavity perturbation corrected for nonuniform fields.IEEE Transactions on Microwave Theory and Techniques62 (9): 2149–2159.
25 Krupta, J.A., Geyer, R.G., Baker-Jarvis, J., and Ceremuga, J. (1996). Measurements of the complex permittivity of microwave circuit board substrates using split dielectric resonator and re-entrant cavity techniques.Proceedings of 7th International Conference on Dielectric Materials, Measurements and Applications, Bath, UK (23–26 September 1996), pp. 21–24.
26 Krupta, J., Clarke, R.N., Rochard, O.C., and Gregory, A.P. (2000). Split post dielectric resonator technique for precise measurements of laminar dielectric specimens – measurement uncertainties.Proceedings of 13th International Conference on Microwaves, Radar and Wireless Communications, Wroclaw, Poland (22–24 May 2000), pp. 305–308.
27 Dziurdzia, B., Krupta, J., and Gregorczyk, W. (2006). Characterization of thick-film dielectric at microwave frequencies.
Proceedings of 16th International Conference on Microwaves, Radar and Wireless Communications, Krakow, Poland (22–24 May 2006), pp. 361–364.
28 Cullen, A.L. and Yu, P.K. (1971). The accurate measurement of permittivity by means of an open resonator.Proceedings of the Royal Society of LondonA325: 493–509.
29 Cullen, A.L., Nagenthiram, P., and Williams, A.D. (1972). Improvement in open resonator permittivity measurement.
Electronics Letters8 (23): 577–579.
30 Komiyama, B., Kiyokawa, M., and Matsui, T. (1991). Open resonator for precision measurements in the 100 GHz band.
IEEE Transactions on Microwave Theory and Techniques39 (10): 1792–1796.
31 Hirvonen, T.M., Vainikainen, P., Lozowski, A., and Raisanen, A.V. (1996). Measurement of dielectrics at 100 GHz with an open resonator connected to a network analyzer.IEEE Transactions on Instrumentation and Measurement45 (4):
780–786.
32 Afsar, M.N., Ding, H., and Tourshan, K. (1999). A new open resonator technique at 60 GHz for permittivity and loss tangent measurement of low-loss materials.Proceedings of 1999 IEEE International Microwave Symposium, Anaheim, CA (13–19 June 1999), pp. 1755–1758.
33 Afsar, M.N., Moonshiram, A., and Wang, Y. (2004). Assessment of random and systematic errors in millimeter-wave dielectric measurement using open resonator and Fourier transform spectroscopy systems.IEEE Transactions on Instru- mentation and Measurement53 (4): 899–906.
34 Ghodgaonkar, D.K., Varadan, V.V., and Varadan, V.K. (1989). A free-space method for measurement of dielectric con- stants and loss tangents at microwave frequencies.IEEE Transactions on Instrumentation and Measurement37 (3):
789–793.
35 Osman, N., Leigh, R., and Free, C.E. (2009). Characterization of LTCC material at G-band.Proceedings of 42nd Interna- tional Symposium of Microelectronics, San Jose, CA (1–5 November 2009), pp. 260–267.
36 Troughton, P. (1968). High Q-factor resonators in microstrip.Electronics Letters4 (24): 520–522.
37 Yu, C.-C. and Chang, K. (1997). Transmission-line analysis of a capacitively coupled microstrip ring resonator.IEEE Transactions on Microwave Theory and Techniques45 (11): 2018–2024.
38 Bray, J.R. and Roy, L. (2003). Microwave characterization of a microstrip line using a two-port ring resonator with an improved lumped-element model.IEEE Transactions on Microwave Theory and Techniques51 (5): 1540–1547.
39 Owens, R.P. (1976). Curvature effect in microstrip ring resonators.Electronics Letters12 (14): 356–357.
40 Faria, J.A.B. (2009). A novel approach to ring resonator theory involving even and odd mode analysis.IEEE Transactions on Microwave Theory and Techniques57 (4): 856–862.
41 Hopkins, R. and Free, C.E. (2008). Ultra-wideband slotline dispersion measurements using ring resonator.Electronics Letters44 (21): 1262–1264.
42 Benarabi, B., Bayard, B., Kahlouche, F. et al. (2017). Asymmetric coplanar ring resonator (ACPW) for microwave charac- terization of silver composite conductors.IEEE Transactions on Microwave Theory and Techniques65 (6): 2139–2144.
43 Ghione, G. and Goano, M. (1997). The influence of ground plane width on the ohmic losses of coplanar waveguides with finite lateral ground planes.IEEE Transactions on Microwave Theory and Techniques45 (9): 1640–1642.
k k
127