By Professor Syed Idris Syed Hassan Sch of Elect. & Electron Eng Engineering Campus USM Nibong Tebal SPS Penang Microwave Circuit Design
Introduction 10 weeks lecture + 4 weeks ADS simulation Assessments :8 tests + 2 ADS assignments + 1 final examination Class : lecture rest (tea break) lecture test
Dates 06/04/02 Morning 20/04/02 Morning 27/04/02 Morning 04/05/02 Morning 11/05/02 Morning 18/05/02 Morning 25/05/02 Morning 08/06/02 Morning 15/06/02 Morning 22/06/02 Morning 29/06/02 morning 06/07/02 Morning 20/07/02 Morning 27/07/02 Morning
Syllabus Transmission lines Network parameters Matching techniques Power dividers and combiners Diode circuits Microwave amplifiers Oscillators Filters design Applications Miscellaneous
References David M Pozar,Microwave Engineering- 2 nd Ed., John Wiley, 1998 E.H.Fooks & R.A.Zakarevicius, Microwave Engineering using microstrip circuits, Prentice Hall,1989. G. D. Vendelin, A.M.Pavio &U.L.Rohde, Microwave circuit design-using linear and Nonlinear Techniques, John Wiley, W.H.Hayward, Introduction to Radio Frequency Design, Prentice Hall, 1982.
Transmission Line
Equivalent Circuit RRLL C G Lossy line Lossless line
Analysis From Kirchoff Voltage Law Kirchoff current law (a) (b)
Analysis Let’s V=V o e j t, I = I o e j t Therefore then a b Differentiate with respect to z
Analysis The solution of V and I can be written in the form of where Let say at z=0, V=V L, I=I L and Z=Z L Therefore and e f c d
Analysis Solve simultaneous equations ( e ) and (f ) Inserting in equations ( c) and (d) we have
Analysis But and Then, we have and * **
Analysis Or further reduce or For lossless transmission line, = j since
Analysis Standing Wave Ratio (SWR) node antinode Ae - z Be z Reflection coefficient Voltage and current in term of reflection coefficient or
Analysis For loss-less transmission line = j By substituting in * and **,voltage and current amplitude are Voltage at maximum and minimum points are and Therefore For purely resistive load g h
Analysis Other related equations From equations (g) and (h), we can find the max and min points Maximum Minimum
Important Transmission line equations ZoZo ZLZL Z in
Various forms of Transmission Lines
Parallel wire cable Where a = radius of conductor d = separation between conductors
Coaxial cable Where a = radius of inner conductor b = radius of outer conductor c = 3 x 10 8 m/s a b
Micro strip w hehe rr t t=thickness of conductor Substrate Conducted strip Ground
Characteristic impedance of Microstrip line Where w=width of strip h=height and t=thickness
Microstrip width For A>1.52 For A<1.52
Simple Calculation Approximation only
Microstrip components Capacitance Inductance Short/Open stub Open stub Transformer Resonator
Capacitance ZoZo ZoZo Z oc For
Inductance ZoZo ZoZo Z oL For
Short Stub ZoZo Z ZoZo ZoZo ZLZL
Open stub ZoZo Z ZoZo ZoZo ZLZL
Quarter-wave transformer ZoZo ZoZo ZTZT Z mx/min ZLZL x in radian At maximum point
Quarter-wave transformer in radian at minimum point
Resonator Circular microstrip disk Circular ring Short-circuited /2 lossy line Open-circuited /2 lossy line Short-circuited /4 lossy line
Circular disk/ring a feeding a * These components usually use for resonators
Short-circuited /2 lossy line n /2 Z in ZoZo where = series RLC resonant cct
Open-circuited /2 lossy line n /2 Z in ZoZo = parallel RLC resonant cct where
Short-circuited /4 lossy line /4 Z in ZoZo = parallel RLC resonant cct where
Rectangular waveguide a b Cut-off frequency of TE or TM mode Conductor attenuation for TE 10
Example Given that a= 2.286cm, b=1.016cm and x S/m. What are the mode and attenuation for 10GHz? Using this equation to calculate cutoff frequency of each mode
Calculation TE 10 a=2.286mm, b=1.016mm, m=1 and n=0,thus we have Similarly we can calculate for other modes
Example TE 10 TE 20 TE 01 TE GHz13.123GHz14.764GHz16.156GHz Frequency 10Ghz is propagating in TE 10. mode since this frequency is below the GHz (TE 20 ) and above 6.561GHz (TE 10 )
continue or
Evanescent mode Mode that propagates below cutoff frequency of a wave guide is called evanescent mode Wave propagation constant is Where k c is referred to cutoff frequency, is referred to propagation in waveguide and is in space j = attenuation =phase constant When f 0 < f c, But Since no propagation then The wave guide become attenuator
Cylindrical waveguide a TE mode Dominant mode is TE 11
continue a TM mode TM 01 is preferable for long haul transmission
Example Find the cutoff wavelength of the first four modes of a circular waveguide of radius 1cm Refer to tables TE modes TM modes 1 st mode 2 nd mode 3 rd &4 th modes
Calculation 1 st mode Pnm= 1.841, TE 11 2 nd mode Pnm= 2.405, TM 01 1 st mode Pnm= 3.832, TE 01 and TM 11
Stripline w b
Continue On the other hand we can calculate the width of stripline for a given characteristic impedance
Continue Where t =thickness of the strip