Microwave Circuit Design

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- 2nd 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, 1990. W.H.Hayward, Introduction to Radio Frequency Design, Prentice Hall, 1982.

Transmission Line

Equivalent Circuit R L R L C G Lossy line Lossless line

From Kirchoff Voltage Law Analysis From Kirchoff Voltage Law Kirchoff current law (a) (b)

Analysis then Let’s V=Voejwt , I = Ioejwt Therefore b a Differentiate with respect to z

Analysis The solution of V and I can be written in the form of c d where and Let say at z=0 , V=VL , I=IL and Z=ZL Therefore f e and

Analysis Solve simultaneous equations ( e ) and (f ) Inserting in equations ( c) and (d) we have

Analysis and But Then, we have * ** and

For lossless transmission line , g= jb since a=0 Analysis or Or further reduce For lossless transmission line , g= jb since a=0

Standing Wave Ratio (SWR) Analysis antinode Standing Wave Ratio (SWR) Reflection coefficient node Ae-gz Begz Voltage and current in term of reflection coefficient or

Analysis For loss-less transmission line g = jb By substituting in * and ** ,voltage and current amplitude are g h Voltage at maximum and minimum points are and Therefore For purely resistive load

Analysis Other related equations From equations (g) and (h), we can find the max and min points Maximum Minimum

Important Transmission line equations Zin ZL Zo

Various forms of Transmission Lines

Parallel wire cable Where a = radius of conductor d = separation between conductors

Coaxial cable b a Where a = radius of inner conductor b = radius of outer conductor c = 3 x 108 m/s

Micro strip Conducted strip t Substrate he er w Ground t=thickness of conductor

Characteristic impedance of Microstrip line w=width of strip h=height and t=thickness Where

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 Zoc Zo Zo For For

Inductance ZoL Zo Zo For For

Short Stub Zo Zo Zo ZL Z

Open stub Zo Zo Zo ZL Z

Quarter-wave transformer l/4 x ZT ZL Zo Zo Zmx/min At maximum point q in radian

Quarter-wave transformer at minimum point q in radian

Resonator Circular microstrip disk Circular ring Short-circuited l/2 lossy line Open-circuited l/2 lossy line Short-circuited l/4 lossy line

* These components usually use for resonators Circular disk/ring feeding a a * These components usually use for resonators

Short-circuited l/2 lossy line Zin = series RLC resonant cct Zo b a =nl/2 where

Open-circuited l/2 lossy line Zin = parallel RLC resonant cct Zo b a =nl/2 where

Short-circuited l/4 lossy line Zin = parallel RLC resonant cct Zo b a =l/4 where

Rectangular waveguide b a Cut-off frequency of TE or TM mode Conductor attenuation for TE10

Using this equation to calculate cutoff frequency of each mode Example Given that a= 2.286cm , b=1.016cm and s=5.8 x 107S/m. What are the mode and attenuation for 10GHz? Using this equation to calculate cutoff frequency of each mode

Calculation TE10 a=2.286mm, b=1.016mm, m=1 and n=0 ,thus we have Similarly we can calculate for other modes

Example TE20 TE01 TE11 TE10 6.562GHz 13.123GHz 14.764GHz 16.156GHz Frequency 10Ghz is propagating in TE10.mode since this frequency is below the 13.123GHz (TE20) and above 6.561GHz (TE10)

continue or

Evanescent mode Mode that propagates below cutoff frequency of a wave guide is called evanescent mode Wave propagation constant is Where kc is referred to cutoff frequency, g is referred to propagation in waveguide and b is in space When f0< fc , But g = a +jb a=attenuation b=phase constant Since no propagation then The wave guide become attenuator

Cylindrical waveguide TE mode Dominant mode is TE11

continue a TM mode TM01 is preferable for long haul transmission

Example Refer to tables TM modes TE modes Find the cutoff wavelength of the first four modes of a circular waveguide of radius 1cm 2nd mode Refer to tables TM modes TE modes 3rd &4th modes 3rd &4th modes 1st mode

Calculation 1st mode Pnm= 1.841, TE11 2nd mode Pnm= 2.405, TM01 1st mode Pnm= 3.832, TE01 and TM11

Stripline b w

Continue On the other hand we can calculate the width of stripline for a given characteristic impedance

t =thickness of the strip Continue Where t =thickness of the strip