Steer. M. B. Trew.RJ. "Microwave devices The Electrical Engineering Handbook Ed. Richard c. dorf Boca raton crc Press llc. 2000
Steer, M.B., Trew, R.J. “Microwave Devices” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
39 Microwave Devices Characterization of passive elements Transmission Line Sections.Discontinuities. Impedance Transformers Terminations. Attenuators. Microwave Resonators. Tuning Michael B. steer ements. Hybrid Circuits and Directional Couplers. Filters Ferrite Components.Passive Semiconductor Devices 39.2 Active microwave Devices Robert ].Trew Semiconductor Material Properties. Two-Terminal Active Case Western Reserve University Microwave Devices Three-Terminal Active Microwave Devices 39.1 Passive microwave devices Michael B Steer Wavelengths in air at microwave and millimeter-wave frequencies range from 1 m at 300 MHz to 1 mm at 300 GHz and are comparable to the physical dimensions of fabricated electrical components. For this reason circuit components commonly used at lower frequencies, such as resistors, capacitors, and inductors, are not readily available above 10 GHz. The available microwave frequency lumped elements have dimensions of around mm. The relationship between the wavelength and physical dimensions enables new classes of distributed components to be constructed that have no analogy at lower frequencies. Components are realized by disturbing the field structure on a transmission line, resulting in energy storage and thus reactive effects. Electric(E)field isturbances have a capacitive effect and the magnetic(H)field disturbances appear inductive. Microwave components are fabricated in waveguide, coaxial lines, and strip lines. The majority of circuits are constructed sing strip lines as the cost is relatively low and they are highly reproducible due to the photolithographic hniques used. Fabrication of waveguide components requires precision machining but they can tolerate higher power levels and are more easily realized at millimeter-wave frequencies(30-300 GHz)than either coaxial or microstrip components. Characterization of Passive elements Passive microwave elements are defined in terms of their reflection and transmission properties for an incident wave of electric field or voltage Scattering(S)parameters are based on traveling waves and so naturally describe hese properties. As well they are the only ones that can be measured directly at microwave frequencies. s parameters are defined in terms of root power waves which in turn are defined using forward and backward traveling voltage waves. Consider the N port network of Fig 39.1 where the nth port has a reference transmission ine of characteristic impedance Zo and of infinitesimal length. The transmission line at the nth port serves to separate the forward and backward traveling voltage(V+ and Vm)and current(It and In)waves. The reference characteristic impedance matrix, Z, is a diagonal matrix, Z,= diag(Zol-.Zom. ZoN), and the root power waves at the nth port, a, and bn, are defined by c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 39 Microwave Devices 39.1 Passive Microwave Devices Characterization of Passive Elements • Transmission Line Sections • Discontinuities • Impedance Transformers • Terminations • Attenuators • Microwave Resonators • Tuning Elements • Hybrid Circuits and Directional Couplers • Filters • Ferrite Components • Passive Semiconductor Devices 39.2 Active Microwave Devices Semiconductor Material Properties • Two-Terminal Active Microwave Devices • Three-Terminal Active Microwave Devices 39.1 Passive Microwave Devices Michael B. Steer Wavelengths in air at microwave and millimeter-wave frequencies range from 1 m at 300 MHz to 1 mm at 300 GHz and are comparable to the physical dimensions of fabricated electrical components. For this reason circuit components commonly used at lower frequencies, such as resistors, capacitors, and inductors, are not readily available above 10 GHz. The available microwave frequency lumped elements have dimensions of around 1 mm. The relationship between the wavelength and physical dimensions enables new classes of distributed components to be constructed that have no analogy at lower frequencies. Components are realized by disturbing the field structure on a transmission line, resulting in energy storage and thus reactive effects. Electric (E) field disturbances have a capacitive effect and the magnetic (H) field disturbances appear inductive. Microwave components are fabricated in waveguide, coaxial lines, and strip lines. The majority of circuits are constructed using strip lines as the cost is relatively low and they are highly reproducible due to the photolithographic techniques used. Fabrication of waveguide components requires precision machining but they can tolerate higher power levels and are more easily realized at millimeter-wave frequencies (30–300 GHz) than either coaxial or microstrip components. Characterization of Passive Elements Passive microwave elements are defined in terms of their reflection and transmission properties for an incident wave of electric field or voltage. Scattering (S) parameters are based on traveling waves and so naturally describe these properties. As well they are the only ones that can be measured directly at microwave frequencies. S parameters are defined in terms of root power waves which in turn are defined using forward and backward traveling voltage waves. Consider the N port network of Fig. 39.1 where the nth port has a reference transmission line of characteristic impedance Z0n and of infinitesimal length. The transmission line at the nth port serves to separate the forward and backward traveling voltage (Vn + and Vn – ) and current (In + and I n –) waves. The reference characteristic impedance matrix, Z0 is a diagonal matrix, Z0 = diag(Z01…Z0n…Z0N), and the root power waves at the nth port, an and bn , are defined by a V Z b V Z (39.1) n n n n n n = = + 0 0 and – Michael B. Steer North Carolina State University Robert J. Trew Case Western Reserve University
n ,1,b In, bn VN,IN,bN FIGURE 39.1 N port network with reference transmission lines used in defining S parameters. In matrix form b= z-v-=Y V (39.2) b where (394) (395) and the characteristic admittance matrix Yo and Zo Now S parameters can be formally defined b= Sa (39.6) Thus, Y0V-= SY V+ and so V-= y-SYoV+. This reduces to v-=SV* when all of the reference transmission lines have the same characteristic impedance. S parameters can be related to other network parameters after first considering the relationship of total port voltage V=[V.Vn.VN and current I=[I. I.INT to forward and backward voltage and current waves =V++V d i=i+i (39.7) where I*=Y,V+=Y 2a and F=-YoV-=-Y0b. The development of the relationship between S parameters and other network parameters is illustrated by considering Y parameters defined by I=YV (39.8) Using traveling waves this becomes I++l (399) c 2000 by CRC Press LLC
© 2000 by CRC Press LLC In matrix form (39.2) (39.3) where (39.4) (39.5) and the characteristic admittance matrix Y0 and Z0 –1. Now S parameters can be formally defined: b = Sa (39.6) Thus, Y0 1/2V– = SY0 1/2V+ and so V– = Y0 –1/2SY0 1/2V+. This reduces to V– = SV+ when all of the reference transmission lines have the same characteristic impedance. S parameters can be related to other network parameters after first considering the relationship of total port voltage V = [V1…Vn…VN]T and current I = [I1…In…IN]T to forward and backward voltage and current waves: (39.7) where I+ = Y0V+ = Y0 1/2a and I– = –Y0V– = –Y0 1/2b. The development of the relationship between S parameters and other network parameters is illustrated by considering Y parameters defined by I = YV (39.8) Using traveling waves this becomes FIGURE 39.1 N port network with reference transmission lines used in defining S parameters. a Z V VV b Z V YV == == -+ + -- - 0 1 2 0 1 2 0 1 2 0 1 2 , , V Za Y a V Zb Y b == == +- - - 0 1 2 0 1 2 0 1 2 0 1 2 and a b = ºº [ ] aaa bbb 1 1 nN nN = ºº [ ] T T , , V V = ºº [ ] = ºº [ ] + +++ - - - VVV VVV 1 1 nN nN T T , . – VV V II I = + =+ + - +- and I I YV V Y V V YV V +- + - +- +- += + ( ) ( - ) = + ( ) ( .) (.) 39 9 39 10 0
Y(1+Yo1"sx ) v Y=Y(1-Yosy 1+Yo 2) Alternatively(39.10)can be rearranged as (Y +YV=(Yo-YV (3913) )(Y-Yv (39.14) b Y)(Y-Y) Comparing this to the definition of S parameters, (39.6), leads to S=Y( Y+r)(Y-YY/ (39.16) For the usual case where all of the reference transmission lines have the same characteristic impedance Zo 1/YoY=Yo(1-S)(1 +S)- and S=(Y +y-(Yo-y The most common situation involving conversion to and from S parameters is for a two port with both ports having a common reference characteristic impedance Zo Table 39. 1 lists the most common conversions S parameters require that the reference impedances be specified. If they are not it is assumed that it is 50 $2 They are commonly plotted on Smith Charts- polar plots with lines of constant resistance and reactance I Vendelin et al In Fig. 39.2(a)a travelling voltage wave with phasor Vi is incident at port 1 of a two-port passive element reflected by Z, to if Z T=v/V=s1+s2s2/(1-s2I2), I2=(z1-20)(z1+z) More convenient measures of reflection and transmission performance are the return loss and insertion loss as they are relative measures of power in transmitted and reflected signals. In decibels RETURN LOSS =-20 log T(dB) INSERTION LOSS =-20 log t(dB) The Zin=Zo(1+T/1-D)
© 2000 by CRC Press LLC Alternatively (39.10) can be rearranged as Comparing this to the definition of S parameters, (39.6), leads to (39.16) For the usual case where all of the reference transmission lines have the same characteristic impedance Z0 = 1/Y0, Y = Y0(1 – S)(1 + S)–1 and S = (Y0 + Y)–1(Y0 – Y). The most common situation involving conversion to and from S parameters is for a two port with both ports having a common reference characteristic impedance Z0. Table 39.1 lists the most common conversions. S parameters require that the reference impedances be specified. If they are not it is assumed that it is 50 W. They are commonly plotted on Smith Charts — polar plots with lines of constant resistance and reactance [Vendelin et al.]. In Fig. 39.2(a) a travelling voltage wave with phasor V1 + is incident at port 1 of a two-port passive element. A voltage V1 – is reflected and V2 – is transmitted. V2 – is then reflected by ZL to produce V2 + . V2 + is zero if ZL = Z0. The input voltage reflection coefficient transmission coefficient and the load reflection coefficient More convenient measures of reflection and transmission performance are the return loss and insertion loss as they are relative measures of power in transmitted and reflected signals. In decibels RETURN LOSS = –20 log G1 (dB) INSERTION LOSS = –20 log T (dB) The input impedance at port 1, Zin, is related to G by Y 1 Y SY V Y 1 Y SY V Y Y 1 Y SY 1 Y SY - + - + - - - ( - ) = + ( ) = - ( )( + ) ( . ) ( . 39 11 39 12 0 0 1 2 0 1 2 0 1 2 0 1 2 0 0 1 2 0 1 2 0 1 2 0 1 2 1 ) Y Y V Y Y V V Y Y Y Y V Y b Y Y Y Y Y a 0 0 0 1 0 0 1 2 0 1 0 0 1 2 39 13 39 14 39 15 ( + ) = - ( ) = + ( ) ( - ) = + ( ) ( - ) - + - - + - - - ( . ) ( . ) ( . ) S = + Y (Y Y) (Y - Y)Y - - 0 1 2 0 1 0 0 1 2 G G 1 1 1 11 12 21 22 = = + (1 - ) - + V V s s s s L , T = V V 2 1 - + GL L L = - (Z Z0 0 ) (Z + Z ) Z Z in = 0 (1 + G G 1 1 - 1 )
TABLE 39.1 Two-Port S Parameter Conversion Chart for Impedance, Z, Admittance, Y, and Hybrid, H, Parameters z1=z12 Z 6=(z1+1)(2+1)-Z12 8=(1-S1)(1-S2)-S1Sx -联+1-2列动+S)s)+ Z12=2S26 S21=2Z2x/6 =2S Z1+1)2-1)-2l Sa1+S2)+S12S216 Y Y12 =Y2 6=(1+s1)(+S2)-S2S2 x=-s)+S2)+SS]6 +y 6 +S,川1-S H H:=H (+H)1+ (1-S1)(1+S2)+S /6 +H)-B1)+比H161=Ss)-ss] Note: The Z, Y" and H parameters are normalized to zo- 20 2 PORT 1 PORT 2 FIGURE 39.2 Incident, reflected and transmitted traveling voltage waves at(a)a passive microwave element and(b)a The reflection characteristics are also described by the voltage standing wave ratio(VSWR), a quantity that can be measured using relatively simple equipment. The VSWR is the ratio of the maximum voltage amplitude or the imput transmission line(yi+/vi) to the minimum voltage amplitude(v1l-Mvil Thus, VSWR=(1+r)/1-D c 2000 by CRC Press LLC
© 2000 by CRC Press LLC The reflection characteristics are also described by the voltage standing wave ratio (VSWR), a quantity that can be measured using relatively simple equipment. The VSWR is the ratio of the maximum voltage amplitude on the imput transmission line to the minimum voltage amplitude . Thus, TABLE 39.1 Two-Port S Parameter Conversion Chart for Impedance, Z, Admittance, Y, and Hybrid, H, Parameters S In Terms of S Z Y H Note: The Z¢, Y¢ and H¢ parameters are normalized to Z0. FIGURE 39.2 Incident, reflected and transmitted traveling voltage waves at (a) a passive microwave element and (b) a transmission line. z zZ z zZ ¢ = ¢ = 11 11 0 12 12 0 z zZ z zZ ¢ = ¢ = 21 21 0 22 22 0 d = ( ) Z Z ZZ ¢ + ( ) ¢ + - ¢ ¢ 11 22 12 21 1 1 d= - ( ) 1 1( ) - - 11 22 12 21 S S SS S Z Z ZZ 11 11 22 12 21 = ( ) ¢ - 1 1 ( ) ¢ + - ¢ ¢ [ ] d ¢ = + ( )( ) - + [ ] z S S SS 11 11 22 12 21 1 1 d S Z 12 12 = 2 ¢ d Z S ¢ = 12 12 2 d S Z 21 21 = 2 ¢ d Z S ¢ = 21 21 2 d S Z Z ZZ 22 11 22 12 21 = ( ) ¢ + 1 1 ( ) ¢ - - ¢ ¢ [ ] d ¢ = - ( )( ) + + Z S S SS 22 11 22 12 21 [ ] 1 1 d Y YZ Y YZ ¢ = ¢ = 11 11 0 12 12 0 Y YZ Y YZ ¢ = ¢ ¢ = 21 21 0 22 22 0 d= + ( ) 1 1 ¢ ( ) + ¢ = ¢ ¢ 11 22 12 21 Y Y YY d= + ( ) 1 1( ) + - 11 22 12 21 S S SS S Y Y YY 11 11 22 12 21 = - ( ) 1 1 ¢ ( ) + ¢ + ¢ ¢ [ ] d ¢ = - ( )( ) + + Y S S SS 11 11 22 12 21 [ ] 1 1 d S Y 12 12 = -2 ¢ d Y S ¢ = - 12 12 2 d S Y 21 21 = -2 ¢ d Y S ¢ = - 21 21 2 d S Y Y YY 22 11 22 12 21 = + ( ) 1 1 ¢ ( ) - ¢ + ¢ ¢ [ ] d ¢ = + ( )( ) - + Y S S SS 22 11 22 12 21 [ ] 1 1 d H HZ H H ¢ = ¢ = 11 11 0 12 12 H H H HZ ¢ = ¢ = 21 21 22 22 0 d= + ( ) 1 1 ¢ ( ) + ¢ - ¢ ¢ H H HH 11 22 12 21 d= - ( ) 1 1( ) + + 11 22 12 21 S S SS S H H HH 11 11 22 12 21 = ( ) ¢ - 1 1 ( ) ¢ + - ¢ ¢ [ ] d ¢ = + ( )( ) + - H S S SS 11 11 22 12 21 [ ] 1 1 d S H 12 12 = 2 ¢ d H S ¢ = 12 12 2 d S H 21 21 = -2 ¢ d H S ¢ = - 21 21 2 d S H H HH 22 11 22 12 21 = + ( ) 1 1 ¢ ( ) - ¢ + ¢ ¢ [ ] d ¢ = - ( )( ) - - H S S SS 22 11 22 12 21 [ ] 1 1 d V V 1 1 + - ( ) + V V 1 1 + - ( ) - VSWR = 1 1 1 1 ( + G G ) ( - )