SETFLCE DIELECTRIC FIGURE 39. 3 Sections of transmission lines used for interconnecting components:(a)waveguide tapered section (b)waveguide E-plane bend, (c)waveguide H-plane bend, (d)waveguide twist, and (e)microstrip taper. Most passive devices, with the notable exception of ferrite devices, are reciprocal and so Spy=Sap. A loss-less sp 1, which is a statement of power cons Most microwave circuits are designed to minimize the reflected energy and maximize transmission at least over the frequency range of operation. Thus, the return loss is high and the VSwR =1 for well-designed circuits. A terminated transmission line such as that in Fig. 39.2(b) has an input impedance z.=Z ZL+ jZo tanh yd Zo+ jz, tanh yo Thus, a short section(Ya < 1)of a short circuited(Z=0)transmission line looks like an inductor and capacitor if it is open circuited(Z,= oo). When the line is a half wavelength long, an open circuit is at the input to the line if the other end is short circuited Transmission line sections The simplest microwave circuit element is a uniform section of transmission line which can be used to introduce a time delay or a frequency-dependent phase shift. Other line segments for interconnections include bend corners,twists, and transitions between lines of different dimensions(see Fig 39.3). The dimensions and shapes are designed to minimize reflections and so maximize return loss and minimize insertion loss Discontinuities The waveguide discontinuities shown in Fig. 39. 4(a)-(f) illustrate most clearly the use of E and H field distu bances to realize capacitive and inductive components. An E-plane discontinuity[ Fig. 39. 4(a)] can be modeled approximately by a frequency-dependent capacitor. H-plane discontinuities [Figs. 39.4(b)and (c)] resemble inductors as does the circular iris of Fig. 39.4(d). The resonant waveguide iris of Fig. 39.4(e) disturbs both the E and H fields and can be modeled by a parallel LC resonant circuit near the frequency of resonance Posts in waveguide are used both as reactive elements [Fig. 39.4(f)] and to mount active devices [Fig. 39.4(g).The equivalent circuits of microstrip discontinuities [Figs. 39.4(k)-o)) are again modeled by capacitive elements if the E field is interrupted and by inductive elements if the H field(or current)is interrupted. The stub shown in Fig. 39.4() presents a short circuit to the through transmission line when the length of the stub is / 4.When the stubs are electrically short(<< A 4)they introduce shunt capacitances in the through transmission line
© 2000 by CRC Press LLC Most passive devices, with the notable exception of ferrite devices, are reciprocal and so Spq = Sqp. A loss-less passive device also satisfies the unitary condition: which is a statement of power conservation indicating that all power is either reflected or transmitted. Most microwave circuits are designed to minimize the reflected energy and maximize transmission at least over the frequency range of operation. Thus, the return loss is high and the VSWR ª 1 for well-designed circuits. A terminated transmission line such as that in Fig. 39.2(b) has an input impedance Thus, a short section (gd << 1) of a short circuited (ZL = 0) transmission line looks like an inductor and a capacitor if it is open circuited (ZL = •). When the line is a half wavelength long, an open circuit is presented at the input to the line if the other end is short circuited. Transmission Line Sections The simplest microwave circuit element is a uniform section of transmission line which can be used to introduce a time delay or a frequency-dependent phase shift. Other line segments for interconnections include bends, corners, twists, and transitions between lines of different dimensions (see Fig. 39.3). The dimensions and shapes are designed to minimize reflections and so maximize return loss and minimize insertion loss. Discontinuities The waveguide discontinuities shown in Fig. 39.4(a)–(f) illustrate most clearly the use of E and H field disturbances to realize capacitive and inductive components. An E-plane discontinuity [Fig. 39.4(a)] can be modeled approximately by a frequency-dependent capacitor. H-plane discontinuities [Figs. 39.4(b) and (c)] resemble inductors as does the circular iris of Fig. 39.4(d). The resonant waveguide iris of Fig. 39.4(e) disturbs both the E and H fields and can be modeled by a parallel LC resonant circuit near the frequency of resonance. Posts in waveguide are used both as reactive elements [Fig. 39.4(f)] and to mount active devices [Fig. 39.4(g)]. The equivalent circuits of microstrip discontinuities [Figs. 39.4(k)–(o)] are again modeled by capacitive elements if the E field is interrupted and by inductive elements if the H field (or current) is interrupted. The stub shown in Fig. 39.4(j) presents a short circuit to the through transmission line when the length of the stub is lg/4. When the stubs are electrically short (<< lg/4) they introduce shunt capacitances in the through transmission line. FIGURE 39.3 Sections of transmission lines used for interconnecting components: (a) waveguide tapered section, (b) waveguide E-plane bend, (c) waveguide H-plane bend, (d) waveguide twist, and (e) microstrip taper. Sp pq S 2 = 1, Z Z Z jZ d Z jZ d L L in = + + 0 0 0 tanh tanh g g
SVERSE H-PLAN HI+ 山 FIGURE 39.4 Discontinuities Waveguide discontinuities:(a)capacitive E-plane discontinuity,(b)inductive H-plane dis- continuity,(c)symmetrical inductive H-plane discontinuity,(d)inductive post discontinuity,(e)resonant window discon- tinuity,(f)capacitive post discontinuity(g) diode post mount, and(h)quarter-wave impedance transformer. Microstrip discontinuities:(i)quarter-wave impedance transformer, ()open microstrip stub, (k)step, (I)notch, (m)gap, (n)crossover, and(o)bend. Impedance Transformers Impedance transformers are used to interface two sections of line with different characteristic impedances The smoothest transition and the one with the broadest bandwidth is a tapered line as shown in Fig. 39. 3(a) and(e). This element tends to be very long and so step terminations called quarter-wave impedance transformers ee Fig. 39.4(h)and (i) are sometimes used although their bandwidth is relatively small centered on the frequency at which I=n 4. Ideally, Zo Terminations In a termination, power is absorbed by a length of lossy material at the end of a shorted piece of transmission line [Fig. 39.5(a)and(c)). This type of termination is called a matched load as power is absorbed and reflections are very small irrespective of the characteristic impedance of the transmission line. This is generally preferred the characteristic impedance of transmission lines varies with frequency, particularly so for waveguides. When the characteristic impedance of a line does not vary much with frequency, as is the case with a coaxia line, a simpler smaller termination can be realized by placing a resistor to ground [Fig. 39.5(b) Attenuators Attenuators reduce the level of a signal traveling along a transmission line. The basic construction is to make the line lossy but with a characteristic impedance approximating that of the connecting lines so as to reduce reflections. The line is made lossy by introducing a resistive vane in the case of a waveguide [Fig. 39.5(d)] replacing part of the outer conductor of a coaxial line by resistive material [Fig. 39.5(e)l, or covering the line into the transmission line is controlled, a variable attenuator is achieved, e.g, Fig. 39 material introduced by resistive material in the case of a microstrip line [Fig. 39.5(f). If the amount of lossy c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Impedance Transformers Impedance transformers are used to interface two sections of line with different characteristic impedances. The smoothest transition and the one with the broadest bandwidth is a tapered line as shown in Fig. 39.3(a) and (e). This element tends to be very long and so step terminations called quarter-wave impedance transformers [see Fig. 39.4(h) and (i)] are sometimes used although their bandwidth is relatively small centered on the frequency at which l = lg/4. Ideally, Z0,2 = Terminations In a termination, power is absorbed by a length of lossy material at the end of a shorted piece of transmission line [Fig. 39.5 (a) and (c)]. This type of termination is called a matched load as power is absorbed and reflections are very small irrespective of the characteristic impedance of the transmission line. This is generally preferred as the characteristic impedance of transmission lines varies with frequency, particularly so for waveguides. When the characteristic impedance of a line does not vary much with frequency, as is the case with a coaxial line, a simpler smaller termination can be realized by placing a resistor to ground [Fig. 39.5(b)]. Attenuators Attenuators reduce the level of a signal traveling along a transmission line. The basic construction is to make the line lossy but with a characteristic impedance approximating that of the connecting lines so as to reduce reflections. The line is made lossy by introducing a resistive vane in the case of a waveguide [Fig. 39.5(d)], replacing part of the outer conductor of a coaxial line by resistive material [Fig. 39.5(e)], or covering the line by resistive material in the case of a microstrip line [Fig. 39.5(f)]. If the amount of lossy material introduced into the transmission line is controlled, a variable attenuator is achieved, e.g., Fig. 39.5(d). FIGURE 39.4 Discontinuities. Waveguide discontinuities: (a) capacitive E-plane discontinuity, (b) inductive H-plane discontinuity, (c) symmetrical inductive H-plane discontinuity, (d) inductive post discontinuity, (e) resonant window discontinuity, (f) capacitive post discontinuity, (g) diode post mount, and (h) quarter-wave impedance transformer. Microstrip discontinuities: (i) quarter-wave impedance transformer, (j) open microstrip stub, (k) step, (l) notch, (m) gap, (n) crossover, and (o) bend. Z Z 0, , 1 0 3
MICROSTRIP LOSSY MATERIAL IGURE 39.5 Terminations and attenuators: (a) waveguide matched load,(b)coaxial line resistive termination, (c)microstrip matched load,(d)waveguide fixed attenuator,(e)coaxial fixed attenuator,()microstrip attenuator, and (g)waveguide variable attenuator. Microwave resonators In a lumped element resonant circuit, stored energy is transferred between an inductor which stores Resonators are described in terms of their quality factor tnagnetict ry period. Microwave resonators f the same way, exchanging energy stored in electric and ms but with the energy stored Q=2r6 Maximum energy stored in the resonator at f o (39.17) Power lost in the cavity where fo is the resonant frequency. The Q is reduced and thus the resonator bandwidth is increased by the power lost due to coupling to the external circuit so that the loaded Q Maximum energy stored in the resonator at fa QL= 21o Power lost in the cavity and to the external circuit (39.18) 1/Q+1/Q where Qext is called the external QQ, accounts for the power extracted from the resonant circuit and is typical large. For the simple response shown in Fig. 39.6(a)the half power(3 dB )bandwidth is f/Q2. Near resonance the response of a microwave resonator is very similar to the resonance response of a parallel or series R, L, C resonant circuit [Fig. 39.6(f)and(g). These equivalent circuits can be used over a narrow frequency range. Several types of resonators are shown in Fig. 39.6. Figure 39.6(b)is a rectangular cavity resonator coupled to an external coaxial line by a small coupling loop. Figure 39.6(c)is a microstrip patch reflection resonator c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Microwave Resonators In a lumped element resonant circuit, stored energy is transferred between an inductor which stores magnetic energy and a capacitor which stores electric energy, and back again every period. Microwave resonators function the same way, exchanging energy stored in electric and magnetic forms but with the energy stored spatially. Resonators are described in terms of their quality factor (39.17) where f0 is the resonant frequency. The Q is reduced and thus the resonator bandwidth is increased by the power lost due to coupling to the external circuit so that the loaded Q (39.18) where Qext is called the external Q. QL accounts for the power extracted from the resonant circuit and is typically large. For the simple response shown in Fig. 39.6(a) the half power (3 dB) bandwidth is f0/QL. Near resonance the response of a microwave resonator is very similar to the resonance response of a parallel or series R, L, C resonant circuit [Fig. 39.6(f) and (g)]. These equivalent circuits can be used over a narrow frequency range. Several types of resonators are shown in Fig. 39.6. Figure 39.6(b) is a rectangular cavity resonator coupled to an external coaxial line by a small coupling loop. Figure 39.6(c) is a microstrip patch reflection resonator. FIGURE 39.5 Terminations and attenuators: (a) waveguide matched load, (b) coaxial line resistive termination, (c) microstrip matched load, (d) waveguide fixed attenuator, (e) coaxial fixed attenuator, (f) microstrip attenuator, and (g) waveguide variable attenuator. Q f f = Ê Ë Á ˆ ¯ ˜ 2 0 0 p Maximum energy stored in the resonator at Power lost in the cavity Q f f Q Q L = Ê Ë Á ˆ ¯ ˜ = + 2 1 1 1 0 0 p Maximum energy stored in the resonator at Power lost in the cavity and to the external circuit ext / /