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
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 Z
0n
and of infinitesimal length. The transmission line at the nth port serves to
separate the forward and backward traveling voltage (V
n
+
and V
n
–
)and current (I
n
+
and I
n
–
)waves. The reference
characteristic impedance matrix, Z
0
is a diagonal matrix, Z
0
= diag(Z
01
…Z
0n
…Z
0N
), and the root power waves
at the nth port, a
n
and b
n
, are defined by
(39.1)aVZ bVZ
nnn nnn
==
+
00
and
–
Michael B. Steer
North Carolina State University
Robert J. Trew
Case Western Reserve University
? 2000 by CRC Press LLC
In matrix form
(39.2)
(39.3)
where
(39.4)
(39.5)
and the characteristic admittance matrix Y
0
and Z
0
–1
. Now S parameters can be formally defined:
b = Sa (39.6)
Thus, Y
0
1/2
V
–
= SY
0
1/2
V
+
and so V
–
= Y
0
–1/2
SY
0
1/2
V
+
. 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
1
…V
n
…V
N
]
T
and current I = [I
1
…I
n
…I
N
]
T
to forward and backward voltage and current waves:
(39.7)
where I
+
= Y
0
V
+
= Y
0
1/2
a and I
–
= –Y
0
V
–
= –Y
0
1/2
b. 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.
aZV VV bZV YV== ==
-+ + -- -
0
12
0
12
0
12
0
12
,,
VZaYa VZbYb== ==
+- - -
0
12
0
12
0
12
0
12
and
ab=??
[]
=??
[]
aaa bbb
nN nN11
TT
,,
VV=??
[]
=??
[]
+ +++ - - -
VVV VVV
nN nN
,.
–
VV V II I=+ =+
+- -
and
II YVV
YV V YV V
+- + -
+- +-
+= +
( )
-
( )
=+
( )
(.)
(.)
39 9
39 10
0
? 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 Z
0
=
1/Y
0
, Y = Y
0
(1 – S)(1 + S)
–1
and S = (Y
0
+ Y)
–1
(Y
0
– 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 Z
0
. 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 V
1
+
is incident at port 1 of a two-port passive element.
A voltage V
1
–
is reflected and V
2
–
is transmitted. V
2
–
is then reflected by Z
L
to produce V
2
+
. V
2
+
is zero if Z
L
= Z
0
.
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 G
1
(dB) INSERTION LOSS = –20 log T (dB)
The input impedance at port 1, Z
in
, is related to G by
Y1YSYV Y1YSYV
Y Y1 Y SY 1 Y SY
-+ -+
--
-
-
( )
=+
( )
=-
( )
+
( )
(.)
(.
3911
3912
00
12
0
12
0
12
0
12
00
12
0
12
0
12
0
12
1
)
YYVYYV
VYYYYV
YbYYYYYa
00
0
1
0
0
12
0
1
00
12
3913
3914
3915
+
( )
=-
( )
=+
( )
-
( )
=+
( )
-
( )
-+
-
-
+
-
-
-
(.)
(.)
(.)
SYYYYYY=+
( )
-
( )
-
-
0
12
0
1
00
12
GG
1111 1221 2
1==+-
( )
-+
VV sss s
L
,
T=VV
21
-+
G
LL L
ZZZZ=-
( )
+
( )
00
ZZ
in
=+-
( )
011
11GG
? 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 Z
0
.
FIGURE 39.2 Incident, reflected and transmitted traveling voltage waves at (a) a passive microwave element and (b) a
transmission line.
￠ = ￠ =zzZ zzZ
11 11 0 12 12 0
￠ = ￠ =zzZ zzZ
21 21 0 22 22 0
d= ￠ +
()
￠ +
()
- ￠￠ZZ ZZ
11 22 12 21
11 d= -
()
-
()
-11
11 22 12 21
SSS
SZ Z ZZ
11 11 22 12 21
11= ￠ -
()
￠ +
()
- ￠￠
[]
d ￠ =+
()
-
()
+
[]
zSSS
11 11 22 12 21
11 d
SZ
12 12
2= ￠ d ￠ =ZS
12 12
2 d
SZ
21 21
2= ￠ d ￠ =ZS
21 21
2 d
SZ Z ZZ
22 11 22 12 21
11= ￠ +
()
￠ -
()
- ￠￠
[]
d ￠ =-
()
+
()
+
[]
ZSSS
22 11 22 12 21
11 d
￠ = ￠ =YYZ YYZ
11 11 0 12 12 0
￠ = ￠￠=YYZ YYZ
21 21 0 22 22 0
d= + ￠
()
+ ￠
()
= ￠￠11
11 22 12 21
YYY d= +
()
+
()
-11
11 22 12 21
SSS
SYYY
11 11 22 12 21
11=-￠
()
+ ￠
()
+ ￠￠
[]
d ￠ =-
()
+
()
+
[]
YSSS
11 11 22 12 21
11 d
SY
12 12
2=- ￠ d ￠ =-YS
12 12
2 d
SY
21 21
2=- ￠ d ￠ =-YS
21 21
2 d
SYYY
22 11 22 12 21
11=+￠
()
- ￠
()
+ ￠￠
[]
d ￠ =+
()
-
()
+
[]
YSSS
22 11 22 12 21
11 d
￠ = ￠ =HHZ HH
11 11 0 12 12
￠ = ￠ =HH HHZ
21 21 22 22 0
d= + ￠
()
+ ￠
()
- ￠￠11
11 22 12 21
HHHH d= -
()
+
()
+11
11 22 12 21
SSS
SH H HH
11 11 22 12 21
11= ￠ -
()
￠ +
()
- ￠￠
[]
d ￠ =+
()
+
()
-
[]
HSSS
11 11 22 12 21
11 d
SH
12 12
2= ￠ d ￠ =HS
12 12
2 d
SH
21 21
2=- ￠ d ￠ =-HS
21 21
2 d
SHHH
22 11 22 12 21
11=+￠
()
- ￠
()
+ ￠￠
[]
d ￠ =-
()
-
()
-
[]
HSSS
22 11 22 12 21
11 d
VV
11
+-
+
()
VV
11
+-
-
()
VSWR = 1 1
11
+
( )
-
( )
GG
? 2000 by CRC Press LLC
Most passive devices, with the notable exception of ferrite devices, are reciprocal and so S
pq
= S
qp
. 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 ? 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 (g
d
<< 1) of a short circuited (Z
L
= 0) transmission line looks like an inductor and a
capacitor if it is open circuited (Z
L
= ￥). 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 distur-
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(j) presents a short circuit to the through transmission line when the length of the stub is l
g
/4. When
the stubs are electrically short (<< l
g
/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.
S
ppq
S
2
1=,
ZZ
ZjZ d
ZjZ d
L
L
in
=
+
+
0
0
0
tanh
tanh
g
g
? 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 = l
g
/4. Ideally, Z
0,2
=
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 39.4Discontinuities. 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, (j) open microstrip stub, (k) step, (l) notch, (m) gap, (n) crossover,
and (o) bend.
ZZ
0103,,
.
? 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 f
0
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 Q
ext
is called the external Q. Q
L
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 f
0
/Q
L
.
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.
Qf
f
=
?
è
?
?
?
÷
2
0
0
p
Maximum energy stored in the resonator at
Power lost in the cavity
Qf
f
QQ
L
=
?
è
?
?
?
÷
=
+
2
1
11
0
0
p
Maximum energy stored in the resonator at
Power lost in the cavity and to the external circuit
ext
//
? 2000 by CRC Press LLC
This resonator has large coupling to the external circuit. The coupling can be reduced and photolithographically
controlled by introducing a gap as shown in Fig. 39.6(d) for a microstrip gap-coupled transmission line
reflection resonator. The Q of a resonator can be dramatically increased by using a high dielectric constant
material as shown in Fig. 39.6(e) for a dielectric transmission resonator in microstrip. One simple application
of a cavity resonator is the waveguide wavemeter [Fig. 39.6(h)]. Here the resonant frequency of a rectangular
cavity is varied by changing the physical dimensions of the cavity with a null of the detector indicating that
the frequency corresponds to the resonant cavity frequency.
Tuning Elements
In rectangular waveguide the basic adjustable tuning element is the sliding short shown in Fig. 39.7(a). Varying
the position of the short will change resonance frequencies of cavities. It can be combined with hybrid tees to
achieve a variety of tuning functions. The post in Fig. 39.4(f) can be replaced by a screw to obtain a screw
tuner which is commonly used in waveguide filters. Sliding short circuits can be used in coaxial lines and in
conjunction with branching elements to obtain stub tuners. Coaxial slug tuners are also used to provide
adjustable matching at the input and output of active circuits. The slug is movable and changes the characteristic
impedance of the transmission line. It is more difficult to achieve variable tuning in passive microstrip circuits.
One solution is to provide a number of pads as shown in Fig. 39.7(c) which, in this case, can be bonded to the
stub to obtain an adjustable stub length. Variable amounts of phase shift can be inserted by using a variable
length of line called a line stretcher, or by a line with a variable propagation constant. One type of waveguide
variable phase shifter is similar to the variable attenuator of Fig. 39.5(d) with the resistive material replaced by
a low-loss dielectric.
FIGURE 39.6Microwave resonators: (a) resonator response, (b) rectangular cavity resonator, (c) microstrip patch reso-
nator, (d) microstrip gap-coupled reflection resonator, (e) transmission dielectric transmission resonator in microstrip,
(f) parallel equivalent circuits, (g) series equivalent circuits, and (h) waveguide wavemeter.
FIGURE 39.7Tuning elements: (a) waveguide sliding short circuit, (b) coaxial line slug tuner, (c) microstrip stub with
tuning pads.
? 2000 by CRC Press LLC
Hybrid Circuits and Directional Couplers
Hybrid circuits are multiport components which preferentially route a signal incident at one port to the other
ports. This property is called directivity. One type of hybrid is called a directional coupler, the schematic of
which is shown in Fig. 39.8(a). Here the signal incident at port 1 is coupled to ports 2 and 3 while very little
is coupled to port 4. Similarly, a signal incident at port 2 is coupled to ports 1 and 4 but very little power
appears at port 3. The feature that distinguishes a directional coupler from other types of hybrids is that the
power at the output ports (here ports 2 and 3) is different. The performance of a directional coupler is specified
by three parameters:
Coupling factor = P
1
/P
3
Directivity = P
3
/P
4
Isolation = P
1
/P
4
(39.19)
Microstrip and waveguide realizations of directional couplers are shown in Figs. 39.8(b) and (c) where the
microstrip coupler couples in the backward direction and the waveguide coupler couples in the forward
direction. The powers at the output ports of the hybrids shown in Fig. 39.9 are equal and so the hybrids serve
to split a signal into half as well as having directional sensitivity.
Filters
Filters are combinations of microwave passive elements designed to have a specified frequency response.
Typically, a topology of a filter is chosen based on established lumped element filter design theory. Then
computer-aided design techniques are used to optimize the response of the circuit to the desired response.
FIGURE 39.8Directional couplers: (a) schematic, (b) backward-coupling microstrip directional coupler, (c) forward-
coupling waveguide directional coupler.
FIGURE 39.9Microstrip hybrids: (a) rat race hybrid and (b) Lange coupler.
? 2000 by CRC Press LLC
Ferrite Components
Ferrite components are nonreciprocal in that the insertion loss for a wave traveling from port A to port B is
not the same as that from port B to port A.
Circulators and Isolators
The most important type of ferrite component is a circulator [Fig. 39.10(a) and (b)]. The essential element of
a circulator is a piece of ferrite which when magnetized becomes nonreciprocal, preferring progression of
electromagnetic fields in one circular direction. An ideal circulator has the scattering matrix
(39.20)
In addition to the insertion and return losses, the performance of a circulator is described by its isolation which
is its insertion loss in the undesired direction. An isolator is just a three-port circulator with one of the ports
terminated in a matched load as shown in the microstrip realization of Fig. 39.10(c). It is used in a transmission
line to pass power in one direction but not in the reverse direction. It is commonly used to protect the output
of equipment from high reflected signals. The heart of isolators and circulators is the nonreciprocal element.
Electronic versions have been developed for MMICs. A four-port version is called a duplexer and is used in
radar systems and to separate the received and transmitted signals in a transceiver.
YIG Tuned Resonator
A magnetized YIG (yttrium iron garnet) sphere, shown in Fig. 39.10(d), provides coupling between two lines
over a very narrow bandwidth. The center frequency of this bandpass filter can be adjusted by varying the
magnetizing field.
FIGURE 39.10Ferrite components: (a) schematic of a circulator, (b) a waveguide circulator, (c) a microstrip isolator, and
(d) a YIG tuned bandpass filter.
[]S
S
S
S
=
é
?
ê
ê
ê
ù
?
ú
ú
ú
00
00
00
13
21
32
? 2000 by CRC Press LLC
Passive Semiconductor Devices
A semiconductor diode can be modeled by a voltage-dependent resistor and capacitor in shunt. Thus an applied
dc voltage can be used to change the value of a passive circuit element. Diodes optimized to produce a voltage
variable capacitor are called varactors. In detector circuits a diode’s voltage variable resistance is used to achieve
rectification and, through design, produce a dc voltage proportional to the power of an incident microwave
signal. A controllable variable resistance is used in a PIN diode to realize an electronic switch.
Defining Terms
Characteristic impedance: Ratio of the voltage and current on a transmission line when there are no reflections.
Insertion loss: Power lost when a signal passes through a device.
Reference impedance: Impedance to which scattering parameters are referenced.
Return loss: Power lost upon reflection from a device.
Voltage standing wave ratio (VSWR): Ratio of the maximum voltage amplitude on a line to the minimum
voltage ampitude.
Related Topics
35.3 Wave Equations and Wave Solutions ? 37.2 Waveguides ? 57.3 Applications of Magnetooptic Effects
Reference
G.D. Vendelin, A.M. Pavio, and U.L. Rohde, Microwave Circuit Design Using Linear and Nonlinear Techniques,
New York: Wiley, 1990.
Further Information
The following books provide good overviews of passive microwave components: Microwave Engineering Passive
Circuits by P.A. Rizzi, Prentice-Hall, Englewood Cliffs, N.J., 1988; Microwave Devices and Circuits by S.Y. Liao,
3rd ed., Prentice-Hall, Englewood Cliffs, N.J., 1990; Microwave Theory, Components and Devices by J.A. Seeger,
Prentice-Hall, Englewood Cliffs, N.J., 1986; Microwave Technology by E. Pehl, Artech House, Dedham, Mass.,
1985; Microwave Engineering and Systems Applications by E.A. Wolff and R. Kaul, Wiley, New York, 1988; and
Microwave Engineering by T.K. Ishii, 2nd ed., Harcourt Brace Jovanovich, Orlando, Fla., 1989. Microwave Circuit
Design Using Linear and Nonlinear Techniques by G.D. Vendelin, A.M. Pavio, and U.L. Rohde, Wiley, New York,
1990, provides a comprehensive treatment of computer-aided design techniques for both passive and active
microwave circuits. Microwave Transistor Amplifiers: Analysis and Design, 2nd ed., by G. Gonzalez, Prentice-
Hall, Englewood Cliffs, N.J., 1996.
The monthly journals IEEE Transactions on Microwave Theory Techniques, IEEE Microwave and Guided Wave
Letters, and IEEE Transactions on Antennas and Propagation publish articles on modeling and design of micro-
wave passive circuit components. Articles in the first two journals are more circuit and component oriented
while the third focuses on field theoretic analysis. These are published by The Institute of Electrical and
Electronics Engineers, Inc. For subscription or ordering contact: IEEE Service Center, 445 Hoes Lane,
P.O. Box 1331, Piscataway, New Jersey 08855-1331.
Articles can also be found in the biweekly magazine Electronics Letters and the bimonthly magazine IEE
Proceedings Part H—Microwave, Optics and Antennas. Both are published by the Institute of Electrical Engineers
and subscription inquiries should be sent to IEE Publication Sales, P.O. Box 96, Stenage, Herts. SG1 2SD, United
Kingdom. Telephone number (0438) 313311.
The International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering is a quarterly
journal devoted to the computer-aided design aspects of microwave circuits and has articles on component
modeling and computer-aided design techniques. It has a large number of review-type articles. For subscription
information contact John Wiley & Sons, Inc., Periodicals Division, P.O. Box 7247-8491, Philadelphia, Pennsyl-
vania 19170-8491.
? 2000 by CRC Press LLC
39.2 Active Microwave Devices
Robert J. Trew
Active devices that can supply gain at microwave frequencies can be fabricated from a variety of semiconductor
materials. The availability of such devices permits a wide variety of system components to be designed and
fabricated. Systems are generally constructed from components such as filters, amplifiers, oscillators, mixers,
phase shifters, switches, etc. Active devices are primarily required for the oscillator and amplifier components.
For these functions, devices that can supply current, voltage, or power gain at the frequency of interest are
embedded in circuits that are designed to provide the device with the proper environment to create the desired
response. The operation of the component is dictated, therefore, by both the capabilities of the active device
and its embedding circuit.
It is common to fabricate microwave integrated circuits using both hybrid and monolithic techniques. In
the hybrid approach, discrete active devices are mounted in RF circuits that can be fabricated from waveguides
or transmission lines fabricated using coaxial, microstrip, stripline, coplanar waveguide, or other such media.
Monolithic circuits are fabricated with both the active device and the RF circuit fabricated in the same
semiconductor chip. Interconnection lines and the embedding RF circuit are generally fabricated using micros-
trip or coplanar waveguide transmission lines.
Active microwave devices can be fabricated as two-terminal devices (diodes) or three-terminal devices
(transistors). Generally, three-terminal devices are preferred for most applications since the third terminal
provides a convenient means to control the RF performance of the device. The third terminal allows for inherent
isolation between the input and output RF circuit. Amplifiers and oscillators can easily be designed by providing
circuits with proper stabilization or feedback characteristics. Amplifiers and oscillators can also be designed
using two-terminal devices (diodes), but input/output isolation is more difficult to achieve since only one RF
port is available. In this case it is generally necessary to use RF isolators or circulators.
The most commonly used two-terminal active devices consist of Gunn, tunnel, and IMPATT diodes. These
devices can be designed to provide useful gain from low gigahertz frequencies to high millimeter-wave frequen-
cies. Three-terminal devices consist of bipolar (BJT), heterojunction bipolar (HBT), and field-effect transistors
(MESFETs and HEMTs). These devices can also be operated from UHF to millimeter-wave frequencies.
Semiconductor Material Properties
Active device operation is strongly dependent upon the charge transport characteristics of the semiconductor
materials from which the device is fabricated. Semiconductor materials can be grown in single crystals with
very high purity. The electrical conductivity of the crystal can be precisely controlled by introduction of minute
quantities of dopant impurities. When these impurities are electrically activated, they permit precise values of
current flow through the crystals to be controlled by potentials applied to contacts, placed upon the crystals.
By clever positioning of the metal contacts, various types of semiconductor devices are fabricated. In this section
we will briefly discuss the important material characteristics.
Semiconductor material parameters of interest for device fabrication consist of those involved in charge
transport through the crystal, as well as thermal and mechanical properties of the semiconductor. The charge
transport properties describe the ease with which free charge can flow through the material. For example, the
velocity-electric field characteristics for several commonly used semiconductors are shown in Fig. 39.11. At low
values of electric field, the charge transport is ohmic and the charge velocity is directly proportional to the
magnitude of the electric field. The proportionality constant is called the mobility and has units of cm
2
/V-s.
Above a critical value for the electric field, the charge velocity saturates and either becomes constant (e.g., Si)
or decreases with increasing field (e.g., GaAs). Both of these behaviors have implications for device fabrication,
especially for devices intended for high-frequency operation. Generally, a high velocity is desired since current
is directly proportional to velocity. Also, a low value for the saturation electric field is desirable since this implies
a high-charge mobility. High mobility implies low resistivity and, therefore, low values for parasitic and access
resistances for semiconductor devices.
? 2000 by CRC Press LLC
The decreasing electron velocity with electric field characteristic for compound semiconductors such as GaAs
and InP makes possible active two-terminal devices called transferred electron devices (TEDs) or Gunn diodes.
The negative slope of the velocity versus electric field characteristic implies a decreasing current with increasing
voltage. That is, the device has a negative resistance. When a properly sized piece of these materials is biased
and placed in a resonant cavity, the device will be unstable up to very high frequencies. By proper selection of
embedding impedances oscillators or amplifiers can be constructed.
Other semiconductor materials parameters of interest include thermal, dielectric constant, energy bandgap,
electric breakdown characteristics, and minority carrier lifetime. The thermal conductivity of the material is
important because it describes how easily heat can be extracted from the device. The thermal conductivity has
units of W/cm-K. Generally, high thermal conductivity is desirable. Compound semiconductors, such as GaAs
and InP, have relatively poor thermal conductivity compared to elemental semiconductors such as Si. Materials
such as SiC have excellent thermal conductivity and have uses in high-power electronic devices. The dielectric
constant is important since it affects the size of the semiconductor device. The larger the dielectric constant,
the smaller the device. Electric breakdown characteristics are important since breakdown limits the magnitudes
of the dc and RF voltages that can be applied to the device. This is turn limits the RF power that can be handled
by the device. The electric breakdown for the material is generally described by the critical value of electric
field that produces avalanche ionization. Minority carrier lifetime is important for bipolar devices, such as pn
junction diodes, rectifiers, and bipolar junction transistors (BJTs). A low value for minority carrier lifetime is
desirable for devices such as diode temperature sensors and switches where low reverse bias leakage current is
desirable. A long minority carrier lifetime is desirable for devices such as bipolar transistors. For materials such
as Si and SiC, the minority carrier lifetime can be varied by controlled impurity doping. A comparison of some
of the important material parameters for several common semiconductors is presented in Table 39.2.
FIGURE 39.11Electron velocity versus electric field for several semiconductors. This figure shows the electron velocity in
several common semiconductors as a funcation of electric field strength. At low electric field the electron velocity is ohmic,
as indicated by the linear characteristic. At higher electric field strength the electron velocity saturates and becomes nonlinear.
Compound semiconductors such as GaAs and InP have highly nonlinear behavior at large electric fields.
TABLE 39.2Material Parameters for Several Semiconductors
k (W/cm-K)
Semiconductor E
g
(eV) e
r
@300 K E
c
(V/cm) t
minority
(s)
Si 1.12 11.9 1.5 3 ′ 10
5
2.5 ′ 10
–3
GaAs 1.42 12.5 0.54 4 ′ 10
5
;10
–8
InP 1.34 12.4 0.67 4.5 ′ 10
5
;10
–8
a-SiC 2.86 10.0 4 (1–5) ′ 10
6
;(1–10) ′ 10
–9
b-SiC 2.2 9.7 4 (1–5) ′ 10
6
;(1–10) ′ 10
–9
? 2000 by CRC Press LLC
Two-Terminal Active Microwave Devices
The IMPATT diode, transferred electron device, and tunnel diode are the most commonly used two-terminal
devices. These devices can operate from the low microwave through high millimeter-wave frequencies. They
were the first semiconductor devices that could provide useful RF power levels at microwave and millimeter-
wave frequencies. The three devices are similar in that they are fabricated from blocks of semiconductors and
require two electrodes (anode and cathode) for supplying dc bias. The same electrodes are used for the RF
port, and since only two electrodes are available, the devices must be operated as a one-port network. This is
generally accomplished by mounting the semiconductor in a pin-type package. The package can then be
positioned in an RF circuit or resonant cavity and the top and bottom pins on the package used as the dc and
RF electrical contacts. This arrangement works quite well and packaged devices can be operated up to about
90–100 GHz. For higher-frequency operation, the devices are generally mounted directly into circuits using
microstrip or some other similar technology.
All three devices operate as negative immittance components. That is, their active characteristics can be
described as either a negative resistance or a negative conductance. Which description to use is determined by
the physical operating principles of the particular device.
Tunnel Diodes
Tunnel diodes [Sze, 1981] generate active characteristics by a mechanism involving the physical tunneling of
electrons between energy bands in highly doped semiconductors. For example, if a pn junction diode is heavily
doped, the conduction and valence bands will be located in close proximity and charge carriers can tunnel
through the electrostatic barrier separating the p-type and n-type regions, rather than be thermionically emitted
over the barrier as generally occurs in this type of diode. When the diode is biased (either forward or reverse
bias) current immediately flows and junction conduction is basically ohmic. In the forward bias direction,
conduction occurs until the applied bias forces the conduction and valence bands to separate. The tunnel
current then decreases and normal junction conduction occurs. In the forward bias region where the tunnel
current is decreasing with increasing bias voltage, a negative immittance characteristic is generated. The immit-
tance is called “N-type” because the I-V characteristic “looks like” the letter N. This type of active element is
short-circuit stable and is described by a negative conductance in shunt with a capacitance. Tunnel diodes are
limited in operation frequency by the time it takes for charge carriers to tunnel through the junction. Since
this time is very short (on the order of 10
–12
s) operation frequency can be very high, approaching 1000 GHz.
Tunnel diodes have been operated at hundreds of gigahertz, limited by practical packaging and parasitic
impedance considerations. The RF power available from a tunnel diode is limited (hundreds of milliwatts level)
since the maximum RF voltage swing that can be applied across the junction is limited by the forward turn-
on characteristics of the device (typically 0.6–0.9 V). Increased RF power can only be obtained by increasing
device area to increase RF current, but device area is limited by operation frequency according to an inverse
scaling law. Tunnel diodes have moderate dc-to-RF conversion efficiency (<10%), very low noise figures, and
are useful in low-noise systems applications, such as microwave and millimeter-wave receivers.
Transferred Electron Devices
Transferred electron devices (i.e., Gunn diodes) [Bosch and Engelmann, 1975] also have N-type active char-
acteristics and can be modeled as a negative conductance in parallel with a capacitance. Device operation,
however, is based upon a fundamentally different principle. The negative conductance derives from the complex
conduction band structure of certain compound semiconductors, such as GaAs and InP. In these direct bandgap
materials the central (or G) conduction band is in close energy-momentum proximity to secondary, higher-
order conduction bands (i.e., the X and L valleys). The electron effective mass is determined by the shape of
the conduction bands, and the effective mass is “light” in the G valley but “heavy” in the higher-order X and
L valleys. When the crystal is biased, current flow is initially due to electrons in the light effective mass G valley
and conduction is ohmic. However, as the bias field is increased, an increasing proportion of the free electrons
are transferred into the X and L valleys where the electrons have heavier effective mass. The increased effective
mass slows down the electrons, with a corresponding decrease in conduction current through the crystal. The
net result is that the crystal displays a region of applied bias voltages where current decreases with increasing
voltage. That is, a negative conductance is generated. The device is unstable and, when placed in an RF circuit
? 2000 by CRC Press LLC
or resonant cavity, oscillators or amplifiers can be fabricated. The device is not actually a diode since no pn or
Schottky junction is used. The phenomenon is a characteristic of the bulk material and the special structure
of the conduction bands in certain compound semiconductors. Most semiconductors do not have the conduc-
tion band structure necessary for the transferred electron effect. The term Gunn diode is actually a misnomer
since the device is not a diode. TEDs are widely used in oscillators from the microwave through high millimeter-
wave frequency bands. They have good RF output power capability (milliwatts to watts level), moderate
efficiency (<20%), and excellent noise and bandwidth capability. Octave band tunable oscillators are easily
fabricated using devices such as YIG (yttrium iron garnet) resonators or varactors as the tuning element. Most
commercially available solid-state sources for 60- to 100-GHz operation generally use InP TEDs.
IMPATT Diodes
IMPATT (impact avalanche transit time) diodes [Bhartia and
Bahl, 1984] are fabricated from pn or Schottky junctions. A typical
pn junction device is shown in Fig. 39.12. For optimum RF per-
formance the diode is separated, by use of specially designed layers
of controlled impurity doping, into avalanche and drift regions.
In operation the diode is reverse biased into avalanche breakdown.
Due to the very sensitive I-V characteristic, it is best to bias the
diode using a constant current source in which the magnitude of
the current is limited. When the diode is placed in a microwave
resonant circuit, RF voltage fluctuations in the bias circuit grow
and are forced into a narrow frequency range by the impedance
characteristics of the resonant circuit. Due to the avalanche pro-
cess the RF current across the avalanche region lags the RF voltage
by 90 degrees. This inductive delay is not sufficient, by itself, to
produce active characteristics. However, when the 90 degrees
phase shift is added to that arising from an additional inductive
delay caused by the transit time of the carriers drifting through
the remainder of the diode external to the avalanche region, a
phase shift between the RF voltage and current greater than 90
degrees is obtained. A Fourier analysis of the resulting waveforms
reveals a device impedance with a negative real part. That is, the
device is active and can be used to generate or amplify RF signals.
The device impedance has an “S-type” active characteristic and
the device equivalent circuit consists of a negative resistance in series with an inductor. The device has significant
pn junction capacitance that must be considered, and a complete equivalent circuit would include the device
capacitance in parallel with the series negative resistance-inductance elements. For optimum performance the
drift region is designed so that the electric field throughout the RF cycle is sufficiently high to produce velocity
saturation for the charge carriers. In order to achieve this, it is common to design complex structures consisting
of alternating layers of highly doped and lightly doped semiconductor regions. These structures are called “high-
low,” “low-high-low,” or “Read” diodes, after the man who first proposed their use. They can also be fabricated
in a back-to-back arrangement to form double-drift structures. These devices are particularly attractive for
millimeter-wave applications. IMPATT diodes can be fabricated from most semiconductors, but are generally
fabricated from Si or GaAs. The devices are capable of good RF output power (mW to W) and good dc-to-RF
conversion efficiency (~10–20%). They operate well into the millimeter-wave region and have been operated
as high as 340 GHz. They have moderate bandwidth capability, but have relatively poor noise performance due
to the impact ionization process.
Although the two-terminal active devices are used in many electronic systems, the one-port characteristic
can introduce significant complexity into circuit design. Isolators and circulators are generally required, and
these components are often large and bulky. They are often fabricated from magnetic materials, which can
introduce thermal sensitivities. For these reasons three-terminal devices have replaced two-terminal devices in
many practical applications. Generally, if two-terminal and three-terminal devices with comparable capability
FIGURE 39.12 Diagram showing the struc-
ture for a typical pn junction IMPATT diode.
This particular diode is called a double-drift
device because avalanche breakdown occurs at
the pn junction, which is located in the middle
of the device. When operated in breakdown,
electrons would travel through the n-type
region towards the positive terminal of the bias
source and holes would travel through the p-
type region towards the negative terminal of the
source. The diode, therefore, operates as two
diodes connected in a back-to-back configura-
tion. The frequency capability of the device is
directly proportional to the width of the n and
p regions.
? 2000 by CRC Press LLC
are available, the three-terminal device offers a more attractive design solution and will be selected. Two-terminal
devices are generally only used when a comparable three-terminal device is not available. For this reason
IMPATT and TED devices are used in millimeter-wave applications, where they retain an advantage in providing
good RF power. Tunnel diodes are not often used, except in a few special applications where their low-noise
and wide-bandwidth performance can be used to advantage.
Three-Terminal Active Microwave Devices
The high-frequency performance of three-terminal semiconductor devices has improved dramatically during
the past two decades. Twenty years ago transistors that could provide useful gain at frequencies above 10 GHz
were a laboratory curiosity. Today, such devices are readily available, and state-of-the-art transistors operate
well above 100 GHz. This dramatic improvement has been achieved by advances in semiconductor growth
technology, coupled with improved device design and fabrication techniques. Semiconductor materials tech-
nology continues to improve and new device structures that offer improved high-frequency performance are
continually being reported.
In this section we will discuss the two most commonly employed transistors for microwave applications, the
metal-semiconductor field-effect transistor (MESFET) [Liechti, 1976] and the bipolar transistor (BJT) [Cooke,
1971]. These two transistors are commonly employed in practical microwave systems as amplifiers, oscillators,
and gain blocks. The transistors have replaced many two-terminal devices due to their improved performance
and ease of use. Transistors are readily integrated into both hybrid and monolithic integrated circuit environ-
ments (MICs). This, in turn, has resulted in significantly reduced size, weight, and dc power consumption, as
well as increased reliability and mean time to failure for systems that use these components. Transistors are
easily biased and the two-port network configuration leads naturally to inherent separation between input and
output networks.
Field-Effect Transistors
A cross-sectional view of a microwave MESFET is shown in Fig. 39.13. The device is conceptionally very simple.
The MESFET has two ohmic contacts (the source and drain) separated by some distance, usually in the range
of 3 to 10 mm. A rectifying Schottky contact (the gate) is located between the two ohmic contacts. Typically,
the gate length is on the order of 0.1 to 2 mm for modern microwave devices. The width of the device scales
with frequency and typically ranges from about 1 to 10 mm for power microwave devices to 50 mm for millimeter-
wave devices. All three contacts are located on the surface of a thin conducting layer (the channel) which is
located on top of a high-resistivity, nonconductive substrate to form the device. The channel region is typically
very thin (on the order of 0.1–0.3 mm) and is fabricated by epitaxial growth or ion implantation. In operation,
the drain contact is biased at a specified potential (positive drain potential for an n-channel device) and the
source is grounded. The flow of current through the conducting channel is controlled by negative dc and
superimposed RF potentials applied to the gate, which modulate the channel current and provide RF gain. The
current flow is composed of only one type of charge carrier (generally electrons) and the device is termed
unipolar. The MESFET can be fabricated from a variety of semiconductors, but is generally fabricated from
GaAs. MESFETs fabricated from Si do not work at high frequencies as well as those fabricated from GaAs due
to lower electron mobility in Si (e.g., m
n
;6000 cm
2
/V-s for GaAs and 1450 cm
2
/V-s for Si). The lower electron
mobility in Si produces high source resistance, which seriously degrades the high-frequency gain possible from
the device.
MESFETs can be optimized for small-signal, low-noise operation or for large-signal, RF power applications.
Generally, low-noise operation requires short gate lengths, relatively narrow gate widths, and highly doped
channels. Power devices generally have longer gate lengths, much wider gate widths, and lower doped channels.
Low-noise devices can be fabricated that operate with good gain (;10 dB) and low noise figure (<3 dB) to
above 100 GHz. Power devices can provide RF power levels on the order of watts (W) up to over 20 GHz.
The current gain of the MESFET is indicated by the f
T
of the device, sometimes called the gain-bandwidth
product. This parameter is defined as the frequency at which the short-circuited current gain is reduced to
unity and can be expressed as
? 2000 by CRC Press LLC
(39.21)
where g
m
is the device transconductance (a measure of gain capability) and C
gs
is the gate source capacitance.
High f
T
is desirable and this is achieved with highly doped channels and low capacitance gates. The RF power
gain is also of interest and this performance can be indicated by the unilateral power gain defined as
(39.22)
where U is the unilateral power gain, f is the operating frequency, R
ds
is the drain-source resistance, and R
g
is
the gate resistance. As this expression indicates, large power gain requires a high f
T
, and a large R
ds
/R
g
ratio. The
highest frequency at which the device could be expected to produce power gain can be defined from the
frequency, f, at which U goes to zero. This frequency is called the maximum frequency of oscillation, or f
max
,
and is defined as
(39.23)
A different form of field-effect transistor can be fabricated by inserting a highly doped, wider-bandgap semi-
conductor between the conducting channel and the gate electrode [Drummond et al., 1986]. The conducting
channel is then fabricated from undoped semiconductor. The discontinuity in energy bandgaps between the
two semiconductors, if properly designed, results in free charge transfer from the highly doped, wide-bandgap
semiconductor into the undoped, lower-bandgap channel semiconductor. The charge accumulates at the inter-
face and creates a two-dimensional electron gas (2DEG). The sheet charge is essentially two-dimensional and
allows current to flow between the source and drain electrodes. The amount of charge in the 2DEG can be
controlled by the potential applied to the gate electrode. In this manner the current flow through the device
can be modulated by the gate and gain results. Since the charge flows at the interface between the two materials,
but is confined in the undoped channel semiconductor, very little impurity scattering occurs and extremely
high charge carrier mobility results. The device, therefore, has very high transconductance and is capable of
very high frequency operation and very low noise figure operation. This type of device is called a high electron
mobility transistor (HEMT). HEMTs can be fabricated from material systems such as AlGaAs/GaAs or AlI-
nAs/GaInAs/InP. The latter material system produces devices that have f
T
’s above 300 GHz and have produced
noise figures of about 1 dB at 100 GHz.
FIGURE 39.13 Cross-sectional view of a microwave MESFET. The cross-hatched areas indicate metal electrodes placed
upon the semiconductor to provide for electrical connections. The areas indicated as n
+
are highly doped, highly conducting
regions to reduce ohmic access resistances. The channel contains the region of current flow and the substrate is highly
resistive and nonconducting so that the current flow is confined to the channel.
f
g
C
T
m
gs
=
2p
U
f
f
R
R
Tds
g
=
?
è
?
?
?
÷
1
4
2
f
fR
R
Tds
g
max
=
2
? 2000 by CRC Press LLC
Bipolar Transistors
A cross-sectional view of a bipolar transistor is shown in Fig. 39.14. The bipolar transistor consists of back-to-
back pn junctions arranged in a sandwich structure. The three regions are designated the emitter, base, and
collector. This type of device differs from the field-effect transistors in that both electrons and holes are involved
in the current transport process (thus the designation bipolar). Two structures are possible: pnp or npn,
depending upon the conductivity type common to both pn junctions. Generally, for microwave applications
the npn structure is used since device operation is controlled by electron flow. In general, electron transport
is faster than that for holes, and npn transistors are capable of superior high-frequency performance compared
to comparable pnp transistors. In operation, the base-emitter pn junction is forward biased and the collector-
base pn junction is reverse biased. When an RF signal is applied to the base-emitter junction the junction allows
a current to be injected into the base region. The current in the base region consists of minority charge carriers
(i.e., carriers with the opposite polarity compared to the base material—electrons for an npn transistor). These
charge carriers then diffuse across the base region to the base-collector junction, where they are swept across
the junction by the large reverse bias electric field. The reverse bias electric field in the base-collector region is
generally made sufficiently large that the carriers travel at their saturation velocity. The transit time of the
charge carriers across this region is small, except for millimeter-wave transistors where the base-collector region
transit time can be a significant fraction of the total time required for a charge carrier to travel from the emitter
through the collector. The operation of the transistor is primarily controlled by the ability of the minority
charge carriers to diffuse across the base region. For this reason microwave transistors are designed with narrow
base regions in order to minimize the time required for the carriers to travel through this region. The base
region transit time is generally the limiting factor in determining the high-frequency capability of the transistor.
The gain of the transistor is also significantly affected by minority carrier behavior in the base region. The
density of minority carriers is significantly smaller than the density of majority carriers (majority carrier density
is approximately equal to the impurity doping density) for typical operating conditions and the probability
that the minority charge will recombine with a majority carrier is high. If recombination occurs, the minority
charge cannot reach the base-collector junction but appears as base current. This, in turn, reduces the current
gain capability of the transistor. Narrow base regions reduce the semiconductor volume where recombination
can occur and, therefore, result in increased gain. Modern microwave transistors typically have base regions
on the order of 0.1–0.25 mm.
The frequency response of a bipolar transistor can be determined by an analysis of the total time it takes for
a charge carrier to travel from the emitter through the collector. The total time can be expressed as
FIGURE 39.14Cross-sectional view of a microwave bipolar transistor (BJT). The cross-hatched areas indicate metal
electrodes. The electrode pattern on the surface is interdigitated with the base electrodes connected together at one end and
the emitter electrodes connected together at the other end. Due to the interdigitated structure, there will always be one more
base electrode than the number of emitter electrodes. The n
+
, p, n
–
, and n
c
+
designations indicate the impurity doping type
and relative concentration level. This device has the collector electrode on the bottom of the device.
? 2000 by CRC Press LLC
t
ec
= t
e
+ t
b
+ t
c
+ t￠
c
(39.24)
where t
ec
is the total emitter-collector transit time, t
e
is the base-emitter junction capacitance charging time,
t
b
is the base region transit time, t
c
is the base-collector junction capacitance charging time, and t
c
￠ is the base-
collector region transit time. The total emitter-base time is related to the gain-bandwidth capability of the
transistor according to the relation
(39.25)
Since the bipolar transistor has three terminals, it can be operated in various configurations, depending upon
the electrode selected as the common terminal. The two most commonly employed are the common emitter
(CE) and the common base (CB) configurations, although the common collector (CC) configuration can also
be used. Small-signal amplifiers generally use the CE configuration and power amplifiers often use the CB
configuration.
The current gain for a bipolar transistor is shown in Fig. 39.15. The current gains of the transistor operated
in the CE and CB configurations are called b and a, respectively. As indicated in the figure, the CE current
gain b is much larger than the CB current gain a, which is limited to values less than unity. For modern
microwave transistors a
o
;0.98–0.99 and b
o
;50–60.
A measure of the RF power gain for the transistor is indicated by the unilateral power gain, which can be
expressed as
(39.26)
where U is the power gain, a
o
is the dc CB current gain, r
b
is the base resistance, C
c
is the collector capacitance,
t
ec
is the total emitter-to-collector transit-time, and r
e
is the emitter resistance. The frequency at which U is
FIGURE 39.15Current gains versus frequency for bipolar transistors. The common-emitter and common-base current
gains are designated as b and a, respectively. The subscript “o” indicates the dc value. The gains decrease with frequency
above a certain value. The frequencies where the gains are reduced by 3 dB from their dc values are indicated as the CE and
CB cutoff frequencies, f
b
and f
a
, respectively. The frequency at which the CE current gain is reduced to unity is defined as
the gain-bandwidth product f
T
. Note that the CB current gain is restricted to values less than unity and that the CE current
gain has values that significantly exceed unity.
f
T
ec
=
1
2pt
U
rCf
rC
a
o
bc ec
ec
o
@
+
?
è
?
?
?
÷
a
pt16
22
? 2000 by CRC Press LLC
? 2000 by CRC Press LLC
r
fr
that it has hig
fabr
r
c
bandgap semic
semic
base-emitt
or qualitative measure of the signal. In both traditional manual tuning and in other automated resonance-
tracking systems, the tuning adjustments usually vary the frequencies, but in this case, one does not have
the option of frequency tuning because the frequency of oscillation of the magnetron is not adjustable and
is nominally constant.
The back-and-forth tuning action needed to locate the resonance is provided by an auxiliary tuning
device, which includes a hollow metal rod that is mounted on a loudspeaker outside the cavity and that
protrudes into the cavity, preferably at a position of maximum electric field. An audio oscillator drives the
loudspeaker at a convenient frequency between 30 and 100 Hz, causing the rod to vibrate and thereby impose
a slight modulation on the microwave field in the cavity. A diode across the cavity from the vibrating rod
detects the amplitude modulation on the electric field.
Both the signal from the audio oscillator and the amplified output of the diode are fed to the mixer at
saturating amplitudes, so the low-pass filtered output of the mixer depends only on the difference between
the phases of these two signals. This phase difference is a measure of the deviation from resonance. Thus,
the output of the mixer constitutes an error signal that indicates the adjustment needed to restore the cavity
to resonance. This signal is fed to the motor that drives the plunger to obtain the required tuning adjustment.
educed to unity (f
max
) is the maximum frequency at which the device will have active characteristics. This
equency is
(39.27)
In order to maximize the high-frequency performance of a transistor, it is necessary to design the device so
h current gain (f
T
), low base resistance (r
b
), and low collector capacitance (C
c
).
Bipolar transistors operating to about 20 GHz are generally fabricated from Si. These devices are easily
icated and low cost. They are useful in moderate gain and low to high RF power applications. The have
elatively high noise figure that varies from about 1 dB at 1 GHz to about 4–5 dB at 10 GHz.
An improved high-frequency bipolar transistor can be fabricated using heterostructures of compound semi-
onductors, such as AlGaAs/GaAs [Kroemer, 1982]. These devices have their emitters fabricated from a wide-
onductor (such as AlGaAs) and the remainder of the device fabricated from the lower-bandgap
onductor (GaAs). The wide-bandgap emitter results in improved charge injection efficiency across the
f
f
rC
T
bc
max
=
é
?
ê
ù
?
ú
8
12
p
/
TRACKING A MICROWAVE-CAVITY
RESONANCE BY USE OF VIBRATIONS
microwave heating apparatus that comprises a resonant cavity excited by a magnetron has been
equipped with an automated tuning system (see figure) to maintain resonance. Resonance is a
desirable condition because it maximizes the transfer of power to the material sample that one
seeks to heat. Typically, the cavity becomes detuned from resonance during heating of the sample because
the permittivity of the sample changes with temperature, altering the electromagnetic field in the cavity. A
system like this that automatically compensates for the detuning effect can enhance efficiency and produc-
tivity in microwave processing of materials.
This tuning system, like others, is based on the old-fashioned radio tuning principle, in which one brackets
a resonance by manual back-and-forth actuation of a tuning device while seeking an optimum quantitative
A
er junction into the base region and much improved RF performance. While the operation of standard
i
The effectiveness of the automated tuning system was demonstrated in experiments in which the micro-
wave apparatus was used to heat an alumina rod. The apparatus was operated with a forward microwave
power of 200 W in two cases; one with and one without automatic tuning. Without automatic tuning, the
rod attained an asymptotic temperature of about 600°C in 5 min. With automatic tuning, the temperature
of the rod exceeded 900°C (and was still increasing) in less than 2 min.
This work was done by Martin Barmatz and Ofer Iny of Caltech for NASA’s Jet Propulsion Laboratory.
(Reprinted with permission from NASA Tech Briefs, 20(10), 54, 1996.)
The vibrating rod modulates the electric field in the cavity. The phase difference between the vibrations and the
modulation provides an indication of deviation from resonance and is used to control repositioning of the
plunger to maintain resonance. (Reprinted with permission from NASA Tech Briefs, 20(10), 54, 1996.)
Si bipolar transistors is limited to frequencies less than about 40 GHz, the heterojunction bipolar transistors
(HBTs) can operate in excess of 100 GHz. They are useful in both low-noise and high RF power applications.
The heterostructure concept has recently been applied in Si-based devices using heterostructures using SiGe/S
compounds. These devices show consider promise for high-frequency applications and the transistors have
demonstrated RF performance comparable to that obtained from the AlGaAs/GaAs HBTs.
Comparison of Bipolar Transistor and MESFET Noise Figures
In low-noise applications, GaAs MESFETs are generally preferred to Si bipolar transistors. The MESFET
demonstrates a lower noise figure than the bipolar transistor throughout the microwave frequency range, and
the advantage increases with frequency. This advantage is demonstrated by a comparison of the expressions
for the minimum noise figure for the two devices. The bipolar transistor has a minimum noise figure that can
be expressed as
é ù
? 2000 by CRC Press LLC
(39.28)Fbf
bf
min
@+ + +
?
ê
ê
?
ú
ú
111
2
2
2
where F
min
is the noise figure and
(39.29)
where I
c
is the collector current and the other terms are as previously defined. The minimum noise figure for
the MESFET is
F
min
@ 1 + mf (39.30)
where
(39.31)
where g
m
is the MESFET transconductance, R
g
is the gate resistance, and R
s
is the source resistance.
Comparing these expressions shows that the minimum noise figure increases with frequency quadratically
for bipolar transistors and linearly for MESFETs. Therefore, as operating frequency increases, the MESFET
demonstrates increasingly superior noise figure performance as compared to Si bipolar transistors.
Conclusions
Various active solid-state devices that are useful at microwave and millimeter-wave frequencies have been
discussed. Both two-terminal and three-terminal devices were included. The most commonly used two-terminal
devices are tunnel diodes, transferred-electron devices, and IMPATT diodes. Three-terminal devices consist of
various forms of field-effect transistors and bipolar transistors. Recent advances employ heterostructures using
combinations of different semiconductors to produce devices with improved RF performance, especially for
high-frequency applications. Both two-terminal and three-terminal devices can provide useful gain at frequen-
cies in excess of 100 GHz. Further improvements are likely as fabrication technology continues to improve.
Defining Terms
Active device: A device that can convert energy from a dc bias source to a signal at an RF frequency. Active
devices are required in oscillators and amplifiers.
Charge carriers: Units of electrical charge that when moving produce current flow. In a semiconductor two
types of charge carriers exist: electrons and holes. Electrons carry unit negative charge and have an
effective mass that is determined by the shape of the conduction band in energy-momentum space. The
effective mass of an electron in a semiconductor is generally significantly less than an electron in free
space. Holes have unit positive charge. Holes have an effective mass that is determined by the shape of
the valence band in energy-momentum space. The effective mass of a hole is generally significantly larger
than that for an electron. For this reason electrons generally move much faster than holes when an electric
field is applied to the semiconductor.
Gain: A measure of the ability of a network to increase the energy level of a signal. Gain is generally measured
in decibels. For voltage or current gain: G (dB) = 20 log(S
out
/S
in
), where S is the RF voltage or current
out of and into the network. For power gain G (dB) = 10 log(P
out
/P
in
). If the network has net loss, the
gain will be negative.
Noise figure: A measure of the noise added by a network to an RF signal passing through it. Noise figure can
be defined in terms of signal-to-noise ratios at the input and output ports of the network. Noise figure
is generally measured in decibels and can be defined as F (dB) = 10 log[(S/N)
in
/(S/N)
out
].
One-port network: An electrical network that has only one RF port. This port must be used as both the
input and output to the network. Two-terminal devices result in one-port networks.
b
Ir
f
cb
T
=
40
2
m
f
gRR
T
mg s
=+
25.
()
? 2000 by CRC Press LLC
Three-terminal device: An electronic device that has three contacts, such as a transistor.
Transconductance: A measure of the gain capability of a transistor. It is defined as the change in output
current as a function of a change in input voltage.
Two-port network: An electrical network that has separate RF ports for the input and output. Three-terminal
devices can be configured into two-port networks.
Two-terminal device: An electronic device, such as a diode, that has two contacts. The contacts are usually
termed the cathode and anode.
Related Topic
37.2 Waveguides
References
P.B. Bhartia and I.J. Bahl, Millimeter Wave Engineering and Applications, New York: Wiley-Interscience, 1984.
B.G. Bosch and R.W. Engelmann, Gunn-Effect Electronics, New York: Halsted Press, 1975.
H.F. Cooke, “Microwave transistors: Theory and design,” Proc. IEEE, vol. 59, pp. 1163–1181, Aug. 1971.
T.J. Drummond, W.T. Masselink, and H. Morkoc, “Modulation-doped GaAs/AlGaAs heterojunction field-effect
transistors: MODFET’s,” Proc. IEEE, vol. 74, pp. 773–822, June 1986.
H. Kroemer, “Heterostructure bipolar transistors and integrated circuits,” Proc. IEEE, vol. 70, pp. 13–25, Jan.
1982.
C.A. Liechti, “Microwave field-effect transistors—1976,” IEEE Trans. Microwave Theory and Tech., vol. MTT-
24, pp. 128–149, June 1976.
S.M. Sze, Physics of Semiconductor Devices, 2nd ed., New York: Wiley-Interscience, 1981.
Further Information
Additional details on the various devices discussed in this chapter can be found in the following books:
I. Bahl and P. Bhartia, Microwave Solid State Circuit Design, New York: Wiley-Interscience, 1988.
M. Shur, Physics of Semiconductor Devices, Englewood Cliffs, N.J.: Prentice-Hall, 1990.
S.M. Sze, High-Speed Semiconductor Devices, New York: Wiley-Interscience, 1990.
S. Tiwari, Compound Semiconductor Device Physics, San Diego: Academic Press, 1992.
S. Wang, Fundamentals of Semiconductor Theory and Device Physics, Englewood Cliffs, N.J.: Prentice-Hall, 1989.
? 2000 by CRC Press LLC
