CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
IMPATT DIODE POWER ACCUMULATOR
A thesis submitted in partial satisfaction of the requirements for the degree of Master of Science in
Engineering
by
Steven Eugene ~amilton /
June, 1979 The Thesis of Steven Eugene Hamilton is approved:
Steven D. Gavazza
Edmond S. Gillespie~
California State University, Northridge
ii TO MY LOVING WIFE AND CHILDREN
iii TABLE OF CONTENTS
Page ABSTRACT ix Section I INTRODUCTION 1 Section II ACTIVE CIRCUIT DESIGN 3 Section III SINGLE DIODE WAVEGUIDE OSCILLATOR 14 Section IV HI-PAC DESIGN 20 Section V POWER COMBINER PERFORMANCE 46
Section VI CONCLUSIONS 57 REFERENCES 59 APPENDIX A DIODE CHARACTERIZATION 62 LIST OF TABLES v LIST OF FIGURES vi
iv f '
LIST OF TABLES
. TABLE 1 Power and Efficiency Versus Rc p4~e 2 Power and Efficiency Results 52 Al Varian Diode VSX9251 AD 99 A2 Diode Comparison 100
v LIST OF FIGURES
Figure Page 1 IMPATT Diode 5 (a) Structure {b) Field Profile (c) Electron Energy (d) Voltage Wave Form (e) Injected and External Current 2 Equivalent Circuit of Diode and Load 8 (a) Diode Chip and Load (b) Packaged Diode and Load
·3 Coaxial Oscillator 10 (a) Structure {b) Equivalent Circuit 4 Design Curves for a Single Step 12 Transformer 5 Single Diode Waveguide Oscillator 15 (a) Side View (b) End View 6 Equivalent Circuit of Single Diode 17 Waveguide Oscillator
7 Kurokawa Waveguide Oscillator End View 21 8 Kurokawa Waveguide Oscillator Top View 22
9 24 Diode HiPac 24 10 Module Configuration 26 (a) Kurokawa Module (b) HiPac Module 11 Cross-Sectional View of Diode 27
12 Module Spacing for HiPac 29
13 Waveguide TE011 Mode Cavity 31 14 Power Versus Current for Different 36 Circuit Load
vi Figure pjge 15 Equivalent Circuit of HiPac 16 Power and Efficiency Versus Current 40 for Rc < Ropt 17 Power and Efficiency Versus Current 41 for Rc = Ropt 18 Power and Efficiency Versus Current 42 for Rc > Ropt 19 IMPATT Oscillator Test Set-up 45
20 Assembled End View of HiPac 47 21 Disassembled View of HiPac 48 22 Power and Efficiency Versus Current 49 8 Diodes in HiPac 23 Comparison of HiPac Performance to so Eight Times Single Diode Data 24 Power and Efficiency Versus Current 53 4 Diodes in HiPac 25 Power and Efficiency Versus Current 54 2 Diodes in HiPac 26 Mechanical Tuning Bandwidth of HiPac 56 Al Low-High-Low Diode 64 (a) Doping Profile (b) Electric Field A2 Hie;h-Low Diode 65 (a) Doping Profile (b) Electric Field
A3 Cross Section of High-Low Diode 66 A4 High-Low Diode 67 (a) Layer Definition (b) Electric Field AS Mean Life to Failure 76 A6 Cross-Sectional View of Diode 78 A7 Doping Profile of High-Low Diode 82
vii Figure AB C-V Plot of High-Low Diode PB~e A9 Equivalent Circuit of Packaged Diode 90 AlO Equivalent Circuit of the Packaged 92 Diode and Load Reactance
viii ABSTRACT
IMPATT DIODE POWER ACCUMULATOR by Steven Eugene Hamilton Master of Science in Engineering
This thesis presents the development of a new type of
I~ATT diode power accumulator. The design has twice the capacity of similar accumulators of the same size. The circuit offers high combining efficiency, reduced thermal interaction and broad tuning bandwidth. The basic concepts of IMPATT oscillators are dis cussed. A single diode version of the power accumulator is presented in detail along with an equivalent circuit. A technique to optimize IMPATT oscillators is covered with experimental verification. The power combiner performance is demonstrated utilizing 2, 4 and 8 diodes. The broad tuning bandwidth of the combiner is presented for the eight diode configuration only. The optimum performance of a power combiner is attained when all the diodes, to be combined, have similar characteristics. To achieve the optimum condition, a
ix technique is presented which determines if the diodes are suitable for combiner application.
X SECTION I INTRODUCTION
The development of solid state microwave sources has experienced tremendous growth over the past ten years. Their high reliability, low cost and small volume are characteristics which attract many designers. Solid state sources have been developed for communications, space and radar systems to replace low and medium power tube type transmitters. The principal devices responsible for solid state growth have been FETs and IMPATTs*. These devices have all served as the fundamental building blocks in the new solid state components. Within the past six years the IMPATT diode has clearly set the pace for solid state technology by replacing several tube type transmitters. This has been accomplished by the development of many new devices and power combining circuits. Recently, improvements in combiner power level have been attained only through the development of higher power diodes. This presents a problem to the solid state design er in that future requirements will exceed the capability
* FET is an acronym for Field Effect Transistor. IMPATT is an acronym for Impact and Transit Time Device.
1 ~'·
2
of present combining techniques. To maintain their growth, solid state designers have resorted to utilizing circuits which can potentially meet future requirements by combining larger numbers of diodes; unfortunately, the new circuits operate at reduced efficiency, require increased fabrica tion cost and exhibit reduced reliability. The aforemen tioned characteristics reduce the advantages that solid state sources have over other transmitter technologies. It is the object of this thesis to reclaim some of the desirable characteristics of solid state sources and, in addition, to satisfy future power requirements. To accom plish this task, a new combining technique has been developed which is capable of summing more devices than was previously attainable. This technique offers high combin ing efficiency and greater reliability than other designs. In order to demonstrate the new combiner circuit, three oscillators were designed and fabricated. The design utilizes a waveguide cavity with a plurality of coaxial modules located along the cavity walls. IMPATT diodes are located at one end of a coaxial transmission line with a bias filter at the other end. The test results are presented both in tabular and graphical form to illustrate the circuits capability and to compare its performance against previously developed technology. A simple model will be presented to discuss the various characteristics of the new circuits, hereafter referred to as HiPac. ~··
SECTION II ACTIVE CIRCUIT DESIGN
A. Introduction The design of an active circuit utilizing negative resistance devices is a complicated process. The param eters which must be considered involve areas of semi conductor physics and standard microwave circuit technol ogy. Unfortunately, the non-linearity of the device, which makes it useful, also prevents closed form solutions in large signal analysis. In addition, as one strives for high power sources, devices are typically combined in complex microwave circuits. These circuits usually have mutual coupling interactions which are as equally difficult to analyze as the active device. In this section, several aspects of the design will be presented, although only those subjects pertinent to the design process will be discussed. Approximations and limits will be presented as required, and more detailed studies will be referenced.
B. IMPATT Diode The type of device used in this study is a gallium arsenide IMPATT [1] [2]. The GaAs IMPATT is the highest efficiency device in the IMPATT family [3] [4]. Silicon
3 4
and indium phosphide materials are also used in construct ing IMPATT diodes; but they operate at half the efficiency of GaAs. As previously stated, the IMPATT diode is a negative resistance device. The negative resistance occurs as a result of a 180° phase difference which is developed be tween the ac current and voltage within the device. The diode is essentially composed of two constituents: (1) the avalanche zone and (2) the drift zone (also known as depletion zone). Consider the simple P+N N+ diode shown in Figure la, with reverse bias applied as indicated. Within the diode, an electric field profile, as shown in Figure lb, is developed. The high field, which exists between x1 and x2 , establishes the avalanche zone. In this region avalanche breakdown occurs which generates hole electron pairs. The region between x2 and x3 is called the drift zone, where the field is high enough to maintain constant drift velocity but not high enough for avalanche to occur. Figure lc shows the energy band diagram under breakdown conditions. The holes generated in the avalanche zone go into the p+ region while the electrons are injected into the N region, drift zone. If an ac voltage, as shown in Figure ld, is applied to the diode, via noise or some other stimulus, the electric field will change periodically with time around some average value. The rate of impact ionization will follow the change in field almost 5
14--- DRIFTZONE ~
p+ N N+ -1 I i I ~+ ~~-- AVALANCHE ZONE (a) Structure
ELECTRIC FIELD ~ p+ I N N+ I I X x 1 x 2 x3 DISTANCE (b) Field Profile
ELECTRON ENERGY
DISTANCE (c) Electron Energy
AC VOLTAGE
8 = Wt
(d) Voltage Wave Form
CURRENT
T 2T (e) Injected and External Currents
Figure 1. lmpatt Diode 6
instantaneously. However, the carrier density does not follow the field change in unison because the generation of carriers depends on the number already generated. So when the field is maximum, carrier generation is still increas ing and does not peak until after the field has decreased by some amount. Thus we have the carrier density peak lagging the ac voltage by about 90° (see Figure ld and le). The injected electrons then enter the drift zone where, because of the field, they travel at a saturated or scattering-limited velocity. Figures ld and le show that the remaining phase shift is provided by the drift zone where the drifting carriers become 180° out of phase with the ac voltage. The length of the drift zone is designed to be about one-half cycle of the desired operating fre quency, and the induced external current is as illustrated in Figure le. This explanation is extremely elementary and was used to give physical insight into IMPATT operation. To com plete this description, one would have to study the effects of ionization rates, doping profile, saturated velocity, etc. Papers covering these topics have been presented in great detail and thus will not be covered here [5] [6] [7]. Appendix A will present further information on the doping profile and internal dimensions of the diode used in this study. The appendix is presented in order to explain how the tolerances on doping and internal dimensions affect 7
microwave performance.
C. Condition for Oscillation
The condition for oscillation, for a negative resist ance device, has been described by several authors [8] [9] [10] and is given by
Z'd + Z'c = 0 (1) where Zd is the impedance of the diode at a reference plane and Z~ is the impedance of the circuit at the same refer ence plane. The impedances Zd and Z~ are presented as
zd = Rd - jXd
Z'c = R'c + J·x• c·
Figure 2a shows an equivalent circuit of the diode chip connected to a matched load impedance. Figure 2b is an equivalent representation of the packaged diode with mounting parasitics connected to the matched load. It is important to recognize that the package and mount para sitics contribute to the impedance at port B which is normally the actual diode/circuit interface. The exact model of the package and mount parasitics will not be con sidered here but have been presented in many papers [11] 8
A I
I A (a) Diode Chip and Load
A B I I Lp
CpT -;x, T... _--<0>------...&.---0>------T..... -ixc I I A B (b) Packaged Diode and Load
Figure 2. Equivalent Circuit of Diode and Load 9
[12]. The important concept here is that Zd, at port A, is transformed via 1p and Cp to an impedance Zd at port B. Where zd is given by
(2)
Since Zd has changed form, Zc must also be modified in order for Equation (1) to be satisfied. The circuit imped
ance Z~ can now be represented as
(3)
Where Zc is the new circuit impedance which matches Zd.
D. Oscillator Design
To develop an understanding of oscillator design, let us consider the simple coaxial oscillator illustrated in Figure 3a. In this circuit, the 50 ohm transmission line is the circuit load impedance. A transmission line of impedance ZT transforms the circuit load impedance to one that satisfies Equation (1) at port B. Usually informa tion is provided by the diode manufacturer in which Zd is given; for our diode, Zd = -1.0 + j5.0. From Equation (1) the impedance presented at port B by the load impedance must be Zc = 1.0 - j5.0. To obtain Zc, a line transformer 10
B
DIODE TRANSFORMER TRANSMISSION LINE
(a) Structure
B C
TRANSFORMER TRANSMISSION ZT LINE
(b) Equivalent Circuit
Figure 3. Coaxial Oscillator 11
of impedance ZT and length L is used to transform the load impedance to Zc· To determine ZT, one may use the trans mission line equation or, more simply, the graph provided by the Hewlett-Packard Company, which is shown in Figure 4. The real and imaginary components of Zc are located on the graph, and the intersection of these lines defines ZT and L. The graph was developed for a load impedance of 50 ohms. In operation, the oscillator will probably not operate in accordance with the design requirements. Toierances on diode package parameters and various fring ing effects usually degrade the performance from ideal. If the manufacturer does not provide data which gives Zd, then one will have to measure this impedance. Active diode impedance measurement requires a large complex measuring system and a computer. The measurement system and associated computer programs have been described by many papers [13] [14] [15] [16] and will not be presented. A simpler de technique can be employed to determine an approximation of Zd; this method requires only the use of a capacitance bridge and a de power supply. Initially the capacitance Cb of the packaged diode is measured at or near the breakdown voltage. The value of diode reactance at a specific frequency, f, can then be calculated by
(4) 12
30 ZT 22.3 20
15.81 10 9 8 7 6 5 4
3 a u 2 a:
1.or------;------+~~~~-7~-+~~*-~~~=r~~~~;-----~ 0.9 0.8 0.7~-----4------+~~~~~~~~~~~~~~~~~~~----~ 0.6 0.5 1------+----: 0.4
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1.1'1\ Figure 4. Design Curves for a Single Step Transformer 13
The value of Rd does not vary extensively from one diode type to another. Typically, Rd has a range between -1.0 and -2.0 ohms; with this fact, one arbitrarily selects Rd. Since changes in the original design are frequently required, this technique is both expedient and economical. SECTION III SINGLE DIODE WAVEGUIDE OSCILLATOR
A. Introduction
The fundamental theory used in development of HiPac is based on the design of a popular single diode waveguide oscillator (SDWO). The SDWO was conceived by Harkless [17] and was developed by Magalhaes and Kurokawa [18] [19]. The SDWO has been used in the development of stable low-noise oscillators because of the controls over stability afforded to the designer. The SDWO basically operates like HiPac but with fewer diodes and in a much simpler form. Thus it will be useful to understand the SDWO before presenting the design of the HiPac.
B. SDWO Description
The SDWO, shown in Figure 5, essentially consists of a coaxial line, hereafter denoted as module, and a high Q cavity resonator. The cavity length is determined by the distance between the short circuit and the inductive iris. The module contains a diode and transformer at one end, a coupling section in the center, and an RF termination at the other end. Basically, the power is coupled from the
14 15
BIAS
RF TERMINATION
--oUTPUT n ~~A0c"u~T ~/- \ IRIS D CAVITY/ RESONATOR
DIODE ANSFORMER
(a) Side View
MODULE-CAVITY { COUPLING LTY RESONATOR
(b) End View)
Figure 5. Single Diode Waveguide Oscillator 16
module to the cavity and coupled from the cavity to the load, through the iris. The frequency of oscillation is determined by the length of the transformer and the posi tion of the short circuit. The impedance required to satisfy Equation (1) is obtained in the following manner: The load impedance, which is the characteristic impedance of the waveguide, is transformed by the iris to the cavity module interface. The impedance at the cavity-module interface is transformed to the diode, thus satisfying Equation (1).
C. Equivalent Circuit Near the resonant frequency of the cavity, the SDWO may be represented by the equivalent circuit shown in Figure 6. Port C is the diode-transformer interface, port A is the cavity-module interface at mid-height of the wave guide, and port B is the connection to the load. The impedance ZT represents the transformer, z1 is the RF termination, and ZL is the load. M1 is the module-cavity coupling, M0 is the cavity-load coupling, and R-L-C repre sents the cavity. It can be shown [20] [21] that, at the resonant fre quency, the coupling factors can be represented as
(5) 1-
'
...... -.....) 18
(6) where ~l is the module-cavity coupling, and ~2 is the cavity-load coupling. By simple manipulation of the equivalent circuit, it is seen that
Rc = [<1 + ~2 ) I (1 + 2~ + ~ 2 >] ~ = (2~1 ~2) I [<1 + 2 ~1 + ~2> <1 + ~2>J (8) where Rc is defined by (3) and ~ is the efficiency of the circuit. The circuit efficiency is defined as the ratio of power delivered to ZL relative to the power available at port A. D. SDWO Optimization The parameter ~l is mainly determined by the position of the module within the cavity and the geometry at that interface. It is important to note that a standing wave exists in the module; therefore, for maximum value of ~ 1 , the diode should be located at the position N Xl4 from mid height of the cavity where N is an odd integer. Because ~l is defined by the position of the module within the cavity, ~ 2 is usually the variable adjusted to maximize the effi ciency. The adjustment of ~ 2 affects both the efficiency and the value of Rc· To maintain the required value of Rc, 19 as ~2 is adjusted for maximum efficiency, it may be neces sary to adjust ZT, see Equation (7). An important condi tion to be considered is when ZT is less than 8 ohms. At that point, ZT may be physically unrealizable, and the efficiency will be less than that predicted by (8). Ideally the value of Rc is adjusted to maximize the power produced by the diode; however, ~l and ~2 are found to be interdependent. Therefore, the design usually has to be iterated several times before maximum power and maximum circuit efficiency are attained. A measurement technique described by Tjassens [22] can be used to determine Pl and ~2 . A more rigorous analytical approach has been described by Davydova and Danyushevskiy [23]. When the circuit is employed as a stable oscillator, ~ 2 is made small. This increases the external Q of the circuit and hence stabil ity. For stable operation, the efficiency of the circuit is essentially traded for stability. HiPac will differ in this respect, because it will be adjusted for maximum efficiency and then injection-locked for stability. SECTION IV HI-PAC DESIGN A. Introduction HiPac is an extension of a multiple diode oscillator developed by Kurokawa [24] [25]. Both designs incorporate the basic technology of the SDWO, namely, the magnetic coupling of a module to a cavity resonator. Kurokawa located a module on each side of a waveguide across the narrow dimension as shown in Figure 7. In addition, he positioned other modules in similar planes spaced by Ag/2, as illustrated in Figure 8. As shown in Figure 8, Kurokawa was able to combine twelve modules in this fashion. The combining efficiency he attained was approximately 77% at a power level of 10.5 watts CW in X-band. This oscillator was the first of its type produced in this country and only preceded by Tager [26] [27] of the U. S. S. R. While Kurokawa's circuit is useful, it is also large and cannot compete with the newer cylindrical combiners. A cylindrical combiner at mid X-band can sum the power from ' 18 modules within a 1.0-inch diameter cavity. The high density packing of modules, though, does lead to thermal interaction between modules, which typically dissipate 20 21 Figure 7. Kurokawa Waveguide Oscillator End View 22 SHORT CIRCUIT \ IRIS MODULE WAVEGUIDE FLANGE Figure 8. Kurokawa Waveguide Oscillator Top View 23 30-40 watts each. If one wanted to combine 18 or more diodes, the simple cylindrical combiner, which is operated in the TMQ10 mode, is limited by its diameter and the size of the diode. To overcome this problem, radial line combiners have been designed which have larger diameters and can combine more modules. Unfortunately, these combiners require mode sup pression, since several modes which do not couple to the output are generated. In addition, these combiners are marginally stable and operate at reduced efficiency. To overcome the stability, thermal and combining limitations of the previous circuits, HiPac was developed. B. HiPac Configuration HiPac essentially doubles the diode capacity of Kuro kawa's circuit by positioning two modules on each sidewall of the waveguide cavity rather than one as shown in Figure 9. In the HiPac configuration, each diode has only one close neighbor; thus, a thermal advantage is realized over cylindrical combiners. The stability of the HiPac circuit is not affected by the use of two closely spaced modules, since no higher order degenerate modes are propagated. The combining limits combined to other circuits is greater, be cause one can simply make the circuit longer to combine more modules. -sHORT CIRCUIT t IRIS TWIN t MODULES WAVEGUIDE FLANGE Figure 9. 24 Diode Hi Pac ~"" 25 The differences between Kurokawa's circuit and HiPac are confined to module position, diode location, and RF termination. In Kurokawa's circuit, the module is posi tioned along the sidewall of the cavity where the magnetic field is maximum. In addition the diode is located 3/4A from the mid-height of the waveguide, as shown in Figure lOa. The HiPac design positions the modules on either side of the maximum magnetic field with the diodes located A/4 from mid-height of the waveguide (Figure lOb). Kurokawa terminates his module with a matched load, and HiPac uses a mismatched load as shown in Figure 10. C. Design In the following paragraph, an X-band design example will be provided to describe the basic structure of HiPac. The modules in HiPac are 0.125 inches in diameter and are separated by 0.150 inches center to center. The diameter of the module is determined by the physical size of the diode. The diode used in the design is a Microwave Associates type 46072 IMPATT, shown in Figure 11. The separation between the modules is determined by compromise between physical and electrical constraints. It is desir able to have the modules as close as possible for the electrical constraint but separated for the physical requirement. In this design, the separation between a 26 WAVEGUIDE CAVITY .,.,..~ / -/--- / MAGNETIC FIELD 3/4>. AMPLITUDE DISTRIBUTION __.TRANSFORMER (a) Kurokawa Module WAVEGUIDE CAVIT\ t DIODE (b) HiPac Module Figure 10. Module Configuration 27 0.100 METAL CAP WIRE MESH DIODE CHIP CERAMIC RING HEAT SINK ----3-48 UNG-2A Figure 11. Cross-Sectional View of Diode 28 f' ' module pair is 0.025 inches. If this spacing is reduced, tighter dimensional tolerances will be required. The module pairs are separated by Ag/2 as shown in Figure 9. The design frequency is 9.25 GHz. The waveguide cavity width is 0.9 inches, and the height of the cavity is 0.4 inches. With the given parameters, the value of Ag can be determined by (9) Ag = The parameter A is the free space wavelength, which equals c/f, where c is the velocity of light and f is the design frequency. The parameter 'a' is the width of the wave guide. For the given conditions, Ag = 1.809 inches and Ag/2 is 0.905 inches. Figure 12 illustrates the module design which is repeated along the length and on both sides of the waveguide cavity. Since the modules are located off the peak of the mag netic field, it is necessary to determine how this affects performance. The waveguide cavity operates in the TE 0 rn mode. Since the field is periodic, it is only necessary to examine the complex field representation of a TE011 mode cavity. The field components for the TE 011 mode are given by [28] CAVITY SIDEWALL 0.905 CENTER LINE: --7 WAVEGUIDE CAVITY Figure 12. Module Spacing for Hi Pac \0"' ·~ 30 Ex = Eo sin , y cos 1T z (10) a c Hy = Ja Eo sin , y cos , z (11) 77[b2 + c2]~ a c Hz = -Jc Eo cos , y sin 1T z (12) 7} [ b2 + c 2]~ b c Figure 13 illustrates the geometry of the TE011 cavity. To examine the reduction in coupling by the placement of modules off of the maximum magnetic field point, let y = 0 in Equations (10), (11), and (12). The only field term re maining is Hz. If Equation (12) is normalized to remove the constants, Hz becomes (13) c A g • At Z = Ag/4 maximum coupling is realized, but in our case z = A.g/4 + ~' (14) where ~is one-half the module spacing in wavelengths. Since the reduction in coupling will be the same on either side A_&, only one side needs to be considered. For the 4 31 > .....>. -~ u ~ '"0 0 -< ::2: -0 tJ.: ~ ~ '"0 -~ ~ ::::~ M e X = -~ CD u.. ~ N 32 given design .1 = 0.041 .\g, so that Z = .!.....& + 0.041 ,\g which 4 results in Hz= 0.967. The maximum coupling then, to a given module, can be considered to be reduced by the reduc tion in Hz. In this example, Hz is reduced 3.3% from the maximum case, Hz = 1.0. As a worse case, one might expect the maximum efficiency to also be reduced by this amount. From Equation {8), it is found that a reduction of 3.3% in $ 1 results in an efficiency reduction of less than 0.3%. To design the module transformer, one must first approximate the impedance presented at the module-cavity interface. Initially one-half the characteristic impedance of the waveguide is selected. The impedance is given by 120 ;;b (15) For our case, A= 1.276, a = 0.900, and b = 0.400, there fore, Zme = 237.55 ohms. Then, by assuming that ZT is a quarter wave line transformer, the impedance is given by {16) where Zc = 1.0, from {3), this results in ZT = 15.41 ohms. To determine the physical dimensions of ZT, the following equation, which defines the impedance of a coaxial line, is used 33 _ 60 .fn b Z - --r (17) f r ~ a . In Equation (17), 'b' is the module diameter and 'a' is the diameter of the coaxial center conductor. The parameter fr is the dielectric constant of the material used between the center conductor and module diameter. In this example, a = 0.083 inches, b = 0.125 inches, and fr = 2.53 (rexo lite} from which Z = 15.41 ohms. The RF termination used in this design was made from Eccosorb MF - 124, a high-loss dielectric (175 dB/inch). The impedance of this load is established by the desired stability and efficiency of the circuit. For maximum effi ciency, the impedance should be zero, but then the circuit would be unstable. If the load is matched to the 50 ob~s transmission line, the circuit would be stable. The module efficiency is given by "~me = (18) where Zme is the impedance at the module-cavity interface and z1 is the termination impedance. For example, if Zmc = 237.55 ohms and z1 =50 ohms, then "~me= 82.6%. For the design example, a termination impedance of 25 ohms was used; therefore, "~me = 90.5%. Since the RF termination 34 does not match the coaxial line impedance, its position is critical. The location is typically set to be A/2 from the face of the termination to mid-height of the cavity. The length of the termination is determined by the desired amount of attenuation of the RF energy incident at the load face. In the example, the length was 0.350 inches which results in 61.3dB of attenuation. The cavity short circuit is positioned Ag/4 from the last module pair. The position of the short circuit deter mines the resonant frequency of the cavity. In addition, it indirectly establishes the coupling of the modules to the cavity. The coupling is altered by the position of the short because the short circuit establishes an electro magnetic boundary. The location of the electric and mag netic fields in the cavity are set by the short circuit position. By moving the short, one also moves the fields; but with the module location fixed within the cavity, the coupling of the module to the cavity is affected. The exact effect was described earlier when the module-cavity coupling was discussed. The output coupling is determined by the iris, shown in Figure 9. In this example, an inductive iris was used. The width of the iris opening determines the amount of coupling between the oscillator cavity and load. For this example, a width of 0.385 inches was used. The adjustment of the iris affects both the impedance, which is ! ' l 35 transformed to the diode, and the combining efficiency. A discussion on how to determine the correct width of the iris will be presented later. D. Optimization The procedure for setting the coupling and optimum transformer is as follows: For a given module transformer, adjust the iris and short position for maximum power, then check the diode threshold current. The threshold current is the current amplitude where the combiner initially oscillates. For each diode type, there is an optimum threshold current and maximum operating current for maximum power, as shown in Figure 14. If the threshold current is too low, as Ithl' the resulting power saturates before !max is achieved. Correspondingly, if the threshold is too high, as shown by Ith3 , Pmax is not obtained. The Ithl condition is obtained by underloading the diode, and Ith3 is caused by overloading the diode. Plots of power versus current are very useful for the optimization of the design. This is because optimum diode loading can be obtained for reduced circuit efficiencies. The tolerance, surface conditions and flatness of mating parts must follow good microwave practice. Losses due to poor short circuits or cavity roughness all reduce Q0 of the resonator and hence the combining efficiency. 36 POWER (WATTS) Iop (AMPS) Figure 14. Power Versus Current for Different Circuit Load 37 E. Equivalent Circuit The HiPac circuit has the same characteristics as Kurokawa's circuit; therefore, they will have the same equivalent circuit. The equivalent circuit of HiPac is shown in Figure 15. Where M1 , ---, Mn represents the module-to-cavity coupling of the individual modules to the cavity. Since the analysis of this circuit has been done by Kurokawa and Davydova [19] [23], it will not be pre sented. The principal difference between Kurokawa's cir cuit and HiPac is the required coupling of the output load, ~2· Let the impedance at the module cavity interface be ~c' for one diode in the oscillator, and the required loading by the output be RL. Then, for "N" modules, each of which requires an impedance ~c' a much larger value of RL will be required which is equal to N~. The larger value of RL is obtained by increasing the output coupling, ~2· F. Diode All of the tests conducted with HiPac used a Microwave Associates diode, MA - 46072. This diode is a single drift, low-high-low GaAs-pulsed IMPATT. Typically this device produces 9.0 watts of peak power at 1/3 duty factor. The dc-to-RF efficiency of the diode is approximately 15.5%. The efficiency and power characteristics of the ....JXd L A c ZLOAO ~------_j Mo ~ Ml ....JXd Figure 15. Equivalent Circuit of Hi Pac w 00 39 diodes are a function of the circuit loading. The optimum performance is attained when Re {zc} equals Ropt' where Ropt is the optimum loading on the device. Figures 16, 17 and 18 depict the type of performance one would attain with Rc < Ropt' Rc = Ropt and Rc > Ropt· Once a diode has been characterized in a test circuit to determine Ropt' the information can then be used to determine what load is present on the device in any other circuit. This is accomplished by observing Ith' where Ith is the threshold current at which oscillations begin. Table 1 summarizes the diode performance from Figures 16, 17 and 18. As shown in Table 1, the performance varies considerably with Rc. It is also noticed that Ith is pro portional to Rc. Thus, if one uses the diodes in another circuit and sets the Ith = 270ma, by varying Rc, optimum performance can be obtained. There are two cases in which the optimum setting of Rc will not yield optimum performance: 1) if the circuit causes parasitic oscillation, and 2) if the diode jumps to a new operating point as the current is increased. Both of the exceptions are easily recognizable. The first case is distinguished by subharmonic and/or tone pair oscillations which can be observed on a spectrum analyzer. The second case can be identified by plotting the power-versus-current curve and observing any definite changes in slope. If the diode jumps to a new operating point, the power curve will 00'· IT:''· 40 3.0 ....------., 2.5 14 2.0 12 ..,; -- ,.-"' -- / / 10 / de- RF EFFICIENCY~/ 'r/ PRF (%) (AVE 1.5 / 8 WATTS) / / / 6 1.0 4 0.2 0.4 0.6 0.8 1.0 laP (AMPS) Figure 16. Power and Efficiency Versus Current for Rc < RoPT 41 3,0 ..------. 2.5 16 14 / 2.0 / 12 / de- RF / 10 fJ / (%) PRF EFFICIENCY / (AVE 1.5 B WATTS) ~/ / / 6 / 1,0 4 0,5 0.2 0.4 0.6 0.8 1.0 laP (AMPS) Figure 17. Power and Efficiency Versus Current for Rc = RoPT 42 3.0 .------, 2.5 14 2.0 12 ....-:: / / 10 / EFFICIENCY PRF '-y/ de- RF (AVE 1.5 8 17 _WATTS) / (%) / / 6 / / 1.0 / 4 / / 2 0.5 0.2 0.4 0.6 0.8 1.0 lQp (AMPS) Figure 18. Power and Efficiency Versus Current for Rc > RoPT Table 1. Power and Efficiency Versus Rc AVE DC-RF 1 POWER EFFICIENCY loP TH Rc (WATTS) '1(%) (AMPS) (AMPS) (OHMS) 2.30 12.6 1.0 0.22 < ROPT 2.80 16.6 1.0 0.27 "ROPT 2.40 12.4 1.0 0.31 > RoPT +="' VJ 44 noticeably change; this is usually accompanied by a fre quency jump as well. The power and efficiency characteristics were obtained by placing the diodes in a coaxial oscillator circuit. Figures 16, 17 and 18 represent the average values for the eight diodes used during this study. The block diagram of the test setup used is shown in Figure 19. This type of measuring system is typically required when working with IMPATT devices. 45 OSCILLOSCOPE PULSE GENERATOR CURRENT VOLTAGE POWER SPECTRUM PROBE PROBE METER ANALYZER DC POWER SUPPLY 1-- BAND PULSE PASS MODULATOR FILTER ~ HIGH IMPATT XX X> SECTION V POWER COMBINER PERFORMANCE A. Introduction To demonstrate the combining performance of HiPac, an eight diode version was fabricated. (See Figures 20 and 21). The unit was tested as a free-running oscillator in three different configurations. Measurements were con ducted using two, four and eight diodes in the combiner. Data is presented which gives a comparison of the circuit performance of the eight diode combiner with that of eight times the single diode performance. This data will be used to determine the combining efficiency of HiPac. B. HiPac Performance The HiPac combiner was optimized and characterized with the use of the setup shown in Figure 19. It was operated at 1/3 duty factor with a pulse repetition fre quency of 250kHz. The combiner was initially optimized with eight diodes; the power and efficiency characteristic is shown in Figure 22. The power and efficiency characteristic of HiPac com bining eight diodes is compared in Figure 23 to Figures 17 46 47 Figure 20. Assembled End View of HiPac 48 Figure 21. Disassembled View of HiPac ~·· 49 24 22 20 18 16 14 12 PRF (AVE 12 10 WATTS) 11~_,.. de- RF 10 / 8 11 / (%) / 8 / 6 / / 6 4 4 2 0 0.2 0.4 0.6 0.8 1.0 1.2 lop (AMPS) Figure 22. Power and Efficiency Versus Current 8 Diodes in Hi Pac I ·---- 50 51 and 18. Figure 17 is referenced since it represents the optimum condition for the diodes. Figure 18 is used be cause it has a similar threshold level as the HiPac com- biner with eight diodes. In Figure 23 it is shown that the loading on HiPac is greater than Ropt' since the power curve of HiPac follows that of eight times Figure 18. A summary of the HiPac performance is given in Table 2. The only area which needs explanation is the determination of the combining efficiency, ~c' which is defined as ~HiPac (19) where ~ HiPac is the dc-to-RF efficiency of HiPac, and sd is the dc-to-RF efficiency of a diode. If ~sd of the optimized diode is used for the evaluation of (19), then ~c = 76%. If ~sd for the case where Rc is greater than Ropt is used, then ~c = 94%. Figure 23 indicates that the diodes in HiPac were not optimally loaded. This condition can be corrected by lowering the impedance of the diode transformer in accordance with Equation (17). Figures 24 and 25 show the performance of HiPac when 4 and 2 diodes are combined. The performance was optimized for each case by adjusting the output coupling. The fre quency, transformers and short position were all main tained, at the same values as used during the eight diode Table 2. Power and Efficiency Results :! NUMBER NUMBER AVE OF OF DC-RF COMBINING TWIN DIODES s'OP VOP Poe PRF EFFICIENCY EFFICIENCY MODULES COMBINED. (AMPS) (VOLTS) (WATTS) (WATTS) "7% • '7C (%)" 1 2 1.0 58.0 38.7 3.4 8.8 58/71.0 2 4 1.0 58.0 77.3 8.8 11.1 72190 I ! 4 8 1.0 58.1 157.3 18.4 11.7 76/94 ------ • SEE TEXT FOR DEFINITIONS VI N 53 12 11 10 9 8 7 12 PRF (AVE 6 10 WATTS) 5 //. 8 / de- RF / 77 / (%) 4 / 6 / / 4 3 / 2 2 0~----'-~------~------~------~------~--~ 0.2 0.4 0.6 0.8 1.0 1.2 loP (AMPS) Figure 24. Power and Efficiency Versus Current 4 Diodes in Hi Pac 54 6r------, 5 4 12 PRF (AVE 3 10 WATTS) 8 de- RF 1'/ (%) 2 6 4 2 0~----~~------~------~------~------~~~ 0.2 0.4 0.6 0.8 1.0 1.2 loP (AMPS) Figure 25. Power and Efficiency Versus Current 2 Diodes in Hi Pac ~·· 55 ,, . operation, for each case tested. The results of the four diodes case are similar to that of the eight diode case, but the two diode configuration is very different. The reason for this difference is found in Equation (8) and the output coupling factor. As the output coupling, ~ 2 , is reduced, for a fixed value of ~1 , the combining efficiency is reduced. Since the coupling, ~ 2 , is proportional to the number of diodes combined, as fewer diodes are combined in this circuit, with a fixed ~1 , rye is reduced. The final characteristic measured on HiPac was the mechanical tuning bandwidth. The short position, which is the principal frequency-determining element, was varied in order to determine the RF power as a function of frequency as shown in Figure 26. This test was conducted using the eight diode configuration. No adjustments other than the short circuit position were made. The results indicate a relatively flat power band of 240rnHz and a full band per formance of 360mHz. The broad band nature of this circuit suggests that a varactor might be included in the design, so that the circuit may be used as a voltage-controlled oscillator. 2no.------, 18.0 16.0 I~ 240 MHz 0.5dB POWER VARIATION iii ~ 12.0 ~ w ~ 10.0 u. a: Q. 8.0 360 MHz 1.38 dB POWER VARIATION OL------~------L------~------~ 8.665 8.765 8.865 8.965 9.025 FREQUENCY IGHz) Figure 26. Mechanical Tuning Bandwidth of Hi Pac V1 0\ SECTION VI CONCLUSIONS A new type of power combiner has been developed. The diode capacity has been doubled over previously developed circuits without a noticeable reduction in efficiency. The waveguide cavity is a low-loss circuit capable of handling high power levels. The physical separation of the module pairs reduces thermal interaction, thus, the power dissi pation per unit area of heat sink is reduced, when compared to a cylindrical combiner. The tunable bandwidth of HiPac is greater and exhibits less power variation than similar power level combiners. This suggests that the HiPac could be used as a high power voltage tunable oscillator. The design of the unit is relatively simple, but good microwave construction techniques must be utilized. The use of usual microwave tolerances on the mechanical parts will ensure repeatable performance. The optimization of HiPac is easily accomplished by using the procedure out lined in Section IV. The performance of HiPac is dependent on the consist ency of the diodes. A diode selection technique should be used to ensure that all diodes operate the same in a given circuit. A theoretical analysis of GaAs IMPATT diodes is 57 58 presented in Appendix A. The analysis presents a technique which can predict the RF performance of the aforementioned diodes through the use of easily obtainable de parameters. REFERENCES 1. Read, W. T., "A Proposed High-Frequency Negative Resistance Diode," Bell System Tech. J., val. 37, pp. 401-446, March 1958. 2. Irvin, J. C., "GaAs Avalanche Microwave Oscillators," IEEE Trans. on Elec. Dev., ED-13, pp. 208-210, Jan. 1966. 3. Armstrong, L., "High Efficiency X-band GaAs IMPATT Diodes," IEEE Trans. on Elec. Dev., ED-15, p. 938, Nov. 1968. 4. Salmer, G., et al., "Theoretical and Experimental Study of GaAs IMPATT Oscillator Efficiency," Jour. of App. Phy., vol. 44, No. 1, pp. 314-324, Jan. 1973. 5. Haddad, G. I., et al., "Basic Principles and Proper ties of Avalanche Transit-Time Devices," IEEE Trans. on MTT, val. MTT-18, No. 11, pp. 752-772, Nov. 1970. 6. Misawa, T., "Negative Resistance in P-N Junctions Under Avalanche Breakdown Conditions, Pts. I and II," IEEE Trans. on Elec. Dev., val. ED-13, pp. 137-151, Jan. 1966. 7. Scharfetter, D. L. and H. K. Gummel, "Large-Signal Analysis of a Silicon Read Diode Oscillator," IEEE Trans. on Elec. Dev., ED-16, No. 1, pp. 64-77, Jan. 1969. 8. Kurokawa, K., An Introduction to the Theory of Micro wave Circuits, Chap. 9, Academic Press, New York, 1969. 9. Gibbons, G., Avalanche-Diode Microwave Oscillators, Clarendon Press, Oxford, 1973. 10. Howes, M. J. and D. V. Morgan, Microwave Devices, Chap. 5, John Wiley and Sons, New York, 1976. 11. Eisenhart, R. L., "Take the Trouble Out of Diode Mounting," Microwaves, pp. 78-81, Nov. 1974. 59 60 12. Teraoka, A. E., "TMPATT Oscillator Design," Master's Thesis, Cal. State Univ., Northridge, June 1978. 13. Iperen, B. B. and H. Tjassens, "Measurement of Large Signal Impedance, Optimum AC Voltage and Efficiency of Si pun+, Ge npp+ and GaAs Schotty-Barrier Avalanche Transit-Time Diodes," Proc. of Eighth Int. Conf. on Microwaves and Optical Generation and Amplification, Amsterdam, pp. 7-27 - 7-32, Sept. 1970. 14. Kramer, N. B., "Characterization and Modeling of IMPATT Oscillators," IEEE Trans. on Elec. Dev., ED-15, No. 11, pp. 838-846, Nov. 1968. 15. Dunn, C. N. and J. E. Dalley, "Computer-Aided Small Signal Characterization of IMPATT Diodes," IEEE Trans. on MTT, vol. MTT-17, pp. 691-695, 1969. 16. Gewartowski, J. W. and J. E. Morris, "Active IMPATT Diode Parameters Obtained from Computer Reduction of Experimental Data," IEEE Trans. on MTT, vol. MTT-18, pp. 157-161, 1970. 17. Harkless, E. T., U. S. Patent 3534293, Oct. 13, 1970. 18. Magalhaes, F. M. and K. Kurokawa, "A Single-Tuned Oscillator for IMPATT Characterizations~" Proc. of the IEEE, pp. 831-832, May 1970. - 19. Kurokawa, K. "The Single-Cavity Multiple-Device Oscillators,~ IEEE Trans. on MTT, vol. MTT-19, No. 10, Oct. 1971. 20. Montgomery, C. G., et al., Principles of Microwave Circuits, Chap. 7, McGraw Hill, New York, 1948. 21. Ginzton, E. L., Microwave Measurements, Chap. 9, McGraw Hill, New York, 1957. 22. Tjassens, H., "Circuit Analysis of a Stable and Low Noise IMPATT-Diode Oscillator for X-Band," ACTA Electronics, 17, 2, pp. 181-185, 1974. 23. Davydova, N. S. and Y. Z. Danyushevskiy, "Design of the Electro-Magnetic System of a Multidiode Microwave Amplifier," Telecommunications and Radio Engineering, vol. 31, pp. 96-103, May 1976. 24. Kurokawa, K., "The Single-Cavity Multiple-Device Oscillator," IEEE Trans. on MTT, vol. MTT-19, No. 10, pp. 793-801, Oct. 1971. 61 25. Kurokawa, K. and F. Magalhaes, U. S. Patent 3628171, Dec . 14, 19 71. 26. Tager, A. S. and A. D. Khodnevich, Russian Patent 192252, 1967. 27. Tager, A. S. and A. D. Khodnevich, "IMPATT Diode Oscillators with Electrical Frequency Tuning and Multidiode Oscillators," Radio Engr. and Elec. Physics, vol. 14, No. 3, 1969. 28. Harrington, R. F., Time-Harmonic Electromagnetic Fields, McGraw Hill, New York, 1961. 29. Sze, S. M. and R. M. Ryder, "Microwave Avalanche Diodes," Proceedings of the IEEE, vol. 59, No. 8, pp. 1140-1154, Aug. 1971. 30. Miller, G. L., "A Feedback Method for Investigating Carrier Distributions in Semi Conductors," IEEE Trans. on Elec. Dev., vol. ED-19, No. 10, Oct. 1972. 31. Johnson, W. C. and P. T. Panousis, "The Influence of Debye Lenftth on the C-V Measurement of Doping Profiles,' IEEE Trans. on Elec. Dev., ED-18, No. 10, Oct. 1971. 32. Gordon, B. J., H. L. Stover, and R. S. Harp, "A New Impurity Profile Plotter for Epitaxy and Device," Proceedings of 1970 ASTM Symposium on Silicon Device Processing, June 1970. APPENDIX A DIODE CHARACTERIZATION A. Introduction The characterization of IMPATT diodes has, in the past, been a goal for many designers. The efficient opera tion of power combiner circuits requires that every diode used in the circuit have the same RF characteristics. Most combiner circuits present the same impedance to each diode; thus, if the diodes are different from each other, the overall performance will be suboptimum. Once a power com biner design has been established for production, it is desirable for the production diodes to operate similar to those used in the initial design. There have been many investigations [13] [16] in the past on the characteriza tion of diodes, but these have resulted in slow and expen sive measurement techniques. It is the purpose of this appendix to present a simple de measurement technique which can be used to select diodes. This technique will deter mine whether the diodes will combine efficiently and have repeatable RF performance. At present, this technique is limited to GaAs single-drift diodes with high-low or low high-low profiles. 62 63 B. Diode Design IMPATT diodes are manufactured on a substrate by epi taxial growth techniques which use either liquid or vapor phase reactors. By the use of either process, a substrate is exposed to a dopiant for a period of time, as determined by the growth rate and the desired thickness of that par ticular layer. IMPATT diodes are composed of two main regions, the avalanche and the drift zones. The doping levels and lengths of the doped layers determine the characteristics of these two zones. The most efficient diodes are currently doped in a low-high-low or high-low profile shown in Figures Al and A2. Figure A3 illustrates a cross section of typical H-L diode in which the various layers have been accentuated. The function of the indi vidual layers can best be discussed with the use of Figure A4. The p~+ interface forms a junction contact which is typically referred to as a P-N ohmic contact. The ava lanche region is formed by the N+N- interface which will be discussed in more detail later. The N- region is referred to as the drift zone, with the N++ acting as a buffer and the ~ the substrate. As shown in Figure A3, the epitaxial layers are much smaller than the substrate. This fact, coupled with the sensitivity of the design to the doping levels, demands that the most exacting manufacturing techniques be 64 X EPITAXIAL LAYER ------4..~1 SUBSTRATE (a) Doping Proflle X r- Wa _..,.,..... , .. ____ Wd (b) Electric Field Figure Al. Low-High-Low Diode 65 ~------~X EPITAXIAL LAYER -----t•~l SUBSTRATE (a) Doping ProfJ.le E1 j~.------~.. ~~------~x w --t•... wd - · 8 .....j .,_ ____ · (b) Electric Field Fiplre A2. lfilh-Low Diode l - GOLO CONTACT SUBSTRATE GOLD CONTACT HEAT SINK 301J.M 1 ~>nnmm>mm>>>>>>11111>1~~~::::A::::::.::JjMp+ REGION 1.0 IJ.M Figure A3. Crossection of High-Low Diode 0\ 0'1 67 N++ SUBSTRATE I I GOLD GOLD CONTACT .....-- CONTACT (a) Layer Defmition \ E FIELD V/CM (b) Electric Field Figure A4. High-Low Diode 68 utilized. As a basic review of the parameters that affect IMPATT performance, let us consider the two zones. In order for avalanche to occur, the field must reach a par ticular value which is realized with a high level of doping in the N+ region. For efficiency, the length of this zone must be very narrow in order to keep the voltage (Va) across this region small. The efficiency is given by (Al) where Vd is the voltage across the drift zone. The doping of the N- layer keeps the field high enough to maintain the scattering limited velocity. This level must not be so large that the field extends into the buffer and substrate layers, a condition known as punch through. Operation of an IMPATT in punch through will cause the diode to fail. In addition, the N- layer must be designed for a particu lar frequency as given by (A2) where W is the length of the N- region, and Vs is the scattering limited velocity (for GaAs Vs = 9.0 x 106 em/sec). A long N- layer leaves undepleted material ~··- 69 during operation which causes there to be a series resist ance and a corresponding reduction in efficiency. The buffer layer serves to provide a pure high doped region which is used to compensate for some of the defects found in the substrate material. The epitaxial growth process is not currently used to manufacture substrate material be cause of the substrate's size and the fact that epitaxial growth is slow. The frequency and efficiency characteristics of a diode have been shown to be affected by the internal dimensions of the device; now it will be shown how the power level is established. The optimum profile is based , on the diode operating at a particular current density, J 0 2 , typically 1000 Amps cm- • For a desired power level, P0 one must adjust the area of the diode to yield (A3) where "A" is the area of the diode, and V0 P is the operat ing voltage of the diode which is given by (A4) where Vb is the breakdown voltage. The parameter V'is the volt-temperature characteristic of the material. The fac tor ~T is the operating temperature of the diode minus the 70 ambient temperature at which Vbr is measured. The param eter I 0 p is the operating current and Rsc is the space change resistance. Thus, for high power levels, the area must be large; but there are limits to be imposed on the area and maximum P • 0 It is known that the area of the diode is inversely proportional to the impedance of the device, so that large areas result in low values of Zd. Consequently, Zd could reach a limiting value below which it cannot be properly matched by the circuit impedance Zc. The condition for oscillation states that Zd + Zc = 0. (AS) Consider a circular diode with radius 'r' and represent Zd as (A6) It can be shown [1] [29] that w 1 - cos ( v;) (A7) • 71 and 2 -1 -JXd = (1rr w C) {A8) where c = l (A9) and W depletion width (em) A area of diode (cm2) l dielectric permittivity (Farads/em) w operating frequency (radians/sec) "'r avalanche resonant frequency (radians/sec) Vs scattering limited velocity {em/sec). At a particular frequency, w , Equations (A7) and (A8) 0 reduce to WK. (AlO) -JXd = (A "'o C) -1 (All) • where K is constant at w0 It can be shown that K is w approximated by -1/2. The negative sign occurs because 0 72 is greater than wr. The device only has negative resist ance at frequencies greater than wr, so that -w (Al2) At w • 2 0 If the operating frequency is near the designed frequency of the diode, w can be expressed as w Vs)/W. From 0 0 = (" Equation (AS), Rc = -Rd and JXc = JXd and, upon substitu tion of JXc and Rc into (All) and (Al2) respectively, one obtains -w (Al3) Rc = 2 At w 0 -1 = w XC (A 0 C) (Al4) = 2 If A "r and w0 = (" Vs)/W is substituted into (Al3) and (Al4), the new equations are in terms of the diode radius 'r' given by (Al5) and 73 w (Al6) If Equation (A9) is substituted into (Al6}, it becomes (Al7) From Equation (Al5), r 2 is given by w2 (Al8} r2 =----- 2" 2 £ Vs Rc By use of Equation (Al7), one finds that r 2 is also given by (Al9} 1r £ V s X c Since r 2 must be the same for Equations (A18) and (Al9}, they can be equated, i.e., 2 w2 4 w (A20} = 2 2 f vs Rc 1T f v s XC 74 or 1 4 (A21) ---=- thus (A22) In actual circuits, obtaining a value for Rc that is prac tical becomes the limiting factor. This fact is demon strated through the use of the transformer equation (A23) If Zo = SOn, Rc = 0.50, then ZT = sn which is difficult to achieve. If Rc = O.Sn is substituted into Equation (Al8), one obtains the maximum value of 'r' in terms of W, given by r = 103.1 W. (A24) For an X-band diode, W is usually 4~m, so r = 412.2~m. In addition to the limitation on output power due to the impedance of the device, there is also a limitation due 75 to thermal properties of the device. The factor ~T occur ring in Equation (A4) is the rise in temperature of the diode junction above ambient temperature. The reliability of the device is determined by the junction temperature Tj, as shown in Figure AS, and thus must be considered in the design. Manufacturers recommend that T. be maintained less J than 270°c; and, therefore, they design diodes for a Tj = 200°c. This provides a mean failure time greater than 106 hours. Tj is defined as (A25) where ~T arises from the device efficiency, input de power and the thermal resistance (et) of the device. Equation {A25) can be rewritten as (A26) (A27) Typical values of 8t for high power GaAs devices, mounted on copper heat sinks, range from 8.5 - 11.0. If it is assumed that 8t = 10° c/watt, Pde = 23 watts, 7J = 24% and Tamb = 25° c, then one finds that Tj = 200° c. To deter mine the maximum RF power that can be produced at the upper , temperature limit, one can solve Equation (A26) for P0 76 ' ' 300~------~ MEAN LIFE (HOURS) Figure AS. Mean Life to Failure 77 where = 7J (T; - Tamb) (A28) p (1 - 7]) (Jt Substitution of the values 7J = 24%, Tamb = 25° c, Tj = 270° c and et = 10° c/w, into Equation (A26), one finds that P 6.13 watts. If one computes the power 0 = based on Equation (A3) and uses the largest diode radius attainable, with V0 P = 40 volts, it is found that P0 = 213.0 watts. In comparing the two power levels, it is seen that there is a thermal limitation on the amount of power that can be produced. C. dc-to-RF Correlation With the previous discussion, the development of the relationships between the RF performance and de character istics can begin. The doping levels and layer thicknesses have been shown to be the most important parameters. The doping profiles shown in Figures Al and A2 provide this information, under the assumption that the diode diameter is known. Typically, a circuit designer only works with the packaged device, shown in Figure A6. Upon testing the commercially available diodes, a designer may notice performance differences between the diodes and slight to 78 0.100 r- 0.060 __., :-~---~1_--r-- METALCAP I WIREMESH I DIODECHIP L---+'1 -"t'--- J. CERAMICRING --~~----~-----4- T HEAT SINK ----3-48UNc-2A Figure A6. Cross-Sectional View of Diode 79 major tuning may be required. The frequency may differ by as much as 500mHz or the efficiency can vary as much as 5%. All of the above differences may occur while meeting or exceeding a required specification provided by the manu facturer. On the other hand, if the parameters of the test circuit are fixed and the diodes are retested, one would observe larger performance variations. Most likely, some diodes would not meet the manufacturer's specification when tested in this condition. It is the intent of this section to present a method of predetermining a diode's RF performance based on simple de measurements. It will be assumed that a diode type has been selected and optimized in a given circuit. Further, it will be required that the predicted performance of the diodes be restricted to the aforementioned circuit. The idea is that power combiner circuits present the same impedance to each diode. Therefore, in trying to attain repeatable optimum performance, the diodes are required to have the same RF characteristics. The doping profile, diode junction diameter and cur rent density define the RF characteristics of a device. We will assume that the diode is always operated at the proper current density, and that the junction diameter is easily attainable from the manufacturer. Next, the doping profile must be defined. Several papers [30] [31] [32] have been written describing the measurement of the profile. All of ~·· 80 these techniques require a knowledge of the junction area and a measurement of the capacitance-versus-voltage (C-V) characteristic of the device. Typically a microprosser is used in conjunction with a capacitance meter to generate the doping profile. For the typical circuit designer, most of the information provided by the doping profile is unfamiliar and, without a knowledge of solid state physics, it is useless. Nevertheless, it is important that a designer be capable of specifying the parameters of the diode, so that its RF performance will be reproducible. Specifications such as minimum power and efficiency are not adequate to guarantee repeatable performance. To accomplish this task, the capacitance of the device will be examined, since this is a quantity that most designers understand and can easily measure. The basic idea will be to develop relationships between operating characteristics, profile and capacitance. The depletion-layer capacitance of a diode is given by A ( (A29) c = w ' which is the standard capacitance equation for two parallel plates of area 'A' and separation 'W' • With a diode, the equivalent plate separation 'W' varies as the voltage is changed. So the diode capacitance is given by 81 ~ q ( N 12 (A30) c=A [z (Vi + V) J where q electron charge (1.602 x lo-19 coul) ( dielectric constant (1.062 x lo-12 fds/cm2) impurity density (em -3) build in potential for one-sided abrupt junctions (volts) v bias voltage (+ reverse bias, - forward bias) w depletion width (em) A area of the junction (cm2) Equation (A30) is only valid for a constant value of N (uniform doping). In this treatment, a diode with a high low doping profile will be examined. In addition, only the reverse biased case will be considered so that Equation (A30) becomes q ( N l~ (A31) c= A [z (Vi + V)J Before proceeding, a high-low doping profile and the corresponding C-V curve, which are shown in Figures A7 and AB respectively, will be discussed. The voltage points along the doping profile correspond to the voltages on the C-V curve. As the bias voltage is increased, the 82 1017 8 6 4 - 7.0 2 r> I :E 1016 ~ Clz 8 ii: 0 0 6 4 2 1015~------~~------~----~--~--~------~------~----~--~~ 0.1 1.0 10.0 DEPTH CMICRONSI Figure A 7 Doping Profile of High-Low Diode 83 II) '0 ....0 0 ~ ~ 0 ~ .s::I ....00 :I: c,... ~ 0 ...1 0 ...0 > =-- >.u 00 < II).... .~ ~ ICJVYV::I OOid 84 1 capacitance decreases in a manner proportional to v-~ until it reaches the end of the uniformly doped high region. The region between the high and low doped layers is called the abrupt junction. The capacitance then changes as v-l/3 ; i.e. , 1/3 (A32) rl qa€2] C a =A 12 (Vi + V) where 'a' is the doping gradient between the regions. As the bias is further increased, the diode is depleted into the low doped material and the capacitance once again is proportional to V -~. The important points to consider are the levels of doping and the length of the doped layers. To define the high doping level (NH), let us consider Equation {A30) with V = o. The capacitance for this condi- tion will be defined as co and is given by (A33) co = A [q , Na r 2 vi . If Equation (A33) is rewritten to determine NH, one obtains (A34) 2 V·~ q ( 85 Since c0 can be measured, and all the other parameters are known, thus NH is determined. To obtain the low doping level (NL), let V = Vb, in Equation (A30), and define this capacitance as Cb, which is given by (A35) The parameter Vb is the breakdown voltage of the diode. If Equation (A35) is solved for NL, one obtains (A36) q l With the measurement of ~ and, since all the other param eters are known, NL is obtained. Since the doping level is independent of the area of the diode, the parameter 'A' can be factored out by taking the ratio NH/NL, which is given by (A37) For a GaAs diode, Vi = 1.2 volts. Equation (A37) repre sents the ratio of the doping levels determined directly from the capacitance and voltage characteristic. 86 To develop the relationship between the RF character- istics and capacitance values, let us consider the device efficiency which is given by (A38) in which Va equals the de voltage across the avalanche region and Vd is the equivalent de voltage across the drift region. The voltages expressed in terms of the electric field and respective layer length are (A39) (A40) where Ea and Ed are the average electric fields in ava lanche and drift regions respectively. For the avalanche region (A41) and for the drift region 87 (A42) q NH La where W = La + Ld, Emax = 1.5 Ea, Ea = l Upon sub- stitution of Equations (A41) and (A42) into (A39) and (A40) one obtains or q NH La 2 (A43) Va = ~ --==-~ l and (A44) The efficiency can then be defined with the use of Equations (A43) and (A44) as (A45) 88 where La is the length of the avalanche region and is expressed as A( {A46) The parameter Cs is the point shown in Figure A8; it is the capacitance at the beginning of the abrupt region. The drift length, Ld, is given by (A47) where W is the total depletion length determined by (A48) w =- The substitution of Equations (A46) and (A48} into (A47) yields (A49) Upon substitution of Equations (A37) and (A46) and (A49} into (A45), one obtains 89 (ASO) 1 .,., =- 7T 2 cb - (Cs - cb) + ___v...;;;i;:...._c..;;;.o ____ ~ v. (Vi + Vb) (Cs ~) ~ - The diode efficiency is now in terms of easily measured quantities. Since the efficiency of the device has been derived, it is now possible to determine the maximum RF power. This is achieved by use of Equation (A28) and, since the diode power is thermally limited, (A28) To determine the power, one only requires the efficiency (T'/), thermal resistance (Ot), and the maximum operating temperature (Tj). The next dc-to-RF correlation to be derived is the relative frequency difference. Let us consider Figure A9 as the equivalent circuit of the packaged diode. In Figure A9(a), the diode chip represented by Rand C, where ~ and Cp are the package parameters. For the purpose of simplifying the analysis, let R = 0, since it is typically less than -1.0 . By eliminating R, the circuit now has 90 R CT c, I 0 I (a) A A 4 I 'VYV" 0 J c,II 1 0 I (b) A A 4 I 'V'V'Y"' 0 C+~l 1 0 I (c) A .figure A9 Equivalent Circuit of Packaged Diode 91 the form shown in Figure A9(b) which, in turn, reduces to Figure A9(c). The resulting L-C circuit, in Figure A9(c), must resonate at a desired frequency with the load circuit reactance to satisfy the condition for oscillation. If the load is capacitive and is represented by Cc, as shown in Figure AlO, one can solve for the resonant frequency, f 0 . Since the reactive elements of the circuit, in Figure 10, must sum to zero at the resonant frequency, one obtains -j j (A51) ------+ J 2" fo ~- ---- = o. 2 "fo (c + cP) 2" fo cc The resonant frequency of the circuit, if found to be 1 {A52) The value of Cc can be determined by measuring the circuit reactance {Xc} and substituting it into 1 (A53} The parameter {C + CP) is determined by measuring the capacitance of the diode at the breakdown voltage, thus 92 c•c,ll~------~o~--]1- cc I A Figure AIO Equivalent Circuit of The Packaged Diode and Load Reactance 93 (AS4) The substitution of Equation (AS4) into (AS2) yields (ASS) Equation (ASS) describes the operating frequency of a diode in terms of its package inductance, breakdown capacitance, and the load circuit capacitance. Diodes to be used in power combiner circuits will all have the same load capaci- tance, Cc. Thus, variation in operating frequency can only be caused by variations in the package inductance and/or breakdown capacitance. Typically the package inductance does not change from diode to diode. Therefore, only changes in Cb will affect the operating frequency. To determine the sensitivity of fo to variations in ~, it is necessary to define a reference diode. The reference diode will operate at frequency fr with a breakdown capacitance cbr" The frequency difference between the reference diode and any other diode, that operates at some frequency f 0 with breakdown capacitance ~' is obtained by simple manip ulation of Equation (ASS) and yields {AS6) f r - fo = f r 94 Equation (A56) represents the change in frequency one can expect to measure between diodes of the same type tested in the same circuit but with different values of breakdown capacitance. The final diode characteristic to simplify, in terms of measured quantities, is the real part of its impedance, R. The small-signal expression is given by 1 (A57) R--- where the transit angle is defined as (ASS) (} = and Vs is the scattering-limited velocity. The two right hand factors in Equation (A57) can be approximated by -1/2. With this approximation, Equation (A57) reduces to 95 -1 (A59) R=--- 2.WCb. The expression for cb is given by {A60) cb = A _q_N.;;;;;,L_)J~ [-2 {V + V since Vi is much smaller than Vb, Equation (A60) reduces to (A61) to include most of the diode parameters in (A61) and expansion of vb is presented through vb = va + vd. {A62) The parameters Va and Vd are from Equations (A43) and (A44). By substitution of Equation (A43) and (A44) into {A62), Vb becomes (A63) 1 q NL [NH L~ + NH La (W - La) 2 ( NL NL If Equations (A37), (A46), and (A49) are substituted into 96 I ' Equation (A63) and the resultant equation substituted in (A61), one obtains V· ) 1 (A64) cb +~Vb . (s ~)l~ = [(~:Y (vi Cs cb Cs cb The final expression for R is obtained by substitution of (A64) into (A59), which yields D. Summary of Equations The following relationships have been developed be- tween the RF characteristics and de measurements . (A66) ., = 1 ----....,2_1____ 1 " 1 + K1 C0 -K=--K-.:;__K__c_b___ K-:=-~ J 1 2 3 p = 7J (Tj - Tamb) (A67) (l-7J) ot (A68) 97 (A69) 4rrF where The above equations can be used by the circuit designer to determine a specification for a given diode. Once a diode with desirable RF characteristics has been selected, the designer can measure the values of C , Cb, 0 cs, vb, cc and the operating frequency. The diode param eters can then be varied until a range of reasonable tolerances are determined. A tolerance analysis was conducted on a GaAs single drift, high-low diode. The result of this exercise is described as follows: 1. Tolerance on Cb determines AF; 2. Ratio of C0 /Cb mainly determines ~' PRF, and R; 98 3. Tolerance on Cs affects R, ~, and PRF' effect is greater for low ratios of C0 /Cb; 4. Tolerance on Vb greatly affects R with reduced effects on ~ and PRF. In determining a specification, it is suggested that the tolerances be established in the following manner: 1. Set vb to restrict R variation; 2. ,Set Co/Cb for max/min~; 3. Set cb for allowable frequency differences; 4. Set cs for R variation. For the aforementioned diode, the parameters and toler ances, listed in Table Al, were successfully implemented. , It should be recognized that ~' P0 ~F and R are approximations to the actual values. The results of the tolerance study indicate the equations do predict trends quite accurately. All tolerances described in Table Al were verified by measuring good and bad diodes. The veri fication is clearly demonstrated by the data presented in Table A2. The correlation between the theoretical and measured values shown in Table A2 are typical and were taken from a sample of over 200 diodes. Table Al. Varian Diode VSX9251 AD PARAMETER VALVE vb 33.0 ± 1.5 VOLTS Co/Cb 18.6 ± 2.0 cb 3.85 ± 0.25 Pfd cs 27.5 ± 2.0 Pfd 22.0 ± 2.0% PRF"' 5.1 ± 0.33 WATTS AF 186.0 MHz R -3.0 ± 0.4 OHMS \0 \0 Table A2. Diode Comparison THEORETICAL EXPERIMENTAL DIODE PARAMETERS VALUES VALUES Co t.F PRF AF PRF R cb cs vb R CASE (Pfd) (Pfd) (Pfd) (VOLTS) (%)"' (MHz) WATTS %"' (MHz) (WATTS) (OHMS) 1 72.5 3.9 25.5 31 23.8 0 5.0 -2.99 23.1 0 4.9 -2.9 2 77.0 3.6 26.5 39 24.6 -20 5.2 -3.24 25.0 -30 5.5 -3.2 3 56.5 4.0 20.0 34 19.8 +35 3.9 -2.50 18.7 +40 3.8 -2.7 4 74.5 5.1 30.0 38 17.5 +338 3.4 -1.77 15.2 +300 2.75 -2.7 1-' 0 0