Intrapulse frequency variation in a W-band pulsed IMPATT diode.
Currently, the silicon IMPATT diode is the most powerful solidstate source at W-band frequencies and is being used in several developmental high performance mm-wave systems, such as missile seekers, precision guided weapons and tracking radars.(1) When operated with short bias current pulses of 50 to 100 ns and low duty cycle (< 1 percent), IMPATT diodes can deliver sufficiently high peak powers.(2) The present status of peak power capability of the Si IMPATT diodes is 42 W.(3) Commercially, devices are available with up to 20 W of peak power.(4)
One of the inherent features of the pulsed IMPATT diode oscillator is the frequency chirp, that is, the intrapulse frequency variation. This effect is the direct consequence of the diode junction temperature increase within the pulse on-period that results in the variation of device impedance, and hence the intra-pulse variation of oscillation frequency. Several circuit applications of IMPATT diode devices, such as injection locking and power combining, require minimal chirp. In contrast, a precise and controllable chirp, that is with linearly varying frequency within the RF pulse, can be used to design high performance radars with improved range resolution using the pulse compression technique.(5) The chirp characteristics, although an inherent device feature, can be optimized by proper bias current waveform shaping.(2)
This paper presents a simple device-circuit interaction model to compute the intrapulse frequency variation for the most commonly used W-band pulsed IMPATT diode oscillator configuration. Experimental results for a commercial device are presented and compared with the model predicted response.
Device-Circuit Interaction Model Configuration
A commonly used W-band pulsed IMPATT diode oscillator is shown in Figure 1. The device is mounted at the bottom of a reduced-height waveguide and is coupled to the waveguide through a cylindrical post. The bias is provided through this post in conjunction with an RF choke. The circuit is matched to the device by selecting the height of the reduced-height waveguide and the post diameter. Finer tuning can be obtained using a precision moveable back short. The reduced-height waveguide is matched to the full height WR-10 waveguide through a cascaded section [lambda]/4 impedance transformer.
Defining [Z.sub.C] = [R.sub.C] + j[X.sub.C] as the equivalent circuit impedance at the device terminals and [Z.sub.DP] = [R.sub.DP] + j[X.sub.DP] as the packaged device impedance, the conditions for circuit controlled steady-state oscillations(6) are RDP is negative and [X.sub.DP](f) + [X.sub.C](f) = 0 (1) for the oscillation frequency and [R.sub.DP](f,A) + [R.sub.C](f) = 0 (2) for the amplitude A of steady-state oscillation. In addition, for oscillation to start and grow -[R.sub.DP] > [R.sub.C] (at small signal level) (3)
Finally, oscillation stability requires that
[MATHEMATICAL EXPRESSION OMITTED] The device and circuit impedances must be known in order to compute the oscillation frequency.
The post-waveguide mounting structure has been discussed in detail previously(7) and an equivalent circuit was derived, as shown in Figure 2. In this work, computer software to compute the circuit impedance [Z.sub.C] at the diode terminals has been developed.
Device-circuit interaction of the oscillator depends on the large signal device impedance. This impedance is difficult to model accurately, especially for W-band IMPATT diodes that operate at high current density.(8) An approximate closed-form expression for a single drift structure diode has been reported previously.(9) In this work, a modified form of this expression that suits the DDR structure has been used and is given as
[MATHEMATICAL EXPRESSION OMITTED] where [omega] = angular frequency [[omega].sub.a] (u) = RF voltage dependent avalanche frequency
The RF voltage dependent avalanche frequency is given by
[MATHEMATICAL EXPRESSION OMITTED] where
[MATHEMATICAL EXPRESSION OMITTED] where [alpha]' = first derivative of the ionization coefficient [alpha] w.r.t. the electric field [v.sub.s] = saturation drift velocity [J.sub.0] = DC current density [theta] = transit angle [I.sub.0] (u) and [I.sub.1] (u) = modified Bessel functions [C.sub.D] = [epsion]A/W = depletion capacitance W = depletion width A = area of the device [epsion] = semiconductor material's relative dielectric constant
E?? corresponds to the maximum amplitude of the RF field at the avalanche region and is assumed to be 0.4 times the DC breakdown field.(10)
In Equations 5 and 5a, W, [alpha] and [v.sub.s] are the three parameters that are sensitive to the junction temperature of the device. When the device is operated in the pulsed mode, the device junction temperature and these three parameters, vary within the pulse width, resulting in the variation of the large signal device impedance within the pulse. This time varying device impedance causes frequency chirp. The temperature dependence of these parameters has been adequately considered in this analysis.
The depletion width W at the operating conditions is given by
[MATHEMATICAL EXPRESSION OMITTED] where [W.sub.0] = depletion width at zero current density and at room temperature [T.sub.0] [[beta].sub.T] = fractional change of breakdown voltage with temperature T = operating junction temperature [N.sub.B] = doping density q = electronic charge
The fractional change of breakdown voltage with temperature has been taken(2) as 5 x [10.sup.-4] in this work. This quantity can be experimentally measured. The temperature dependence of [alpha](11) and [v.sub.s](12) have been assigned values previously reported.
Figure 3 shows the W-band IMPATT diodes packaged in a miniature quartz ring with a cross gold ribbon connecting the chip to the package top and its equivalent circuit. The package parasitics, although distributed in nature, can be modeled(13) by an inductance [L.sub.p] representing the gold ribbon and a capacitance [C.sub.p] representing the quartz housing. [R.sub.S] represents the parasitic series resistance that includes resistances due to [n.sup.+] substrate, contact layers, undepleted epilayers and the package loss.
Intrapulse Junction Temperature Profile
The precise knowledge of junction temperature within the short (100 ns) pulse can be obtained from the transient thermal analysis of the IMPATT diode structure, as shown in Figure 4. The exact analysis of the problem is extremely difficult and can only be tackled numerically.(14) In this work, several simplifying assumptions have been made, including linear flow of heat is from the device junction to the heat sink, heat flow through the bonding ribbons is negligibly small, the entire heat is generated at the device junction plane and the single pulse approximation is valid when the duty factor is < 1 percent. Physically, during the initial portion of the bias pulse, the heat generated at the junction travels through the silicon material and the gold metalization layer only. The heat sink will not be effective until the heat flux reaches it. The time needed for the generated heat flux at the p-n junction to reach the heat sink interface is [tau], the thermal time constant of the chip, which includes the Si and Au layers. Further, practical W-band silicon pulsed IMPATT diodes have thin layers of Si and Au. Under these conditions, an approximate formula for calculating the transient junction temperature rise has been given previously.(15) For time t < [tau], the rise in junction temperature is given by
[MATHEMATICAL EXPRESSION OMITTED] where R = thermal resistance of chip C = thermal capacitance P = power dissipated at the junction of the device [tau] = thermal time constant (R x C) erfc = the complimentary error function,
[MATHEMATICAL EXPRESSION OMITTED]
For time t [greater than or equal to] [tau], the chip has been heated and the contribution of heat sink also comes into the picture. The expression for the transient temperature rise at the heat sink interface can be obtained from a previous work(16) and is given by
[MATHEMATICAL EXPRESSION OMITTED] where [t.sub.1] = t - [tau] K = thermal conductivity of the heat sink material k = the material's diffusivity
For t > [tau], the chip has been sufficiently heated and the temperature rise across the chip can now be described by a lumped parameter model(17) given by
[MATHEMATICAL EXPRESSION OMITTED]
The total junction temperature rise of the device is given by [delta] [T.sub.j] = [delta] T (chip) + [delta] T (HS) (10)
Method of Computation
For a given dissipated power (operating voltage * operating current -- generated RF power) and known device structure, the junction temperature at any time t within the pulse on period ([t.sub.ON]) is computed from Equation 7 for t < [tau] and from Equations 8 to 10 for [tau] [less than or equal to] t [less than or equal to] [t.sub.ON]. Knowing the junction temperature and details of the device structure, the chip impedance [Z.sub.D] is calculated from the approximate large signal impedance expression given by Equation 5. The packaged device impedance [Z.sub.DP] is then computed using the values of the package parasitic elements.
For the given circuit parameters, the circuit impedance [Z.sub.C] at the device terminals is computed from the developed software based on the equivalent circuit previously given.(7) The frequency of oscillation is obtained from Equation 1. The conditions as given by Equation 3 and 4 also need to be satisfied. This procedure is repeated for different values of time t within the intra-pulse period to obtain the RF frequency profile.
Figure 5 shows the plot of the circuit reactance [X.sub.C] and negative of the packaged device reactance -[X.sub.DP] vs. frequency for two values of junction temperatures, one at 27[degrees] C corresponding to the start of pulse and the other at 250[degrees] C corresponding to the end of pulse. The oscillation frequency is 92.17 GHz at the beginning of the pulse and 91.47 GHz at the end.
Theoretical and Experimental Results
For presentation of data, a typical W-band reduced-height waveguide IMPATT diode oscillator consisting of a 5 W Si DDR ([n.sup.+] -n-p-[p.sup.+]) IMPATT diode was considered. The typical device parameters as obtained from the manufacturer are listed in Table 1.
TABLE 1 TYPICAL DEVICE PARAMETERS
Junction diameter 82 [micro]m Doping density 1.2 x [10.sup.17]/[cm.sup.3] Epilayer thickness 0.3 [micro]m [p.sup.+] layer thickness 0.2 [micro]m Gold layer thickness 1 [micro]m Operating current 5.35 A Operating voltage 20 V Package inductance 0.5 nH Package capacitance 0.13 pF
The diode parasitic series resistance [R.sub.S] is taken as 0.4 [omega].(18) The heat sink material used is diamond embedded in copper. The bias pulse considered was a flat top pulse of 100 ns width and a PRF of 10 kHz. Thermal time constant for the chip (p and [p.sup.+] Si layers plus Au layer) was 22 ns and the calculated operating current density was 100 KA/[cm.sup.2].
The circuit has a reduced-height waveguide height = 0.51 mm, a post radius = 0.35 mm, a 1.85 mm position of back short from diode and a waveguide width = 2.54 mm.
Figure 6 shows the bias current pulse, the computed junction temperature, and the calculated and measured frequency. The frequency profile indicates that the RF frequency decreases as the junction temperature increases and most of the frequency variation is near the start of the pulse. The chirp bandwidth as obtained theoretically is 700 MHz.
The measured RF frequencies at the start, middle and near the end of the pulse were obtained by displaying the detected RF pulse envelope on an oscilloscope and by observing the power dip on the displayed pulse profile at the corresponding points by using a high Q calibrated precision absorption wavemeter. The experimentally measured chirp bandwidth is 800 MHz. The measured frequency profile follows the trend of the theoretical frequency profile.
This paper has presented a simple device-circuit interaction model to compute the intrapulse frequency variation for pulsed IMPATT diodes operating with a flat-top (rectangular) bias current pulse. The model-predicted response agrees reasonably well with the measured data. Sometimes mm-wave IMPATT diode operations with controllable chirp requires proper modulator current pulse shaping. As an example, an upward ramping bias current pulse reduces the chirp bandwidth.(2) To compute the chirp response for any pre-defined modulator waveform, the outlined method can easily be extended.
Although the measured RF frequency and chirp bandwidth agrees reasonably well with the model predicted data, the slight difference may be due to the fact that the exact device impedance model at a large signal level was not available. The model used for computing the junction temperature was not a rigorous one and lacked the accurate modeling of package parasitic elements at W-band, machining tolerances of the oscillator parts and nonideal functioning of the RF choke and waveguide short.
The authors are grateful to the director of SPL for his kind permission to publish this work.
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|Author:||Ray, U.C.; Gupta, A.K.|
|Date:||Apr 1, 1994|
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