Simulation and Optimization of a Quarterwave Transformer for a W- Band Reducedheight Type IMPATT Oscillator

Simulation and Optimization of a

Quarter-wave Transformer for a W- Band

Reduced-height Type IMPATT Oscillator

ARIJIT DAS

Centre of Millimeter-wave Semiconductor Devices and Systems, University of Calcutta, 1, Girish Vidyaratna Lane, Kolkata 700009, West Bengal, India

arijitdas_83@rediffmail.com

Abstract—Millimeter-wave frequencies are gaining importance for applications in solid state transmitters for radar, radiometry, or short-range communication systems. The high-power pulsed IMPATT diode has been proven to be best suitable for these applications. The most commonly used mm-wave IMPATT oscillator is a reduced-height waveguide circuit cross coupled with a coaxial line. The mounting parasitics at millimeter-waves usually limit output power and efficiency of these kinds of oscillators. In the current paper the author has carried out modeling, simulation and optimization of a quarter-wave step transformer section for a W-band reduced height type IMPATT oscillator by using High Frequency Structure Simulator (HFSS). Also an easy method of designing and optimizing a tapered impedance transformer section has also been investigated using HFSS.

Keywords: Millimeter-wave; IMPATT; Reduced Height;, Resonant Cavity Oscillator; Quarter-wave Impedance Transformer

1 Introduction

At millimeter-wave frequencies, there is great interest in solid state transmitters for radar, radiometry, or short-range communication systems. The high-power pulsed IMPATT diode has been proven to be the key element for these applications. Beside exact controllable semiconductor technology, packaging and circuit mounting techniques are important factors for optimum performance. The mounting parasitics at millimeter-waves cause a transformation of the active diode impedance and usually limit output power and efficiency. Therefore it is important to minimize the resistive parasitics associated with the diode chip and its mounting connections. The use of package parasitics for impedance matching, however, shows that the often-stated demand of minimum parasitics does not automatically lead to the best RF performance results [4].

The Electrical and Mechanical tuning of MM-wave IMPATT diodes have been discussed in the literature by many workers. The most commonly used mm-wave IMPATT oscillator is a reduced-height waveguide circuit cross coupled with a coaxial line. The diode is mounted at the end of the coaxial line. This is schematically shown in the figure 1.

In this paper the author has carried out modeling, simulation and optimization of the impedance transformer section (Both Step type and tapered type) of W-band reduced height type IMPATT oscillator by using as High Frequency Structure Simulator (HFSS) software and the results have been compared.

Fig 1. Schematic Diagram of a Reduced Height type Resonant Cavity

BIAS ANODIZED ALUMINIUM (RF CHOKE)

REDUCED HEIGHT W/G WR - 10

POST

2 Simulation of Step Type Quarter-Wave Transformer 2.1. Theory

Quarter-wave transformers have numerous applications such as impedance transformers, reactance coupled filters, short-line low-pass filters, branch guide directional couplers etc. If the attenuation constant for flat response of pass-band is considered, the TEM-mode coupled-transmission-line directional coupler becomes analytically equivalent to quarter-wave transformer [Fig. 2].

The realization of transmission-line discontinuities by impedance steps is equivalent to their realization by means of ideal impedance inverters. The main difference is that while impedance steps can be physically realized over a wide band of frequencies (for small steps), ideal impedance inverters can be approximated over only limited band width.

Fig 2. Quarter wave Transformer Schematics

For a quarter-wave transformer realized by transmission line discontinuities the fractional bandwidth is given by ,

(1)

where λg1 and λg2 are the longest and the shortest guide wavelengths, respectively, in the pass band of the quarter-wave transformer. The length, L, of each section is nominally one quarter wavelength at centre frequency and is given by,

(2)

where the center frequency is defined as that frequency at which the guide wavelength λg is equal to λg0. For a non dispersive transmission line, considering the free space wavelength λ, the 3 dB fractional bandwidth becomes,

(3)

where n is the number of sections of the transformer and R is the over all impedance ratio.

2.2 Correction For Small-Step Discontinuity Capacitance In A Quarter-Wave Waveguide Transformer

A discontinuity in waveguide or coaxial-line cross-section cannot be represented by a change of impedance only, i.e. practical junctions are non-ideal. The equivalent circuit for a small change in inner or outer diameter of

















+

−

=

2

λ

λ

λ

λ

ω

(

)

4

2

L

λ

λ

λ

λ

λ

=

+

=

(

)

R

R

a coaxial line can be represented by an ideal junction shunted by a capacitance, and the same representation is possible for an E-plane step in rectangular waveguide.

This shunt capacitance has only a second-order effect on the magnitude of the junction VSWR, since it contributes a smaller component in quadrature with the already small reflection coefficient of the step. Its main effect is to move the reference planes with real Γ out of the plane of the junction. Since the spacing between adjacent and facing reference planes should be one quarter wavelength at center frequency, the physical junction should be moved the necessary amount to accomplice this. The numerical formula for this displacement given by [3]               + +       − = − − − − i i i i i i i Y Y B Y Y B X 1 1 1 1 tan tan 2 1               + −       − = − − − − i i i i i i i Y Y B Y Y B x 1 1 1 1 _tan tan 2 1 (4) where, Bi is the equivalent shunt susceptance at the step

2.3 Design of Quarter-wave Transformer

Considering the present design purpose, we want to decrease the VSWR. For a given impedance ratio and bandwidth, the VSWR decreases with the increase of the number of intermediate sections. But it also increases the complexity of fabrication as the step height will decrease. As a compromise we take n = 2.

Now for the present case, Diode impedance will be equal to the characteristic impedance of the waveguide section with the shortest height.

The calculated diode impedance = Z0 ≈ 4Ω

The characteristic impedance of a Rectangular waveguide is given by,

(5)

where λg is the guided wavelength, λ0 is the cut-off wavelength, b and a are the length of the narrower and broader wall of the waveguide respectively.

For WR 10, a = 2.54 mm, b = 1.27 mm, λg = 3.2 mm (for 94 GHz), λ0 = 2a = 5.08 mm (for TE10). Then for two intermediate sections, Z3 = 236.7 Ω. We take the heights of the reduced height section is taken to be 0.5 mm for feasibility of fabrication of the cavity and mounting of the diode [5]. The impedance matching is achieved by varying the reactive part of the circuit, i.e. post height and short position. So the heights of the respective sections are given by, b0 = 0.5 mm, b1 = 0.68 mm, b2 = 0.93 mm and b3 = 1.27 mm.

In ideal case the length of each step would have been λg/4 = 0.7975 mm. But the Correction for Small-step Discontinuity Capacitance has to be considered. The calculation was performed with the help of the standard curve for the change of shunt susceptance with the waveguide height. The correction lengths obtained are 0.033 and 0.0457 mm respectively.

Therefore the corrected lengths of the first quarter-wave section should be equal to (0.7975 - 0.033) mm = 0.7645 mm and that of the second quarter-wave section should be equal to (0.7975 - 0.0457) mm = 0.7518 mm. [Fig. 3]

Fig 3. Preliminary Dimension of Quarter wave Transformer

3 HFSS simulation Result for Quarter-wave Transformer

HFSS has three types of solver for a particular structure which are known as DRIVEN MODAL, DRIVEN TERMINAL and EIGENMODE solvers [1]. The HFSS simulation of the structure shown in Fig. 3 was

a

b

Z

377

2

0

λ

λ

=

0.5 mm 0.68 mm 0.93 mm

performed using DRIVEN MODAL type solution and the corresponding S parameters for the input and output terminals were analyzed.

It was observed that the design frequency, i.e the frequency at which S11 is minimum & S21 is maximum, has devieted significantly from 94 GHz. Now for optimization purpose the lengths of the intermidiate steps were changed keeping the heights fixed. The following results and curves [Fig 4-6]were obtained for the various step lengths. The variation between the calculated step lengthand the simulated step length may be due to the approximation used while reading the data from standard curve for the change of shunt susceptance with the waveguide height.

Fig 4. Quarter wave Transformer structure for HFSS simulation

Fig 5. Plot of S11 vs. Frequency

Fig 6. Plot of S21 vs. Frequency

The 3D medium of the impedance steps were considered to be air (instead of vacuum) having a finite conducting boundary of pre assigned width and made of copper. It was found that that the a s21 of -0.0167 dB is obtained at 94 GHz, i.e. if 20 W of power is fed at the reduced height port a output power of 19.923 W will be obtained. The plot of VSWR shows that the value of the same at 94 GHz is as low as 1.0319. The final design dimension of the Quarter-wave transformer is shown in the figure 7.

Calculated Design

Design with Step length = 0.7 mm

Design with Step length = 0.6 mm

Calculated

Design Design with Step length = 0.7 mm

Fig 7. Optimized Dimension of Quarter wave Transformer

4 HFSS Simulation Result For The Tapered Impedance Transformer

Next the tapered Impedance transformer structure was simulated using HFSS. Tapered structure is more suitable for the present purpose as the tapered structure is easy to fabricate but does not involve any noticeable degradation in RF performance. This structure has been used extensively in reported experimental studies [2]. The design of tapered structure is relatively difficult as no mathematical model is readily available to calculate the tapered length for a particular frequency. In the present study, to get an idea of the length of the tapered section required for operation at 94 GHz frequency at first the step impedance stricture was gradually modified by steadily increasing the number of intermediate steps and simulating the RF characteristics at each step. When the number of intermediate steps becomes very large the structure will tend to a tapered structure. It was observed [Fig. 8 and 9] that when the number of intermediate steps was increased from 1 to 8, the total length of the quarter –wave section tends towards 2 mm for operation at 94 GHz frequency. Using this length of 2 mm a tapered structure was created and simulated in HFSS and it was found that the structure has been optimized for the operating frequency ~ 94 GHz. The tapered structure with dimension as well as S11 and S21 profile has been shown in figure 10, 11 and 12 respectively.

Fig. 8. Variation of the length of the Quarter-wave Transformer with the number of Intermediate Steps

0.6 mm

0.6 mm

0.5 mm 0.68 mm 0.93 mm 1.27

Fig. 8. Variation of the length of individual steps with the number of Intermediate Steps

Fig 9. Tapered Impedance Transformer Structure

75.00 80.00 85.00 90.00 95.00 100.00 105.00 110.00 Freq [GHz]

-26.00 -24.00 -22.00 -20.00 -18.00 -16.00 -14.00 -12.00

dB(

S

(W

av

eP

or

t1

,W

av

ePo

rt

1

))

Ansoft Corporation XY Plot 1 HFSSDesign1

m2 m 1

Curve Info dB(S(WavePort1,WavePort1)) Setup1 : Sweep1

Name X Y

m1 93.0000 -24.1330

m2 94.0000 -24.0684

Fig 10. S11 Vs Frequency curve for Tapered Impedance Transformer

2 mm 1.27

75.00 80.00 85.00 90.00 95.00 100.00 105.00 110.00 Freq [GHz]

-0.25 -0.20 -0.15 -0.10 -0.05 0.00

dB(

S

(W

av

ePor

t2

,W

a

v

e

P

or

t1

))

Ansoft Corporation XY Plot 4 HFSSDesign1

m2 m1

Curve Info dB(S(WavePort2,WavePort1)) Setup1 : Sweep1

Name X Y

m1 93.0000 -0.0168

m2 94.0000 -0.0171

Fig 11. S11 Vs Frequency curve for Tapered Impedance Transformer

5 Conclusion

The current paper presents a novel method of simulating the RF characteristics of a reduced height cavity type W-band IMPATT oscillator. Here the author has used both available mathematical model and HFSS simulation software to simulate and optimize the Impedance Transformer for W band Reduced Height cavity structure. Furthermore using the same process a more suitable tapered model, in terms of impedance matching and ease of fabrication has been suggested and analyzed. This model can be used to practically realize such an oscillator in near future.

Acknowledgment

The author wishes to thank the Director, CMSDS for his valuable guidance. The author would also like to express his gratitude to all the staff of CMSDS for their constant support.

References

[1] Ansoft HFSS user guide

[2] Fong T. T., Kuno W H. J; “Millimeter-Wave Pulsed IMPATT Sources”, IEEE Transactions on Microwave Theory and Techniques,

Vol. MTT-27, No. 5, May 1979, pp. 492 – 499

[3] Matthaei G L., Young L & Jones E. M. T. ;“Microwave Filters, Impedance-Matching Networks and Coupling Structures”; Artech

House

[4] Pierzina R. and Freyer E. : 'Power Increase of Pulsed Millimeter-Wave IMPATT Diodes', IEEE. Trans, 1985, MTT-33, pp 1228-1231

[5] Ray U. C., Gupta A. K. and Sen M. N.; “Some aspects of bias current tuning of W-band IMPATT diodes mounted in a reduced-height