Fast and Efficient Synthesis of Multimode Waveguide Components

D.I.Sobolev, G.G. Denisov, A.P. GashturiInstitute of Applied Physics / GYCOM,

Nizhny Novgorod

EC-17, Deurne, 7-10 May 2012

Various waveguide components are widely used in plasma heating and diagnostics setups: mode converters, tapers, DC breaks.

Every percent of transmission/conversion efficiency matters: relatively low power dissipated in the wrong place may cause a big problem.

Sometimes dimensions are very restricted. Special methods of synthesis are required to

satisfy all conditions.

The goal

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

Synthesis principles

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

1. Deformation of the waveguide surface at each iteration step is defined by two field distributions calculated using boundary conditions at the input and output of the waveguide.

E1H1

E-2H-2

S1S2

S0

l

S’

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

2. Deformation satisfies the integral equation written for a specific field representation.

Deformation at each step is small enough to satisfy the equivalent boundary condition

Lorentz lemma could be written for the two field distributions

Conversion efficiency change after the deformation is

A similar integral equation can be written for any type of field representation

tHnikllEgradttE n

V

mmee

S

dVHjHjEjEjc

dSnHEHE

12211221

1221

4

2121,0

nnSEEHHikFdSFlP

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

3. Solution of the integral equation is found in accordance with the restrictions imposed on the waveguide deformation.

For the chosen value of the guidance parameter ΔP the deformation norm is minimized

Writing the first variation with Lagrange multipliers, we get the solution. In the simplest case it is

sconstraint lGeometrica

ImIm

ReRe

min

0

0

0

2

PdSFl

PdSFl

dSl

S

S

S

,ReIm

,ImRe

2ImReImRe

ImReRe

2ImReImRe

ImReIm

NNN

PNPN

NNN

PNPN

.ImRe

,ImRe

0

00

ImRe

2

Im

2

Re

S

SS

dSFFN

dSFNdSFN,ImRe FFl

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

These principles summarize our experience in waveguide synthesis since 2004.

Any field analysis method can be used for synthesis:• Coupled wave equations• Mode matching• Time domain methods (FDTD)• Surface integral equations (EFIE+MLFMA)

Only several tens of field calculations are required. Over 50 components were synthesized and tested. Additional techniques were developed to optimize the

efficiency over a large bandwidth and to reduce the diffraction losses in gaps to their theoretical minimum (in DC breaks and miter bends) .

Practical use

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

Smooth-wall waveguide broadband taper-converter from H11 mode to HE11 mode of corrugated waveguide.

Operating bandwidth 85-100 GHz, length 180 mm, diameter from 3.6 mm to 38 mm.

Calculated efficiency over 97%, measured efficiency over 95%.

Synthesized units

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

Corrugated waveguide taper-converter from H11 mode of smooth waveguide to nearly Gaussian wave beam with flat phase front.

Operating frequency 53.5 GHz, length 234 mm, diameter from 4 mm to 80 mm.

Calculated efficiency over 99%.

The converter is extremely short: its length is only 3 times more than the diameter (shown here in close perspective).

Synthesized units

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”

Smooth-wall waveguide converter from H11 mode to H03 mode. Consists of H11-H01 converter (left) and H01-H03 taper (right). Operating frequency 42 GHz, total length 650 mm, diameter from 10

mm to 85 mm. Calculated efficiency over 98%, measured efficiency over 95%

(mostly due to Ohmic losses).

Synthesized units

Synthesized units

Low-loss miter bend for HE1,1 mode.

Consists of two identical converters (length of one converter is 19 cm) and a mirror (gap length is 7 cm).

Operating frequency 84 GHz, input and output converter radius 15.875 mm.

Value of diffraction losses is ≈ 0.4%.

Synthesized units

Exotic converter of E0,1 mode to H0,1 mode (these are not coupled directly). Conversion through the intermediate rotating H4,1 mode.

Frequency 10 GHz, radius 54 mm, length 30 cm. Chosen for the nice Er field graph.

Methods developed in IAP can be used to synthesize highly efficient and at the same time compact waveguide components.

The methods are very fast: even complicated converters can be calculated on a typical PC.

Over 50 different waveguide components synthesized and fabricated.

Measured results are in excellent agreement with the calculations.

Conclusion

D.I.Sobolev, G.G. Denisov, A.P. Gashturi “Fast an d Efficient Synthesis of Multimode Waveguide Components”