output power of 25 mW with 25% efficiency was obtained. At a maximum output power of 30mW (with 6 V drain voltage) the DC to RF conversion efficiency was 23%. The threshold drain voltage for oscillation was about 1.2 V.

40 r 1 Lo 1 I

! 3 5 3 5 t 61 3 2 10

5

0

r / .30

/ #

0 1 2 3 L 5 6 7 drain voltage, V

Fig. 5 Performance of 40 GHz oscillator -0- output power -A- efficiency

In conclusion, high performance Q-band GaAs power MESFETs used as oscillators have achieved record eficiency and power density performances at Q-band. At 34 GHz, a DC to RF conversion efficiency of 30% was obtained with an output power of 33mW using a 75 x 0.25pm device. A similar output power was achieved at 40GHz with an efi- ciency of 25%. The corresponding power densities were in excess of 0.4W per millimetre of gate width. This level of oscillator performance makes it attractive for implementation of GaAs MESFET oscillators in millimetre-wave subsystems.

Acknowledgments: The authors wish to thank H. D. Shih for the supply of GaAs material, K. Bradshaw for e-beam litho- graphy, and N. Camilleri and M. Wurtele for the help in testing. For technical assistance, they thank S . F. Goodman, L. P. Graff, J. M. Ramzel, and P. A. Tackett, and for editing assistance they thank J. Fuller.

H. Q. TSERNG B. KIM Texas Instruments Incorporated Central Research Laboratories PO Box 655936, MIS 134 Dallas, T X 75265, U S A

24th November 1987

References

1 GEDDFS, J., SOKOLOV, v., CONTOLATIS, T., ABROKWAH, J., and LARSON, w.: ‘High efficiency GaAs MBE power FETs for Ka-band. IEEE 1984 Microwave and Millimetre-wave Monolithic Circuits Sym- posium Digest, pp. 87-90

2 KIM, B., TSERNG, H. Q., and SHIH, H. u.: ‘Millimeter-wave GaAs FETs prepared by MBE, I E E E Electron Device Lett., 1985,

3 KOBIKI, M., MITSUI, Y., SASAKI, Y., KOMARU, M., SEINO, K., and TAKAGI, T.: ‘A Ka-band GaAs power MMIC. IEEE 1985 Microwave and Millimetre-Wave Monolithic Circuits Symposium Digest, pp.

4 KIM, B., MACKSEY, H. M., TSERNG, H. Q., SHIH, H. D., and CAMILLERI, N.: ‘Millimeter-wave monolithic GaAs power FET amplifier’. 1986 GaAs IC Symposium Tech. Digest, pp. 61-63

5 KIM, B., MACKSEY, H. M., TSERNG, H. Q., SHIH, H. D., and CAMILLERI, N.: ‘mm-wave monolithic GaAs power FET amplifiers’, Microwave J . , March 1987, pp. 153-163

6 TAYLOR, G . e . , ERON, M., BECHTLE, D. w., LIU, s. G., and CAMISA, R. L.: ‘High-efficiency 35-GHz GaAs MESFET’s’, IEEE Trans., 1987,

7 TSERNG, H. Q., and KIM, B.: ‘High-efficiency Q-band GaAs FET

8 TSERNG, H. Q., and KIM, B.: ‘11OGHz GaAs FET oscillator’, ibid.,

9 TSERNG, H. Q., and KIM, B.: ‘A 115GHz monolithic GaAs FET oscillator’. 1985 GaAs IC Symposium Technical Digest, pp. 11-13

10 EVANS, D. H.: ‘High-efficiency Ka- and Ku-band MESFET oscil- lators’, Electron. Lett., 1985, 21, pp. 254255

E D M , pp. 1-2

31-34

ED-34, pp. 1259-1262

oscillator’, Electron. Lett., 1984,20, pp. 297-298

1985,21, pp. 178-179

FIBRE PROBE FAR-FIELD TECHNIQUE FOR MODE-FIELD D l A M ETER MEASUREMENT OF SINGLE-MODE FIBRES

Indexing terms: Opticalfibres, Optical measurement

A far-field pattern (FFP) technique using an optical fibre probe to measure the mode-field diameters of single-mode fibres is described. The endface separation between the test fibre and the probe fibre can be reduced to a tenth of the fibre/detector separation in the conventional scanning detec- tor method.

Introduction: The mode-field diameter (MFD) of a single- mode fibre is an important parameter to be measured. There are several methods’-4 of measuring the MFD. For a one- dimensional far-field technique’.’ it is easy to construct the measuring set-up, and it is extensively used in many factories. The far-field power intensity P(0) is measured as a function of the far-field angle 0 by rotationally scanning a small detector. The MFD can be calculated by

D, = (i/2n)(2 1 OP(0) dO 1 03P(0) do)*’’ (1) 0 0

where i is the ~ a v e l e n g t h . ~ The endface separation between the fibre under test (FUT) and the detector has been empiri- cally chosen to be 80mm for a l00pm-diameter detector’ or 100 mm for a 500 pm-diameter detector.*

Fresnel diflraction integration: In the cylindrical co-ordinate system shown in Fig. I , the power intensity at point Q can be expressed by Fresnel diffraction integration as

x exp [ - k p cos 8/(2So)]p d p (2)

where A’ is a constant, p is the radial co-ordinate of the FUT endface, u(p) is the field distribution on the FUT endface, k is the wave number, J , is a 0th-order Bessel function, and So is the endface separation between the FUT and the detector surface. Using local co-ordinates ( r , 4) on the detector surface, the total far-field power detected by the detector can be given by

Pde) = I A‘ j j j u(p)Jo(kp sin

r 4 ~

x exp [ - k p cos 8’/(2R)]p d p d 4 rdr 1’ (3)

where 0’ = cos- ((So + r cos 4) sin O/R), R = (r’ sin’ 4 + ( S o + r cos 4)’)’’’. The MFD is estimated by substituting the detected far-field power PT(0) instead of the Fraunhofer dif- fraction intensity Pf(0) into eqn. 1. The estimation errors by numerical simulation for detectors with diameters of 0, 50, 100, 200, 300, 500, and 1000pm are shown in Fig. 2 by the

I Q

-3 X

FUT endface 148011)

Fig. 1 Co-ordinates for far-field intensity calculations

84 ELECTRONICS LETTERS 21st January 1988 Vol. 24 No. 2

solid lines. The curve for a zero-diameter detector shows that the difference between Fresnel and Fraunhofer diffractions becomes negligible in the region where the separation is more than 3mm. For a 100pm-diameter detector, the endface separation can be reduced to 3.4 mm if an MFD measurement error of 0.05 pm is allowed.

0 25 E 1 g - 0

P

E 0 2 5

z ul B

1 0-1 10 0 IO‘ 107 endface separatlon, rnm

Fig. 2 MFD estimation errors as a function of the endface separation between the FUT and the detector ( a probefibre)

Solid lines are computed results A, A experimental results obtained by a rotational scanning detec- tor method 0 experimental results obtained by linear scanning fibre probe method

Scanning detector method: The MFD is measured as a func- tion of the endface separation for a step-profile single-mode fibre by the rotational scanning detector method. The MFD estimation errors are plotted in Fig. 2 as A and A, detectors are Ge-APD (100 pm dia.) and GaInAs pin (80 pm dia.) respec- tively. The minimum endface separation which gives an MFD error of less than 0.05pm is about 50mm for each detector. This separation is about 14 times greater than the numerical expectations. This difference comes from the fact that detec- tors are sensitive even in the area outside the central detection area of the ring ohmic contact, and that the power integrated in this outer area is sometimes greater than the power detected in the centre area. The surface sensitivity distribution of the Ge-APD used in the experiment is shown in Fig. 3. Effective detector diameters of these small detectors are gener- ally greater than the detector diameters typically specified.

Fig. 3 Detector surface sensitivity of a Ge-APD

Scanning jibre probe method: The endface separation in the scanning detector method may be reduced by simulating a pinhole on the detector surface. We refined the method as follows: an optical fibre with a high numerical aperture con- nected to a detector functions as a pinhole, and the fibre is scanned instead of the detector. Furthermore, we used linear scanning instead of rotational scanning for ease of construc- tion. The measuring set-up is shown in Fig. 4. In this case, the detected power PA@) must be replaced by PA@, given by

PAe) = PAexs; + d2)/s;/cos e = p ~ e y c o s ~ e (4)

where d is the axial offset between the FUT and the fibre probe, (Si + d 2 ) / S i is a distance factor, and l/cos 0 is an inclination factor. The MFD estimation error as a function of the endface separation is plotted in Fig. 2 as 0, where the

probe fibre has a core diameter of 80pm and a numerical aperture of 0.22. When the allowable MFD measurement error is 0.05pm, the minimum endface separation is 4mm. This separation is about a tenth of that in the conventional scanning detector method. The minimum endface separation is close to the numerical result. A 4mm endface separation f 1 mm scanning width and a 20pm step resolution, corre- sponding to an angle resolution, give a scanning angle range of k0.25 radians and an angular resolution of 0.005 radians respectively.

fihrp

stage photodiode + L- I

computer

Fig. 4 Measuring set-up for the linear scanning jibre probe technique

When the fibres under test are dispersion-shifted single- mode fibres, greater scanning angles will be required than for these conventional step-profile single-mode fibres2 Then, a step-index fibre with a numerical aperture of 0.4 has to be used as the fibre probe.

Conclusion: A combination of a linear scanning translation and a step-index fibre with a high numerical aperture is effec- tive for MFD measurement of single-mode fibres. The required endface separation is about a tenth of that in the conventional rotational scanning detector method. The mea- surement set-up can be easily and compactly constructed, and measurements can be made faster than with a conventional set-up. Furthermore, there is no need to know the surface sensitivity distribution of the detector in constructing an MFD measurement set-up.

K. YAMASHITA 24th November 1987 M. TATEDA N T T Transmission Systems Laboratories Tokai, Ibaraki 319-11, Japan

References

1 OHASHI, M., KITAYAMA, K., and SEIKAI, s.: ‘Mode field diameter mea- surement conditions for fibers by transmitted field pattern method’, J . Lightwaue Technol., 1985, LT-4, pp. 109-115 ANDERSON, T. W., SHAH, V., CURTIS, L., JOHNSON, I. A., and KILMER, P. I. : ‘Mode-field diameter measurement for single-mode fibers with non-Gaussian field profiles’, ibid., 1987, LT-5, pp. 21 1-217 OTIEN, G. w., KAPRON, P. F., and OLSON, c. T.: ‘Mode-field diameters of single-mode fiber by knife-edge scanning in the far field’, ibid., 1986, LT-4, pp. 1576-1579 SMITH, K. D., and WFSTWIG, A. R. : “on-Gaussian fitting of variable aperture far-field data and waveguide dispersion from multi- wavelength measurement of mode radius’. Tech. Dig. OFC ’85, 1985, paper TuB2 PETERMANN, K.: ‘Constraints for fundamental mode spot size for broadband dispersion-compensated single mode fibers’, Electron. Lett., 1983, 19, p. 712

2

3

4

5

SIGNAL ESTIMATION THROUGH THE MEAN OF THE LOG

Indexing terms: Noise, Signal urocessinq. Sianal detection

We discuss and illustrate a method for the determination of a signal amplitude, detected in the presence of noise, based on the measurement of the mean of the logarithm of its inten- sity.

Signals are almost invariably corrupted by the presence of noise, whose power and distribution function may well not be known. An estimate of the amplitude of the uncorrupted

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