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Results and discussion: To evaluate the
performance of the
rrequency selective surfaces, measurements were made in
the T E and T M planes of incidence at 22" using a Martin
Puplett interferometer with a swept frequency range of 80200GHz. The diplexers were positioned at the waist of a
Gaussian beam which produced an edge taper lower than
-40dB at 89 GHz. The measurement technique was designed
to simulate the normal operation of the FSS in the feed chain.
Fig. 2 shows the measured and predicted swept frequency
transmission response of the two FSS for T M incidence at 22".
Good agreement is demonstrated in both cases. For the waveguide array the measured loss in the transmission band varied
between -0.6 and -0.3dB a t 148.5 and 151.5GHz, respectively. Because the effective bandwidth is narrow (- 3%), and
the rolloff very steep, a machining accuracy considerably
better than
10pm would be required t o achieve a symmetric
low loss performance at the band edges. In contrast the transmission band of the double square FSS is broad ( - 1lo/"), and
even though the centre frequency was measured to be
-154GHz, the loss over the prescribed range of frequencies
was less than 0.2dB. The reflection losses for both FSSs were
less than 0.2dB, and again computed results showed good
agreement with the experimental values.
The sensitivity of the passband to the angle of incidence is
summarised in Table 1 using computed results at 0, 22 and
Both FSSs satisfy our design criteria except at 45' T E
where the passband of the waveguide array is shifted below
the 148.5-151.5 GHz range. For applications requiring linear
polarisation only, the T M orientation is preferable because
broader relatively stable passbands are generated. Table 1
shows that the waveguide array has a bandwidth that varies
between 3 and 6.5% at 0 and 45" incidence, respectively. For
the double square FSS the bandwidth varies between 9 and
12% over the same angular range. For operation in the circular polarisation mode the performance of the FSS is limited
by divergence of the transmission bands in the orthogonal
planes and/or narrowing in the T E plane. Table I shows for
example that at 45" incidence the waveguide array is unusable
whereas the double square FSS gives a bandwidth of -6%.
The rejection band (87.5-91.5GHz) of the waveguide array is
unaffected by the incident angle because the individual waveguides comprising the array were designed to he far below
cutoff. For the double square FSS the common reflection
band is determined by that generated in the T M plane. Our
results show however that virtually no degradation occurs
over the angular range W 5 " due to the relatively broad band
over which the elements reflect the incident energy.
Conclusions: The performances of a waveguide and a double
square printed FSS have been compared at large incident
angles in the millimetric band. It is shown that the passband
of the printed element FSS is much broader and relatively
insensitive to the incident angle in both the T E and TM
planes. The selection of a device for a particular application
will additionally be influenced by the required rejection and
mechanical characteristics.
Acknowledgments: We thank W. J. Hall and R. J. Martin for
useful discussions, A. C. de C. Lima for running some of the
software, and M. J. Archer for writing one of the computer
models used in this study. The printed element FSS was fabricated by the Materials Science Department at the BAe
Sowerby Research Centre. This work was supported by a
British Aerospace, Space Systems research grant.
3rd March 1992
R Cahill (Systems and Payloads Department, British Aerospace (Space
Systems) PLC, FPC 320, PO Box 5, Filton, Bristol BSI2 7QW. United
E. A. Parker ( T h e Electronic Engineering Laboratories, T h e Unioersify
o f K e n t , Canterbury, Kent C T 2 7 N T , United Kingdom)
R., and PARKER, E. A ' 'Crosspolar levels of ring arrays in
reflection at 45 incidence: influence of lattice spacing', Electron.
Lett., 1982. 18, pp. 1060-1061
J. r.:
'Frequency selective surfaces'. ICAP 83, IEE Conf. Publ. 219, 1983,
pp. 459-463
C ~ N c.
, c : 'Transmission of microwaves through perforated flat
plates of finite thickness', IEEE Trans., 1973, MTT-21, pp. 1-6
HAMDY, s. M. A., and PARKER, E. A.:'Current distribution on the
elements of a square loop frequency selective surface', Electron.
Lett., 1982, 18, pp. 624-626
frequency, GHr
h' Dun,te\ and
j'. K
Indexing terms Magnetostatic waves, Microwave oscillators
Multimode oscillation at up to 15 frequencies and a modelocking regime in a magnetostatic backward volume wave
delay line oscillator have been realised At 3 53GHz central
frequency the mode-locked oscillator generated 1-10 ns long
coherent pulses with 53 ns pulse repetition period.
Fig. 2 Sweptfrequency transmission response berween 80 and 200GHz
U Waveguide FSS: TM incident at 22
b Double square FSS: TM incidence at 22
A calculated
ELECTRONICS LETTERS 9th April 1992 Vol. 28 No. 8
Introduction: Solid state microwave oscillators, containing a
magnetostatic wave (MSW) delay line in the feedback loop,
have been intensively studied [I, 21. The possibility of electrical tuning over a wide frequency range, low phase noise and
planar structure make them very attractive for applications in
microwave devices and communication systems [3].
In previous research attention has mainly focused on singlemode oscillators. Also the wideband nature of MSWs allows a
multimode regime to he realised [l, 4, 51, which may be used
for frequency net oscillation or for coherent radio pulse oscillation.
We present a more detailed investigation of multimode
oscillation and, for the first time, realisation of active synchronisation of the mode phases in an MSW delay line oscillator.
Oscillator design: The oscillator consisted of a GaAsmonolithic transistor amplifier (frequency range f = 3-4 GHz,
voltage controlled: gain coefficient G = 18-25dB and output
power saturation level P, = 3-5 mW), planar directional
coupler (B = -4dB) and wideband magnetostatic backward
volume wave (MSBVW) delay line in the feedback loop. The
delay line was realised on yttrium-iron-garnet (YIG) film
(dimensions 25 x 3 x 0.02mm3, saturation magnetisation
1750Gs, FMR linewidth AH = 0.5Oe) prepared by LPE technology on a nonmagnetic substrate. Two microstrip transducers of 50pm width and 3mm length deposited on the film
surface at a distance y = 4mm apart were used to excite and
to receive the MSWs.
The DC magnetic field of H = 7150e strength created hy
an SmCo, permanent magnet was applied tangentially and
perpendicularly to the transducers. For harmonic field modulation with a magnitude up to h - 200e and frequency
F = 2-30 MHz we used an electromagnetic coil wound on the
structure. The MSBVW delay line exhibited an amplitude
response bandwidth of Af = 380 MHz at - 30dB level with a
minimum insertion loss of -13dB and output signal phase
changing up to 32 mad.
Experimental results and discussion: For gain coefficient
G < 20dB, only a singlemode oscillation of the frequency
f = 3535MHz with output power P,, = 2mW existed. For
G = 20-23dB, stable multimode oscillation at up to 15 frequencies (see Fig. l a ) was observed. The distance between
modes increased from 17 to 22 MHz with an increase of frequency. Total output power reached Po., = 2.4-3 mW.
f r e q u e n c y , GHz
Fig. 1 Measured and calculated multimode oscillation spectra
a Measured
b Calculated
The oscillation frequencies may be found from the phasebalance condition: qIcfN)
+ ( p 2 c f N ) + q3cfN)
= 2nN, where
'pl = k ( f ) y , ", q 3 are the phase shifts in the delay line, in the
connection lines and in the amplifier, respectively, N = 1, 2 .. .
is the mode number, and &(f)is the MSBVW wavenumber.
Phase shifts q , ( f ) and q 3 ( f )have been measured and
approximated within the 3.3-3.8 GHz frequency range by
where E = 2.2, I = 5cm are the dielectric penetration and the
length of the connection lines, and c = 3 x 108m/s. The
dependence q , ( f )is given by the well known MSBVW dispersion equation.
Fig. Ib demonstrates good agreement between the measured and calculated oscillation spectra.
Note that nonequidistance of the spectrum is mainly caused
by the nonlinearity of the MSBVW delay line phase response.
The real distribution of the mode intensities arises from the
mode competition process and is determined by the real
amplitude and phase responses of the oscillator components.
The mode-locking regime in the oscillator described was
obtained by harmonic modulation of the field strength with
frequency F = 19 MHz. After modulation, the spectrum
spread to 330 MHz, the intensities of central modes decreased
by 1-2dB and the distance between them became equal to the
modulation frequency. With that the oscillator generated shot
pulses shown in Fig. 2 a The pulse repetition period was equal
to T = 53ns, the pulse lengths were 6t = 7-1011s and mean
oscillation power reached P, = 2mW.
Fig. 2 Observed oscillator output pulses and calculated pulse envelope
Output pulses
b Pulse envelope
The mode-locking principle, we believe, is based on the
dependence of specific MSW properties on the magnetic field
strength. As shown in Reference 6,the harmonic field modulation H = H, + h cos (2nFt) resulted in the MSW phase
modulation and gave rise to the appearance of harmonics of
frequencies f N f nF ( n = 1, 2 . .. is the mode number) at the
delay line output.
In the multimode oscillation regime the harmonics arise
near each eigenmode. Provided nF is equal to the intermode
interval AfN the harmonics act as an external force and carry
out the mode-locking. The number of locked modes is determined by the magnitude of the modulation field h.
The envelope of the pulses is given by
where N , < N < N,, and A: and q; are the amplitudes and
the phases of locked modes of the numbers from NI to N,.
With that it should be taken into account that external
pumping results in the establishment of exactly defined
nonzero initial phases qg of the modes under consideration.
These phases may be calculated using the equations for amplitude A(/) and phase Q ( f ) responses for oscillator loop:
A ( f ) = [I + ezu(f)Y
- 2eQ'f)Ycos {k(f)Y}l-
a(/) = 2ny AH/v, are the group velocity
where vg = 271
and attenuation coefficient of MSW, respectively,
y = 2.8 MHz/Oe, the gyromagnetic ratio.
Fig. 26 shows the theoretical pulse envelope for measured
amplitudes A: and calculated phases q: for five central
modes. It can be seen that the MSW phase response nonlinearity explains well the nonsymmetry of the radio pulse
Note, that the central frequency of coherent radio pulses
may be tuned within amplifier range by changing the field
strength. The pulse length is controlled by adjusting the delay
line parameters and modulation field strength. A more wideband nondispersive MSW delay line should be used for
shorter-pulse oscillation.
Passive mode-locking may be realised by including an
MSW signal-to-noise enhancer [3] in the oscillator loop.
5th February 1992
S . N.Dunaev and Y. K. Fetisov (Moscow Institute ofRudio Engineering, Electronics and Automution, Vernadskogo 78, Moscow 117454,
ELECTRONICS LETTERS 9th April 1992 Vol. 28 No. 8
BROWN, 0.:‘Tunable magnetostatic surface wave
oscillator’,Electron. Lett., 1976, 12, pp. 209-210
ISHAK, w.: ‘4-20GHz magnetostatic-wave delay-line oscillator’,
Electron. Lett., 1983, 19, pp. 930-931
ADAM, I. 0.:
‘Analog signal processing with microwave magnetics’,
Proc. I E E E , 1988,76, pp. 159-171
CASTERA, 1. P . : ‘Tunable magnetostatic surface-wave-oscillators’,
l E E E Trans., 1978, M A G 1 4 , pp. 826-828
S E T H A m , 1. c., and STIGLITZ, M. R.: ‘Magnetostatic wave oscillator
frequencies’,J . Appl. Phys., 1981,52, pp. 2273-2275
FETISOV, Y. K.: ‘Microwave signal processing and forming using
dynamic magnetostatic wave devices’. Proc. 20th Microwave
European Conf.,Budapest, 1990, Vol. 2, pp. 1142-1 144
decomposition as each subsequent decimation on a filtered
image generates a batch of bandpass DCT coefficients.
The pyramids of the decimated images are each filtered by a
weighting function based on a cosine summation hence it is
called the ‘cosine pyramid’. The hierarchy set of error signals
which are essentially the remaining DCT coeficients is
referred hereafter as the ‘DCT pyramid’ which epitomises the
idea of encapsulating DCT within a pyramidal data structure.
The image coding technique introduced here results in data
compression by encoding the DCT pyramid as illustrated in
Fig. 1. Notice that the apex level, the final decimated image, is
simply DCT coded.
reconstructed reconstructed
c o s ~ wpyramid DC T pyramid
apex level
DCT pyramid cosine pyramid
coefficient (/ccefflclent
extraction quantisation Padding--
K. H. Tan a n d M. G h a n b a r i
Indexing terms: Image processing, Codes and coding, Signal
An image coding technique using the discrete cosine transform within a pyramidal data structure is described. A distinct feature is the in built capability to correct blocking
effects at low bit rates employing noninteger decimation.
I n t r o d u c t i o n : The property of the discrete cosine transform
(DCT) is that when it is applied to natural images most of the
energy is concentrated at lower frequencies. This property can
be exploited by retaining only M coeficients from an original
of N . The technique of manifesting DCT coding within a pyramidal data structure to be described here relies on this ability
to perform decimation in the transform domain.
Decimation of a sample block of size N by a ratio of M/N,
where M < N, is achieved by performing an N-point DCT
analysis (forward transform) followed by a n M-point DCT
synthesis (reverse transform) using the first M coeficients,
denoted hereafter by N + M. Obviously both integer and
noninteger ratios are possible in just one operation. The synthesised picture elements, pixels, are equivalently derived by
subsampling a filtered version of the original sequence at
intervals of N/M samples. This filtered sequence is derived by
convolving a periodic symmetrically extended original
N-point data block with a weighting function that is based on
a cosine summation [l]. The spread of the filter function
broadens as the decimation factor increases. This is consistent
with the requirement for a narrower passband as the sampling
rate is reduced t o avoid aliasing effects. DCT decimation
inherently provides the corresponding lowpass filtering
required according to the decimation rate. This makes it a
potentially powerful tool.
C o n c e p t : A DCT decimated image can be interpolated, again
through the DCT domain, to recover a n image that closely
resembles the original. This is achieved by performing an
M-point DCT transform on the decimated image followed by
padding with zero coeficients from M to N - 1 positions
before a n N-point reverse transform. A two-dimensional DCT
domain decimation technique can be realised from the onedimensional case by performing an N x M block transform in
the horizontal direction first followed by the vertical. Decimation is then obtained by extracting the lower P x Q coeficients from the M x N coellicients for a P x Q reverse
transform this time initiating from the vertical direction.
The decimation process effectively decomposes an image
into two distinct components of differing characteristics. They
are a lowpass filtered image reconstructed from the low frequency transform coeficients and a set of highpass DCT coefficients. A pyramidal data structure is then generated by
successive decimation that implicitly embodies sub-band
Vol. 28
No. 8
Fig. I Summary of procedure of using three level DCT pyramid as
image coder
Two significant advantages of coding the DCT pyramid as
opposed to the classical Laplacian pyramid [Z] are identified.
First, the error signal elements are in the DCT domain rather
than the pixel domain for the Laplacian pyramid. The high
compaction efficiency of the two-dimensional DCT would
force most of the picture information content into the decimated image, especially when the pixel-to-pixel correlation is
high. This in turn reduces the importance of the DCT
pyramid and coarser quantisation can be applied to achieve a
lower entropy. Secondly, assuming the area of the original
image to be A, the total image area of the DCT pyramid is
always equal to A, regardless of the rate of decimation or the
number of levels in the pyramid. For the Laplacian pyramid,
the error area approximates 4/3A, when n , the number of
levels in the pyramid, is greater than 4. Clearly, this makes the
DCT pyramid attractive for compact coding.
A key feature of the coding scheme just outlined is the
drastic reduction of blocking effects at low bit rates; a degradation which is inherent in DCT. The mechanism involved is
the overlapping effects of the DCT blocks during the decimation and interpolation processes at the various levels of the
pyramid. If noninteger decimation with different block sizes
and decimation factors at each level of the pyramid is
employed, then the interpolated blocks would have different
block lengths and the edges of the blocks are nonaligned.
Should blocking occur in the reconstructed picture at a level
of the pyramid, at the next stage of interpolation, due to the
nonalignment of the blocks, the edges are smoothed by the
filtering of the basis vectors of the DCT. As a consequence
edges appear smoother and block boundaries are removed.
Experiment results und f i n d i n g s ; The entropy for each level of
the DCT pyramid after quantisation was calculated. The bit
rate for the image is the sum of these entropies weighted by
their sample density.
Fig. 2b shows an image of ‘Trevor’ coded at 0,20bit/pixel
using noninteger decimation scheme at three levels of the
cosine pyramid. The decimation ratios used for the horizontal
and vertical directions were 8 + 4; 11 + 6; 8 + 4 and 8 + 3;
9 + 5 ; 12 + 6, respectively. The image is much less blocky
than that coded via the conventional DCT at the same bit
rate as shown in Fig. 2u. The selective quantisation of the
sub-bands has preserved a significant amount of detail which
is clearly evident from the background. The ringing around
the edges of the ‘Trevor’ image demonstrates the lowpass filtering effects of DCT decimation as described previously.
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