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where the g, and go are the transconductanceand output conductance of corresponding transistors, C,, is the gate-source capacitance. In the above derivation, we neglect the gate-drain
capacitance and finite impedance of the current sources Zb and 4.
From eqn. 1, R, is very small since its value is a second-order
effect. So we also neglect this series resistor in the following derivation of the self-resonant frequency of the active inductor (a,)
and intrinsic quality factor (Q):
2
Wt
- gmlgm2 = wtlwta
~
Q
-E
-4,
Rp
1
Cgsl c g s 2
-
(2)
with ql, at2the unity current-gain frequency of M1 and M2,
respectively. A drawback of this active inductor is its low Q value.
From eqn. 2, the intrinsic Q value of the active inductor will
increase with atland decrease with at2.Note wI1 and q2are proportional to dZ,where Z is biasing current. It is preferred that transistor M1 has higher unity-gain frequency than M2, therefore one
approach to increase the intrinsic Q value is to increase the biasing
current of M1 while keeping that of M2 constant. The extra biasing current Z,will come from the negative impedance circuit @IC)
which will be addressed immediately. The CCO circuit is shown in
Fig. 2. PMOS transistors M1-2a, b are two active inductors, V, is
a DC biasing voltage for the CG transistors. Mbl-3 are current
sources to provide biasing currents for the active inductor pair.
Vb
b
9
I
I
‘c
.
’
frequency is tuned by changing the biasing currents of the active
inductors (Z, in Fig. 2), thus the equivalent inductance value is
tuned while the capacitance is kept the same. Assuming the total
capacitance from input stages of NIC and output buffer is C,, the
oscillating frequency can be expressed as
where k is a factor determined by the spec ratios of Mla (or b)
and M2a (or b), respectively. To test the CCO, an output buffer
stage with 50Q match has been designed (not shown in Fig. 2). A
transformer is employed on the PCB as a balun circuit for test
equipments.
Measurement results: This circuit has been fabricated in a 0 . 3 5 ~
CMOS process and hosted in a plastic TQFP package. The circuit
occupies a very small area (100 x 1 2 0 ~due
) to the use of active
inductors. With 3V power supply, a very wide tuning range (from
100 to 900MHz) has been achieved. The phase noise and output
power for the above tuning range have been shown in Fig. 3. As
can be seen from this Figure, more than 15dBcHz phase-noise
difference exists between the two ends of the tuning range. The
decrease of output power at high frequency is mainly caused by
the output buffer. At the high frequency end, the phase noise is
not good enough for most wireless applications.Nevertheless, this
circuit may find applications with a relaxed requirement on phase
noise and where a wide tuning range is preferred.
0 IEE 2001
14 February 2001
Electronics Letters Online No: 20010347
D 01: IO.1049/el:20010347
Y. Wu and M. Ismail (Analog VLSI Laboratory, Department of
Electrical Engineering, Ohio State University, 2015 Neil Ave.,
Columbus, OH43210, USA)
E-mail: [email protected]
H. Olsson (Radio Electronics Laboratory, Department of Electronics,
Royal Institute of Technology, SE16440, Kista, Sweden)
References
HARA, s., TOKUMITSU, T., TANAKA, T., and AIKAWA, M.:‘Broad-band
microwave active inductor and its application to miniaturized
wide-band amplifiers’, ZEEE Trans. Microw. Theory Tech., 1988,
36, pp. 1920-1924
2 ISMAIL, M., WASSENAR, R . , and MORRISON, w.: ‘A high-speed
continuous-time bandpass VHF filter in MOS technology’. Proc.
IEEE ISCAS, 1991, Vol. 3, pp. 1761-1764
3 KAUNISTA, R.: ‘Active inductors for GaAs and bipolar
technologies’, Analog Integr. Circuits Signal Process., 1995, 1, pp.
35-48
4 w u , ~ . , ISMAIL, M., and OLSSON,H.:
‘A novel CMOS fully
differential inductorless RF bandpass filter’. Proc. IEEE ISCAS,
2000, Vol. 4, pp. 149-152
1
Fig. 2 CMOS current controlled oscillator (CCO)
105
1 -5
Simple, low-cost control of unity-powerfactor boost pre-regulator
0. Lbpez, L. Garcia de Vicuiia and M. Castilla
frequency, MHz
A simple design for the control circuit of a unity-power-factor
Isss/31
Fig. 3 Measured phase noise at 500kHz offset and oscillator output
power
-0- phase noise
-Apower
boost pre-regulator is presented. The controller operates in
continuous conduction mode and avoids the use of an analogue
multiplier and the sensing of the line voltage. The proposed circuit
is an interesting solution when high-efficiency and low-cost
control circuitry are required.
The NIC circuit is composed of a cross-coupled differential pair
Mnl, 2. To satisfy the start-up condition of the oscillator, the negative resistance of NIC must overcome the damping resistance of
the active inductors and will generate positive poles in s-plane.
With the increase of oscillation amplitude, the large-signal
response of NIC will bring the poles to left-half plane. A constantamplitude oscillation is built when the NIC cancels all the damping resistance. In the CCO circuit, no varactors are employed. The
Introduction: In singlephase power supply systems, the most popular power-factor pre-regulator (PFP) topology is the boost converter, due to its simplicity, low cost, and the continuous character
of its input current. In this topology, two control techniques have
been traditionally used, namely the voltage follower control and
the multiplier approach [l].
In the voltage follower control, the input current follows the
line voltage automatically when the boost converter operates at
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12th Aoril7001
Vol. 37
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473
the boundary between the continuous-conduction mode (CCM)
and the discontinuous-conductionmode. In that case, a specific
control circuitry is needed to force such operation. Moreover,
other features include variable switching frequency and high current stress, which cause high line-current ripple and low efficiency
for medium- and high-power applications.
The multiplier approach is commonly used in CCM operation
when high efficiency is required. In this approach, an active control makes the input current follow the line voltage, using an analogue multiplier to generate the line-current reference signal. This
element, however, increases the nonlinearities and the complexity
of the control circuitry. Although at present it is possible to use
integrated solutions, such as UC3854, the cost of such circuits is
slightly higher [2].
Recently, the quasi-steady-state approach has been proposed in
the literature for pulsewidth modulation (PWM) controllers to
avoid the use of an analogue multiplier [3, 41. Based on this
approach, in this Letter we propose an alternative control implementation using sliding mode control theory. The proposed controller operates in CCM and avoids the use of an analogue
multiplier, a clock generator, and the sensing of the line voltage.
,
.
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.
.
:
$:
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. . , . . . . . . . . . . . . . . , ...I... . .
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I
~ 0 0 x ~Ch4
.
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2.00A
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M50
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4.2V
1017/41
Fig. 4 Transient response during step change in load from 135 to 270 R
Top trace: control variable K [CH3]
Middle trace: output voltage [CHl]
Bottom trace: line current [CH4]
Control design: The input current of a PFP must follow the shape
of the line voltage as a resistor, and simultaneously the average
value of the output voltage ((V,)) must be regulated to a reference
Both control goals can be achieved if the inductor
value (V,
current satisfies the following relation (see Fig. 1):
res>.
.
IKnI
ZL = -
(1)
Re,
Fig. 1 Simplified control diagram
2000pH
where iL is the inductor current of the converter and &, is the
emulated resistor the values of which are related to the input
power and the output voltage. The value of kgmust be controlled
to make the average value of the output voltage (V,) follow a reference value V, ref.
The control scheme consists of both an outer control loop,
which regulates the value of the emulated resistor, and an inner
control loop, which is used to make the input current follow a reference value (I VJIReq).
To implement the relation (eqn. l), avoiding the sensing of the
line voltage and the use of an analogue multiplier, the quasisteady-state approach is considered. According to this approach,
the ratio between the line and the output voltage can be approximated by the voltage conversion ratio of a D C D C boost converter. Therefore, the following relationship can be used in the
control design
MUR1560
where (U) is the average value of the control variable U during a
switching period (U = 0 when MI is on and U = 1 when MI is off).
Substituting eqn. 2 for eqn. 1 yields a new expression of the
control goal
.
v o . (U)
2L 11 (3)
Re,
Taking into account that iL and VJRe, are nearly constant during
a switching period, the relation (eqn. 3) can be approximated by
(ZL - K U ) N 0
(4)
'
,
,
Chl
-
.
lOOV
.
,
where K is defined as VJ&,, and it is a new control variable
which is used to regulate the output voltage.
To achieve the unity-power-factor, the expression (eqn. 4) must
be satisfied when the sliding regime is reached. The expression of
the required sliding surface can be deduced by identifying the
invariance condition S = 0 with eqn. 4:
..
2.00A
s = (iL - K . U )
1017/31
Fig. 3 Steady-state input waveforms
Top trace: line voltage [CHI]
Bottom trace: line current [CH4]
47 4
(5)
Note that this sliding surface will satisfy the transversal condition
if a first-order lowpass filter is used to calculate the average value
of iL - K.u during a switching period. The control law associated
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12thApril2007
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No. 8
with this surface is deduced by using the reaching condition, S.S < 0
[5], which yields
U = { 1 when S > 0
0 when S < 0
Moreover, a proportional-integralcontrol of K has been used to
make the output voltage be regulated to a reference value Vo
K = Kp(Voref - V O ) + KI
/t(vo,.ef
-V
W
ated-emissions above 1GHz typically have lower field-strength levels compared with those below IGHz, so an antenna system
having a lower antenna factor (AF) is required. An offset-fed parabolic reflector operated as a CAR can be considered as an alternative to replace the conventional double-ridged horn antenna. Here
we consider the AF of such an antenna.
(6)
Figs. 1 and 2 show the block diagram and the physical implementation of the proposed controller, respectively. To implement
the sliding surface, a first-order lowpass filter, an analogue multiplexer, and a proportional-integral controller have been used.
Finally, the state of MI is determined by a hysteresis comparator,
according to the control law deduced above. Note that a single
low-cost integrated circuit is used, resulting in a very simple and
cheap solution.
Results and conclusions: Fig. 3 shows the experimental line voltage
and line current in the steady state. As expected, the line current
tracks the shape of the line voltage with a slight distortion. Fig. 4
shows the dynamic behaviour of the converter when the load was
subject to a sudden change from 135 to 270Q. The amplitude of
the line current varies to regulate the output voltage to the reference value.
These results demonstrate that the proposed control circuit can
be used to control the boost PFP and that it is an interesting alternative to unity-power-factor integrated control circuits.
0 IEE 2001
21 February 2001
Electronics Letters Online No: 20010359
DOI: 10.1049/el:20010359
0. Lbpez, L. Garcia de VicuAa and M. Castilla (Department of
Electronics Engineering, Universidad Politecnica de Cataluria, AV.
Victor Balaguer s/n, Vilanova i la Geltru 08800, Spain)
E-mail: [email protected]
References
SEBASTIAN, J., JAUREGUIZAR, M., and UCEDA, J.: ‘An overview of
power factor correction in single-phase off-line power supply
systems’. IECON’94, 1994, pp. 1688-1693
‘UC3854 controlled power factor correction circuit
design’. Unitrode Application Note, U-134
JOEL, D., GEGNER, P., and LEE, c.Q.:‘Linear peak current mode
control: a simple active power factor correction control technique
for continuous conduction mode’. Proc. PESC’96, June 1996, pp.
196-202
LAI, z., and SMEDLEY, K.M.: ‘A family of continuous-conductionmode power-factor-correction controllers based on the general
pulse-width modulator’, IEEE Trans. Power Electron., 1998, 13,
(3), pp. 501-510
YUNG, J.Y., GAO, w., and HUNG, J.c.: ‘Variable structure control: a
survey’, IEEE Trans. Ind. Electron., 1993, 40, pp. 2-22
10
20
30
40
50
60
HPBW of feed, deg
70
80
18067’11
Fig. 1 Dependence of correction factor on HPB W of feed
Analytical formulation: Consider a CAR operated as a field
source. The plane-wave field is created by collimating the spherical-waveform of a feed with an offset-fed parabolic reflector. The
approximate power density in the aperture can be computed if it is
assumed that the plane wave is confined with uniform power density in the collimated region. The approximation can be corrected
by a correction factor ( C q derived from the feed radiation pattern. An equal power density can be produced at a specified distance R from an antenna with the same input power and an
appropriate gain. This gain can be considered as the effective gain
of the CAR associated with the distance R . By reciprocity, the
effective gain can then be converted to an antenna factor [l] for
the CAR associated with a distance R , i.e.:
TODD, P.c.:
Antenna factor of compact antenna range
for EMC measurements above 1GHz
Y.-C. Chung, A.C. Marvin and A.J. Rowel1
A formula is proposed for measuring the antenna factor of an
offset-fed parabolic reflector operated as a compact antenna range
(CAR) by considering the plane-wave approximation and fielddistribution in the collimated region. The antenna factor is
determined from the half power beamwidth (HPBW) of the feed,
the physical geometry of the reflector and a field-distribution
correction factor. The proposed formula is in good agreement
with the measured results using a standard double-ridged hom
antenna as the feed. The formula can be used to design CARSfor
EMC applications.
Introduction: The upper frequency of unwanted radiated-emission
measurements is being expanded above lGHz because of the
higher clock frequencies of modem electronic products. The radi-
ELECTRONICS LETTERS
12th April 2001
where fMHzis the frequency in MHz, R is the distance, d is the
diameter of the collimated region, and CF is a correction factor
for the field distribution in the collimated region. The distance R
is required as the response of the CAR is independent of distance
along its radiation axis within the collimated region, whereas the
field radiated by a source in free-space is dependent on the distance between the field observation point and the source.
The field distribution function across the aperture of the CAR,
which determines the correction factor CF, can be adequately
described by only considering the amplitude taper [2] across the
projected aperture. This is due to the feed pattern and space attenuation between the feed and reflector surface. The correction factor is obtained through numerical integration that includes an
asymmetrical field-distribution function due to offset feeding.
Fig. 1 shows the correction factor of the offset-fed parabolic
reflector used for experiments, where the feed pattern is assumed
to be parabolic in dB as Kelleher’s approximation [3]. It can be
seen that the correction factor is 0.7 to 7.5dB for variation of the
half-power beamwidth (HPBW) of 10-80”. The broader HPBW
has a lower correction factor due to the more uniform distribution
in the collimated region.
Experimental results and discussions: Experiments were performed
using a commercial offset-fed parabolic reflector and a doubleridged horn as a feed. The reflector system has the dimensions
shown in Fig. 2. Computed values of the antenna factor are given
in Fig. 3. The HPBW data used for calculations range from 66” at
lGHz to 34” at 1OGHz. They were obtained from the feed horn
manufacturer’scatalogue.
The antenna factor of the reflector system for a 3m equivalent
distance can be determined using the measured received-voltage
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