Showing papers on "Balun published in 2013"

A Wideband, Wide Scanning Tightly Coupled Dipole Array With Integrated Balun (TCDA-IB)

Abstract: A key challenge in the design of wideband dipole phased arrays is the design of equally wideband baluns which are sufficiently compact to fit within the unit cell (typically in the linear dimension at low frequencies). In this paper, we exploit the reactance of a compact Marchand balun as an impedance matching network for each array element. The elimination of bulky external baluns results in a significant reduction of size, weight and cost, while the bandwidth is simultaneously improved by over 30%, compared to standard feeding techniques. In this manner, a tightly coupled dipole array with an integrated balun (TCDA-IB) is developed which achieves 7.35:1 bandwidth (0.68 - 5.0 GHz) while scanning to ±45° in all directions, subject to . In a dual-polarization configuration, the TCDA-IB has low cross polarization of over the majority of the band. Measured results are presented for a prototype 8 × 8 element TCDA-IB, showing good agreement with simulation.

SAW-less analog front-end receivers for TDD and FDD

Abstract: In cellular receivers, out-of-band blockers are generally managed by surface-acoustic-wave (SAW) filters between the antenna and the low-noise amplifier (LNA). For Time Division Duplexing (TDD), such as GSM, the SAW can be removed if the receiver can handle very large interferers (e.g. in GSM 0dBm 20 MHz away) [1]. Generally SAW filters also perform differential to single-ended (SE) conversion (balun). Once the SAW is removed an SE transceiver eliminates the external balun, reducing cost and attenuation. For the same sensitivity, a SAW-less SE transceiver can have a noise figure (NF) 2 to 3dB higher than a classical one. An SE LNA could be susceptable to couplings from supply and substrate, which are usually rejected through symmetry. Therefore it should become symmetric as closely as possible to the input pin. A SAW-less differential transceiver [2] can also be appealing if it has an NF close to that of classical transceivers. This is because it can have better sensitivity in TDD (a balun attenuates less than a SAW) and it can be very flexible, being usable for both FDD (where duplexers are differential) and TDD.

Broadband Balanced Frequency Doublers With Fundamental Rejection Enhancement Using a Novel Compensated Marchand Balun

Abstract: In this paper, a novel compensation technique is proposed to improve the imbalance of a Marchand balun due to the unequal odd- and even-mode phase velocities of the coupled lines. Using this method, the fundamental rejection of the balanced doubler with the Marchand balun can be effectively enhanced. Two single-balanced doublers using the improved Marchand balun are designed, fabricated, and measured to verify the concept in CMOS processes. One doubler for 15–36-GHz possesses $-$ 10-dB conversion gain with the 3-dB bandwidth of 82.4% and the fundamental rejection of 33 dB. The other doubler for 95–150 GHz achieves $-$ 7.9-dB conversion gain with the 3-dB bandwidth of 45% and the fundamental rejection of 30 dB. With the proposed compensation technique, these frequency doublers feature wide bandwidths and high fundamental rejections.

UWB Low-Profile Tightly Coupled Dipole Array With Integrated Balun and Edge Terminations

Abstract: Tightly coupled phased arrays (TCPAs) provide UWB performance due to their strong inter-element coupling. However, in finite tightly coupled phased array realizations, mutual coupling is reduced near the array edges, causing the edge elements to become narrowband. To address this issue, a nonuniform array excitation scheme, referred to as “characteristic mode (CM) excitation,” was recently proposed. A more practical alternative for designing UWB tightly coupled phased arrays is proposed here. In this paper, we present a strategy that employs uniform excitation of the central array elements and short-circuits the periphery elements. We report that at least for medium size arrays, this approach provides up to 3 dB more gain and 50% higher efficiency than typical resistive termination. This concept is demonstrated using a 7 × 7 linearly polarized dipole array, 60.96 cm × 60.96 cm (2' × 2') in size, for operation from 200 MHz-600 MHz. Feeding of the active elements is challenging due to several constraints on the feed design, including balanced to unbalanced transitions, impedance transformations, common mode suppression, compact size, low cost, etc. To address these issues we propose a novel array feed using a compact, ultrawideband balun (with 10:1 bandwidth for VSWR ). Simulated and measured data are provided for broadside and 30 scan in the H-plane.

Microwave energy-delivery device and system

Abstract: A microwave ablation device including a cable assembly configured to connect a microwave ablation device to an energy source and a feedline in electrical communication with the cable assembly. The microwave ablation device further includes a balun on an outer conductor of the feedline, and a temperature sensor on the balun sensing the temperature of the balun.

A 60-GHz CMOS Sub-Harmonic RF Receiver With Integrated On-Chip Artificial-Magnetic-Conductor Yagi Antenna and Balun Bandpass Filter for Very-Short-Range Gigabit Communications

Abstract: This paper presents a first reported 60-GHz CMOS sub-harmonic RF receiver with an integrated on-chip artificial-magnetic-conductor (AMC) Yagi antenna and a balun bandpass filter (BPF) fabricated in 90-nm technology. The on-chip antenna with an AMC structure can reduce the substrate loss and increase the antenna radiation efficiency and power gain. The on-chip balun BPF combines the integrated design of the balun and RF BPF to reduce the circuit size and the insertion loss. The sub-harmonic receiver is adopted to mitigate the dc offset problem. The probe-station based on-wafer continuous wave wireless transmission test is conducted $(R=1~{\hbox{m}})$ and the measured total receiving conversion gain ${\rm CG}_{\rm ant+Rx}$ and output third-order intercept point of the integrated RF receiver (with the on-chip AMC antenna and the balun BPF) are 16.2 dB and 3 dBm at 60 GHz, respectively. In error vector magnitude/bit error rate (BER) tests, the measured maximum data rate is 1.152 Gb/s in the 16QAM mode at a 25-cm wireless link (transmitting ${\rm EIRP}=23~{\hbox{dBm}}$ ) approximately with a BER of ${\hbox{10}}^{-3}$ . The presented integrated RF receiver will be very useful for the design of a 60-GHz fully integrated CMOS single-chip radio for very-short-range communication applications.

A Magnetic-Field Resonant Probe With Enhanced Sensitivity for RF Interference Applications

Abstract: High-sensitive field probes are highly desirable for radio-frequency (RF) interference studies, where ultralow noise levels are of interest. By incorporating an LC resonant circuit in a differential-loop probe, together with a Marchand balun, a magnetic-field probe with enhanced sensitivity is developed. Its equivalent circuit model and design methodology are established. The design is validated by measurements. The measured relative sensitivity in terms of |S21| of the proposed probe increases by approximately 8.63 dB at the resonant frequency of 1.575 GHz compared to that of a conventional design. The advantage of the proposed probe is validated through its application in the measurement of a microstrip trace and a real-world cell phone design.

Dual-Band Circularly Polarized Annular-Ring Microstrip Antenna for GNSS Applications

Abstract: A dual-band circularly polarized antenna fed by four apertures that covers the bands of GPS (L1, L2, L5), Galileo (E5a, E5b, E1, E2, L1), and GLONASS (L1, L3) is introduced. A lotus-shaped aperture is added to optimize the coupling between the microstrip lines and the rings. Three wideband planar baluns are used to achieve good axial ratio (lower than 2.1 dB in both bands) and VSWR (41.2%). The measured results of the annular-ring microstrip antenna show good performance of a dual-band operation, and they confirm the validity of this design, which meets the requirement of Global Navigation Satellite System (GNSS) applications.

RF Surface Receive Array Coils: The Art of an LC Circuit

Abstract: The radiofrequency (RF) receive array coil is a complicated device with many inductors and capacitors and serves as one of the most critical magnetic resonance imaging (MRI) electronic devices It directly determines the achievable level of signal-to-noise ratio (SNR) Simply put, however, the RF coil is nothing but an LC circuit The receive array coil was first proposed more than 20 years ago, evolving from a simple arrangement with a few electronic channels to a complicated system of 128 channels, enabling highly sophisticated parallel imaging, at different field strengths This article summarizes the basic concepts pertaining to RF receive coil arrays and their associated SNR and reviews the theories behind the major components of such arrays This includes discussions of the intrinsic SNR of a receive coil, the matching circuits, low-noise preamplifiers, coupling/decoupling amongst coils, the coupling between receive and transmit coils, decoupling via preamplifiers, and baluns An 8-channel receive array coil on a cylindrical former serves as a useful example for demonstrating various points in the review

A CMOS 77-GHz Receiver Front-End for Automotive Radar

Abstract: This paper presents the design of a receiver (Rx) front-end for automotive radar application operating at 76-77 GHz. The Rx employs a double conversion architecture, which consists of a five-stage low-noise amplifier (LNA), a sub-harmonic mixer (SHM), and a double-balanced passive mixer (PSM). By adopting this architecture, millimeter-wave frequency synthesizer design can be relaxed. In the LNA layout, the output of each stage is positioned close to the input of the follow stage, thus creating a LC resonance load. As a result, complex interstage matching networks is simplified. The SHM driven by a 38-GHz local oscillator (LO) is adopted to avoid push/pull effect and power consumption of the voltage-controlled oscillator. A PSM is utilized for the second conversion since it consumes no dc current and has low flickering noise. To connect the singled-ended LNA and SHM, a 77-GHz balun is designed; and for driving the SHM, two 38-GHz baluns and an in-phase/quadrature coupler to provide quadrature 38-GHz LO are designed. The proposed Rx is implemented in a 65-nm CMOS technology and measurement results show 16-dB voltage gain and 13-dB calculated noise figure while dissipating 23.5 mA from a black 1.2-V supply.

A 76–84 GHz SiGe Power Amplifier Array Employing Low-Loss Four-Way Differential Combining Transformer

Abstract: This paper presents holistic design of a novel four-way differential power-combining transformer for use in millimeter-wave power-amplifier (PA). The combiner with an inner radius of 25 μm exhibits a record low insertion loss of 1.25 dB at 83.5 GHz. It is designed to simultaneously act as a balanced-to-unbalanced converter, removing the need for additional BALUNs typically required in differential circuits. A complete circuit comprised of a power splitter, two-stage differential cascode PA array, a power combiner as well as input and output matching elements was designed and realized in SiGe technology with fT/fmax 170/250 GHz. Measured small-signal gain of at least 16.8 dB was obtained from 76.4 to 85.3 GHz with a peak 19.5 dB at 83 GHz. The prototype delivered 12.5 dBm output referred 1 dB compression point and 14 dBm saturated output power when operated from a 3.2 V dc supply voltage at 78 GHz.

Balun's effect on the measurement of transmission characteristics for intrabody communication channel

Abstract: Intrabody communication (IBC) is a promising technology that enables the improvement of digital healthcare devices. IBC uses the human body as a transmission media, and the accurate transmission model is important for the design of transceivers. In the measurements of transmission characteristics, baluns have been widely used to separate the grounds of transmitter and receiver. In this work, we analyze the balun's effect on the measured results of capacitive IBC channel. Baluns and balun boards used in our measurements have the parasitic common-mode capacitances, ranging from 1.1 to 32 pF, which affects the measured transmission level of the IBC channel, leading to a significant difference of about 40 dB.

220–250-GHz Phased-Array Circuits in 0.13- $\mu{\hbox {m}}$ SiGe BiCMOS Technology

Abstract: This paper describes the design of 220-250-GHz phased-array circuits in 0.13- μm BiCMOS technology. The design aspects of the active and passive devices that are used in the phased-array systems, such as balun, Wilkinson divider, and branch-line coupler, are presented in details. A millimeter-wave vector modulator is designed to support both amplitude and phase control for beam-forming applications. The designed circuits are integrated together to form a four-channel 220-250-GHz phased-array chip. Each channel exhibits 360° phase control with 18 dB of amplitude control. The entire chip draws 167 mA from a 3.3-V supply. The millimeter-wave phase shifting and the low-power consumption makes it ideal for highly integrated scalable beam-forming systems for both imaging, radiometry, and communication applications.

Design of a Wideband Balun Using Parallel Strips

Abstract: A wideband balun designed by exact synthesis is presented in this letter. The designed balun has a symmetrical four-port structure with one port open-ended. It consists of a wideband impedance transformer and a broadband phase inverter, which is realized by connecting bottom and top layer parallel strip through two via holes. To design the wideband impedance transformer, an S-plane highpass prototype has been exactly synthesized with third-order Chebyshev response. The proposed design procedure is very flexible, and it can be easily scaled for other frequency bands. A wideband parallel strip balun operating from 0.72 to 2.05 GHz is fabricated and tested to verify the design concepts. The measured results match well with the design theory.

A 1- to 10-GHz RF and Wideband IF Cross-Coupled Gilbert Mixer in 0.13- $\mu\hbox{m}$ CMOS

Abstract: A modified Gilbert-cell mixer exhibiting both wideband radio-frequency (RF) and wideband IF performance is presented. With the proposed common-gate RF stage with the cross-coupled complementary transistors, a measured conversion gain of 3-8 dB over an RF band of 1-10 GHz is demonstrated, together with an RF input return loss better than 10 dB. The proposed mixer also incorporates wideband active local oscillator (LO) and IF baluns for matching and testing purposes. An IF bandwidth from 100 MHz to 1 GHz is achieved with a conversion gain variation of less than 2 dB. The measured output return loss within the IF band is better than 10 dB. Fabricated in a standard 0.13- μm CMOS technology, the chip only draws 7 mA from a 1.2-V supply due to the current reuse in the proposed RF stage. The measured input referred 1-dB compression point IP1-dB, third-order input intercept point IIP3, and single-sideband noise figure are better than -16 dBm, - 7 dBm, and 15 dB throughout the entire RF band.

Wideband active balun lna topology with narrow-band filtering and noise cancelling

Abstract: The present invention provides a wideband active balun LNA topology with narrow-band filtering and noise cancelling. The amplifier includes three transconductance stages, a feedback network, and a load. The first and second transconductance stages are connected in parallel to receive the input signal. The differential output of the first transconductance stage is fed back to voltage input through a differential-to-single-end-end feedback network, while the output of the first transconductance, passing through the third transconductance, is added to the output of the second transconductance stage in proper phase. The present invention accomplish both wideband low-noise amplification and narrow-band filtering without inserting interface stages, thereby improving the linearity and noise performance of the whole circuit. Noise cancellation technique is implemented in differential way to ensure the low noise figure. The present invention also achieves single-end to differential conversion with balanced output and superior second order linearity performance.

General Compensation Method for a Marchand Balun With an Arbitrary Connecting Segment Between the Balance Ports

Abstract: For a Marchand balun, the output imbalance due to the inevitable physical separation between the balance ports is a problem. In this paper, a general compensation method to cope with this imbalance issue is proposed with rigorous analysis and design formulas. The compensation relies on two intentionally shortened coupling sections and a pair of short-circuited transmission lines as the terminations. The proposed method is able to deal with a long connecting segment between the balance ports as long as the coupling sections are tight enough at the desired frequencies. The theory and formulation are first treated using transient analysis with multiple reflections/couplings between the networks. Design graphs are summarized and three examples are fabricated, validated, and discussed to demonstrate the design flexibility the proposed method provides.

An Ultra-Low Power $V$ -Band Source-Driven Down-Conversion Mixer With Low-Loss and Broadband Asymmetrical Broadside-Coupled Balun in 90-nm CMOS Technology

Abstract: This paper proposes a microwatt source-driven down-conversion mixer with broadband asymmetrical broadside-coupled baluns in a 90-nm CMOS low-power process. The forward body biased (FBB) technique reduces the threshold voltage (VTH) and supply voltage for operation in the near weak inversion region in millimeter-wave mixer designs. To effectively reduce the size of the chip, an asymmetrical broadside-coupled balun is developed with a bandwidth of 103 GHz (from 34 to 137 GHz) with a low insertion loss of 3.66 dB (3 dB for an ideal balun) at 58 GHz. The chip area of the balun is 0.016 mm2. The proposed FBB mixer has a 4.2-dB peak conversion gain and a 14.3-dBm input third-order intercept point at 55 GHz under a 2-dBm local-oscillator power. The dc power of the FBB mixer core is only 139 W, while it draws a 278-μA dc current from a 0.5-V supply. The fabricated FBB mixer, comprising two asymmetrical broadside-coupled baluns, and all of test pads and dummy blocks, occupies an area of 0.72 mm2. An FoMMixer1 that is obtained using the ultra-low power consumption FBB mixer is as high as 23.4.

Wide-Bandwidth Power-Combining and Inverse Class-F GaN Power Amplifier at X-Band

Abstract: In this paper, we present a wide bandwidth power amplifier (PA) utilizing a Marchand balun to achieve power combining and inverse class-F (class-F-1) matching. We have used a 4-to-1 balun and its out-of-band characteristics to achieve matching at the second and third harmonic for differential class-F-1 operation. Thus, the balun simultaneously acts as a combiner and harmonic matching network. The experimental results demonstrate that the prototype PA achieves an output power of 41.5 dBm at the 1-dB compression point (P1 dB), power-added efficiency of 55%, and gain of 10 dB over a fractional bandwidth of 40% from 8 to 12 GHz. Due to the differential operation, the class-F-1 PA has also achieved a measured second harmonic distortion of -50 dBc.

Decade bandwidth high-efficiency GaN VHF/UHF power amplifier

Abstract: This work discusses the design of a GaN power amplifier demonstrating high efficiency over more than a decade bandwidth using coaxial baluns and transformer matching networks to achieve over a 50MHz-500 MHz bandwidth. The power amplifier demonstrates a power added efficiency of 83%-64% over full bandwidth with 15 dB compressed gain at peak PAE.

Broadband high PAE GaN push-pull power amplifier for 500MHz to 2.5 GHz operation

Abstract: A broadband push-pull power amplifier with power added efficiency (PAE) greater than 47% from 500 MHz to 25 GHz is reported The power amplifier comprises two GaN integrated circuits whose outputs are combined with a broadband balun to achieve power up to 20W Each IC contains two stacked GaN HEMTs and is designed to employ a load impedance of 25Ω without any reactive matching in order to achieve broadband operation To provide a better input impedance match to 25Ω and to reduce gain variation over frequency, an RC feedback network is used Measurements, under CW excitation, demonstrated greater than 63% power added efficiency at select frequencies and greater than 47% over the entire bandwidth

A Modified Marchand Balun Configuration With Tunable Phase Balance

Abstract: In this letter, a novel modified Marchand balun configuration with tunable phase balance is analyzed and verified experimentally. It is proposed to add a shunt susceptance in between the two couplers of the Marchand balun. This allows for a change in the phase balance which, to first order, is linear with the susceptance, while the magnitude balance is kept constant. To verify the proposed configuration, a lumped element Marchand balun has been fabricated using a SiGe BiCMOS technology. The balun design is centered around 9.4 GHz, with an insertion loss of 6.0 dB. The phase difference between the output ports can be changed from 175.8° to 183 ° whereas the magnitude imbalance is kept almost constant at 0.3 dB. The balun performs well in the range from 7 to 11 GHz, where it is possible to tune the phase to exactly 180°.

Analysis, Design, Modeling, and Characterization of Low-Loss Scalable On-Chip Transformers

Abstract: A few important design choices for a low-loss scalable on-chip transformer are discussed, the most important one being that the capacitive and inductive couplings should be aligned to minimize insertion loss. The importance of these design choices is illustrated both theoretically as well as experimentally. In particular, for the first time the performance of these on-chip transformers is verified with four-port S -parameter measurements taken up to 67 GHz. With that, an insertion loss of only 0.6 dB up to 30 GHz is demonstrated. To facilitate the use of these low-loss on-chip transformers in the RF integrated-circuit design flow, a scalable compact equivalent-circuit model suitable for all pre-layout circuit simulations is described, which accurately predicts transformation ratios, transmission efficiencies and balun amplitude and phase imbalances.

Triple-Band Marchand Balun Filter Using Coupled-Line Admmittance Inverter Technique

Abstract: This study presents the first reported design and implementation of triple-band Marchand balun filter. The novel balun filter is constructed from the short-circuited coupled line with a triple-band resonator to demonstrate the triple-band admittance inverter characteristic. To improve the amplitude and phase responses within three passbands, the compensation techniques for phase-angle, impedance-matching, and susceptance-slope discrepancies are employed in the balun filter design. Four types of triple-band balun filters with significantly different bandwidths and passband separations are designed and the results are consistent with the specifications. The design procedure for the triple-band Marchand balun filter is established to obtain the amplitude and phase balances in three operating bands with arbitrarily controlled center frequencies and fractional bandwidths. The proposed Marchand balun filter realized by the microstrip coupled-line sections and the defected ground structure stubs is measured and a good agreement among equivalent-circuit calculation, full-wave simulation, and measurement is observed, demonstrating the validity and versatility of the proposed design methodology and balun filter configuration.

LTE broadband dual-polarization antenna oscillator

Abstract: The utility model discloses an LTE broadband dual-polarization antenna oscillator, comprising a printed circuit board, a balun support and a reflective board. A radiation unit is printed on a front surface of the printed circuit board. Every pair of dipoles consists of two annular radiation units which are on the same plane and are arranged in a central symmetry manner. Two centers of two pairs of dipoles are vertical and cross. The adjacent radiation units are 90 DEG equiangular bias and a gap is mounted between the adjacent radiation units. The radiation units forming the pair of dipoles are electrically connected with each other. The printed circuit board and the reflective board are fixed on the balun support disposed between the circuit board and the reflective board. The dual-polarization antenna oscillator provided by the utility model has broad bandwidth and can operate in a frequency scope of 1700-2700 MHz. A VSWR is less than or equal to 1.4. The antenna oscillator can realize 65 DEG and 90 DEG antenna arrays of level 3dB bandwidth and is made of a polytetrafluoroethylene micro-strip board. The oscillator has the advantages of small size, low profile, light weight and good processing consistency and satisfies present mobile-communication development requirements.

Wideband dual-polarized radiation element and antenna of same

Abstract: A wideband dual-polarized radiation element includes two pairs of cross polarized dipoles and baluns which correspondingly feed current to each dipole in a balanced manner. Each dipole includes a pair of unit arms aligned on a top end of the corresponding balun. One end of each unit arm is connected on top of the balun, and the other end of one unit arm is bending inwards to form inward loaded line, and the other unit arm is bending downwards to form downward loaded line. An antenna includes a metal reflector and at least one wideband dual polarized radiation element, which has excellent radiation and polarization performance.

30% PAE W-Band InP Power Amplifiers Using Sub-Quarter-Wavelength Baluns for Series-Connected Power-Combining

Abstract: We present high-efficiency W-band power amplifier (PA) ICs with a new series-connected power combining technique using sub-quarter-wavelength transmission- line baluns. The PAs are implemented in a 0.25μm InP HBT process. At 86GHz, a single-stage PA exhibits 30.4% peak PAE, 20.37dBm Pout and 23GHz 3dB bandwidth. A two-stage PA exhibits 30.2% PAE, and 23.14dBm Pout. These values of PAE represent a 1.2:1 improvement in the state-of-the-art for E- and W- band PAs having similar RF output powers.

Wideband simplified feed for printed log-periodic dipole array antenna

Abstract: A novel simple approach is presented for designing a broadband single layer substrate printed log-periodic dipole array (PLPDA) antenna by using microstrip technology. The PLPDA antenna has the merits of wide bandwidth, low profile and light weight, which should be fed by the balanced line. The balanced line, created by the geometric features of the microstrip, provides a balun with a considerably wide bandwidth with low profile, broad bandwidth and low insertion loss etc. The prototype of the proposed microstrip printed log-periodic array at Ka band is designed and fabricated; the measured data are in good agreement with the simulated results.

A SiGe:C BiCMOS 140 GHz wideband frequency multiplier-by-8 with differential output

Abstract: This paper presents a wideband frequency multiply-by-8 IC for F band FMCW radar application. It combines an active balun, three push-push doubler stages and a buffer stage. The doubler stage uses a transformer for single to differential conversion, with good output balance and compact size. The measured 3 dB output bandwidth of the multiplier is about 30 GHz from 110 GHz to 140 GHz with low harmonics. With 2.5 V power supply, the multiplier can deliver 4.7 dBm output power at 140 GHz and consumes 170 mW.

Full duplex radio frequency interference deleting device and method

Abstract: The invention belongs to the filed of full duplex radio communication interference resistance, and discloses a full duplex radio frequency interference deleting device and method The frequency interference deleting device is composed of a circulator, a power divider, a passive attenuation and delay circuit and a Balun convertor An RF signal output by a transmitting branch circuit is branched off a very small signal by the power divider, after the signal passes through the attenuation and delay circuit, a regenerative interference signal which is equal to a self-interference signal in amplitude and phase, the self-interference signal is leaked on the circulator when the transmitting signal passes through the circulator, the two signals are added to the Balun convertor simultaneously and then are offset mutually, and therefore the purpose that the self-interference generated by the transmitting signal to a receiving branch circuit is eliminated is achieved The passive attenuation and delay circuit is adopted to replace an active isolating method, out-of-band leakage does not occur, and out-of-band interference is greatly reduced