Coupled Lines Research Articles

Highly Sensitive Reflective-Mode Phase-Variation Permittivity Sensors Using Coupled Line Sections

Highly sensitive permittivity sensors operating in reflection and exploiting phase variation are presented in this article. The sensors are one-port structures implemented by means of a pair of coupled lines, the sensitive region, with an appropriate termination. In particular, it is demonstrated that by either short-circuiting the crossed port to the input port of the device (opening the remaining two ports), or opening the crossed port to the input port (terminating the other two ports with a short-circuit), the sensitivity can be driven to very high values, controlled by the coupling factor. For that purpose, the electrical length of the pair of coupled lines must be set to 90 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> when such lines are loaded with the reference (REF) material. Thus, the sensitivity is optimized for dielectric constants (the input variable) in the vicinity of the dielectric constant of the REF material, where the indicated phase condition is fulfilled. The output variable is the phase of the reflection coefficient, an easily measurable quantity. For validation purposes, three prototype sensors are designed and fabricated. The achieved sensitivities in two of the fabricated sensors are as high as 659.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> and 736.0 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> , with figures of merit (FoMs), or ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared-wavelength, of FoM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 9401 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda^2$</tex-math> </inline-formula> and 12 690 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda$</tex-math> </inline-formula> , respectively, i.e., very competitive values. Moreover, the indicated high sensitivities and FoMs have been achieved without the need to add further circuit stages to the sensing region, contrarily to other highly sensitive phase-variation sensors, where sensitivity optimization is achieved at the expense of an increase in the overall sensor size.

Design of UWB Filtering Impedance Transformers and Power Dividers Using Stepped-Impedance Resonators

This study presents a novel design of ultra-wideband (UWB) impedance transformers and power dividers with filtering capabilities. Based on the UWB impedance matching network, the UWB filtering impedance transformers are designed, and the UWB filtering power dividers are achieved by impedance transforming one port of one or more impedance transformers. The transformers consist of a multi-mode stepped-impedance resonator (SIR) and defected ground structures (DGSs). The SIR is tightly coupled to two ports of different impedance levels via the unsymmetrical two-sided coupled lines and DGSs. In addition, two transformers that convert impedance from 50 Ω to 100 Ω are connected to form a UWB power divider with filtering function. The 25 Ω port of an impedance transformer with a 50 Ω to 25 Ω conversion is impedance matched to two 50 Ω ports connected in parallel, resulting in another power divider with filtering function. Thus, two prototype UWB impedance transformers from 50 Ω to 100 Ω and from 50 Ω to 25 Ω are designed and their corresponding power dividers are also designed and fabricated. The simulated and measured results are consistent, demonstrating good features, such as return loss greater than 10 dB and insertion loss less than 4.5 dB in the passband, UWB filtering capacity with out-of-band rejection greater than 20 dB, and compact size smaller than 1.2λ × 2.1λ (λ is the wavelength of the central frequency).

Wideband Filtering Rat-Race Coupler with Shared Triple-Mode Resonator

In this paper, a filtering rat-race coupler (FRC) is presented, which features the merits of a wideband filtering response, good impedance matching at both input and output ports, good isolation, high-frequency selectivity, small in-band phase difference error, a wide stopband, and small size. It was composed of two leading triple-mode resonators, one core section, and two λ/2 open-circuited transmission lines (TLs). The core section consisted of three λ/4 TLs and one λ/4 short-circuited parallel coupled line (CL). The leading triple-mode resonator consisted of one λ/4 short-circuited stub and two λ/4 TLs. By loading the triple-mode resonator as the shared component and combining it with the core section, a wideband filtering response with four transmission poles could be achieved. In addition, two transmission zeros were generated by loading the λ/2 open-circuited TLs to the output ports of the FRC. The working principles of the proposed FRC are analyzed, and equations are derived with parametric analysis. For demonstration, a prototype operating at the center frequency of 1.4 GHz was designed, fabricated, and measured. Measurement results show that a fractional bandwidth of more than 60% was achieved under the criteria of 10 dB return loss and 20 dB isolation. In this bandwidth, the amplitude imbalances and phase difference errors were less than 1 dB and 10°, respectively. Additionally, it also exhibited high selectivity and a wide stopband.

Dual-Band and Wideband Bandpass Filters Using Coupled Lines and Tri-Stepped Impedance Stubs.

In this paper, two bandpass filters-one with a dual-band response and the other with a wideband response-were designed, implemented, and experimented with. The filters are based on the novel combination of series coupled lines and tri-stepped impedance stubs. However, coupled lines along with tri-stepped impedance open stubs (TSIOSs) give a third-order dual passband response. The advantage of dual-band filters using coupled lines and TSIOSs is that they have wide passbands that are close together and separated by a single transmission zero. In contrast, the inclusion of tri-stepped impedance short-circuited stubs (TSISSs) instead of TSIOSs provides a fifth-order wide passband response. The advantage of wideband bandpass filters using coupled lines and TSISSs is that they have a very good selectivity factor. Theoretical analysis was carried out to validate both filter configurations. The tested bandpass filter using coupled lines and TSIOS units had two close wide passbands operating at 0.92 and 1.52 GHz center frequencies, respectively. The dual-band bandpass filter was implemented to operate in GSM and GPS applications. The first passband had a 3 dB fractional bandwidth (FBW) of 38.04%, while the second passband had a 3 dB FBW of 22.36%. The experimental result of the wideband bandpass filter (with coupled lines and TSISS units) had a center frequency of 1.51 GHz with a 3 dB fractional bandwidth of 62.91% and a selectivity factor of 0.90. A good congruence was demonstrated between the full-wave simulated and tested results for both filters.

Wideband quasi-reflectionless bandstop filters using open/shorted coupled lines

AbstractTwo wideband bandstop filters (BSFs) for single and dual-band are proposed and then extended to reflectionless BSFs based on the analysis from input impedance/admittance perspective. Also, topologies of higher-number-stopband input-reflectionless BSF are provided to broaden the design scope. Open/shorted coupled lines are adopted to obtain multi transmission zeros and desired stopband bandwidth by adjusting the even-/odd-mode impedance of coupled lines. Resistor-loaded coupled lines are connected with Port 1 to absorb unwanted signals and obtain input-reflectionless behavior. For validation of the proposed theory analysis, BSFs with corresponding absorptive prototypes are constructed and measured.

Simulation and Experimental Study on Coupling Effect of Fuze under Ultra-wide Spectrum Strong Electromagnetic Pulse

The lack of anti-strong electromagnetic interference ability of fuze has become an important aspect restricting the effectiveness of weapon system. Taking a certain type of fuze as an example, this paper analyzes the coupling mechanism of ultra-wide spectrum transient strong electromagnetic pulse to the fuze, analyzes the action mode of aperture coupling and field line coupling, establishes the mathematical model of space electromagnetic field, and then simulates the effect of aperture coupling and field line coupling of the fuze by using CST Microwave Studio software. It is concluded that the strongest coupling state is when the polarization direction of the electromagnetic field is parallel to the axis of the fuze. Combined with the theory and simulation, the ultra-wide spectrum transient strong electromagnetic pulse simulation system is used to conduct the strong electromagnetic pulse irradiation test, and the electromagnetic pulse effect threshold is obtained. It is concluded that the effect threshold leading to communication failure is about 27~40kV/m, which provides a certain theoretical and experimental basis for fuse strong electromagnetic protection.

Simultaneous Amplitude- and Phase-Tunable Coupler With Wide Phase Tuning Range

In this article, a coupler with simultaneously tunable power division ratio (PDR) and phase difference is proposed based on a multivector summation method. Two groups of varactor diodes are installed on the cross-shaped quarter-wavelength coupled lines to realize the proposed tunable coupler. The horizontal coupled lines serve as the subcouplers to generate multiple vectors, while the vertical coupled lines serve as the phase-tunable units (PTUs) to control the phase of the vectors. The phases of the PTUs can be therefore tuned by the varactor diodes. With a proper combination of the capacitance of the varactor diodes, the amplitude and phase characteristics of the proposed coupler can be controlled independently. For demonstration, a highly tunable coupler operating at 1.8 GHz is designed, fabricated, and measured. The PDR of the coupler can be tuned from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 7 to 1 dB with a 90 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> phase difference, while the phase difference of the coupler can be tuned within a wide range from 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> to 165 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> with equal power division. Better than 10-dB return loss and 15-dB isolation can be observed under different states.

High-directivity and compact microstrip coupler for RF power applications.

A microstrip coupler was designed, fabricated, and tested to monitor the power of the 500MHz kW-level amplifier modules currently installed in an 80-kW solid-state transmitter. The proposed coupler consists of multi-section coupled lines and employs a reverse-coupling scheme, achieving a very compact structure. The dual-side configuration with good termination enables the coupler to have high directivity and wide bandwidth without using any lump components for better temperature stability. Under a low-power test, the measured coupling is 37.69 dB with high directivity from 82 to 700MHz. The coupling is almost independent of the power at 499.65MHz, while the directivity slightly decreases to 33.85 dB at the input power of 1 kW. The maximal insertion loss of 0.08 dB was observed at 1-kW input power. The proposed directional coupler suits many high-power applications, especially in low-frequency regimes.

Theory of Doubly-Shielded Coupled Lines for Directional Couplers of Various Directivity Types With Impedance Transformation

Asymmetric coupled lines (CLs) with double shielding in an inhomogeneous dielectric medium are studied. They have specific properties that allow the creation of impedance-transforming directional couplers with a given directivity type. The proposed models and synthesis techniques take into account both electric asymmetry and dielectric inhomogeneity. Numerical simulations and measurements prove the correctness of the general theory, and the possibility of creating co-, contra-, and trans-directional couplers with impedance-transforming and phase-shifting properties. The results will be useful for finding new design solutions for next-generation microwave circuits.

A New Model to Calculate Contributions of the Distributed Power

Besides metering, a more transparent load with known power distribution is valuable to draft energy strategies, especially in a deregulated power market. Thus, the usage-of-transmission can be considered properly. There are many studies published on related subjects and every research tried to solve a particular part of the problem. There are three basic categories for discussing power distributions: (i) the real power distribution, (ii) the reactive power distribution, and (iii) the loss allocation. These categories were very often treated separately, with the mutual coupling terms, counter flows, and line charging largely neglected. However, we know that these entities are non-separable. These are inter-related entities; the change of one entity will cause the change to every other entity. A good method should consider these entities altogether, while satisfying all electrical theories. This study developed a method to solve the above problem, with all electrical entities solved, satisfying all electrical circuit theories. With several matrix formulations, this method is capable of solving and tracing all electrical entities, including the current flow, the real and reactive power, the counter flow, and the couplings between the active and reactive power. The algorithm can also allocate power distributions and loss among participants effectively. Besides, a line usage idea is formed to allocate the loss to each generator, where counter flows are not necessarily penalized. It can be awarded sometimes. The idea can integrate with the existent tariffs in a deregulated market.

Performance Evaluation of Broadband Characterization of Coupled Transmission Lines Even- and Odd-Mode Propagation Constants Using Differential and Common Mode S-Parameters

This work encompasses some relevant issues that arise when using a broadband method to characterize the even and odd mode propagation constants of symmetric microstrip coupled lines using four-port pure-mode differential and common mode S-Parameters. Correct excitations of differential and common modes play a significant role in experimental results. From these 4-port measurements, parameters corresponding to the even and odd modes can be extracted from the multi-mode generalized S-parameters obtained by the vector network analyzer. Differential and common mode sub-matrices are considered as two independent equivalent 2-port transmission lines. The method will be applied to extract the propagation constants of even and odd modes of coupled microstrip transmission lines. A discussion is included on ensuring the correct excitation of the modes in the structure and avoiding possible unwanted effects such as radiation, that negatively affects the final estimation, both in phase and attenuation. Two figures of merit are defined to evaluate how transitions affect the performance of the method. These figures of merit allow a reasonable estimation of how the final experiment is affected by selected excitation of modes. To assess the theory presented, two sets of seven lines of different lengths are manufactured. The experimental results show an excellent agreement, both with electromagnetic simulations and with the analytical model used, for the phase constant in the improved case of 30° bends, and an improvement in the useful bandwidth of the attenuation constant. This fact verifies the correct functioning of the method. In addition, the measurements are presented in the range of 0.01–67 GHz, which represents a significant advance in bandwidth for this type of structure.

Microwave band-pass filter in frequency reconfiguration with super substrate on cross-coupled line structure for LTE 2500, WiMAX and 5G based internet of things applications

In this paper, the conceptualization of frequency reconfigurable microwave band-pass filter with a super substrate in odd-even method, for Internet of Things (IoT) applications is explained. The prototype consists of band pass filter in cross-coupled line structure with a symmetric structure on dielectric substrate and rectangular slot joining the cross coupled lines. A two different types of super substrate are placed in the rectangular slot one after the other. In parallel to the process, another two different types of dielectric substrate (FR4 epoxy, Rogers RT/duroid 6010 LM (tm)) are placed one after the other above the proposed system producing a total of 6 combinations, each capitulate unique impedance parameters in the transmission poles and transmission zeros. The dimensional framework of the developed design structure have FR4 epoxy (εr = 4.4 and tan δ = 0.02) substrate with 1.6 mm thickness. In the first case, FR4 epoxy substrate is used to place in the rectangular slot in addition the same substrate is placed on top of the prototype. In the second case, slot is covered with Rogers RT/duroid 6010 LM (tm) (εr = 2.2 and tan δ = 0.0009) substrate and the same substrate is placed on the top. When the higher dielectric constant material is used as the addition of substrate the output range of the bandwidths are increased. In all the two cases, the proposed system demonstrates the ability to reconfigure the operating frequencies and bandwidth shifts from LTE 2500 (2496-2690 MHz), WiMAX (2500-2700 MHz, 3400-3600 MHz) to 5 G (3200- 3670 MHz).

Design of wideband antenna using interdigital capacitance

A pair of wideband antenna serve as an impedance transformer for the proposed antenna, which consists of a dipole with periodic capacitive loading. Periodic capacitive loading is achieved at each sector by adding interlaced coupling lines. In order to create a broad impedance bandwidth, the periodic interlaced coupling lines split each arm of the dipole into five portions. Currents are dispersed on the various sections at different frequencies. The suggested antenna is an excellent choice for radar applications since it has a high gain and a low amount of cross polarisation. With the aid of innovative design methods including codirectional inclusion of interdigital capacitance, this research study proposes an interdigital capacitance for wideband (WB) applications interdigital capacitor (IDC). The suggested IDC antenna, which works between 4.70 and 11 GHz, has dimensions of 6.36x6.35x1.6 mm3. This page explores in-depth data on gain over frequency, far field patterns, and surface current distribution on antennas. The suggested antenna's feasibility is shown by simulation data that demonstrates excellent equality on return loss.

A Novel Compact Filtering Antenna for 5.0-GHz WLAN Communication System

The proposed antenna presents a microstrip filter antenna with both filter out-of-band rejection characteristics and antenna radiation characteristics for WLAN communication system. The antenna consists of four U-shaped microstrip resonators, one Γ-shaped antenna, and one parallel coupling line. The Γ-shaped antenna has the filtering function as the last order resonator, and the parallel coupling line integrates the filter and antenna as the conductance converter. After simulation and test, the results show that the center frequency of the filter antenna is 5.25 GHz, the fractional bandwidthis 8.0% (5.0 − 5.42 GHz), the in-band gain changes smoothly, the maximum in-band gain is 3.059 dBi, the gain at 150 MHz outside the passband rapidly decreases to 10.0 dBi, and the overall out-of-band gain drops to below −24 dBi. The filter antenna has a simple structure and thin substrate, which optimizes the overall size of the filter and antenna, reduces the transmission loss between them, and is applicable to the RF front-end of wireless communication systems.

Wideband MIMO Antennas With Enhanced Isolation Using Coupled CPW Transmission Lines

This article presents a wideband printed-monopole antenna pair with enhanced isolation. A clear two-step method based on even-mode (EM) and odd-mode (OM) analyses is developed for antenna decoupling and matching: first, the OM input impedance of the antenna pair is matched by adjusting the element spacing; next, the EM input impedance is matched by adding a coupled TEM transmission line. Those two steps are independent and easy to implement. Notably, the use of a nondispersive coupled transmission line facilitates wideband decoupling and intrinsically allows an extremely small feed-point spacing. The proposed antenna pair is experimentally tested: it offers isolation higher than 20 dB and total efficiency higher than 87% from 3.7 to 7.3 GHz (a fractional bandwidth of 65.5%). The separation between the two feed points is only 5.6 mm ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.069~\lambda $ </tex-math></inline-formula> at 3.7 GHz). Furthermore, we construct a four-element multiple-input–multiple-output (MIMO) array by intersecting orthogonally two of the proposed antenna pairs at their central line, which offer an isolation level better than 20 dB from 3.8 to 7.4 GHz for every two ports. With a straightforward design process, compact feeding structures, and wideband performances, the proposed dual- and four-element MIMO antennas are promising for the fifth-generation wireless communication.

Compact Parallel Coupled Line Microstrip BPF Design for 5G Applications

A compact parallel coupled line microstrip bandpass filter (BPF) for sub-6 GHz fifth generation (5G) applications is designed operating between edge frequencies of 3.40 and 3.80 GHz. The design is designed and simulated by means of the Advanced Design System (ADS) software using the flame retardant-4 (FR-4) board as the substrate. The BPF design applies the insertion loss method (ILM) to generate a parallel coupled line filter structure that performs passband permission and unwanted noise attenuation below 3.40 GHz and above 3.80 GHz, respectively. Consistent and relevant performances in terms of matching impedance, return loss (S11), insertion loss (S21), voltage standing wave ratio (VSWR), far field radiation pattern, gain, directivity, and radiated efficiency promise the microstrip BPF design has a potential for sub-6 GHz 5G applications.

Miniaturized Power Divider With Triple-Band Filtering Response Using Coupled Line

This proposed work describes a miniaturized and simple power divider that uses coupled lines for triple-band filtering. The intended setup included an isolation resistor connecting the output feed lines through Structure-3 and coupled line-based microstrip resonators connected to the input feed line. The presented power divider achieves three passbands with a filtering response. The first and second passbands are achieved by the coupled line that includes Resonator-1 and Resonator-2 of the proposed structure. The third passband is realized due to Resonator-3. Furthermore, by varying the structural parameter of the designed triple-band filtering power divider, the resonance frequencies of all three passbands can be controlled because of changes in their equivalent lumped parameters. The resonance frequency mainly depends on its equivalent inductance and capacitance value. For validation of the simulation result, the filtering power divider structure has been fabricated and tested. The experimental results denote that the prototype has a fractional bandwidth (|S21|<-3 dB) of about 20.0 % (1.1 GHz to 1.35 GHz), 37.0 % (2.0 GHz to 2.9 GHz), and 15.0 % (3.25 GHz to 3.8 GHz) respectively for first, second and third pass-bands. This arrangement shows isolation above 18 dB for all three bands with a downsized of 0.1λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>g</i></sub> × 0.12λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>g</i></sub> (25 mm × 30 mm) according to the operating frequency of the first frequency passband. The triple band performance of the developed component shows a good input reflection coefficient. The operating frequencies, which are suitable for the application of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -band, WLAN, sub-6 GHz band of 5G, which include 1.23 GHz, 2.41 GHz, and 3.55 GHz.

A Novel Design Method for Unequal Coupled Line Dual-band Wilkinson Power Divider

A Novel Design Method for Unequal Coupled Line Dual-band Wilkinson Power Divider

Design and Analysis of a Cascode Distributed LNA With Gain and Noise Improvement in 0.15-μm GaAs pHEMT Technology

This brief presents a 2.0~42.0 GHz ultra-wide bandwidth Cascode distributed low-noise amplifier (CDLNA) MMIC design. With the proposed coupled-line (CL) sections between each drain-artificial transmission line (D-ATML) node and related gate-artificial transmission line (G-ATML) node, the traveling signal is reused to enhance the gain and broaden the operation bandwidth simultaneously. To improve the gain further, the inductive gain peaking has also been employed at each drain of common-source (CS) and common-gate (CG) transistors. Meanwhile, an active termination technique incorporating active and passive elements has been adopted to achieve better noise figure (NF) performance. Employing the proposed techniques, an LNA prototype has been designed and fabricated in a 0.15- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> GaAs E-Mode pHEMT technology with the chip size of 1.53 mm2 including all the pads. From test results, the proposed CDLNA demonstrates a peak gain of 14.1 dB, the best NF of 2.1 dB, a group delay of 102 ± 58.4 ps, and 23.25/14.7 dBm best OIP3/OP1dB, respectively. The total power consumption is 129 mW under 3 V VDD.

A Broadband 10–43-GHz High-Gain LNA MMIC Using Coupled-Line Feedback in 0.15-μm GaAs pHEMT Technology

In this letter, a 10–43-GHz low-noise amplifier (LNA) monolithic microwave integrated circuit (MMIC) is designed in a commercial 0.15- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> GaAs E-mode pseudomorphic high electron mobility transistor (pHEMT) technology. In the proposed LNA circuit, a novel coupled-line (CL)-based positive feedback structure is employed with the bandpass characteristic. By carefully tuning its coupling factor and arm length, the center frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{c}$ </tex-math></inline-formula> and the intensity of the feedback can be controlled, respectively. Subsequently, targeting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{c}$ </tex-math></inline-formula> at the higher cutting edge of the working band leads to compensated gain roll-off and extended bandwidth. Incorporating three-stage common-source (CS) architectures, an LNA prototype is fabricated with a size of 1.05 mm2 including pads. Under 2-V voltage drain drain (VDD), good performance is obtained, including 24.6-dB peak gain with 3-dB bandwidth of 33 GHz, 2.4–3.0-dB noise figure (NF), 54.5 ± 13.8-ps group delay, and 12.3/21.5-dBm best output power at 1 dB gain compression (OP1dB)/output third order intercept point (OIP3). The total dc power is 110 mW.