Real Frequency Technique Research Articles

Systematic design of output filters for audio class-D amplifiers via Simplified Real Frequency Technique

Abstract. In this paper a new filter design concept is proposed and implemented which takes into account the complex loudspeaker impedance. By means of techniques of broadband matching, that has been successfully applied in radio technology, we are able to optimize the reconstruction filter to achieve an overall linear frequency response. Here, a passive filter network is inserted between source and load that matches the complex load impedance to the complex source impedance within a desired frequency range. The design and calculation of the filter is usually done using numerical approximation methods which are known as Real Frequency Techniques (RFT). A first approach to systematic design of reconstruction filters for class-D amplifiers is proposed, using the Simplified Real Frequency Technique (SRFT). Some fundamental considerations are introduced as well as the benefits and challenges of impedance matching between class-D amplifiers and loudspeakers. Current simulation data using MATLAB is presented and supports some first conclusions.

Ultra wideband matching network design for a V-shaped square planar monopole antenna

In this paper, design, manufacture, and measurement of a wideband matching network for a broadband V-shaped square planar monopole antenna (V-SPMA) is presented. Matching network design is unavoidable in most cases even vital to facilitate a maximally flat power transfer gain for an antenna. In the work, a bandpass matching network (BPMN) design is done for a particular square monopole antenna with V-shaped coupling element that has essentially bandwidth increasing effect. Designed BPMN and the antenna forms a VSPMA–BPMN matched antenna structure. “real frequency technique” is employed in the BPMN design. BPMN prototype circuit has been constructed on an FR4 laminate with commercial microwave chip inductors and capacitors. Vector network analyzer gain and reflectance measurements of the matched antenna structure have shown highly compatible results to those of the theoretical design simulations along the passband (~0.8–4.7 GHz). Furthermore, newly proposed distributed capacitor–resistor lossy model for microstrip lines used in the BPMN circuit have exhibited that it can successfully mimic the measured gain and reflectance performance of the matched structure in passband and even in stopband upto 8 GHz. Designed structure can be utilized as a one single wideband broadcasting medium suitable for many communication standards such as GSM, 3G, and Wi-Fi.

High Precision Synthesis of a Richards Immittance Via Parametric Approach

A Richards immitance is a positive real function expressed in terms of the Richards variable λ = tanh(pτ) = Σ+jΩ where p=σ+jω is the classical complex frequency. A Richards immittance can be synthesized as a lossless two port terminated in a resistance as in Darlington's synthesis such that the two-port consists of commensurate transmission lines. In this paper, a high precision method is presented to synthesize a Richards immittance as a lossless two-port constructed with cascade connections of equal length transmission lines, as well as short and open stubs. The new method of synthesis utilizes Bode procedure (or Parametric Method) to correct an immitance function specified in the complex Richards variable λ at each step of the synthesis. It is verified that new technique can synthesize a randomly generated Richards immitance function yielding 25 commensurate lines with the accumulated numerical error less than 10-3. A complete synthesis package is developed in MatLab and successfully integrated with the Real Frequency Technique to design broadband matching networks. Examples are presented to show the merits of the new Richards synthesis tool.

Resistive Second-Harmonic Impedance Continuous Class-F Power Amplifier With Over One Octave Bandwidth for Cognitive Radios

A novel methodology for designing highly-efficient broadband harmonic-tuned power amplifiers (PAs) with more than one octave bandwidth is presented in this paper. Continuous class-F power amplifiers with resistive second-harmonic impedance is for the first time analyzed and employed in a multi-sub-band mode to enhance the bandwidth of a conventional continuous class-F PA. The load-pull method is employed at both fundamental and harmonic frequencies, and the simplified real frequency technique algorithm is used to design and synthesize the PA matching networks. Experimental results show that the fabricated PA operates from 525 to 1325 MHz, with drain efficiency over 70% and output higher than 39 dBm. Digital predistortion is applied to the PA and the adjacent channel power ratio is improved to more than -40 dBc.

A Wideband Doherty Power Amplifier With 100 MHz Instantaneous Bandwidth for LTE-Advanced Applications

In this letter, a 698-862 MHz wideband Doherty power amplifier (DPA) with 100 MHz instantaneous bandwidth is presented. The electrical memory effect of the wideband DPA is reduced by the LC resonant circuits employed in the drain bias networks. The influence of the integrated Doherty combiner is compensated by the broadband output matching networks, which were designed by applying the simplified real frequency technique. Driven with 100 MHz LTE-advanced signals, the adjacent channel leakage ratio (ACLR) and ACLR asymmetry of the proposed DPA at 20 MHz offset are improved by about 4 dB and 3 dB respectively, compared to the wideband DPA with conventional bias networks. After digital predistortion (DPD) linearization, the proposed DPA shows an ACLR of lower than -48 dBc at an average output power of 42.5 dBm, and high drain efficiency of over 42% across the operating frequency range.

A Simplified Broadband Design Methodology for Linearized High-Efficiency Continuous Class-F Power Amplifiers

This paper describes the design approach employed for achieving approximated continuous Class-F power amplifier (PA) modes over wide bandwidths. The importance of the nonlinear device capacitance for wave-shaping the continuous Class-F voltage and current waveforms is highlighted, thus reducing the device sensitivity to second and third harmonic impedance terminations. By identifying the high-efficiency regions on the reactance plane for harmonic band placement, the design can be reduced to a fundamental matching problem. The distributed simplified real frequency technique synthesis algorithm can then be utilized to achieve wideband operation. Using a 10-W Cree GaN HEMT device, greater than 70% efficiency has been measured over a 51% bandwidth from 1.45 to 2.45 GHz, with output powers of 11-16.8 W. The nonlinear PA was then linearized using digital predistortion with 20-MHz long-term evolution and 40-MHz eight-carrier W-CDMA excitation signals, to attain adjacent channel power ratios below -53 and -49 dBc, respectively. To the best of the authors' knowledge, the measured results represent the best performance obtained from a broadband switch-mode PA, and the best linearized switch-mode performance using 20- and 40-MHz modulated signals.

Broadband Doherty Power Amplifier via Real Frequency Technique

A comprehensive method of designing a broadband Doherty power amplifier is presented in this paper. The essential limitations of bandwidth extension of a Doherty power amplifier are discussed based on the proposed structure of the Doherty power amplifier, which also takes the output matching networks of both sub-amplifiers into account. The broadband matching is realized by applying the simplified real frequency technique with the desired frequency-dependent optimum impedances. GaN transistors were selected to implement the circuit structure.

A Multimode/Multiband Envelope Tracking Transmitter With Broadband Saturated Amplifier

A multimode/multiband envelope tracking (ET) transmitter consisting of a hybrid switching amplifier (HSA) and a broadband saturated power amplifier (PA) is developed for operation across 1.3 to 2.7 GHz. For the various standard signals with different bandwidth (BW) and peak-to-average power ratio, the HSA efficiently provides supply signals to the PA by changing the reference value of the hysteresis comparator. The saturated amplifier employs the nonlinear output capacitor to shape the voltage waveform, resulting in the half-sinusoidal or rectangular waveform. Since the nonlinear capacitor generates large out-of-phased second harmonic component with small higher order harmonics, the voltage shaping is mainly carried out by the capacitor and slightly supported by the harmonic loading circuit. Thus, with the harmonic load higher than that of output capacitor, the saturated amplifier can operate with high efficiency. This characteristic enables the saturated PA to operate with broadband characteristic and high efficiency because the design is mainly focused on the fundamental matching problem while the harmonics can be easily kept out of a low efficiency region through the subsequent optimization of the matching circuit. The broadband saturated PA is implemented based on load/source-pull methodology. The broadband matching networks for the high efficiency are synthesized using the simplified real frequency technique. For the BW from 1.3 to 2.7 GHz (70% fractional BW), the measured output power, drain efficiency, and power-added efficiency (PAE) performances are between 39.8-42.0 dBm, 55.8-69.7%, and 51.2-65.3%, respectively. The multimode/multiband ET transmitter with the designed broadband saturated PA is demonstrated at 1.8425-GHz long-term evolution (LTE), 2.14-GHz wideband code division multiple access (WCDMA), and 2.6-GHz mobile world wide interoperability for microwave access (m-WiMAX) applications. This transmitter delivers a PAE of 32.16, 37.24, and 28.75% for LTE, WCDMA, and m-WiMAX applications.

Stable Factorization of Strictly Hurwitz Polynomials

We propose a stable factorization procedure to generate a strictly Hurwitz polynomial from a given strictly positive even polynomial. This problem typically arises in applications involving real frequency techniques. The proposed method does not require any root finding algorithm. Rather, the factorization process is directly carried out to find the solution of a set of quadratic equations in multiple variables employing Newton’s method. The selection of the starting point for the iterations is not arbitrary, and involves interrelations among the coefficients of the set of solution polynomials differing only in the signs of their roots. It is hoped that this factorization technique will provide a motivation to perform the factorization of two-variable positive function to generate scattering Hurwitz polynomials in two variables for which root finding methods are not applicable.

Design of broadband single matching networks

In general commercially available software tools are preferred, to design broadband matching networks for wireless communication systems. But they need a properly selected matching network topology with good initial element values. Therefore, in this paper a new real frequency technique is presented, to generate broadband single matching networks with suitable initial element values. In the proposed method, load impedance is written in terms of ABCD-parameters of the desired matching network and the source resistor. Then, free parameters are optimized which in turn yields the desired matching network with initial element values. It is not needed to select a circuit topology for the matching network, which is the natural consequence of the matching processes. Also, there is no need to select the desired transducer power gain level; the proposed technique naturally provides a gain curve fluctuating around the final available level. Eventually, the initial design is improved by optimizing the performance of the matched system employing the commercially available computer-aided design (CAD) packages. An algorithm and two examples are given, to illustrate the utilization of the proposed technique.

A GENERALIZED DESIGN PROCEDURE FOR A MICROWAVE AMPLIFIER: A TYPICAL APPLICATION EXAMPLE

In this work, a generalized procedure is carried out for the design of a microwave amplifier. First of all, the Performance Data Sheets (PDS) resulted from the active device characterization are used as Feasible Design Target Space (FDTS). Employing the PDS, the compatible (Noise F , Input VSWR Vi, Gain GT ) is determined over the predetermined bandwidth B between fmin and fmax operation frequencies with the source ZS and load ZL terminations as the design target. In the design stage, the Simplified Real Frequency Technique (SRFT) is utilized in the scattering-parameter formulation of the front- and back-end matching two-ports to provide the source and load terminations to the transistor, respectively. As an application example, a novel high technology transistor is chosen and the design targets are determined using the PDSs of the device and its front- and back-end matching two-ports are characterized by the scattering- parameters using the novel SRFT for each design target. Furthermore, the performances of the resulted amplifier circuits are analyzed and compared with the simulated results.

Modeling based real frequency technique

Usually commercially available software tools are used, to design matching networks for wireless communication systems. But a properly selected matching network topology with good initial element values must be supplied to these tools. Therefore, in this paper a modeling-based real frequency technique (M-RFT) is presented, to generate matching networks with initial element values. In the proposed method, output impedance data of the matching network are obtained in terms of ABCD-parameters of the load model. Then, they are modeled which in turn yields the desired matching network with initial element values. It is not needed to select a circuit topology for the matching network, which is the natural consequence of the matching processes. Also, there is no need to select the desired transducer power gain level; the proposed technique naturally provides a gain curve fluctuating around a flat level. Eventually, the initial design is improved by optimizing the performance of the matched system employing the commercially available computer aided design (CAD) packages. An algorithm and example are given, to illustrate the utilization of the proposed technique.

Real frequency wide-band impedance matching with nonminimum reactance equalizers

This paper describes two modifications to the real frequency technique of broadband impedance matching. A fundamental limitation of all broadband matching techniques is that the real and imaginary parts of the equalizer impedance must be related by the Hilbert transform. It is shown that additional degrees of freedom in the Hilbert transform, and thus a better match, can be obtained by employing equalizer impedances with nonminimum reactance and by optimizing the equalizer resistance outside the stated bandwidth. Examples will be presented for a thin wire dipole antenna.

40-Gb/s wide-band MMIC pHEMT modulator driver amplifiers designed with the real frequency technique

With the use GaAs pseudomorphic high electron-mobility transistor technology, the bandwidth performances of Cherry-Hooper driver amplifiers need to be improved. To fulfill these requirements, we propose an original driver circuit topology dedicated to 40-Gb/s optical communication systems. To flatten the transducer gain response of the circuit, passive networks have been added in the design. These networks have been optimized by means of the real frequency technique (RFT). A modified procedure of the classical RFT is introduced to perform the optimization in the presence of an overall resistive feedback.

An Alternative Approach for the Design of Millimetric Wave Drivers for SSB Optical Modulator

For the millimetric wave transport over fiber, one of the most simple ways to eliminate the periodic fading due to chromatic dispersion is to use an optical Single Side Band signal. In accordance with this principle, this paper presents highly linear millimetric amplifiers driving a SSB modulator. For the first time, the real-frequency technique has been successfully applied to the design of the matching networks of 26.5–29.5 GHz and 40.9–41.8 GHz amplifiers.

Multistage solid-state power amplifier design by a new alternative synthesis technique

For the first time, the numerical real-frequency technique has been applied to the design of a nonlinear power amplifier. This synthesis technique does not require any transistor model by directly using measured large-signal S-parameters of the power transistor device. The double power-frequency dependence of these S-parameters requires the use of a bidimensional interpolation (spline functions). With the Levenberg–Marquardt optimization and large-signal S-parameters, a specific CAD program optimizes the added-power in order to synthesize the matching networks of the PA. The simulated and measured results of two S-band power amplifiers validate the new synthesis approach. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 87–98, 2004.

Multistage solid-state power amplifier design by a new alternative synthesis technique

For the first time, the numerical real-frequency technique has been applied to the design of a nonlinear power amplifier. This synthesis technique does not require any transistor model by directly ...

A Computer-Aided Design Technique for Lossless Matching Networks with Mixed, Lumped and Distributed Elements

A computer-aided method for the design of lossless broadband matching networks with lumped elements and commensurate transmission lines is presented. The method is based on combining the simplifield real frequency technique with the algebraic network decomposition by Fettweis. To show the application of the Computer-Aided Design (CAD) approach, an UHF antenna matching problem is solved.

On the design of broad-band loaded wire antennas using the simplified real frequency technique and a genetic algorithm

A novel design methodology for broad-band loaded wire antennas is presented that combines the genetic algorithm and the simplified real frequency technique (SRFT) to remove the requirement of choosing the types of load circuits and matching networks a priori. Analytical expressions for the impedance functions of load circuits and matching networks are obtained in the form of rational polynomials via the SRFT. The location of loads on the antenna and the resistance functions of the load circuits and matching networks are optimized using a genetic algorithm. Maximization of system gain in the azimuth and minimization of voltage standing wave ratio are sought as design objectives. The circuit topologies and the component values are automatically arrived at using Darlington synthesis after the optimization process is complete. Also demonstrated, is the use of this procedure to achieve broad-band operation in the HF band for the unloaded and loaded monopoles assuming electronically switched matching networks.

The Real Frequency Technique Applied to the Synthesis of MMIC Active Filters with Attenuation Poles at Finite Frequencies

This paper reports on several MMIC active filters designed by the real-frequency technique (RFT). RFT provides several advantages over most of the usual techniques: it does not require any active c...