Low-pass Transformation Research Articles

Four-Port Symmetrical Reflectionless Lumped Filter/Diplexer: Prototype and Design Table

It is shown that a well-designed lumped $LC$ loop network with a phase inverter can exhibit perfect reflectionless filtering response at its all four ports. The network is composed of two pairs of symmetrical $LC$ ladder circuits, in which one pair is obtained from lowpass transformation at a prescribed frequency based on a special lowpass prototype, and the other pair is from highpass transformation based on the same prototype at the same frequency. The input power, at any port, is divided into the two adjacent ports in the frequency domain through different paths of the loop. Each path between any two ports nearby can be treated as a mono-functional filter, whereas the adjacent two paths work as two filters with complementary responses. The overall circuit performs as a generalized diplexer without a specified “common” or “separation/combination” port. By using a numerical equation solver, the element values of the reflectionless lowpass/highpass prototype filter of order one, three, five, and seven are given. Then, the values of order nine, eleven, thirteen, and fifteen are obtained by using the optimization method. Other filtering functions such as bandpass/bandstop or dual-band can be easily implemented with the proposed prototype by using the standard frequency transformation method. For verification, two sample filters are fabricated and measured. The experimental data agree well with the predictions.

Lowpass–Bandpass Triplexer Integrated Switch Design Using Common Lumped-Element Triple-Resonance Resonator Technique

This paper presents a lowpass–bandpass triplexer integrated switch using common lumped-element triple-resonance resonator (LE-TRR) technique. First, a lowpass–bandpass triplexer that has one lowpass channel (LPC) and two bandpass channels (BPCs) is designed. The proposed lowpass–bandpass triplexer design method is different from the conventional lowpass–bandpass multiplexer in which the feeding line is designed with lowpass response to combine bandpass structures to form lowpass–bandpass response. In this design, one branch of LE-TRR together with inductors and capacitors and another two branches of LE-TRR together with classical LC resonators are proposed to constitute one LPC and two BPCs, respectively. The LPC design combines the lowpass transformation method and parameters optimization, and two BPCs can be synthesized by classical coupled-resonator filter design theory. The designed lowpass–bandpass triplexer exhibits extremely compact size of ${\text{0.125}}\lambda _{{\rm{g}}} \times {\text{0.086}}\lambda _{{\rm{g}}}$ , and also has merits of low insertion loss, good return loss, wide bandwidth, and high port-to-port isolation. And then, p-i-n diodes are loaded on the lowpass–bandpass triplexer to realize a lowpass–bandpass triplexer integrated switch that combines both the triplexer and microwave switch function. One LPC and two BPCs are able to be switched on / off separately, and the lowpass–bandpass triplexer integrated switch has eight independent states in total. The off -state suppression of LPC is better than 36 dB, and the off -state suppression of two BPCs are better than 46 and 45 dB, respectively.

The Impact of Vertical Measurement Depth on the Information Content of Soil Moisture for Latent Heat Flux Estimation

Abstract This study aims to identify the impact of vertical support on the information content of soil moisture (SM) for latent heat flux estimation. This objective is achieved via calculation of the mutual information (MI) content between multiple soil moisture variables (with different vertical supports) and current/future evaporative fraction (EF) using ground-based soil moisture and latent/sensible heat flux observations acquired from the AmeriFlux network within the contiguous United States. Through the intercomparison of MI results from different SM–EF pairs, the general value (for latent heat flux estimation) of superficial soil moisture observations , vertically integrated soil moisture observations , and vertically extrapolated soil moisture time series [soil wetness index (SWI) from a simple low-pass transformation of ] are examined. Results suggest that, contrary to expectations, 2-day averages of and have comparable mutual information with regards to EF. That is, there is no clear evidence that the information content for flux estimation is enhanced via deepening the vertical support of superficial soil moisture observations. In addition, the utility of SWI in monitoring and forecasting EF is partially dependent on the adopted parameterization of time-scale parameter T in the exponential filter. Similar results are obtained when analyses are conducted at the monthly time scale, only with larger error bars. The contrast between the results of this paper and past work focusing on utilizing soil moisture to predict vegetation condition demonstrates that the particular application should be considered when characterizing the information content of soil moisture time series measurements.

Synthesis of a first-order passive complex filter with band-pass/band-elimination characteristics

In this paper, a new passive complex filter is proposed. In the same fashion as the traditional real band-pass filter, the proposed circuit is also designed through the frequency transformation. In order to obtain the prototype complex filter suitable for passive realization, the extended lowpass---highpass transformation or the bilinear lowpass---lowpass transformation different from the well-known frequency shifting method is adopted. These transformations give two filters; however, the final circuits become identical to each other. The proposed circuit has two output terminals. One is the complex band-pass output, and the other is for the complex band-elimination. The proposed circuit includes a capacitor, an autotransformer or an inductor and termination resistors only. Because the proposed circuit has terminating resistors at both of the input and the output sides, it is suitable for high frequency application. As an example, two first-order complex filters which operate in 100 kHz and 10 MHz are designed and their frequency responses are measured. It is shown that the measured frequency responses agree with the theoretical ones through experiment.

Efficient algorithm for the factorisation of the transfer function of a bandpass filter

The author presents an efficient algorithm for the factorisation of each of the fourth-order polynomials in a bandpass transfer function (arising in lowpass transformation) into the product of two real quadratic factors, simply by solving two quadratic equations. Such factorisation is necessary in the realisation and simulation of the filters. The same algorithm can also be applied to the case of bandreject filters.

Robust ultrasonic range finder-an FFT analysis

An ultrasonic range measurement system has been developed, based on bandpass to lowpass transformation of the impulse response. The impulse response is a sensitive indicator of time delays between signals. In this case the time delay is caused by the propagation of the sound wave between transmitter and receiver. The proposed method features two important advantages, especially usable in robot automation or automated guided vehicle (AGV) application: firstly, it is robust against disturbances with maintenance of high accuracy in the range estimation; secondly, standard signal processor I/O cards can be used due to the reduced analysis frequency interval. Experimental results illustrating the performance of the ultrasonic range system are presented. Some experimental comparisons with the pulse echo method are also made.

General stability analysis of sinusoidal perturbation extrema searching adaptive systems

The stability and response characteristics of extrema seeking adaptive systems, in which sinusoidal perturbations of the adaptive parameter (parameters) provide the derivative action necessary to determine direction and magnitude of the criterion surface gradient at the operating point, are analysed. It is assumed that system variations with time occur slowly as compared with the adaptive loop response time, and that the measured criterion output may be characterized by a general function of the adaptive parameters (usually non-linear) followed by a linear transfer function representing measurement delay. The resulting adaptive control loop is analysed, using modified bandpass to low pass transformation techniques, yielding an equivalent low pass loop in which no perturbation signals appear. This loop is generally non-linear but standard techniques, such as the describing function, may be applied to predict the critical loop gain, the frequency and amplitude of the resulting oscillations, and the required equalization. Several examples are presented which have been simulated on a Pace analogue computer. Predicted and actual results generally compare within 10 per cent, which is within the usual range of describing function accuracy.

Band-Pass Low-Pass Transformation in Variable Networks

An extension of the band-pass low-pass transformation to linear varying-parameter systems is developed. It is shown that this transformation in conjunction with the use of frequency analysis techniques can be applied with advantage to the analysis of a superregenerator operating in the linear mode.