Design principles of frequency multipliers for digital frequency-measuring instruments

Conclusions It will be seen from this review of various methods for multiplying frequency that, in addition to the generally known multipliers which use functional conversion of the input signal, there can also be designed multiplying devices, based on level quantization, on shifting of signals with respect to their phase or time, and on balancing.It should be noted that the output signal of the first group of multipliers has the same shape as their output signal. The frequency multiplication process in devices of the second and third groups can be accompanied by a transformation of the signal shape.The application of a given type of multiplier in digital frequency-measuring instruments depends basically on the maximum permissible variation of the transducer's output frequency. Thus, in transducers with a small deviation it is, probably, advisable to use frequency multipliers of the first group. It is obvious that balancing multipliers whose comparison element consists of a reversible counter are predominantly suitable for transducers with a large frequency deviation.The problem of obtaining the required frequency multiplier characteristics, consisting of their speed of operation and precision, requires a detailed investigation.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 52–55, January, 1967.     

Phase fluctuations in a heterodyne multistage frequency multiplier

Conclusions The inherent phase instability and error of these multipliers are not inferior (as regards frequency stability) to those found in other methods of frequency multiplication.Multiplication with heterodyning is especially justified in frequency comparison of atomic clocks, where the mutual deviation and output frequency instability are much less than the limiting values permissible for undistorted multiplication. A transistorized multiplier is simple, so one can provide reliability over long periods with continuous comparison.The main component in the phase fluctuations in a multiplier is due to noise in the coupling and transformation circuits, so in principle it is possible to improve the stability further via advances in this part of the device.The input stages are of broad bandwidth and have low temperature coefficients, so one can compare frequencies over periods up to 100 sec without thermostatic control without appreciable loss of accuracy.Translated from Izmeritel'naya Tekhnika, No. 11, pp. 41–43, November, 1972.     

Digital Frequency Multiplier for Spectrum Measurement of Periodic Signals

Frequency multipliers find applications in the Fourier and Walsh spectrum measurements of periodic signals. Earlier digital frequency multipliers use two counters: 1) An upcounter which is partitioned into a fractional counter of kbits in cascade with an integral counter. This determines the period of the input signal by the number of clock pulses that are accumulated in a period of the signal. 2) A downcounter which is next fed from the same clock, and which is periodically preset to the contents of the integral counter whenever the downcounter reaches zero. In this process an error is introduced in the output frequency because the fractional counter contents are ignored in the frequency multiplication phase. To minimize this error, a high clock frequency is required so that the fractional count is small compared with the integral count. The maximum output pulse frequency is limited by the speed of the counters used. A new method is described which also uses the contents of the fractional counter. The clock frequency is reduced substantially and the maximum output pulse frequency is limited by the settling time of a D/A converter: If the settling time is 200 ns, the maximum output frequency is ten times that of earlier methods.     

A multi-band fast-locking delay-locked loop with jitter-bounded feature

In this paper, a fast-locking delay-locked loop (DLL) with jitter-bounded feature is presented. In the proposed fast-locking mechanism, a frequency estimator and a programmable voltage circuit are developed to rapidly switch the control node of voltage-controlled delay line to a voltage level near the final required value. After that, the DLL output will be quickly locked by the following charge pumping on the loop filter. In the jitter-bounded approach, two phase-frequency detectors and a tunable delay are employed to hold the output clock jitter between two reference inputs after the DLL is locked. Furthermore, to enhance the flexibility of the presented DLL, a frequency multiplier with fewer active devices is also developed to provide high-frequency clock output for wideband applications. The presented DLL is implemented in a 0.18-μm 1P6M CMOS technology. The active area without contact pads is 0.34 × 0.41 mm(2). A minimum lock time of six clock cycles is measured from no reference input to locked state. The output frequency ranges of the DLL and the frequency multiplier can be measured from 200 to 400 MHz and from 1 to 2 GHz, respectively. The power dissipation of the presented DLL is 31.5 mW at a 1.8 V supply voltage.     

Time dependent model of gain saturation in microchannel plates and channel electron multipliers

We present and discuss a time dependent solution of the transmission line model of a channel electron multiplier, introduced in a previous paper and already solved in steady-state conditions. The model is applicable to all the situations in which the multiplier input current is sufficiently large so that the statistical variations of the gain for each electron can be ignored and it does not apply to photon counting detectors. By introducing the appropriate boundary conditions the time dependent non-linear equations of the model are reduced to an integral equation in implicit form, whose solution can be calculated numerically by a perturbative approach. In this way the multiplying current signal i(z,t) and the voltage V(z,t) are found as functions of the position z along the channel, and of the time t during the pulse itself, for any arbitrary shape of the input current waveform. The important case of the amplification of input current pulses with a short duration compared to the multiplier recovery time is investigated in detail, showing that the non-linear behavior can be entirely described by a general function of a conveniently defined saturation parameter and that this function is characteristic of any uniform channel multiplier. The model is then used to investigate the recovery of the multiplier after a saturating pulse, and it is found that the gain recovery from weak or moderate saturation levels is exponential to a very good approximation, but with a time constant different from the characteristic time constant RC of the multiplier. Finally the case of pulses of arbitrary shape and duration is considered and examples are given of the amplification of step pulses and of a regular sequence of identical pulses. A remarkable feature of the model is that the solution can be calculated from the time shape of the output pulse, rather than from the input. This makes possible to implement methods for pulse restoration, i.e. for recovering the original input pulse shape from a measured saturated output.     

A Fast-Acting Feedback Loop for Pulse Amplitude Ratio Measurement

Design and operating details of a voltage ratio measuring circuit are presented. The circuit employs a wide bandwidth function multiplier as a variable gain amplifier. The denominator voltage activates a feedback loop causing multiplier gain adjustment. Adjustment proceeds until the multiplier output is equal to a Zener reference voltage. The multiplier gain is then equal to the ratio of Zener reference voltage to denominator voltage. Multiplier gain is stored by an integrator serving as a memory. The numerator voltage does not activate the feedback loop, but is simply amplified by the multiplier. The resulting output voltage is the ratio of the input voltages referred to a Zener reference. Null-balance time of 5 ?S allows ratio measurement of 16-kc pulse pairs.     

Improved Analysis of Implicit RMS Detectors

In this paper, the output voltage of the implicit root-mean-square (RMS) detector, which is composed of two voltage-to-current converters, a multiplier/divider, and a low-pass filter and excited by an input voltage comprising a single sinusoid, is approximated using a Fourier cosine series. Using this approximation, closed-form analytical expressions for the output voltage components of the implicit RMS detector are derived. The results obtained are compared with previously published results. This comparison shows that, using the proposed approximation, an improved estimation of the RMS value and the amplitudes of the second- and fourth-harmonic components of the implicit RMS detector can be achieved for any value of the input frequency and is not restricted to large values compared with the cutoff frequency of the low-pass filter.      

A Wide-Band Digitally Controlled Frequency and Phase Multiplier

A method is considered for designing a wide-band digitally controlled frequency and phase multiplier based on nonlinear polynomial transformation of Chebyshev type applied to the initial harmonic signal. The method provides an output signal with a frequency a multiple of the input signal 1. Computer calculations are used to examine the output signal.     

Temporal Talbot effect in fiber gratings and its applications

We show that a temporal effect equivalent to the spatial Talbot effect (self-imaging) applies to the reflection of periodic pulse trains from linearly chirped fiber gratings (LCFG's). For specific input repetition periods the reflected signal is an exact replica of the input signal. Input repetition period values that give rise to this effect depend on the dispersion coefficient of the grating. We propose to use this effect as an alternative for dispersion measurement in LCFG's. Furthermore, by using the properties of the temporal Talbot effect, we can design linear passive devices (LCFG's) for use as frequency multipliers, able to multiply the repetition rate of a given pulse train.     

Mode-locked ring laser with output pulse width of 0.4 ps

The output pulse width of a mode-locked ring laser composed of an erbium-doped fiber amplifier, Mach-Zehnder optical modulator, and optical band-pass filter depends largely on the repetition frequency and the wavelength characteristics of these optical circuit elements. In previous experiments, the output pulse width was in the order of 5 ps at a repetition frequency of 5 GHz. The principal reason was that the narrow passage band of the optical circuit elements made it extremely difficult to generate an ultra-short optical pulse. Consequently, we examined how to narrow the optical pulse width by flattening the wavelength characteristics of these optical circuit elements. Furthermore, we drove the optical modulator in the cavity using a frequency multiplier to operate at an effectively higher frequency By widening the wavelength passage band of all the devices in the optical circuit, we achieved an output pulse width of 0.4 ps at a repetition frequency of 5 GHz; the pulse peak power was more than +23 dBm, and the time-bandwidth product was 0.34. We successfully tested an ultra-short optical pulse source with an output pulse width of 0.4 ps with no external pulse compression using a mode-locked ring laser     

Induction methods used in low temperature physics

A study has been made of induction bridges used in low temperature physics.In Part 1 the design of a mutual inductance bridge of the Hartshorn type is discussed. This design is based on a critical analysis of impurity effects of the different parts of the Hartshorn bridge. With this equipment frequencies up to 0.5 MHz can be used. Two methods have been developed to examine the secondary signal. In one of these use has been made of AD conversion techniques. In the other one, the secondary signal, produced by a superconducting sample, which is generally distorted, is analysed by using a Fourier expansion.In Part 2 equipment is described which enables us to measure the phase and amplitude of the harmonics of the output signal of the bridge. For synchronous detection a reference signal of the same frequency of the harmonic of interest is required. This reference signal is generated from the input signal of the bridge by means of a digital frequency multiplier with programmable multiplication factor N.In Part 3 some experimental results, showing the possibilities of the equipment, on some superconductors are presented.     

多频海底声学原位测试系统在海水中的声源响应及子波分析

多频海底声学原位测试系统是国家海洋局第二海洋研究所自行研制的海底声学原位测试系统。利用声源换能器的等效电路,分析了声源换能器输入终端输入脉冲与输出接收脉冲之间的关系。将系统的低频声源等效为一定半径的球形声源,确定了系统在15kHz时在试验海域海水中的声源换能器的角频率响应和输出回路品质因子。计算了系统理论接收脉冲,结果表明输出接收脉冲并非输入脉冲的简单复制。并与实测接收脉冲进行了比对,理论接受脉冲与实测脉冲在细节上达到了很好的匹配,说明本文确定的各响应参数很好的代表了本系统在海水中的声源响应。     

Measurement of Static AM-PM Conversion in Frequency Multipliers

The generation of very narrow spectral lines in the far-infrared by frequency synthesis from VHF precision sources requires very stringent specifications on the spectral purity of the source and on the phase noise introduced by the synthesizer. The dc measurements of the AM-PM conversion in different multiplier stages are presented in this paper: stages employing transistors, varactors and step-recovery diodes are examined. The results show that a few degrees per dB of input level variation are typical for the AM-PM conversion reported to the input in a simple, carefully built and well tuned multiplier stage employing any of the mentioned solid state devices. This value is shown to be unlikely to degrade more than the expected n2 factor the spectral purity of a signal with AM noise as low with respect to PM noise as it is in the output of a good quartz crystal controlled oscillator; however, such a conversion could become a source of phase noise, with degradation of the spectral purity, for a signal with a slightly worse AM noise.     

Digital-to-analog conversion by pulse-count modulation methods

Three low-cost digital-to-analog converters (DACs) are described and compared. These designs can easily be implemented in an integrated circuit: the conventional pulse-width modulation (PWM) DAC, the new pulse-count modulation (PCM) DAC and the first-order noise shaping (FONS) DAC. All three methods control the ratio of the sum of all pulse durations to the constant total period. As the pulse durations are integral multiples of a unit pulse, all three can be classified as pulse-count modulation methods. Block diagrams of all three DACs consisting of a simple digital circuit and a low-pass filter are presented. For a constant digital input value the worst case ripple of the filter output is used to calculate the cutoff frequency of the low-pass filter. Approximations for the 3 dB cutoff frequency of first-order, second-order and fourth-order Butterworth low-pass filters are given. The dynamic properties are analyzed in the time domain (settling time) and in the frequency domain (unfiltered output spectrum of a full-scale sine wave input). The main influences on the static accuracy are analyzed. A case study demonstrates the abilities of PCM and FONS     

A Pulse Modulator That Can Be Used as an Amplifier, a Multiplier, or a Divider

A pulse modulator that can be used as an amplifier, a multiplier, or a divider is introduced. Some of its desirable features are that it can respond without delay to a change in input signal, it is of very simple construction and it can be used to control either proportional or on-off systems.     

1-3型水泥基压电复合材料传感器的性能

以 123型水泥基压电复合材料作为传感元件制备了水泥基压电复合材料传感器。研究了水泥基压电复合材料传感器的频率响应、 线性性能以及应用于混凝土后的传感性能。结果表明: 当加载频率小于 5 Hz时 , 所有载荷下传感器输出电压的幅值均增大 , 但当加载频率大于 5 Hz时 , 所有载荷下传感器输出电压的幅值几乎与输入载荷频率无关 ; 传感器的输出电压幅值和输入载荷幅值之间存在明显的线性关系。水泥基压电传感器在实际混凝土结构中具有良好的传感特性 , 其输出电压与复杂载荷、 随机载荷和脉冲载荷均呈现明显的一一对应关系 ,且与输入载荷基本同步 , 不存在滞后现象 , 试验输出电压值与理论输出电压值也非常吻合。该传感器非常适合于土木工程结构的健康监测。      

Lagrange constraints for transient finite element surface contact

A new approach to enforce surface contact conditions in transient non-linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss-Seidel method in which non-linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.     

Unified dual-field multiplier in GF(P) and GF(2k)

A scalable unified multiplier for both prime fields GF(P) and binary extension fields GF(2^k), where P=2^m-1 and GF(2^k) is generated by an irreducible all one polynomial. The proposed unified dual-field multiplier uses the LSB-first bit-serial architecture for multiplication in GF(P) and GF(2^k) other than the Montgomery multiplication algorithm, which has been employed by most existing dual-field multipliers. The proposed unified dual-field multiplier costs little space and time complexities. The new multiplier is scalable for operands of any size while other existing dual-field multipliers are only scalable for operands with multiples of m. Furthermore, the proposed multiplier has simplicity, regularity, modularity and concurrency and is very suitable to be implement in VLSI.     

基于增量式光电编码器细分的自适应滤波技术研究

利用光栅副调制原理,在建立了光栅副调制几何光学模型与物理光学模型的基础上,提出了一种针对增量式编码器细分的自适应滤波方法。分析莫尔条纹光电信号输出波形不确定的原因,通过自适应滤波方法将高频信号滤除保留基频信号。自适应滤波效果等价于一个中心频率为基频的窄带带通滤波器,当基频随机变化时其通带也会随之改变。实验证明采用这种自适应滤波技术可以较好地滤除计数信号中除基频外所有高频分量,使莫尔条纹光电信号输出波形趋近于标准正弦波,将信号失真量减小了约7/8。     

Fast Correlation Estimation by a Random Reference Correlator

Fast correlation calculations are needed in many technological and scientific fields. Conventional digital correlators require fast and expensive analog-to-digital converters and digital multipliers. This paper describes the implementation of a fast, inexpensive, and unbiased correlation estimator. The estimator is based on the ternary Random Reference Correlation (RRC). Unbiasness is achieved by the addition of statistically independent, uniformly distributed auxiliary noise sources to the input signals. The use of a ternary quantizer eliminates the need of an A/D converter and multiplier, which are replaced by relatively simple logic circuits. A prototype system is described. Real-time correlations of signals, sampled at a rate of about 4 kHz, were achieved by the prototype system. Correlation errors were found to be in the range of one percent. Increasing the internal clock frequency and using faster logic components will improve system performance to perform real-time correlation calculations of signals sampled at 50 kHz.