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# Multiplier

The multiplier is an electronic device that performs the multiplication of two uncorrelated analog signals. It can multiply two binary numbers, and it is composed of a more basic adder. The multiplier can be realized by using a series of computer arithmetic techniques.

The multiplier is not only used as the main basic unit of analog operations such as multiplication, division, power, and square extraction, but is also widely used in electronic communication systems as modulation, demodulation, mixing, phase discrimination, and automatic gain control; it can also be used for filtering, Waveform formation, frequency control, and other occasions, so it is a versatile circuit. ## Catalogues

### Multiplier principle

The multiplier is an important part of the analog electronic watt-hour meter, and it is also the main source of metering errors. Quantitative research and analysis on the measurement error of the time-division multiplier under harmonic conditions are carried out.

According to the working principle of the time-division multiplier, the theoretical expression of the measurement error under the harmonic conditions is derived, and the measurement is verified through simulation calculation. The error quantifies the accuracy of the expression.

The time-division multiplier watt-hour meter and the digital electronic watt-hour meter are comprehensively compared from the perspective of measurement accuracy and cost. Discuss the rationality of harmonic energy measurement. It provides a theoretical basis for quantitative analysis of the error of the measurement system under harmonic conditions and has reference value for the design of electronic energy meters suitable for measurement under harmonic conditions.

### Type of multiplier

#### Analog multiplier

The analog multiplier is an active non-linear device that multiplies two analog signals (voltage or current). The main function is to realize the multiplication of two uncorrelated signals, that is, the output signal is proportional to the product of the two input signals. It has two input ports, namely X and Y input ports.

The polarity of the two input signals of the multiplier is different, and the polarity of the output signal is also different. If expressed by the XY coordinate plane, the multiplier has four possible working areas, namely four working quadrants, as shown in the figure. If the signal is limited to a voltage of a certain polarity, the multiplier is called a single-quadrant multiplier;

If one of the signals can adapt to both positive and negative polarity voltages, the other can only adapt to unipolar voltages. Voltage is a two-quadrant multiplier; if two input signals can adapt to four polarity combinations, it is called a four-quadrant multiplier. Common products that integrate analog multipliers are BG314, F1595, F1596, MC1495, MC1496, LM1595, LM1596, etc.

#### Hardware multiplier

The basis of the hardware multiplier is the structure of the adder, which is already an essential part of modern computers. The model of the multiplier is based on the "shift and add" algorithm. In this algorithm, each bit in the multiplier produces a local product.

The first local product is generated by the LSB of the multiplier, the second product is generated by the second bit of the multiplier, and so on. If the corresponding multiplier bit is 1, then the local product is the value of the multiplicand; if the corresponding multiplier bit is 0, then the local product is all 0.

Each time the local product is shifted one bit to the left. The multiplier can be expressed in a more general way. Each input, local product number, and result are given a logical name (such as A1, A2, B1, B2), and these names are used as signal names in the circuit schematic. By comparing the signal names in the multiplication example of the schematic, you can find the behavioral characteristics of the multiplication circuit.

In the multiplier circuit, each bit in the multiplier must be ANDed with each bit of the multiplicand, and produce its corresponding product bit. These local products are fed into the array of full adders (half adders can also be used when appropriate), and the adder is shifted to the left and the result of the multiplication is displayed.

The final product term is added to the CLA circuit. Note that some full adder circuits will bring the signal to the carry input (used to replace the carry of adjacent bits). This is the application of a full adder circuit; a full adder adds any three bits at its input.

With the increase in the number of multipliers and multiplicands, the number of adders in the multiplier circuit will increase accordingly. By studying the characteristics of the CLA circuit, a faster addition array can also be developed in the multiplier.

#### Harmonic multiplier

The time division multiplier is an important part of the analog electronic electric energy meter, and it is also the main source of the metering error. In this paper, the measurement error of the time-division multiplier under harmonic conditions is quantitatively studied and analyzed.

According to the working principle of the time-division multiplier, the theoretical expression of the measurement error under the harmonic conditions is deduced and calculated by simulation.

The accuracy of the quantitative expression of measurement error is verified. From the perspective of measurement accuracy and cost, the time-division multiplier watt-hour meter and the digital electronic watt-hour meter are comprehensively compared.

Finally, the rationality of harmonic energy measurement is discussed. It provides a theoretical basis for quantitatively analyzing the error of the measurement system under harmonic conditions and has a reference value for the design of electronic energy meters suitable for measurement under harmonic conditions.

### Multiplier application

An ideal universal multiplier should not impose restrictions on the polarity of any input signal, that is, it should have a circuit capable of completing four quadrant operations. The accuracy and rationality of time-division electric energy measurement are related to the economic accounting of the power grid and involve the economic interests of the three parties.

The electric energy meter is the core part and basic measuring tool of electric energy measurement, and its measurement accuracy is directly related to the accuracy of electric energy measurement. With the increasing application of power electronic technology equipment in the power system, large harmonic distortions have appeared in the voltage and current of the power grid, which has increased the measurement error of the electric energy measurement system.

In-depth and systematic research on the measurement of harmonics on electric energy meters The impact of this has important practical significance and practical value. The multiplier is an indispensable part of the electronic energy meter. The main domestic electronic watt-hour meter uses a time division multiplier (time division multiplier, TDM).

According to the different operating principles of the modulation circuit, TDM can be divided into many types. For example, according to different methods of pulse width modulation conversion on AC signals, it can be divided into triangle wave voltage comparison type, beat square wave control voltage integration type, beat control triangle wave voltage comparison type, and no beat square wave control current integration type.

The TDM measurement method has conducted a preliminary study on the influence of the AC test error and obtained the expression of TDM power measurement, but it is only applicable to the sinusoidal environment and has not been simulated. From the late 1990s to the early 2000s, TDM power measurement methods were widely used, and two main development directions were formed: one was to explore the error of the TDM principle;

the other was to improve TDM method research on the basis of TDM error research There are many TDM instrument errors and how to improve the TDM power measurement method, and there are few studies on the principle error.

The literature studies the errors of three TDM power measurement methods such as triangular wave modulation, but the article only obtains the error expression using the broadband modulation wave, and the expression involves too many variables, which is not conducive to the analysis of the error influence law.

The relationship between the power measurement error of the TDM under sine and non-sine conditions, the realization of the method of using the power measurement error under the sine condition to calculate the error under the non-sine condition, and the quantitative power measurement error under the non-sine condition of the TDM is obtained.

However, this method has been approximated, and the results show that only when the ratio of the pulse frequency of the unmodulated multivibrator to the input signal frequency is greater than 400, the accuracy of the relationship is higher. It can be seen that although relevant research has been carried out on the influence of harmonics on electric energy measurement at home and abroad, most of them only carry out qualitative analysis, and there is no simple and practical error quantification expression.

Based on the analysis of the working principles of TDM with different structures, this paper derives the theoretical expressions of TDM measurement errors under harmonic conditions, which are verified by simulation calculations. Then the TDM electric energy meter is compared with the digital electric energy meter, highlighting the importance of the TDM electric energy meter in most engineering practice.

Finally, from the perspective of measurement mode, how to measure harmonics is reasonable under the condition of harmonics. One of the input quantities X is pulse-width modulated to obtain a pulse signal with a constant frequency but a different duty cycle per cycle, and the width difference between the forward signal part and the reverse signal part during each cycle is proportional to the instantaneous sampling value of the input signal.

Then through the pulse width modulation circuit, the pulse signal is pulse amplitude modulated by another input signal Y, and the final modulation signal is passed through the low-pass filter to obtain the direct current value, which is the active power value.

It mainly includes three parts, namely the pulse width modulation circuit, the pulse amplitude modulation circuit controlled by the output signal of the width modulation circuit, and the low-pass filter circuit.

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